diff --git a/Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb b/Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb new file mode 100644 index 00000000..87c3e72e --- /dev/null +++ b/Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb @@ -0,0 +1,1135 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Probabilistic Programming and Bayesian Methods for Hackers \n", + "========\n", + "\n", + "Welcome to *Bayesian Methods for Hackers*. The full Github repository is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!\n", + "\n", + "#### Looking for a printed version of Bayesian Methods for Hackers?\n", + "\n", + "_Bayesian Methods for Hackers_ is now a published book by Addison-Wesley, available on [Amazon](http://www.amazon.com/Bayesian-Methods-Hackers-Probabilistic-Addison-Wesley/dp/0133902838)! \n", + "\n", + "![BMH](http://www-fp.pearsonhighered.com/assets/hip/images/bigcovers/0133902838.jpg)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Chapter 1\n", + "======\n", + "***" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Philosophy of Bayesian Inference\n", + "------\n", + " \n", + "> You are a skilled programmer, but bugs still slip into your code. After a particularly difficult implementation of an algorithm, you decide to test your code on a trivial example. It passes. You test the code on a harder problem. It passes once again. And it passes the next, *even more difficult*, test too! You are starting to believe that there may be no bugs in this code...\n", + "\n", + "If you think this way, then congratulations, you already are thinking Bayesian! Bayesian inference is simply updating your beliefs after considering new evidence. A Bayesian can rarely be certain about a result, but he or she can be very confident. Just like in the example above, we can never be 100% sure that our code is bug-free unless we test it on every possible problem; something rarely possible in practice. Instead, we can test it on a large number of problems, and if it succeeds we can feel more *confident* about our code, but still not certain. Bayesian inference works identically: we update our beliefs about an outcome; rarely can we be absolutely sure unless we rule out all other alternatives. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### The Bayesian state of mind\n", + "\n", + "\n", + "Bayesian inference differs from more traditional statistical inference by preserving *uncertainty*. At first, this sounds like a bad statistical technique. Isn't statistics all about deriving *certainty* from randomness? To reconcile this, we need to start thinking like Bayesians. \n", + "\n", + "The Bayesian world-view interprets probability as measure of *believability in an event*, that is, how confident we are in an event occurring. In fact, we will see in a moment that this is the natural interpretation of probability. \n", + "\n", + "For this to be clearer, we consider an alternative interpretation of probability: *Frequentist*, known as the more *classical* version of statistics, assumes that probability is the long-run frequency of events (hence the bestowed title). For example, the *probability of plane accidents* under a frequentist philosophy is interpreted as the *long-term frequency of plane accidents*. This makes logical sense for many probabilities of events, but becomes more difficult to understand when events have no long-term frequency of occurrences. Consider: we often assign probabilities to outcomes of presidential elections, but the election itself only happens once! Frequentists get around this by invoking alternative realities and saying across all these realities, the frequency of occurrences defines the probability. \n", + "\n", + "Bayesians, on the other hand, have a more intuitive approach. Bayesians interpret a probability as measure of *belief*, or confidence, of an event occurring. Simply, a probability is a summary of an opinion. An individual who assigns a belief of 0 to an event has no confidence that the event will occur; conversely, assigning a belief of 1 implies that the individual is absolutely certain of an event occurring. Beliefs between 0 and 1 allow for weightings of other outcomes. This definition agrees with the probability of a plane accident example, for having observed the frequency of plane accidents, an individual's belief should be equal to that frequency, excluding any outside information. Similarly, under this definition of probability being equal to beliefs, it is meaningful to speak about probabilities (beliefs) of presidential election outcomes: how confident are you candidate *A* will win?\n", + "\n", + "Notice in the paragraph above, I assigned the belief (probability) measure to an *individual*, not to Nature. This is very interesting, as this definition leaves room for conflicting beliefs between individuals. Again, this is appropriate for what naturally occurs: different individuals have different beliefs of events occurring, because they possess different *information* about the world. The existence of different beliefs does not imply that anyone is wrong. Consider the following examples demonstrating the relationship between individual beliefs and probabilities:\n", + "\n", + "- I flip a coin, and we both guess the result. We would both agree, assuming the coin is fair, that the probability of Heads is 1/2. Assume, then, that I peek at the coin. Now I know for certain what the result is: I assign probability 1.0 to either Heads or Tails (whichever it is). Now what is *your* belief that the coin is Heads? My knowledge of the outcome has not changed the coin's results. Thus we assign different probabilities to the result. \n", + "\n", + "- Your code either has a bug in it or not, but we do not know for certain which is true, though we have a belief about the presence or absence of a bug. \n", + "\n", + "- A medical patient is exhibiting symptoms $x$, $y$ and $z$. There are a number of diseases that could be causing all of them, but only a single disease is present. A doctor has beliefs about which disease, but a second doctor may have slightly different beliefs. \n", + "\n", + "\n", + "This philosophy of treating beliefs as probability is natural to humans. We employ it constantly as we interact with the world and only see partial truths, but gather evidence to form beliefs. Alternatively, you have to be *trained* to think like a frequentist. \n", + "\n", + "To align ourselves with traditional probability notation, we denote our belief about event $A$ as $P(A)$. We call this quantity the *prior probability*.\n", + "\n", + "John Maynard Keynes, a great economist and thinker, said \"When the facts change, I change my mind. What do you do, sir?\" This quote reflects the way a Bayesian updates his or her beliefs after seeing evidence. Even — especially — if the evidence is counter to what was initially believed, the evidence cannot be ignored. We denote our updated belief as $P(A |X )$, interpreted as the probability of $A$ given the evidence $X$. We call the updated belief the *posterior probability* so as to contrast it with the prior probability. For example, consider the posterior probabilities (read: posterior beliefs) of the above examples, after observing some evidence $X$:\n", + "\n", + "1\\. $P(A): \\;\\;$ the coin has a 50 percent chance of being Heads. $P(A | X):\\;\\;$ You look at the coin, observe a Heads has landed, denote this information $X$, and trivially assign probability 1.0 to Heads and 0.0 to Tails.\n", + "\n", + "2\\. $P(A): \\;\\;$ This big, complex code likely has a bug in it. $P(A | X): \\;\\;$ The code passed all $X$ tests; there still might be a bug, but its presence is less likely now.\n", + "\n", + "3\\. $P(A):\\;\\;$ The patient could have any number of diseases. $P(A | X):\\;\\;$ Performing a blood test generated evidence $X$, ruling out some of the possible diseases from consideration.\n", + "\n", + "\n", + "It's clear that in each example we did not completely discard the prior belief after seeing new evidence $X$, but we *re-weighted the prior* to incorporate the new evidence (i.e. we put more weight, or confidence, on some beliefs versus others). \n", + "\n", + "By introducing prior uncertainty about events, we are already admitting that any guess we make is potentially very wrong. After observing data, evidence, or other information, we update our beliefs, and our guess becomes *less wrong*. This is the alternative side of the prediction coin, where typically we try to be *more right*. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Bayesian Inference in Practice\n", + "\n", + " If frequentist and Bayesian inference were programming functions, with inputs being statistical problems, then the two would be different in what they return to the user. The frequentist inference function would return a number, representing an estimate (typically a summary statistic like the sample average etc.), whereas the Bayesian function would return *probabilities*.\n", + "\n", + "For example, in our debugging problem above, calling the frequentist function with the argument \"My code passed all $X$ tests; is my code bug-free?\" would return a *YES*. On the other hand, asking our Bayesian function \"Often my code has bugs. My code passed all $X$ tests; is my code bug-free?\" would return something very different: probabilities of *YES* and *NO*. The function might return:\n", + "\n", + "\n", + "> *YES*, with probability 0.8; *NO*, with probability 0.2\n", + "\n", + "\n", + "\n", + "This is very different from the answer the frequentist function returned. Notice that the Bayesian function accepted an additional argument: *\"Often my code has bugs\"*. This parameter is the *prior*. By including the prior parameter, we are telling the Bayesian function to include our belief about the situation. Technically this parameter in the Bayesian function is optional, but we will see excluding it has its own consequences. \n", + "\n", + "\n", + "#### Incorporating evidence\n", + "\n", + "As we acquire more and more instances of evidence, our prior belief is *washed out* by the new evidence. This is to be expected. For example, if your prior belief is something ridiculous, like \"I expect the sun to explode today\", and each day you are proved wrong, you would hope that any inference would correct you, or at least align your beliefs better. Bayesian inference will correct this belief.\n", + "\n", + "\n", + "Denote $N$ as the number of instances of evidence we possess. As we gather an *infinite* amount of evidence, say as $N \\rightarrow \\infty$, our Bayesian results (often) align with frequentist results. Hence for large $N$, statistical inference is more or less objective. On the other hand, for small $N$, inference is much more *unstable*: frequentist estimates have more variance and larger confidence intervals. This is where Bayesian analysis excels. By introducing a prior, and returning probabilities (instead of a scalar estimate), we *preserve the uncertainty* that reflects the instability of statistical inference of a small $N$ dataset. \n", + "\n", + "One may think that for large $N$, one can be indifferent between the two techniques since they offer similar inference, and might lean towards the computationally-simpler, frequentist methods. An individual in this position should consider the following quote by Andrew Gelman (2005)[1], before making such a decision:\n", + "\n", + "> Sample sizes are never large. If $N$ is too small to get a sufficiently-precise estimate, you need to get more data (or make more assumptions). But once $N$ is \"large enough,\" you can start subdividing the data to learn more (for example, in a public opinion poll, once you have a good estimate for the entire country, you can estimate among men and women, northerners and southerners, different age groups, etc.). $N$ is never enough because if it were \"enough\" you'd already be on to the next problem for which you need more data.\n", + "\n", + "### Are frequentist methods incorrect then? \n", + "\n", + "**No.**\n", + "\n", + "Frequentist methods are still useful or state-of-the-art in many areas. Tools such as least squares linear regression, LASSO regression, and expectation-maximization algorithms are all powerful and fast. Bayesian methods complement these techniques by solving problems that these approaches cannot, or by illuminating the underlying system with more flexible modeling.\n", + "\n", + "\n", + "#### A note on *Big Data*\n", + "Paradoxically, big data's predictive analytic problems are actually solved by relatively simple algorithms [2][4]. Thus we can argue that big data's prediction difficulty does not lie in the algorithm used, but instead on the computational difficulties of storage and execution on big data. (One should also consider Gelman's quote from above and ask \"Do I really have big data?\" )\n", + "\n", + "The much more difficult analytic problems involve *medium data* and, especially troublesome, *really small data*. Using a similar argument as Gelman's above, if big data problems are *big enough* to be readily solved, then we should be more interested in the *not-quite-big enough* datasets. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Our Bayesian framework\n", + "\n", + "We are interested in beliefs, which can be interpreted as probabilities by thinking Bayesian. We have a *prior* belief in event $A$, beliefs formed by previous information, e.g., our prior belief about bugs being in our code before performing tests.\n", + "\n", + "Secondly, we observe our evidence. To continue our buggy-code example: if our code passes $X$ tests, we want to update our belief to incorporate this. We call this new belief the *posterior* probability. Updating our belief is done via the following equation, known as Bayes' Theorem, after its discoverer Thomas Bayes:\n", + "\n", + "\\begin{align}\n", + " P( A | X ) = & \\frac{ P(X | A) P(A) } {P(X) } \\\\\\\\[5pt]\n", + "& \\propto P(X | A) P(A)\\;\\; (\\propto \\text{is proportional to } )\n", + "\\end{align}\n", + "\n", + "The above formula is not unique to Bayesian inference: it is a mathematical fact with uses outside Bayesian inference. Bayesian inference merely uses it to connect prior probabilities $P(A)$ with an updated posterior probabilities $P(A | X )$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Mandatory coin-flip example\n", + "\n", + "Every statistics text must contain a coin-flipping example, I'll use it here to get it out of the way. Suppose, naively, that you are unsure about the probability of heads in a coin flip (spoiler alert: it's 50%). You believe there is some true underlying ratio, call it $p$, but have no prior opinion on what $p$ might be. \n", + "\n", + "We begin to flip a coin, and record the observations: either $H$ or $T$. This is our observed data. An interesting question to ask is how our inference changes as we observe more and more data? More specifically, what do our posterior probabilities look like when we have little data, versus when we have lots of data. \n", + "\n", + "Below we plot a sequence of updating posterior probabilities as we observe increasing amounts of data (coin flips)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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eCYAxhmuvvZYhQ4awYcMGXnnlFf7whz/w3nvvAeDxeJg/fz5btmxh+fLl/Pvf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\n7YPE6CfHe09t27aN+fPn90sDQ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GQORB8bzOM4e8tAiFF5cxsv/1jGNW/t5vF1BWSVtaDT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\nEXNnkxFR5+1quHDqzxeWo396iS9+pyU39D++HqM4fzgzGoh29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EFiYiIjR47klltu6RD/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Xp2eBVpF00xyIGWQoEuUXe9q5+6VjdA8OUxg03rG4nLctno1pkbhpIxJ1/N/rndQd7cEBJaEA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\nMfn8fMmM+7p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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\"\"\"\n", + "The book uses a custom matplotlibrc file, which provides the unique styles for\n", + "matplotlib plots. If executing this book, and you wish to use the book's\n", + "styling, provided are two options:\n", + " 1. Overwrite your own matplotlibrc file with the rc-file provided in the\n", + " book's styles/ dir. See http://matplotlib.org/users/customizing.html\n", + " 2. Also in the styles is bmh_matplotlibrc.json file. This can be used to\n", + " update the styles in only this notebook. Try running the following code:\n", + "\n", + " import json, matplotlib\n", + " s = json.load( open(\"../styles/bmh_matplotlibrc.json\") )\n", + " matplotlib.rcParams.update(s)\n", + "\n", + "\"\"\"\n", + "\n", + "# The code below can be passed over, as it is currently not important, plus it\n", + "# uses advanced topics we have not covered yet. LOOK AT PICTURE, MICHAEL!\n", + "%matplotlib inline\n", + "from IPython.core.pylabtools import figsize\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "figsize(11, 9)\n", + "\n", + "import scipy.stats as stats\n", + "\n", + "dist = stats.beta\n", + "n_trials = [0, 1, 2, 3, 4, 5, 8, 15, 50, 500]\n", + "data = stats.bernoulli.rvs(0.5, size=n_trials[-1])\n", + "x = np.linspace(0, 1, 100)\n", + "\n", + "# For the already prepared, I'm using Binomial's conj. prior.\n", + "for k, N in enumerate(n_trials):\n", + " sx = plt.subplot(len(n_trials) / 2, 2, k + 1)\n", + " plt.xlabel(\"$p$, probability of heads\") \\\n", + " if k in [0, len(n_trials) - 1] else None\n", + " plt.setp(sx.get_yticklabels(), visible=False)\n", + " heads = data[:N].sum()\n", + " y = dist.pdf(x, 1 + heads, 1 + N - heads)\n", + " plt.plot(x, y, label=\"observe %d tosses,\\n %d heads\" % (N, heads))\n", + " plt.fill_between(x, 0, y, color=\"#348ABD\", alpha=0.4)\n", + " plt.vlines(0.5, 0, 4, color=\"k\", linestyles=\"--\", lw=1)\n", + "\n", + " leg = plt.legend()\n", + " leg.get_frame().set_alpha(0.4)\n", + " plt.autoscale(tight=True)\n", + "\n", + "\n", + "plt.suptitle(\"Bayesian updating of posterior probabilities\",\n", + " y=1.02,\n", + " fontsize=14)\n", + "\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The posterior probabilities are represented by the curves, and our uncertainty is proportional to the width of the curve. As the plot above shows, as we start to observe data our posterior probabilities start to shift and move around. Eventually, as we observe more and more data (coin-flips), our probabilities will tighten closer and closer around the true value of $p=0.5$ (marked by a dashed line). \n", + "\n", + "Notice that the plots are not always *peaked* at 0.5. There is no reason it should be: recall we assumed we did not have a prior opinion of what $p$ is. In fact, if we observe quite extreme data, say 8 flips and only 1 observed heads, our distribution would look very biased *away* from lumping around 0.5 (with no prior opinion, how confident would you feel betting on a fair coin after observing 8 tails and 1 head). As more data accumulates, we would see more and more probability being assigned at $p=0.5$, though never all of it.\n", + "\n", + "The next example is a simple demonstration of the mathematics of Bayesian inference. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Bug, or just sweet, unintended feature?\n", + "\n", + "\n", + "Let $A$ denote the event that our code has **no bugs** in it. Let $X$ denote the event that the code passes all debugging tests. For now, we will leave the prior probability of no bugs as a variable, i.e. $P(A) = p$. \n", + "\n", + "We are interested in $P(A|X)$, i.e. the probability of no bugs, given our debugging tests $X$. To use the formula above, we need to compute some quantities.\n", + "\n", + "What is $P(X | A)$, i.e., the probability that the code passes $X$ tests *given* there are no bugs? Well, it is equal to 1, for a code with no bugs will pass all tests. \n", + "\n", + "$P(X)$ is a little bit trickier: The event $X$ can be divided into two possibilities, event $X$ occurring even though our code *indeed has* bugs (denoted $\\sim A\\;$, spoken *not $A$*), or event $X$ without bugs ($A$). $P(X)$ can be represented as:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\\begin{align}\n", + "P(X ) & = P(X \\text{ and } A) + P(X \\text{ and } \\sim A) \\\\\\\\[5pt]\n", + " & = P(X|A)P(A) + P(X | \\sim A)P(\\sim A)\\\\\\\\[5pt]\n", + "& = P(X|A)p + P(X | \\sim A)(1-p)\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have already computed $P(X|A)$ above. On the other hand, $P(X | \\sim A)$ is subjective: our code can pass tests but still have a bug in it, though the probability there is a bug present is reduced. Note this is dependent on the number of tests performed, the degree of complication in the tests, etc. Let's be conservative and assign $P(X|\\sim A) = 0.5$. Then\n", + "\n", + "\\begin{align}\n", + "P(A | X) & = \\frac{1\\cdot p}{ 1\\cdot p +0.5 (1-p) } \\\\\\\\\n", + "& = \\frac{ 2 p}{1+p}\n", + "\\end{align}\n", + "This is the posterior probability. What does it look like as a function of our prior, $p \\in [0,1]$? " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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7uyibiyOF/ZpZBWRr1V5EZMKJqdB394UDz83s79z9X4YeY2Z/k8jAglKPvsRK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\nb6HzgO3HgNeBa23/1vavgauBW4BTgeVDdP8GcGz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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "p = np.linspace(0, 1, 50)\n", + "plt.plot(p, 2 * p / (1 + p), color=\"#348ABD\", lw=3)\n", + "# plt.fill_between(p, 2*p/(1+p), alpha=.5, facecolor=[\"#A60628\"])\n", + "plt.scatter(0.2, 2 * (0.2) / 1.2, s=140, c=\"#348ABD\")\n", + "plt.xlim(0, 1)\n", + "plt.ylim(0, 1)\n", + "plt.xlabel(\"Prior, $P(A) = p$\")\n", + "plt.ylabel(\"Posterior, $P(A|X)$, with $P(A) = p$\")\n", + "plt.title(\"Is my code bug-free?\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see the biggest gains if we observe the $X$ tests passed when the prior probability, $p$, is low. Let's settle on a specific value for the prior. I'm a strong programmer (I think), so I'm going to give myself a realistic prior of 0.20, that is, there is a 20% chance that I write code bug-free. To be more realistic, this prior should be a function of how complicated and large the code is, but let's pin it at 0.20. Then my updated belief that my code is bug-free is 0.33. \n", + "\n", + "Recall that the prior is a probability: $p$ is the prior probability that there *are no bugs*, so $1-p$ is the prior probability that there *are bugs*.\n", + "\n", + "Similarly, our posterior is also a probability, with $P(A | X)$ the probability there is no bug *given we saw all tests pass*, hence $1-P(A|X)$ is the probability there is a bug *given all tests passed*. What does our posterior probability look like? Below is a chart of both the prior and the posterior probabilities. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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OWt2IdIsWLXjqqaf49a9/Tffu3Vm5ciUnnnhihdvG87gq6zt62RlnnMGLL75I\nly5dyM/P59lnny27YPXuu+/mlVdeoUuXLkybNo0zzzyzbL8ePXpwwQUX0L9/f7p27crnn39eq+dF\nREREpCasJhfnxd2Z2RDgAYJ/Fia5+z1R678GPAfkAFnAfe7+dPRxZsyY4f379z/g+IWFheXKFdLt\nG1FLpyw85ZRTkhCRpKvo16mIiIhIqdmzZ5OXl3fAaGDSvlzJzBoADwF5QCHwgZn91d0XRmw2GvjM\n3c8xsyOARWb2nLvvq+CQ1YolkRYRERERSXfJLI/5BrDE3Ve5+17geeDcqG0cOCy8fxiw6WAT9nSk\nEgoREZHMpZp2SaSkjbQDHYDI6TfWECTykR4C/mZmhcChwEVJii0pYr0YVEREkuuOV5elOgTJAGvn\nF/LqjmXceXq3VIciGSiZSXssTgfmuPt3zKwb8LqZHevu5Sbvzs/P54knniAnJweA5s2b07dvX7p2\n7ZqCkEXiU1RUxPLly8vm8y0dmVFbbbVT14Z2FO8tYeUnHwLQundw3dSGhbPVVjvm9q59Jayd/xGE\nSXu6vL7VTu926f2CggIAjj/+ePLy8oiWtAtRzexE4FfuPiRs3wp45MWoZvYy8Ft3fydszwBucfcP\nI48V64WoIulIr1OR9HPHq8v4ongvm3bsTXUoUoe1bJbNEU2zNdIuNZLyC1GBD4DuZnYksA64GBge\ntc0q4LvAO2bWBugJLI+1g0aNGrFp0yZatGih+nFJS8XFxWVTUIpIeurVKr6pfEUAFm0sZsPC2RzR\n/4RUhyIZKmlJu7uXmNm1wGt8NeXjAjMbFaz2x4C7gKfN7ONwt5vdfXOsfbRs2ZLt27dTWFiopL0O\nKSoqonnz5qkOIymysrJo3bp1qsMQERGROiapNe3uPh3oFbXs0Yj76wjq2g/aoYceyqGHHlqTQ0iS\nqVREREQyQWltu0giZPw3ooqIiIiI1HVK2iXlNK+tiIhkgtLZZEQSQUm7iIiIiEiaU9IuKVc6X6mI\niEhdppp2SSQl7SIiIiIiaU5Ju6ScatpFRCQTqKZdEklJu4iIiIhImlPSLimnmnYREckEqmmXRFLS\nLiIiIiKS5pS0S8qppl1ERDKBatolkZS0i4iIiIikOSXtknKqaRcRkUygmnZJJCXtIiIiIiJpTkm7\npJxq2kVEJBOopl0SSUm7iIiIiEiaU9IuKaeadhERyQSqaZdEUtIuIiIiIpLmlLRLyqmmXUREMoFq\n2iWRlLSBXLJOAAAW0ElEQVSLiIiIiKQ5Je2ScqppFxGRTKCadkkkJe0iIiIiImlOSbuknGraRUQk\nE6imXRJJSbuIiIiISJpT0i4pp5p2ERHJBKppl0RqmOoAREREROq67056iEMaNuCQLOOj55qlOhyp\nw+yG4RUuV9IuKTdz5kyNtouISJ23YtNq+mYfxq59xakOReqwJpUsV9IuIiIiUguy9uzhkO1b2L0j\nK9WhSB2mpF3SlkbZRUQkE/Rs0gL2bKV5vz6pDkXqqKI58ytdpwtRRURERETSnJJ2STnN0y4iIplg\n8c7NqQ5BMpiSdhERERGRNKekXVJONe0iIpIJejZpkeoQJIMpaRcRERERSXNK2iXlVNMuIiKZQDXt\nkkgxJ+1mNt7MchMZjIiIiIiIHCiekfYs4FUz+9TMbjGzjvF2ZmZDzGyhmS02s1sq2ebbZjYn7OfN\nePuQukc17SIikglU0y6JFHPS7u4/BdoDtwK5wAIz+5eZXWpmh1a3v5k1AB4CTgeOBoabWe+obZoD\nfwTOcvdjgO/H/EhERERERDJUXDXt7l7i7i+7+3DgRKAV8DSw3syeMLMOVez+DWCJu69y973A88C5\nUduMAKa6+9qwvy/iiU/qJtW0i4hIJlBNuyRSXEm7mX3NzH4Slq28DcwCBgNHAduBV6rYvQOwOqK9\nJlwWqSfQwszeNLMPzOySeOITEREREclEDWPd0MzyCUpb3gYmAi+5++6I9TcCRbUQT3/gO0Az4F0z\ne9fdl9bwuJLGVNMuIiKZoGeTFrBna6rDkAwVc9IOvAdc6+7rK1rp7vvNrE0V+68FciLaHcNlkdYA\nX7j7LmCXmb0NHAeUS9rz8/N54oknyMkJDte8eXP69u1blvyVlluorbbaaqutdixtaAfA5iVzWLux\nMR36DABg7fyPANRWO6b24p2babRne1kZwbxN6wA4rmU7tdWutF16f33xNvZs2crZc+eSl5dHNHP3\nAxZWxMz+6u7RNeiY2TR3vyCG/bOARUAesA54Hxju7gsitukNPAgMARoRlN9c5O7zI481Y8YM79+/\nf0xxS/qbOXOmRttFJKXueHUZXxTvZdOOvfRq1TTV4Ugd1Gnc71i/cQW5exrQ4YS+qQ5H6qiiOfM5\n/E93kpeXZ9Hr4hlpP7WS5d+OZWd3LzGza4HXCGrpJ7n7AjMbFaz2x9x9oZm9CnwMlACPRSfsIiIi\nIiL1TbVJu5n9Jrx7SMT9Ul2BVbF25u7TgV5Ryx6Nat8L3BvrMaXu0yi7iIhkAtW0SyLFMtLeKfzZ\nIOI+gBPMBvOrWo5JREREREQiVJu0u/uPAczsv+7+eOJDkvpGNe0iIpIJFu/cTG58s2mLxKzKpN3M\nOrv7yrA5w8y6VrSduy+v7cBERERERCRQ3Uj7J8Bh4f2lBCUx0VezOpBVy3FJPaJRdhERyQSqaZdE\nqjJpd/fDIu7r8x4RERERkRRQIi4p99WXm4iIiNRdi3duTnUIksGqq2n/D0H5S5Xc/ZRai0hERERE\nRMqprqb9iaREIfWaatpFRCQTqKZdEqm6mvZnkhWIiIiIiIhUrLrymEvc/dnw/v9Utp27P1nbgUn9\noXnaRUQkE2iedkmk6spjhgPPhvcvqWQbB5S0i4iIiIgkSHXlMUMj7p+a+HCkPtIou4iIZALVtEsi\nVTfSXo6ZHQ6cCbQHCoF/uLtenSIiIiIiCRRz4ZWZfQdYCfwUGAiMAVaaWV5iQpP6QvO0i4hIJtA8\n7ZJI8Yy0PwRc6e4vlC4ws+8DfwR613ZgIiIiIiISiOcS5/bA1KhlLwJtay8cqY9U0y4iIpmgZ5MW\nqQ5BMlg8SfuzwOioZVcDf6q9cEREREREJFqVSbuZ/cfM3jazt4F+wH1mtsbMZpnZGuD+cLnIQVNN\nu4iIZALVtEsiVVfT/kRU+/FEBSIiIiIiIhWrbp72Z5IViNRfqmkXEZFMoHnaJZHinae9DfAN4AjA\nSpe7u74RVUREREQkQeKZp/08YBnwG+BRgnnaHwUuSUxoUl+opl1ERDKBatolkeKZPeYu4Mfu3g/Y\nEf68EvgoIZGJiIiIiAgQX9Ke4+7/F7XsGeDSWoxH6iHVtIuISCbQPO2SSPEk7RvCmnaAlWZ2EtAN\nyKr9sEREREREpFQ8SfvjQOmQ6HjgTWAe8HBtByX1i2raRUQkE6imXRIp5tlj3P2eiPt/MrN/A83c\nfUEiAhMRERERkUC8Uz5mAScC7YFC4L1EBCX1i2raRUQkE2iedkmkmJN2MzsWeAloDKwBOgK7zOx8\nd5+XoPhEREREROq9eGranwT+CHRw928AHYCHwuUiB0017SIikglU0y6JFE/S3hN4wN0dIPz5B6BH\nIgITEREREZFAPEn7P4FzopadDfyj9sKR+kg17SIikgk0T7skUpU17Wb2LOBhMwt43sw+AlYDnYAB\nwF8TGqGIiIiISD1X3YWoS6Pan0bcnw+8WrvhSH00c+ZMjbaLiEidt3jnZnLjKmIQiV2VSbu7/zpZ\ngYiIiIiISMXinaf928ClBDPHrAWedfc3ExCX1CMaZRcRkUygedolkWL+DMfMLgdeANYD04B1wBQz\nuyKOYwwxs4VmttjMbqliu4FmttfMLoj12CIiIiIimSqewqubge+5++3u/qi7/xw4LVxeLTNrQDCv\n++nA0cBwM+tdyXbjUL18vaF52kVEJBNonnZJpHiS9pYEF59GWgTEOr/RN4Al7r7K3fcCzwPnVrDd\nGCAf2BBHbCIiIiIiGSuepH0mcL+ZNQUws2bA74H/xrh/B4KpIkutCZeVMbP2wHnu/ghgccQmdZhq\n2kVEJBNonnZJpHiS9quAY4EiM/sc2AocB4yqxXgeACJr3ZW4i4iIiEi9F9PsMWZmQBMgD2gLtAcK\n3X1NHH2tBXIi2h3DZZGOJ/gCJwOOAM4ws73u/rfIjfLz83niiSfIyQkO17x5c/r27Vs2YltaI612\n3Wg/8sgjev7UVlvtlLahHQCbl8xh7cbGdOgzAIC18z8CUFvtmNoztq6k+94GZWUE8zatA+C4lu3U\nVrvSdun99cXb2LNlK2fPnUteXh7RzN0PWFgRM9sBHObu+2Pa4cD9swhq4PMIZp55Hxju7gsq2f4p\n4O/uPi163YwZM7x///4HE4akIX25koik2h2vLuOL4r1s2rGXXq2apjocqYM6jfsd6zeuIHdPAzqc\n0DfV4UgdVTRnPof/6U7y8vIOqDaJpzxmDtDzYINw9xLgWuA14DPgeXdfYGajzOzKinY52L6kblHC\nLiIimUA17ZJI8Xy50r+B6Wb2NMEFpWVJtbs/GcsB3H060Ctq2aOVbPs/ccQmIiIiIpKx4knaTwZW\nAN+KWu5ATEm7SEVUHiMiIplg8c7N5MZVxCASu2qT9nCKx18A24HZwN3uvjvRgYmIiIiISCCWfwf/\nCJwNLAAuBO5NaERS72iUXUREMoFq2iWRYknahwCnufvNwBnAWYkNSUREREREIsWStDdz93UA7r4a\naJ7YkKS++WqeZBERkbpr8c7NqQ5BMlgsF6I2NLNT+erbSaPbuPsbiQhORERERERiS9o3UH52mE1R\nbQe61mZQUr+opl1ERDJBzyY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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "colours = [\"#348ABD\", \"#A60628\"]\n", + "\n", + "prior = [0.20, 0.80]\n", + "posterior = [1. / 3, 2. / 3]\n", + "plt.bar([0, .7], prior, alpha=0.70, width=0.25,\n", + " color=colours[0], label=\"prior distribution\",\n", + " lw=\"3\", edgecolor=colours[0])\n", + "\n", + "plt.bar([0 + 0.25, .7 + 0.25], posterior, alpha=0.7,\n", + " width=0.25, color=colours[1],\n", + " label=\"posterior distribution\",\n", + " lw=\"3\", edgecolor=colours[1])\n", + "\n", + "plt.ylim(0,1)\n", + "plt.xticks([0.20, .95], [\"Bugs Absent\", \"Bugs Present\"])\n", + "plt.title(\"Prior and Posterior probability of bugs present\")\n", + "plt.ylabel(\"Probability\")\n", + "plt.legend(loc=\"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that after we observed $X$ occur, the probability of bugs being absent increased. By increasing the number of tests, we can approach confidence (probability 1) that there are no bugs present.\n", + "\n", + "This was a very simple example of Bayesian inference and Bayes rule. Unfortunately, the mathematics necessary to perform more complicated Bayesian inference only becomes more difficult, except for artificially constructed cases. We will later see that this type of mathematical analysis is actually unnecessary. First we must broaden our modeling tools. The next section deals with *probability distributions*. If you are already familiar, feel free to skip (or at least skim), but for the less familiar the next section is essential." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "_______\n", + "\n", + "## Probability Distributions\n", + "\n", + "\n", + "**Let's quickly recall what a probability distribution is:** Let $Z$ be some random variable. Then associated with $Z$ is a *probability distribution function* that assigns probabilities to the different outcomes $Z$ can take. Graphically, a probability distribution is a curve where the probability of an outcome is proportional to the height of the curve. You can see examples in the first figure of this chapter. \n", + "\n", + "We can divide random variables into three classifications:\n", + "\n", + "- **$Z$ is discrete**: Discrete random variables may only assume values on a specified list. Things like populations, movie ratings, and number of votes are all discrete random variables. Discrete random variables become more clear when we contrast them with...\n", + "\n", + "- **$Z$ is continuous**: Continuous random variable can take on arbitrarily exact values. For example, temperature, speed, time, color are all modeled as continuous variables because you can progressively make the values more and more precise.\n", + "\n", + "- **$Z$ is mixed**: Mixed random variables assign probabilities to both discrete and continuous random variables, i.e. it is a combination of the above two categories. \n", + "\n", + "#### Expected Value\n", + "Expected value (EV) is one of the most important concepts in probability. The EV for a given probability distribution can be described as \"the mean value in the long run for many repeated samples from that distribution.\" To borrow a metaphor from physics, a distribution's EV as like its \"center of mass.\" Imagine repeating the same experiment many times over, and taking the average over each outcome. The more you repeat the experiment, the closer this average will become to the distributions EV. (side note: as the number of repeated experiments goes to infinity, the difference between the average outcome and the EV becomes arbitrarily small.)\n", + "\n", + "### Discrete Case\n", + "If $Z$ is discrete, then its distribution is called a *probability mass function*, which measures the probability $Z$ takes on the value $k$, denoted $P(Z=k)$. Note that the probability mass function completely describes the random variable $Z$, that is, if we know the mass function, we know how $Z$ should behave. There are popular probability mass functions that consistently appear: we will introduce them as needed, but let's introduce the first very useful probability mass function. We say $Z$ is *Poisson*-distributed if:\n", + "\n", + "$$P(Z = k) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k=0,1,2, \\dots $$\n", + "\n", + "$\\lambda$ is called a parameter of the distribution, and it controls the distribution's shape. For the Poisson distribution, $\\lambda$ can be any positive number. By increasing $\\lambda$, we add more probability to larger values, and conversely by decreasing $\\lambda$ we add more probability to smaller values. One can describe $\\lambda$ as the *intensity* of the Poisson distribution. \n", + "\n", + "Unlike $\\lambda$, which can be any positive number, the value $k$ in the above formula must be a non-negative integer, i.e., $k$ must take on values 0,1,2, and so on. This is very important, because if you wanted to model a population you could not make sense of populations with 4.25 or 5.612 members. \n", + "\n", + "If a random variable $Z$ has a Poisson mass distribution, we denote this by writing\n", + "\n", + "$$Z \\sim \\text{Poi}(\\lambda) $$\n", + "\n", + "One useful property of the Poisson distribution is that its expected value is equal to its parameter, i.e.:\n", + "\n", + "$$E\\large[ \\;Z\\; | \\; \\lambda \\;\\large] = \\lambda $$\n", + "\n", + "We will use this property often, so it's useful to remember. Below, we plot the probability mass distribution for different $\\lambda$ values. The first thing to notice is that by increasing $\\lambda$, we add more probability of larger values occurring. Second, notice that although the graph ends at 15, the distributions do not. They assign positive probability to every non-negative integer." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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dua5fy1rOY3lQWXpGU287fj+otzw9jZaj/X6I1qvl5Odhw4ZkYktXVxezZs1i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\nWLDAr1i+J8dMn5LjvWmss7uXAyZPYNp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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "import scipy.stats as stats\n", + "a = np.arange(16)\n", + "poi = stats.poisson\n", + "lambda_ = [1.5, 4.25]\n", + "colours = [\"#348ABD\", \"#A60628\"]\n", + "\n", + "plt.bar(a, poi.pmf(a, lambda_[0]), color=colours[0],\n", + " label=\"$\\lambda = %.1f$\" % lambda_[0], alpha=0.60,\n", + " edgecolor=colours[0], lw=\"3\")\n", + "\n", + "plt.bar(a, poi.pmf(a, lambda_[1]), color=colours[1],\n", + " label=\"$\\lambda = %.1f$\" % lambda_[1], alpha=0.60,\n", + " edgecolor=colours[1], lw=\"3\")\n", + "\n", + "plt.xticks(a + 0.4, a)\n", + "plt.legend()\n", + "plt.ylabel(\"probability of $k$\")\n", + "plt.xlabel(\"$k$\")\n", + "plt.title(\"Probability mass function of a Poisson random variable; differing \\\n", + "$\\lambda$ values\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Continuous Case\n", + "Instead of a probability mass function, a continuous random variable has a *probability density function*. This might seem like unnecessary nomenclature, but the density function and the mass function are very different creatures. An example of continuous random variable is a random variable with *exponential density*. The density function for an exponential random variable looks like this:\n", + "\n", + "$$f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0$$\n", + "\n", + "Like a Poisson random variable, an exponential random variable can take on only non-negative values. But unlike a Poisson variable, the exponential can take on *any* non-negative values, including non-integral values such as 4.25 or 5.612401. This property makes it a poor choice for count data, which must be an integer, but a great choice for time data, temperature data (measured in Kelvins, of course), or any other precise *and positive* variable. The graph below shows two probability density functions with different $\\lambda$ values. \n", + "\n", + "When a random variable $Z$ has an exponential distribution with parameter $\\lambda$, we say *$Z$ is exponential* and write\n", + "\n", + "$$Z \\sim \\text{Exp}(\\lambda)$$\n", + "\n", + "Given a specific $\\lambda$, the expected value of an exponential random variable is equal to the inverse of $\\lambda$, that is:\n", + "\n", + "$$E[\\; Z \\;|\\; \\lambda \\;] = \\frac{1}{\\lambda}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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or15PqGcxAK4hzJK7H2bl/3sMF4lkuHUiIiIi0tm0W029mU0B7nfOnR+d/hrg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\nXMeJQGAedxoH/HECEQSpZMAs1befC8JWWxDg3uYynipNtD4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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "a = np.linspace(0, 4, 100)\n", + "expo = stats.expon\n", + "lambda_ = [0.5, 1]\n", + "\n", + "for l, c in zip(lambda_, colours):\n", + " plt.plot(a, expo.pdf(a, scale=1. / l), lw=3,\n", + " color=c, label=\"$\\lambda = %.1f$\" % l)\n", + " plt.fill_between(a, expo.pdf(a, scale=1. / l), color=c, alpha=.33)\n", + "\n", + "plt.legend()\n", + "plt.ylabel(\"PDF at $z$\")\n", + "plt.xlabel(\"$z$\")\n", + "plt.ylim(0, 1.2)\n", + "plt.title(\"Probability density function of an Exponential random variable;\\\n", + " differing $\\lambda$\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### But what is $\\lambda \\;$?\n", + "\n", + "\n", + "**This question is what motivates statistics**. In the real world, $\\lambda$ is hidden from us. We see only $Z$, and must go backwards to try and determine $\\lambda$. The problem is difficult because there is no one-to-one mapping from $Z$ to $\\lambda$. Many different methods have been created to solve the problem of estimating $\\lambda$, but since $\\lambda$ is never actually observed, no one can say for certain which method is best! \n", + "\n", + "Bayesian inference is concerned with *beliefs* about what $\\lambda$ might be. Rather than try to guess $\\lambda$ exactly, we can only talk about what $\\lambda$ is likely to be by assigning a probability distribution to $\\lambda$.\n", + "\n", + "This might seem odd at first. After all, $\\lambda$ is fixed; it is not (necessarily) random! How can we assign probabilities to values of a non-random variable? Ah, we have fallen for our old, frequentist way of thinking. Recall that under Bayesian philosophy, we *can* assign probabilities if we interpret them as beliefs. And it is entirely acceptable to have *beliefs* about the parameter $\\lambda$. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Inferring behaviour from text-message data\n", + "\n", + "Let's try to model a more interesting example, one that concerns the rate at which a user sends and receives text messages:\n", + "\n", + "> You are given a series of daily text-message counts from a user of your system. The data, plotted over time, appears in the chart below. You are curious to know if the user's text-messaging habits have changed over time, either gradually or suddenly. How can you model this? (This is in fact my own text-message data. Judge my popularity as you wish.)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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09CjG7DKsbe1Jpd25Q+PsB0vukCZ7K3fu7X7daub+ypx7mTn3dDox+xkzZtDT\n01P35PcmRTYQEd+WdF1+/8V89j3APwygHTsCP5QU+X6vjYhbJd0HXCdpEvAEcPwAtmlmZlYKjb5R\n1N8mamb1FOqoS9oIeLnqPsAzEbGq6I4i4jFgnULziHgWOLy/9V2jnkanvescLJx7Os4+jcGQe+Ub\nRev50tGjknTUB0Punci5p1O27IuO+vIa2cWja90krZD0mKRLJG3ZqkaamZmZmQ02RTvq/0L2ZURH\nAPsARwK3A58ETgPeDlzaigZWeBz1NCoXQVh7Ofd0nH0azj0N556Gc0+nbNkXKn0BzgTGRcSSfPqR\nvLb8dxGxl6RZwO9a0kIzMzMzs0Go6Bn1rYAhNfOGAMPz+wuB1zWrUfW4Rj2NstVydQvnno6zT8O5\np+Hc03Du6ZQt+6Jn1K8m+0bRycA8YFfgDGBK/vgRwMPNb56ZmZmZ2eBU9Iz6J4Cvkg3H+BXgfcDX\nyGrUAe4EDml666q4Rj2NstVydQvnno6zT8O5p+Hc03Du6ZQt+6LjqK8Cvp7f6j3+cjMbZWZmZmY2\n2BU6oy7pREn75PffKOkuSXdKelNrm7eGa9TTKFstV7dw7uk4+zScexrOPQ3nnk7Zsi9a+vJ54Nn8\n/iXAvcBdwP+0olFmZmZmZoNd0Y769hGxSNIWwETgU8BnqfNNo63iGvU0ylbL1S2cezrOPg3nnoZz\nT8O5p1O27IuO+vK0pFHAaODeiFghaQig1jXNzMzMzGzwKtpR/xzZFxqtBE7I5x0OzGxFo+pxjXoa\nZavl6hbOPR1nn4ZzT8O5p+Hc0ylb9kVHffm2pOvy+y/ms+8hG67RzMzMzMyarGiNeqWDvomkXSTt\nQtbJL7z+hnKNehplq+XqFs49HWefhnNPw7mn4dzTKVv2hc6oSzocuBzYveahADZucpvMzMzMzAa9\nomfErwT+A9gK2LTqtlmL2rUO16inUbZarm7h3NNx9mk49zScexrOPZ2yZV+0o74FcFVEvBARK6tv\nA92hpI0kzZB0Uz69jaRbJT0s6RZJwwe6TTMzMzOzblO0o/4V4JOSmjEc4xnAA1XT5wC3RcTewB3A\nufVWco16GmWr5eoWzj0dZ5+Gc0/Duafh3NMpW/ZFO+o/AD4MLJH0aPVtIDuTtCtwNHBF1exjgSn5\n/SnAcQPZppmZmZlZNyo6jvoNwN3A9cBLG7C/rwCfAKrLW3aMiEUAEbFQ0g71VnSNehplq+XqFs49\nHWefhnPtpaAVAAAfFElEQVRPw7mn4dzTKVv2RTvqewD7R8Sq9d2RpHcDiyKiV9KhDRaNejNvuOEG\nrrjiCkaMGAHA8OHDGT169OrAKx9leLrc08P2HAPA0jlZqdNWe41daxpGdVR7u2l6zjMvAtsD6+bf\nO30ay7Yb0lHt9bSnO2W6d/o0ls55ap3Xq9q/n0avb73Tn2bMcUc0dX+dko+nPe3ptadnzZrFkiVL\nAJg7dy7jx4+np6eHehRRt1+89kLSNcCUiLit34X73sZ/AB8AXgNeBwwDfgiMBw6NiEWSdgLujIh9\nate/5JJLYtKkSeu7e1tPU6dOXX1wtcPM+cv4xM2z+3z8S0ePYswuw9rWnlTanTs0zn6w5A5psrdy\n5170datZf2PNfJ0sc+5l5tzT6cTsZ8yYQU9PT93rQDcpuI3NgZsk3Q0sqn4gIk4qsoGIOA84D0DS\nIcBZEfFBSRcDpwAXAScDNxZsk5mZmZlZ1yraUb8/v7XChcB1kiYBTwDH11vINeppdNq7zsHCuafj\n7NNw7mk49zSc+8AsWLqCxS+8UvexHbbcjJ232rzwtsqWfaGOekR8ppk7jYi7gLvy+88Chzdz+2Zm\nZmbWHRa/8ErDsrGBdNTLpujwjKtJ+mkrGtIfj6OeRuUiCGsv556Os0/Duafh3NNw7umULfsBd9SB\ng5veCjMzMzMzW0vRGvVqzfh20gFzjXoaZavl6hbOPR1nn4ZzT8O5p+Hcm69RHTusqWUvW/br01H/\nSNNbYWZmZma2nhrVsUN5a9kLlb5IWj1kYkR8t2r+/7WiUfW4Rj2NstVydQvnno6zT8O5p+Hc03Du\n6ZQt+6I16of1Mf/QJrXDzMzMzMyqNCx9kfTZ/O5mVfcr9iQb97wtXKOeRtlqubqFc0/H2afh3NNw\n7mk493TKln1/Neq75T83qroPEMA84IIWtKnrFL3AwczMzNrP/6etUzXsqEfEqQCSfhMR32xPk+rr\n7e1l3LhxKZuw3sp8gcPUqVNL9+6zGzj3dJx9Gs49Deeeaff/aeeeTtmyL1qj/lLtDGXObXJ7zMzM\nzMyM4h318yV9X9I2AJL2BKYCR7esZTVco55Gmd51dhPnno6zT8O5p+Hc03Du6ZQt+6Id9bHAUuAP\nkj4H3Av8BDikVQ0zMzMzMxvMCnXUI2I5cB7wHPAp4CbgwohY1cK2rcXjqKdRtvFGu4VzT8fZp+Hc\n03DuaTj3dMqWfdEvPHo3MBO4E9gP2Bu4W9IeLWybmZmZmdmg1d/wjBVfB06OiF8ASJpIdmb9PmDb\nFrVtLa5RT6NstVzdwrmn4+zTcO5pOPc0nHs6Zcu+aEd9v4h4rjKRl7x8TtJPi+5I0ubAr4DN8v3e\nEBGfyS9Q/T4wEngcOD4ilhTdrpm1j8caNjMza5+iNerPSdpW0gclfRJA0i7A4qI7iogVwGERsT/Z\nxal/JWkCcA5wW0TsDdwB1B3y0TXqaZStlqtbdGrulbGG+7o16sSXRadm3+2cexrOPQ3nnk7Zsi90\nRl3SIcAPyEpdDgIuBt4AfBx4T9GdRcSL+d3N830HcCxrRo+ZAvySrPNuZmZmHaDRp2n+JK0c/ByW\nU9HSl0uBEyLidkmVEpjfAhMGsjNJGwG/A/YCvhYR90raMSIWAUTEQkk71FvXNepplK2Wq1s493Sc\nfRrOPY2iuTf65s5O/nbtTpXiePdzmCnba03RcdR3j4jb8/uR/3yF4h39bMWIVXnpy67ABEn7Vm1v\n9WID2aaZmZmZWTcq2tF+QNKREXFL1bzDgVnrs9OIWCrpl8BRwKLKWXVJO9FH3fvkyZMZOnQoI0aM\nAGD48OGMHj169TujSs1Rp04vnZPV2G+119i606nb19d0ZV679jdszzEN84JRHZVPq6Yvu+yyth/f\nc555EdgeWDf/3unTWLbdkEHx/NQe+6nbM1imZ82axWmnndYx7RnIdO/0aSyd81Sfr+9F/n56pz/N\nmOOOaOr+mnm8F3l96JTno9mvfwN9fjr1eC9y/C1YuoJb77gLgLETDgSy57cyvcOWmzHnD/e2pb2t\n+v+U4v9r7fSsWbNYsiQbN2Xu3LmMHz+enp4e6lFE/yewJf0l2TeR/hQ4HriarDb92Ii4t98NZNvY\nDng1IpZIeh1wC3AhWX36sxFxkaSzgW0iYp0a9UsuuSQmTZpUZFcdZ+b8ZX1+3ATZR05jdhnWxhYV\nN3Xq1NUHVzuUOatmanfu0Dj7Su6D4flJkb2VO/eifxdF/saaub8iiuberLZ3qna/tvk1fmCa2fZO\nfK2ZMWMGPT09qvfYJkU2EBH3SNoP+ADwLWAeMCEinhxAO3YGpuR16hsB34+ImyXdA1wnaRLwBNkb\ngXW4Rj2NTjuYW6ETL7AZDLl3KmefhnNPw7mn4dzTKVv2hTrqkj4eEf9JNtpL9fwzI+LLRbYREbOA\ncXXmP0tWRmOWhC+wMTMzs05U9GLST/cx/9+b1ZD+eBz1NKrrF619nHs6zj4N556Gc0/DuadTtuwb\nnlGX9M787saSDgOq62f2BJa1qmFmZmZmZoNZf6UvV+Y/tyCrTa8IYCHwL61oVD2uUU+jbLVc3cK5\np+Ps03DuaTj3NJx7OmXLvmFHPSL2AJB0dUSc1J4mmZml04kXF5uZlU2j11Lw62lRRUd9Sd5J7+3t\nZdy4da5FtRbrxGGMBgPnns6td9zFtc9sX/cxX1zcOj7m03DuaQyG3BsN1ADpXk/Lln3Ri0nNzMzM\nzKyNStNRd416GmV619lNnHs6lW/js/byMZ+Gc0/DuadTtuz77KhLOqbq/qbtaY6ZmZmZmUHjM+rf\nqbr/51Y3pD8eRz2Nso032i2cezq906elbsKg5GM+DeeehnNPp2zZN7qYdKGkjwIPAJvUGUcdgIi4\no1WNMzMzMzMbrBp11E8BPgucAWzG2uOoVwTZFx+1XJEa9WYOBeRhhTJlq+XqFs49nbETDuTaBiMV\nWGv4mE/Duafh3NMpW/Z9dtQj4jfA4QCSZkfEqLa1aj01cyigTh1WyMzMzMwGh0KjvlQ66ZJGSDpQ\n0m6tbda6XKOeRtlqubqFc0/HNepp+JhPw7mn4dzTKVv2hb7wSNJOwPeBA8kuLN1W0j3AP0TE/Ba2\nz8ysKVzOZmbtUOS1xqyoQh114OvATODoiFguaSjwH/n8Yxqu2SQeRz2NstVydQvn3nxFy9lco56G\nj/k0nHvzFXmtce7plC37oh31icDOEfEqQN5Z/yTwVMtaZh2h6FnIRsv5TOXA+eyvmW0ovy6bpbeh\nn7AU7ag/B7yZ7Kx6xd7A8wXXR9KuwNXAjsAq4JsR8V+StiErqxkJPA4cHxFLatfv7e1l3LhxRXdn\nTXLrHXdx7TPb9/l45SxkozMIvvB24Irmbs2X1aj3nb21xtSpU0t3pqvTFXlddu5pOPd02p19kU9Y\nGil0MSlwMXCbpAslnSbpQuAX+fyiXgPOjIh9yWrd/1nSm4BzgNsiYm/gDuDcAWzTzMzMzKwrFR31\n5ZvACcB2wHvyn++LiMuL7igiFkZEb37/BeBBYFfgWGBKvtgU4Lh667tGPY2xEw5M3YRBybmn4+zT\n8NnFNPba7wBmzl/W523B0hWpm9iVfLynU7bsi5a+VL6BtCnfQippd2AscA+wY0QsyvexUNIOzdiH\nmZmZNebvDDHrbIU76s0iaUvgBuCMiHhBUtQsUjsNwOTJkxk6dCgjRowAYPjw4YwePXr1O6OpU6cy\n55kXqdSWLp2Tjbu+1V5jV0/3Tn+aMccdsXp5YK31q6d7p09j6Zyn1lq/enu906exbLshfa5fO12v\nPdXT/a2farqSaV/th1GF8iq6v2F7jmmYV2V/zf59272//qZvuPoKli7ZumnHX5HpRn8/lf2len5a\n/ftVvz5UjuVGv9+Nt9zJ8y+9uvrse2Xs9cr047PuY9uhm3bU79/p07NmzeK0007rmPYMZLro/4tG\nfz+t+P9UZH+Njvfq1+8irw/tzn+v/Q5g8QuvrPP3V5k+4p2HrK7D72977e4//GbBnLYf70WPv2b1\nV5r5/6KZ/58uu+yydfqPzch3IMfDi/Nns/Kl5QBcOHU573rHgfT09FCPIur2i1tC0ibAT4CfRcTk\nfN6DwKERsSgfr/3OiNindt1LLrkkJk2a1HD7M+cv6/fMwJhdhhVqa6duq92m/OjWfi9qHLPLsIa/\nY6dn1ay2N1PR3JupSA5lPpaLtr1R9t2QQ6cq88V1RY+Hdr9OFtlfu1/jm6lT/08X2dayR2e2/Xhv\n92t8u7Y10La3+7WmSLtWLvwTPT09qvd4u8+ofwt4oNJJz90EnAJcBJwM3FhvRdeop1HmMaVTDHHY\nrOHQypx7Cs0chs7Zp9GpnfRuH+Kwmce7h5UtrlOP98GgbNkX/WbSj0fEf9aZf2ZEfLngNg4C3g/M\nkvR7shKX88g66NdJmgQ8ARxftPFmjaSovfQwlWk4d2sVH1vFud7drPmKDs/46T7m/3vRHUXEryNi\n44gYGxH7R8S4iPh5RDwbEYdHxN4RcURE1B2bvbe3t95sa7FKrZ+1l3NPx9mnUanrtPby8Z6Gj/d0\nypZ9wzPqkt6Z391Y0mFAdf3MnsCyVjXMzJrDH0ebWdl0e8mRWVH9lb5cmf/cgqy+vCKAhcC/tKJR\n9bhGPQ3X66bRzNz9cfTA+JhPo2x1o92iU4/3bi858vGeTtmyb9hRj4g9ACRdHREntadJZmaDhz/x\nMCuPZp3p99+9FVXoYtLqTrqkjWoeW9XsRtXT29vLuHHj2rErq5LVL/Y9dJe1hnNPp93Z+xOPTJmH\nZywzv9YMTLPO9N96x139Dos5GP7uUyjba02hi0kljZM0TdJy4NX89lr+08zMzMzMmqzoqC9TgDuB\n8WQXke4J7JH/bAvXqKdR+aY3ay/nno6zL27B0hXMnL+sz9uCpSsKb6tMZ7i6iY/3NJx7OmV7rSn6\nhUcjgU9FO7/G1MzMOprLdszMWqtoR/2HwBHALS1sS0OuUS+umRepuH4xDeeejrNvviIX4DWzbrTI\n/nwxX8bHexrOPZ2y1agX7ahvAfxQ0lSyYRlX82gwncdnucysk7R7qL0i+/PrpJmVQdEa9QeAi4Bf\nA3Nqbm3hGvU0XEeXhnNPx9mnUaYzXN3Ex3sazj2dsr3WFB2e8TOtboj5m9jMrPVc8mFm1lgnvU4W\n6qhLemdfj0XEHc1rTt8GQ416J34Tm+vo0nDu6XR79p1a8lG2utFu0e3He6dy7ukUea3ppNfJojXq\nV9ZMbw9sBjxJG4donDl/Wd35PgNk1p066axGSs7BzDqJKwAy7cihaOnLHtXTkjYG/h2o33NugbFj\nx3bc2ebBYOyEA7m2wbtKaw3nnklxVqMTs++kszut4rPpaXTi8T4YlD33TqwAKKqZrzXtyKHoxaRr\niYiVwBeAT25wC8zMzMzMbB1FS1/qeRewqujCkq4E/hpYFBH75fO2Ab5P9oVKjwPHR8SSeuv39vYC\n+29Ac219uI6u+YqUMRTN3R8/Np+P+TRco57GYDjeO/F1cjDk3qnK9lpT9GLSeUD1t5IOIRtb/fQB\n7Osq4L+Bq6vmnQPcFhEXSzobODefZ9a1ipQxNGNbnf7xo5lZO/h10sqs6Bn1D9RMLwceiYilRXcU\nEVMljayZfSxwSH5/CvBL+uiojx07lv+dUXRv3auZZwaKbKuZdXRFziQ3Y1vdcCa57PWLZebs0yjT\nGa5ukuJ47/bX7yL8OpNO2V5ril5MeheApI2AHcnKVwqXvTSwQ0QsyvexUNIOTdhmV2vmmYFO+rbA\nyj6bsS2fITEz61x+/TYrrmjpyzDga8AJwKbAq5L+F/hYXzXl6yn6emDy5Mk8On8Fm2+zEwAbv24o\nQ3YZxVZ7Zd9YOnXqVOY88yKVmq+lc3oBVj++dE4vvdOfZsxxR6xeHta8s6qd7p0+jaVznlpr/ert\n9U6fxrLthvS5fu10vfZUT/fX/sr+hu05ptDv16z9VZbpa3swqlBeRZ+fyre1tWt//eVV2V9/z29l\nulnPzw1XX8HSJVv3e/y1+3hotL/1yWtD8qzeXzOPh8q2NmR/zX59KLq/vfY7gMUvvJLXv6759sPe\n6dPY+nWbcuyRhxXaX4rnZ9asWZx22mkD2v/6vn43+/Wh6PNT9O+1Wf+fiuyv0fHeqteHDX1+2r2/\nVhwPsx+6H7Y7tND+2vF62un/L5q5v8suu4zRo0ev9/6acTy8OH82K19aDsCFU5fzrnccSE9PD/UU\nLX35b2AoMBp4guzizy8A/wWcXHAb9SyStGNELJK0E7C4rwUPOeQQFqzq+2LSiRMnMmz+stUfJVUC\nqdhqr7GMnTBqreVr1682dsKBbPXMmnf8tdsbO+FAxuwyrPD26rVnIO2v7K8ylnx/v1+z9jfnR7cW\n2l5/eQ30+em0/fX3/Famm/X8jHrTvvz2me37fDzV8dBof7Xba8Z00f112vHX7NeHovubOX9ZfqYy\nO3bWfLS+/VqfWLXjeB9I+5t1vAxkfymOh6J/r836/9Sprw8b+vy0e3+tOB4AfvtM39sbyPHQ7v9P\nKf5fNHN/1Z309dlfM46H6mXOOXoUKxf+ib4UHZ7xKOCDEfFIRKyIiEeAU/P5A6H8VnETcEp+/2Tg\nxr5WHDt2bF8PWQtVXlCsvZx7Os4+jbLVjXYLH+9pOPd0yvZaU/SM+stkp2ieqJq3HbCi6I4kfRc4\nFNhW0lzgfOBC4HpJk/JtH190e2bWuXyxmJmZ2YYr2lG/AviFpC+zpvTl34DLi+4oIt7Xx0OHF1nf\n46in4bFe0yh77mW+WKzs2ZdV2cY27hY+3tNw7umU7bWmaEf9C8B84H3ALvn9i4FvtahdLeWzfWZm\nZmbW6QrVqEfmWxFxeES8Of95ZUT0OUpLszWzRr1ytq/erdE434OR6+jScO7pOPs0ynSGq5v4eE/D\nuadTtteaQh11Sf8l6e01894u6dLWNMvMzMzMbHArWvpyIvDxmnm/A34E/GtTW9SHTq1R7/YyGtfR\npTEYcm/mN9U202DIvhPdeMud7D56fJ+Pd8PraRHt/p/i4z0N555Ot9aoB+uefd+4zrxBp8wXzZml\n1MxvqrXye/6lV/s9HgbD66n/p5hZtaId7buBz0vaCCD/eUE+vy08jnoarqPLLFi6gpnzl/V5W7C0\n8EilhTj3dJqZfaPjptnHTLO1u+0+5tNw7mk493TKdDYdip9RPwP4CbBA0hPACGAB8J5WNcyskxQ5\n++szXVarzGdHy9x2M7NuUXTUlyeBccCxwJeA44C35vPbIqtRt3bL6uis3Zx7Os4+DeeehnNPw7mn\nM3Xq1NRNGJCiZ9SJiFXAPfnNzMzMzKxU/rz8VWbOX1b3sU68aL00F4O6Rj0N19Gl4dzTcfZpOPc0\nnHsazj2d3UePL9V36RQ+o25mZmZm7dPtQ0Bb/0rTUe/UcdS7ncd6TcO5p+Ps03DuaTj3NIrm7ou6\nm69sx3xpSl/MzMzMzAaT0nTUXaOehuvo0nDu6Tj7NJx7Gs49DeeeTtmyL01H3czMzMxsMHGNujVU\ntlqubuHc03H2aRTJvdGFdeCL69aHj/c0mpm7/y4GpmzHfEd01CUdBVxKdob/yoi4qHaZ2bNnw57u\nqLfb7Ifuh+0OTd2MQce5p+Ps0yiSu78huPl8vKfRzNz9dzEwZTvmk5e+SNoI+CpwJLAvcKKkN9Uu\nt3z58nY3zYAXltX/UgBrLeeejrNPw7mn4dzTcO7plC375B11YALwp4h4IiJeBf4XODZxm8zMzMzM\nkuqEjvrrgXlV00/m89aycOHCtjXI1lj41Lz+F7Kmc+7pOPs0nHsazj0N555O2bJXRKRtgPR3wJER\n8U/59AeACRHxserlTjvttKgufxkzZoyHbGyD3t5e55yAc0/H2afh3NNw7mk493Q6Ifve3l5mzpy5\nenrMmDGcddZZqrdsJ3TU/xK4ICKOyqfPAaLeBaVmZmZmZoNFJ5S+3AuMkjRS0mbAPwA3JW6TmZmZ\nmVlSyYdnjIiVkj4K3Mqa4RkfTNwsMzMzM7OkOuGMOhHx84jYOyLeEBEXVj8m6ShJD0l6RNLZqdo4\nGEi6UtIiSX+omreNpFslPSzpFknDU7axG0naVdIdku6XNEvSx/L5zr6FJG0u6beSfp/nfn4+37m3\ngaSNJM2QdFM+7dzbQNLjkmbmx/30fJ6zbzFJwyVdL+nB/LX+bc69tSS9MT/OZ+Q/l0j6WNly74iO\nel+KjrFuTXMVWdbVzgFui4i9gTuAc9vequ73GnBmROwLHAj8c36cO/sWiogVwGERsT8wFvgrSRNw\n7u1yBvBA1bRzb49VwKERsX9ETMjnOfvWmwzcHBH7AGOAh3DuLRURj+TH+TjgrcBy4IeULPeO7qjj\nMdbbKiKmAs/VzD4WmJLfnwIc19ZGDQIRsTAievP7LwAPArvi7FsuIl7M725OVgoYOPeWk7QrcDRw\nRdVs594eYt3//c6+hSRtBRwcEVcBRMRrEbEE595OhwNzImIeJcu90zvqhcZYt5baISIWQdahBHZI\n3J6uJml3srO79wA7OvvWyssvfg8sBH4REffi3NvhK8AnyN4YVTj39gjgF5LulfSP+Txn31p7AM9I\nuiovw7hc0hCcezudAHw3v1+q3Du9o26dJ+14nl1M0pbADcAZ+Zn12qydfZNFxKq89GVXYIKkfXHu\nLSXp3cCi/FOkuuMG55x7axyUlwIcTVZmdzA+5lttE2Ac8LU8++Vk5RfOvQ0kbQocA1yfzypV7p3e\nUX8KGFE1vWs+z9pnkaQdASTtBCxO3J6uJGkTsk76NRFxYz7b2bdJRCwFfgkchXNvtYOAYyQ9CnwP\neKeka4CFzr31ImJB/vNp4EdkJaY+5lvrSWBeRNyXT/+ArOPu3Nvjr4DfRcQz+XSpcu/0jrrHWG8/\nsfZZrpuAU/L7JwM31q5gTfEt4IGImFw1z9m3kKTtKlf7S3od8C6y6wOcewtFxHkRMSIi9iR7Tb8j\nIj4I/Bjn3lKShuSf3CFpKHAEMAsf8y2Vl1nMk/TGfFYPcD/OvV1OJDspUFGq3JN/M2l/JB1FdrV0\nZYz1C/tZxdaTpO8ChwLbAouA88nOuFwP7AY8ARwfEc+namM3knQQ8Cuyf5iR384DpgPX4exbQtJo\nsguJNspv34+IL0j6C5x7W0g6BDgrIo5x7q0naQ+yUS+CrBzj2oi40Nm3nqQxZBdPbwo8CpwKbIxz\nb6n8WoAngD0jYlk+r1THe8d31M3MzMzMBqNOL30xMzMzMxuU3FE3MzMzM+tA7qibmZmZmXUgd9TN\nzMzMzDqQO+pmZmZmZh3IHXUzMzMzsw7kjrqZWQlIOlfS5W3c39R87Od6jx0iaV6L9/9bSfu0ch9m\nZp1uk9QNMDMzkLSM7ItoAIYCK4CV+byPRMQX29iWvwaWRsTMBou1+ks4vgR8Dnhvi/djZtaxfEbd\nzKwDRMSwiNgqIrYi+7a8d1fN+15/6zfZ/wdc0+Z91voxcJikHRK3w8wsGXfUzcw6j/LbmhnS+ZKu\nye+PlLRK0imS5kr6s6SPSBovaaakZyX9d836kyQ9kC/7M0kj6u5Y2hR4J3BX1bwtJH073+4fgQNq\n1jlb0mxJSyX9UdJxlW3l+9u3atntJS2XtG1++7Gk5/LlVu8zIlYAvwOOXL8IzczKzx11M7PyqC03\nmQCMAk4ALgXOI+tkvwU4XtLBAJKOBc4BjgO2B+4G+jpL/wZgZUTMr5p3AbBHfjsSOLlmndnAQfmn\nAZ8BviNpx4h4Nd/PB6qWPRG4LSL+DJwFzAO2BXbI21/tQaBunbyZ2WDgjrqZWTkF8NmIeCUibgOW\nA9+LiD/nney7gf3zZT8CfDEiHomIVcCFwFhJu9XZ7tbAspp5fw98PiKWRMRTwH+t1ZCIH0TEovz+\n9cCfyN5EAFwNvK9q8Q/m8wBeBXYG9oiIlRHx65r9LsvbY2Y2KLmjbmZWXour7r8ELKqZ3jK/PxKY\nnJeuPAv8mayj//o623wOGFYzbxfgyarpJ6oflHSSpN/nJSzPAfsC2wFExHRgeT5SzN7AXmT15wAX\nA3OAW/PSmbNr9jsMeL7+r25m1v3cUTcz637zyEaO+Yv8tk1EbBkR99RZdjYgSTtXzZsPVJ99H1m5\nk9e6Xw6cnm93G+B+1q6xn0J2Jv2DwA0R8QpARCyPiI9HxF7AMcCZkg6rWm8foNHIM2ZmXc0ddTOz\nclL/i6z2deA8SW8GkDRcUt1hD/O68tuAQ6pmXw+cK2lrSbsCH616bCiwCnhG0kaSTiWrka92LfA3\nwPtZU/aCpHdL2iufXAa8lm8LSZsDbwV+MYDf08ysq7ijbmbWeYqMUV67TJ/TEfEjsrr0/5X0PPAH\n4KgG274cOKlq+jPAXOAx4OdUdbYj4kHgEuAeYCFZ2cvUtRoS8SQwI7sb1Y+9AbgtH0P+18DXIqIy\n8ssxwJ0RsbBBO83MupoiWv2dFWZmVjaS7gY+2s+XHg1ke1cCT0XEpwsuPw34UEQ80Iz9m5mVkTvq\nZmbWUpJ2Jzujvn9EPNF4aTMzq3Dpi5mZtYykz5KV2lzsTrqZ2cD4jLqZmZmZWQfyGXUzMzMzsw7k\njrqZmZmZWQdyR93MzMzMrAO5o25mZmZm1oHcUTczMzMz60DuqJuZmZmZdaD/HznQjkjM7w2rAAAA\nAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 3.5)\n", + "count_data = np.loadtxt(\"data/txtdata.csv\")\n", + "n_count_data = len(count_data)\n", + "plt.bar(np.arange(n_count_data), count_data, color=\"#348ABD\")\n", + "plt.xlabel(\"Time (days)\")\n", + "plt.ylabel(\"count of text-msgs received\")\n", + "plt.title(\"Did the user's texting habits change over time?\")\n", + "plt.xlim(0, n_count_data);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before we start modeling, see what you can figure out just by looking at the chart above. Would you say there was a change in behaviour during this time period? \n", + "\n", + "How can we start to model this? Well, as we have conveniently already seen, a Poisson random variable is a very appropriate model for this type of *count* data. Denoting day $i$'s text-message count by $C_i$, \n", + "\n", + "$$ C_i \\sim \\text{Poisson}(\\lambda) $$\n", + "\n", + "We are not sure what the value of the $\\lambda$ parameter really is, however. Looking at the chart above, it appears that the rate might become higher late in the observation period, which is equivalent to saying that $\\lambda$ increases at some point during the observations. (Recall that a higher value of $\\lambda$ assigns more probability to larger outcomes. That is, there is a higher probability of many text messages having been sent on a given day.)\n", + "\n", + "How can we represent this observation mathematically? Let's assume that on some day during the observation period (call it $\\tau$), the parameter $\\lambda$ suddenly jumps to a higher value. So we really have two $\\lambda$ parameters: one for the period before $\\tau$, and one for the rest of the observation period. In the literature, a sudden transition like this would be called a *switchpoint*:\n", + "\n", + "$$\n", + "\\lambda = \n", + "\\begin{cases}\n", + "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", + "\\lambda_2 & \\text{if } t \\ge \\tau\n", + "\\end{cases}\n", + "$$\n", + "\n", + "\n", + "If, in reality, no sudden change occurred and indeed $\\lambda_1 = \\lambda_2$, then the $\\lambda$s posterior distributions should look about equal.\n", + "\n", + "We are interested in inferring the unknown $\\lambda$s. To use Bayesian inference, we need to assign prior probabilities to the different possible values of $\\lambda$. What would be good prior probability distributions for $\\lambda_1$ and $\\lambda_2$? Recall that $\\lambda$ can be any positive number. As we saw earlier, the *exponential* distribution provides a continuous density function for positive numbers, so it might be a good choice for modeling $\\lambda_i$. But recall that the exponential distribution takes a parameter of its own, so we'll need to include that parameter in our model. Let's call that parameter $\\alpha$.\n", + "\n", + "\\begin{align}\n", + "&\\lambda_1 \\sim \\text{Exp}( \\alpha ) \\\\\\\n", + "&\\lambda_2 \\sim \\text{Exp}( \\alpha )\n", + "\\end{align}\n", + "\n", + "$\\alpha$ is called a *hyper-parameter* or *parent variable*. In literal terms, it is a parameter that influences other parameters. Our initial guess at $\\alpha$ does not influence the model too strongly, so we have some flexibility in our choice. A good rule of thumb is to set the exponential parameter equal to the inverse of the average of the count data. Since we're modeling $\\lambda$ using an exponential distribution, we can use the expected value identity shown earlier to get:\n", + "\n", + "$$\\frac{1}{N}\\sum_{i=0}^N \\;C_i \\approx E[\\; \\lambda \\; |\\; \\alpha ] = \\frac{1}{\\alpha}$$ \n", + "\n", + "An alternative, and something I encourage the reader to try, would be to have two priors: one for each $\\lambda_i$. Creating two exponential distributions with different $\\alpha$ values reflects our prior belief that the rate changed at some point during the observations.\n", + "\n", + "What about $\\tau$? Because of the noisiness of the data, it's difficult to pick out a priori when $\\tau$ might have occurred. Instead, we can assign a *uniform prior belief* to every possible day. This is equivalent to saying\n", + "\n", + "\\begin{align}\n", + "& \\tau \\sim \\text{DiscreteUniform(1,70) }\\\\\\\\\n", + "& \\Rightarrow P( \\tau = k ) = \\frac{1}{70}\n", + "\\end{align}\n", + "\n", + "So after all this, what does our overall prior distribution for the unknown variables look like? Frankly, *it doesn't matter*. What we should understand is that it's an ugly, complicated mess involving symbols only a mathematician could love. And things will only get uglier the more complicated our models become. Regardless, all we really care about is the posterior distribution.\n", + "\n", + "We next turn to PyMC, a Python library for performing Bayesian analysis that is undaunted by the mathematical monster we have created. \n", + "\n", + "\n", + "Introducing our first hammer: PyMC\n", + "-----\n", + "\n", + "PyMC is a Python library for programming Bayesian analysis [3]. It is a fast, well-maintained library. The only unfortunate part is that its documentation is lacking in certain areas, especially those that bridge the gap between beginner and hacker. One of this book's main goals is to solve that problem, and also to demonstrate why PyMC is so cool.\n", + "\n", + "We will model the problem above using PyMC. This type of programming is called *probabilistic programming*, an unfortunate misnomer that invokes ideas of randomly-generated code and has likely confused and frightened users away from this field. The code is not random; it is probabilistic in the sense that we create probability models using programming variables as the model's components. Model components are first-class primitives within the PyMC framework. \n", + "\n", + "B. Cronin [5] has a very motivating description of probabilistic programming:\n", + "\n", + "> Another way of thinking about this: unlike a traditional program, which only runs in the forward directions, a probabilistic program is run in both the forward and backward direction. It runs forward to compute the consequences of the assumptions it contains about the world (i.e., the model space it represents), but it also runs backward from the data to constrain the possible explanations. In practice, many probabilistic programming systems will cleverly interleave these forward and backward operations to efficiently home in on the best explanations.\n", + "\n", + "Because of the confusion engendered by the term *probabilistic programming*, I'll refrain from using it. Instead, I'll simply say *programming*, since that's what it really is. \n", + "\n", + "PyMC code is easy to read. The only novel thing should be the syntax, and I will interrupt the code to explain individual sections. Simply remember that we are representing the model's components ($\\tau, \\lambda_1, \\lambda_2$ ) as variables:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pymc as pm\n", + "\n", + "alpha = 1.0 / count_data.mean() # Recall count_data is the\n", + " # variable that holds our txt counts\n", + "lambda_1 = pm.Exponential(\"lambda_1\", alpha)\n", + "lambda_2 = pm.Exponential(\"lambda_2\", alpha)\n", + "\n", + "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=n_count_data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the code above, we create the PyMC variables corresponding to $\\lambda_1$ and $\\lambda_2$. We assign them to PyMC's *stochastic variables*, so-called because they are treated by the back end as random number generators. We can demonstrate this fact by calling their built-in `random()` methods." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Random output: 64 5 12\n" + ] + } + ], + "source": [ + "print(\"Random output:\", tau.random(), tau.random(), tau.random())" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@pm.deterministic\n", + "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", + " out = np.zeros(n_count_data)\n", + " out[:tau] = lambda_1 # lambda before tau is lambda1\n", + " out[tau:] = lambda_2 # lambda after (and including) tau is lambda2\n", + " return out" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This code creates a new function `lambda_`, but really we can think of it as a random variable: the random variable $\\lambda$ from above. Note that because `lambda_1`, `lambda_2` and `tau` are random, `lambda_` will be random. We are **not** fixing any variables yet.\n", + "\n", + "`@pm.deterministic` is a decorator that tells PyMC this is a deterministic function. That is, if the arguments were deterministic (which they are not), the output would be deterministic as well. Deterministic functions will be covered in Chapter 2. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "observation = pm.Poisson(\"obs\", lambda_, value=count_data, observed=True)\n", + "\n", + "model = pm.Model([observation, lambda_1, lambda_2, tau])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The variable `observation` combines our data, `count_data`, with our proposed data-generation scheme, given by the variable `lambda_`, through the `value` keyword. We also set `observed = True` to tell PyMC that this should stay fixed in our analysis. Finally, PyMC wants us to collect all the variables of interest and create a `Model` instance out of them. This makes our life easier when we retrieve the results.\n", + "\n", + "The code below will be explained in Chapter 3, but I show it here so you can see where our results come from. One can think of it as a *learning* step. The machinery being employed is called *Markov Chain Monte Carlo* (MCMC), which I also delay explaining until Chapter 3. This technique returns thousands of random variables from the posterior distributions of $\\lambda_1, \\lambda_2$ and $\\tau$. We can plot a histogram of the random variables to see what the posterior distributions look like. Below, we collect the samples (called *traces* in the MCMC literature) into histograms." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 40000 of 40000 complete in 6.5 sec" + ] + } + ], + "source": [ + "# Mysterious code to be explained in Chapter 3.\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(40000, 10000, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "lambda_1_samples = mcmc.trace('lambda_1')[:]\n", + "lambda_2_samples = mcmc.trace('lambda_2')[:]\n", + "tau_samples = mcmc.trace('tau')[:]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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xLjdW0wfbNH7EaH1Q/2aLy826qefAjwZXVfo4zuOReTwyj0fm8cg8HWjoUdLe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\nRESkgWlCnzPVouVPfZ4/9Xn+VM+dP/V5/jS25E9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o963x9u9oeaLs3223266JP2LECFpa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\nGmu6QlEEjwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 10)\n", + "# histogram of the samples:\n", + "\n", + "ax = plt.subplot(311)\n", + "ax.set_autoscaley_on(False)\n", + "\n", + "plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of $\\lambda_1$\", color=\"#A60628\", normed=True)\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(r\"\"\"Posterior distributions of the variables\n", + " $\\lambda_1,\\;\\lambda_2,\\;\\tau$\"\"\")\n", + "plt.xlim([15, 30])\n", + "plt.xlabel(\"$\\lambda_1$ value\")\n", + "\n", + "ax = plt.subplot(312)\n", + "ax.set_autoscaley_on(False)\n", + "plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", normed=True)\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim([15, 30])\n", + "plt.xlabel(\"$\\lambda_2$ value\")\n", + "\n", + "plt.subplot(313)\n", + "w = 1.0 / tau_samples.shape[0] * np.ones_like(tau_samples)\n", + "plt.hist(tau_samples, bins=n_count_data, alpha=1,\n", + " label=r\"posterior of $\\tau$\",\n", + " color=\"#467821\", weights=w, rwidth=2.)\n", + "plt.xticks(np.arange(n_count_data))\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.ylim([0, .75])\n", + "plt.xlim([35, len(count_data) - 20])\n", + "plt.xlabel(r\"$\\tau$ (in days)\")\n", + "plt.ylabel(\"probability\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Interpretation\n", + "\n", + "Recall that Bayesian methodology returns a *distribution*. Hence we now have distributions to describe the unknown $\\lambda$s and $\\tau$. What have we gained? Immediately, we can see the uncertainty in our estimates: the wider the distribution, the less certain our posterior belief should be. We can also see what the plausible values for the parameters are: $\\lambda_1$ is around 18 and $\\lambda_2$ is around 23. The posterior distributions of the two $\\lambda$s are clearly distinct, indicating that it is indeed likely that there was a change in the user's text-message behaviour.\n", + "\n", + "What other observations can you make? If you look at the original data again, do these results seem reasonable? \n", + "\n", + "Notice also that the posterior distributions for the $\\lambda$s do not look like exponential distributions, even though our priors for these variables were exponential. In fact, the posterior distributions are not really of any form that we recognize from the original model. But that's OK! This is one of the benefits of taking a computational point of view. If we had instead done this analysis using mathematical approaches, we would have been stuck with an analytically intractable (and messy) distribution. Our use of a computational approach makes us indifferent to mathematical tractability.\n", + "\n", + "Our analysis also returned a distribution for $\\tau$. Its posterior distribution looks a little different from the other two because it is a discrete random variable, so it doesn't assign probabilities to intervals. We can see that near day 45, there was a 50% chance that the user's behaviour changed. Had no change occurred, or had the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many days were plausible candidates for $\\tau$. By contrast, in the actual results we see that only three or four days make any sense as potential transition points. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Why would I want samples from the posterior, anyways?\n", + "\n", + "\n", + "We will deal with this question for the remainder of the book, and it is an understatement to say that it will lead us to some amazing results. For now, let's end this chapter with one more example.\n", + "\n", + "We'll use the posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le 70$ ? Recall that the expected value of a Poisson variable is equal to its parameter $\\lambda$. Therefore, the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n", + "\n", + "In the code below, let $i$ index samples from the posterior distributions. Given a day $t$, we average over all possible $\\lambda_i$ for that day $t$, using $\\lambda_i = \\lambda_{1,i}$ if $t \\lt \\tau_i$ (that is, if the behaviour change has not yet occurred), else we use $\\lambda_i = \\lambda_{2,i}$. " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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/MXPmTF544QUmTJhAWlqab/k9e/bw8ssvc+LECRYsWMDGjRvp2rUr0dHRdOrU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\n9fdWjQ+H+vspe3+t6A+NDrU/lP35FPF5UeT+Brd5sPsroj9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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "# tau_samples, lambda_1_samples, lambda_2_samples contain\n", + "# N samples from the corresponding posterior distribution\n", + "N = tau_samples.shape[0]\n", + "expected_texts_per_day = np.zeros(n_count_data)\n", + "for day in range(0, n_count_data):\n", + " # ix is a bool index of all tau samples corresponding to\n", + " # the switchpoint occurring prior to value of 'day'\n", + " ix = day < tau_samples\n", + " # Each posterior sample corresponds to a value for tau.\n", + " # for each day, that value of tau indicates whether we're \"before\"\n", + " # (in the lambda1 \"regime\") or\n", + " # \"after\" (in the lambda2 \"regime\") the switchpoint.\n", + " # by taking the posterior sample of lambda1/2 accordingly, we can average\n", + " # over all samples to get an expected value for lambda on that day.\n", + " # As explained, the \"message count\" random variable is Poisson distributed,\n", + " # and therefore lambda (the poisson parameter) is the expected value of\n", + " # \"message count\".\n", + " expected_texts_per_day[day] = (lambda_1_samples[ix].sum()\n", + " + lambda_2_samples[~ix].sum()) / N\n", + "\n", + "\n", + "plt.plot(range(n_count_data), expected_texts_per_day, lw=4, color=\"#E24A33\",\n", + " label=\"expected number of text-messages received\")\n", + "plt.xlim(0, n_count_data)\n", + "plt.xlabel(\"Day\")\n", + "plt.ylabel(\"Expected # text-messages\")\n", + "plt.title(\"Expected number of text-messages received\")\n", + "plt.ylim(0, 60)\n", + "plt.bar(np.arange(len(count_data)), count_data, color=\"#348ABD\", alpha=0.65,\n", + " label=\"observed texts per day\")\n", + "\n", + "plt.legend(loc=\"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our analysis shows strong support for believing the user's behavior did change ($\\lambda_1$ would have been close in value to $\\lambda_2$ had this not been true), and that the change was sudden rather than gradual (as demonstrated by $\\tau$'s strongly peaked posterior distribution). We can speculate what might have caused this: a cheaper text-message rate, a recent weather-to-text subscription, or perhaps a new relationship. (In fact, the 45th day corresponds to Christmas, and I moved away to Toronto the next month, leaving a girlfriend behind.)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Exercises\n", + "\n", + "1\\. Using `lambda_1_samples` and `lambda_2_samples`, what is the mean of the posterior distributions of $\\lambda_1$ and $\\lambda_2$?" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# type your code here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. What is the expected percentage increase in text-message rates? `hint:` compute the mean of `lambda_1_samples/lambda_2_samples`. Note that this quantity is very different from `lambda_1_samples.mean()/lambda_2_samples.mean()`." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# type your code here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3\\. What is the mean of $\\lambda_1$ **given** that we know $\\tau$ is less than 45. That is, suppose we have been given new information that the change in behaviour occurred prior to day 45. What is the expected value of $\\lambda_1$ now? (You do not need to redo the PyMC part. Just consider all instances where `tau_samples < 45`.)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# type your code here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "\n", + "- [1] Gelman, Andrew. N.p.. Web. 22 Jan 2013. [N is never large enough](http://andrewgelman.com/2005/07/31/n_is_never_larg/).\n", + "- [2] Norvig, Peter. 2009. [The Unreasonable Effectiveness of Data](http://static.googleusercontent.com/media/research.google.com/en//pubs/archive/35179.pdf).\n", + "- [3] Patil, A., D. Huard and C.J. Fonnesbeck. 2010. \n", + "PyMC: Bayesian Stochastic Modelling in Python. Journal of Statistical \n", + "Software, 35(4), pp. 1-81. \n", + "- [4] Jimmy Lin and Alek Kolcz. Large-Scale Machine Learning at Twitter. Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data (SIGMOD 2012), pages 793-804, May 2012, Scottsdale, Arizona.\n", + "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. ." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [conda env:bayes]", + "language": "python", + "name": "conda-env-bayes-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter1_Introduction/Ch1_Introduction_PyMC3.ipynb b/Chapter1_Introduction/Ch1_Introduction_PyMC3.ipynb new file mode 100644 index 00000000..ef7a601f --- /dev/null +++ b/Chapter1_Introduction/Ch1_Introduction_PyMC3.ipynb @@ -0,0 +1,1068 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Probabilistic Programming\n", + "=====\n", + "and Bayesian Methods for Hackers \n", + "========\n", + "\n", + "##### Version 0.1\n", + "\n", + "`Original content created by Cam Davidson-Pilon`\n", + "\n", + "`Ported to Python 3 and PyMC3 by Max Margenot (@clean_utensils) and Thomas Wiecki (@twiecki) at Quantopian (@quantopian)`\n", + "___\n", + "\n", + "\n", + "Welcome to *Bayesian Methods for Hackers*. The full Github repository is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Chapter 1\n", + "======\n", + "***" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Philosophy of Bayesian Inference\n", + "------\n", + " \n", + "> You are a skilled programmer, but bugs still slip into your code. After a particularly difficult implementation of an algorithm, you decide to test your code on a trivial example. It passes. You test the code on a harder problem. It passes once again. And it passes the next, *even more difficult*, test too! You are starting to believe that there may be no bugs in this code...\n", + "\n", + "If you think this way, then congratulations, you already are thinking Bayesian! Bayesian inference is simply updating your beliefs after considering new evidence. A Bayesian can rarely be certain about a result, but he or she can be very confident. Just like in the example above, we can never be 100% sure that our code is bug-free unless we test it on every possible problem; something rarely possible in practice. Instead, we can test it on a large number of problems, and if it succeeds we can feel more *confident* about our code, but still not certain. Bayesian inference works identically: we update our beliefs about an outcome; rarely can we be absolutely sure unless we rule out all other alternatives. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### The Bayesian state of mind\n", + "\n", + "\n", + "Bayesian inference differs from more traditional statistical inference by preserving *uncertainty*. At first, this sounds like a bad statistical technique. Isn't statistics all about deriving *certainty* from randomness? To reconcile this, we need to start thinking like Bayesians. \n", + "\n", + "The Bayesian world-view interprets probability as measure of *believability in an event*, that is, how confident we are in an event occurring. In fact, we will see in a moment that this is the natural interpretation of probability. \n", + "\n", + "For this to be clearer, we consider an alternative interpretation of probability: *Frequentist*, known as the more *classical* version of statistics, assume that probability is the long-run frequency of events (hence the bestowed title). For example, the *probability of plane accidents* under a frequentist philosophy is interpreted as the *long-term frequency of plane accidents*. This makes logical sense for many probabilities of events, but becomes more difficult to understand when events have no long-term frequency of occurrences. Consider: we often assign probabilities to outcomes of presidential elections, but the election itself only happens once! Frequentists get around this by invoking alternative realities and saying across all these realities, the frequency of occurrences defines the probability. \n", + "\n", + "Bayesians, on the other hand, have a more intuitive approach. Bayesians interpret a probability as measure of *belief*, or confidence, of an event occurring. Simply, a probability is a summary of an opinion. An individual who assigns a belief of 0 to an event has no confidence that the event will occur; conversely, assigning a belief of 1 implies that the individual is absolutely certain of an event occurring. Beliefs between 0 and 1 allow for weightings of other outcomes. This definition agrees with the probability of a plane accident example, for having observed the frequency of plane accidents, an individual's belief should be equal to that frequency, excluding any outside information. Similarly, under this definition of probability being equal to beliefs, it is meaningful to speak about probabilities (beliefs) of presidential election outcomes: how confident are you candidate *A* will win?\n", + "\n", + "Notice in the paragraph above, I assigned the belief (probability) measure to an *individual*, not to Nature. This is very interesting, as this definition leaves room for conflicting beliefs between individuals. Again, this is appropriate for what naturally occurs: different individuals have different beliefs of events occurring, because they possess different *information* about the world. The existence of different beliefs does not imply that anyone is wrong. Consider the following examples demonstrating the relationship between individual beliefs and probabilities:\n", + "\n", + "- I flip a coin, and we both guess the result. We would both agree, assuming the coin is fair, that the probability of Heads is 1/2. Assume, then, that I peek at the coin. Now I know for certain what the result is: I assign probability 1.0 to either Heads or Tails (whichever it is). Now what is *your* belief that the coin is Heads? My knowledge of the outcome has not changed the coin's results. Thus we assign different probabilities to the result. \n", + "\n", + "- Your code either has a bug in it or not, but we do not know for certain which is true, though we have a belief about the presence or absence of a bug. \n", + "\n", + "- A medical patient is exhibiting symptoms $x$, $y$ and $z$. There are a number of diseases that could be causing all of them, but only a single disease is present. A doctor has beliefs about which disease, but a second doctor may have slightly different beliefs. \n", + "\n", + "\n", + "This philosophy of treating beliefs as probability is natural to humans. We employ it constantly as we interact with the world and only see partial truths, but gather evidence to form beliefs. Alternatively, you have to be *trained* to think like a frequentist. \n", + "\n", + "To align ourselves with traditional probability notation, we denote our belief about event $A$ as $P(A)$. We call this quantity the *prior probability*.\n", + "\n", + "John Maynard Keynes, a great economist and thinker, said \"When the facts change, I change my mind. What do you do, sir?\" This quote reflects the way a Bayesian updates his or her beliefs after seeing evidence. Even — especially — if the evidence is counter to what was initially believed, the evidence cannot be ignored. We denote our updated belief as $P(A |X )$, interpreted as the probability of $A$ given the evidence $X$. We call the updated belief the *posterior probability* so as to contrast it with the prior probability. For example, consider the posterior probabilities (read: posterior beliefs) of the above examples, after observing some evidence $X$:\n", + "\n", + "1\\. $P(A): \\;\\;$ the coin has a 50 percent chance of being Heads. $P(A | X):\\;\\;$ You look at the coin, observe a Heads has landed, denote this information $X$, and trivially assign probability 1.0 to Heads and 0.0 to Tails.\n", + "\n", + "2\\. $P(A): \\;\\;$ This big, complex code likely has a bug in it. $P(A | X): \\;\\;$ The code passed all $X$ tests; there still might be a bug, but its presence is less likely now.\n", + "\n", + "3\\. $P(A):\\;\\;$ The patient could have any number of diseases. $P(A | X):\\;\\;$ Performing a blood test generated evidence $X$, ruling out some of the possible diseases from consideration.\n", + "\n", + "\n", + "It's clear that in each example we did not completely discard the prior belief after seeing new evidence $X$, but we *re-weighted the prior* to incorporate the new evidence (i.e. we put more weight, or confidence, on some beliefs versus others). \n", + "\n", + "By introducing prior uncertainty about events, we are already admitting that any guess we make is potentially very wrong. After observing data, evidence, or other information, we update our beliefs, and our guess becomes *less wrong*. This is the alternative side of the prediction coin, where typically we try to be *more right*. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Bayesian Inference in Practice\n", + "\n", + " If frequentist and Bayesian inference were programming functions, with inputs being statistical problems, then the two would be different in what they return to the user. The frequentist inference function would return a number, representing an estimate (typically a summary statistic like the sample average etc.), whereas the Bayesian function would return *probabilities*.\n", + "\n", + "For example, in our debugging problem above, calling the frequentist function with the argument \"My code passed all $X$ tests; is my code bug-free?\" would return a *YES*. On the other hand, asking our Bayesian function \"Often my code has bugs. My code passed all $X$ tests; is my code bug-free?\" would return something very different: probabilities of *YES* and *NO*. The function might return:\n", + "\n", + "\n", + "> *YES*, with probability 0.8; *NO*, with probability 0.2\n", + "\n", + "\n", + "\n", + "This is very different from the answer the frequentist function returned. Notice that the Bayesian function accepted an additional argument: *\"Often my code has bugs\"*. This parameter is the *prior*. By including the prior parameter, we are telling the Bayesian function to include our belief about the situation. Technically this parameter in the Bayesian function is optional, but we will see excluding it has its own consequences. \n", + "\n", + "\n", + "#### Incorporating evidence\n", + "\n", + "As we acquire more and more instances of evidence, our prior belief is *washed out* by the new evidence. This is to be expected. For example, if your prior belief is something ridiculous, like \"I expect the sun to explode today\", and each day you are proved wrong, you would hope that any inference would correct you, or at least align your beliefs better. Bayesian inference will correct this belief.\n", + "\n", + "\n", + "Denote $N$ as the number of instances of evidence we possess. As we gather an *infinite* amount of evidence, say as $N \\rightarrow \\infty$, our Bayesian results (often) align with frequentist results. Hence for large $N$, statistical inference is more or less objective. On the other hand, for small $N$, inference is much more *unstable*: frequentist estimates have more variance and larger confidence intervals. This is where Bayesian analysis excels. By introducing a prior, and returning probabilities (instead of a scalar estimate), we *preserve the uncertainty* that reflects the instability of statistical inference of a small $N$ dataset. \n", + "\n", + "One may think that for large $N$, one can be indifferent between the two techniques since they offer similar inference, and might lean towards the computationally-simpler, frequentist methods. An individual in this position should consider the following quote by Andrew Gelman (2005)[1], before making such a decision:\n", + "\n", + "> Sample sizes are never large. If $N$ is too small to get a sufficiently-precise estimate, you need to get more data (or make more assumptions). But once $N$ is \"large enough,\" you can start subdividing the data to learn more (for example, in a public opinion poll, once you have a good estimate for the entire country, you can estimate among men and women, northerners and southerners, different age groups, etc.). $N$ is never enough because if it were \"enough\" you'd already be on to the next problem for which you need more data.\n", + "\n", + "### Are frequentist methods incorrect then? \n", + "\n", + "**No.**\n", + "\n", + "Frequentist methods are still useful or state-of-the-art in many areas. Tools such as least squares linear regression, LASSO regression, and expectation-maximization algorithms are all powerful and fast. Bayesian methods complement these techniques by solving problems that these approaches cannot, or by illuminating the underlying system with more flexible modeling.\n", + "\n", + "\n", + "#### A note on *Big Data*\n", + "Paradoxically, big data's predictive analytic problems are actually solved by relatively simple algorithms [2][4]. Thus we can argue that big data's prediction difficulty does not lie in the algorithm used, but instead on the computational difficulties of storage and execution on big data. (One should also consider Gelman's quote from above and ask \"Do I really have big data?\")\n", + "\n", + "The much more difficult analytic problems involve *medium data* and, especially troublesome, *really small data*. Using a similar argument as Gelman's above, if big data problems are *big enough* to be readily solved, then we should be more interested in the *not-quite-big enough* datasets. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Our Bayesian framework\n", + "\n", + "We are interested in beliefs, which can be interpreted as probabilities by thinking Bayesian. We have a *prior* belief in event $A$, beliefs formed by previous information, e.g., our prior belief about bugs being in our code before performing tests.\n", + "\n", + "Secondly, we observe our evidence. To continue our buggy-code example: if our code passes $X$ tests, we want to update our belief to incorporate this. We call this new belief the *posterior* probability. Updating our belief is done via the following equation, known as Bayes' Theorem, after its discoverer Thomas Bayes:\n", + "\n", + "\\begin{align}\n", + " P( A | X ) = & \\frac{ P(X | A) P(A) } {P(X) } \\\\\\\\[5pt]\n", + "& \\propto P(X | A) P(A)\\;\\; (\\propto \\text{is proportional to })\n", + "\\end{align}\n", + "\n", + "The above formula is not unique to Bayesian inference: it is a mathematical fact with uses outside Bayesian inference. Bayesian inference merely uses it to connect prior probabilities $P(A)$ with an updated posterior probabilities $P(A | X )$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Mandatory coin-flip example\n", + "\n", + "Every statistics text must contain a coin-flipping example, I'll use it here to get it out of the way. Suppose, naively, that you are unsure about the probability of heads in a coin flip (spoiler alert: it's 50%). You believe there is some true underlying ratio, call it $p$, but have no prior opinion on what $p$ might be. \n", + "\n", + "We begin to flip a coin, and record the observations: either $H$ or $T$. This is our observed data. An interesting question to ask is how our inference changes as we observe more and more data? More specifically, what do our posterior probabilities look like when we have little data, versus when we have lots of data. \n", + "\n", + "Below we plot a sequence of updating posterior probabilities as we observe increasing amounts of data (coin flips)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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eCYAxhmuvvZYhQ4awYcMGXnnlFf7whz/w3nvvAeDxeJg/fz5btmxh+fLl/Pvf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wRqdfl452Ar7xxsxaRXmJ/p4KycOJZkx5FkHb0rhnKFSVskN4Q30T6zXn+QrTVdfFTWzqdVXQNO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NU3s3NeXFfOj4Kj59yhTmTCrPcMTZt3VDXa5DyDkz48Sacq44ZQqXLZrE7Jrk5EN/2HGIe576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\nRCQyNSBERERERCSy/weqJ/a7T99jYQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\"\"\"\n", + "The book uses a custom matplotlibrc file, which provides the unique styles for\n", + "matplotlib plots. If executing this book, and you wish to use the book's\n", + "styling, provided are two options:\n", + " 1. Overwrite your own matplotlibrc file with the rc-file provided in the\n", + " book's styles/ dir. See http://matplotlib.org/users/customizing.html\n", + " 2. Also in the styles is bmh_matplotlibrc.json file. This can be used to\n", + " update the styles in only this notebook. Try running the following code:\n", + "\n", + " import json\n", + " s = json.load(open(\"../styles/bmh_matplotlibrc.json\"))\n", + " matplotlib.rcParams.update(s)\n", + "\n", + "\"\"\"\n", + "\n", + "# The code below can be passed over, as it is currently not important, plus it\n", + "# uses advanced topics we have not covered yet. LOOK AT PICTURE, MICHAEL!\n", + "%matplotlib inline\n", + "from IPython.core.pylabtools import figsize\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "figsize(11, 9)\n", + "\n", + "import scipy.stats as stats\n", + "\n", + "dist = stats.beta\n", + "n_trials = [0, 1, 2, 3, 4, 5, 8, 15, 50, 500]\n", + "data = stats.bernoulli.rvs(0.5, size=n_trials[-1])\n", + "x = np.linspace(0, 1, 100)\n", + "\n", + "# For the already prepared, I'm using Binomial's conj. prior.\n", + "for k, N in enumerate(n_trials):\n", + " sx = plt.subplot(len(n_trials)/2, 2, k+1)\n", + " plt.xlabel(\"$p$, probability of heads\") \\\n", + " if k in [0, len(n_trials)-1] else None\n", + " plt.setp(sx.get_yticklabels(), visible=False)\n", + " heads = data[:N].sum()\n", + " y = dist.pdf(x, 1 + heads, 1 + N - heads)\n", + " plt.plot(x, y, label=\"observe %d tosses,\\n %d heads\" % (N, heads))\n", + " plt.fill_between(x, 0, y, color=\"#348ABD\", alpha=0.4)\n", + " plt.vlines(0.5, 0, 4, color=\"k\", linestyles=\"--\", lw=1)\n", + "\n", + " leg = plt.legend()\n", + " leg.get_frame().set_alpha(0.4)\n", + " plt.autoscale(tight=True)\n", + "\n", + "\n", + "plt.suptitle(\"Bayesian updating of posterior probabilities\",\n", + " y=1.02,\n", + " fontsize=14)\n", + "\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The posterior probabilities are represented by the curves, and our uncertainty is proportional to the width of the curve. As the plot above shows, as we start to observe data our posterior probabilities start to shift and move around. Eventually, as we observe more and more data (coin-flips), our probabilities will tighten closer and closer around the true value of $p=0.5$ (marked by a dashed line). \n", + "\n", + "Notice that the plots are not always *peaked* at 0.5. There is no reason it should be: recall we assumed we did not have a prior opinion of what $p$ is. In fact, if we observe quite extreme data, say 8 flips and only 1 observed heads, our distribution would look very biased *away* from lumping around 0.5 (with no prior opinion, how confident would you feel betting on a fair coin after observing 8 tails and 1 head). As more data accumulates, we would see more and more probability being assigned at $p=0.5$, though never all of it.\n", + "\n", + "The next example is a simple demonstration of the mathematics of Bayesian inference. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Bug, or just sweet, unintended feature?\n", + "\n", + "\n", + "Let $A$ denote the event that our code has **no bugs** in it. Let $X$ denote the event that the code passes all debugging tests. For now, we will leave the prior probability of no bugs as a variable, i.e. $P(A) = p$. \n", + "\n", + "We are interested in $P(A|X)$, i.e. the probability of no bugs, given our debugging tests $X$. To use the formula above, we need to compute some quantities.\n", + "\n", + "What is $P(X | A)$, i.e., the probability that the code passes $X$ tests *given* there are no bugs? Well, it is equal to 1, for a code with no bugs will pass all tests. \n", + "\n", + "$P(X)$ is a little bit trickier: The event $X$ can be divided into two possibilities, event $X$ occurring even though our code *indeed has* bugs (denoted $\\sim A\\;$, spoken *not $A$*), or event $X$ without bugs ($A$). $P(X)$ can be represented as:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\\begin{align}\n", + "P(X ) & = P(X \\text{ and } A) + P(X \\text{ and } \\sim A) \\\\\\\\[5pt]\n", + " & = P(X|A)P(A) + P(X | \\sim A)P(\\sim A)\\\\\\\\[5pt]\n", + "& = P(X|A)p + P(X | \\sim A)(1-p)\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have already computed $P(X|A)$ above. On the other hand, $P(X | \\sim A)$ is subjective: our code can pass tests but still have a bug in it, though the probability there is a bug present is reduced. Note this is dependent on the number of tests performed, the degree of complication in the tests, etc. Let's be conservative and assign $P(X|\\sim A) = 0.5$. Then\n", + "\n", + "\\begin{align}\n", + "P(A | X) & = \\frac{1\\cdot p}{ 1\\cdot p +0.5 (1-p) } \\\\\\\\\n", + "& = \\frac{ 2 p}{1+p}\n", + "\\end{align}\n", + "This is the posterior probability. What does it look like as a function of our prior, $p \\in [0,1]$? " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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0e062s+dEW6S4b+dkW3fM55iSn8nCSFG/sDyPheW5TNfEmwlHPfoiIiIiY1R/P/3uE+3s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\nduCWiHgxw7AtIym/W64Gbi/6ScU5EfFmRiFbhiT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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "p = np.linspace(0, 1, 50)\n", + "plt.plot(p, 2*p/(1+p), color=\"#348ABD\", lw=3)\n", + "#plt.fill_between(p, 2*p/(1+p), alpha=.5, facecolor=[\"#A60628\"])\n", + "plt.scatter(0.2, 2*(0.2)/1.2, s=140, c=\"#348ABD\")\n", + "plt.xlim(0, 1)\n", + "plt.ylim(0, 1)\n", + "plt.xlabel(\"Prior, $P(A) = p$\")\n", + "plt.ylabel(\"Posterior, $P(A|X)$, with $P(A) = p$\")\n", + "plt.title(\"Are there bugs in my code?\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see the biggest gains if we observe the $X$ tests passed when the prior probability, $p$, is low. Let's settle on a specific value for the prior. I'm a strong programmer (I think), so I'm going to give myself a realistic prior of 0.20, that is, there is a 20% chance that I write code bug-free. To be more realistic, this prior should be a function of how complicated and large the code is, but let's pin it at 0.20. Then my updated belief that my code is bug-free is 0.33. \n", + "\n", + "Recall that the prior is a probability: $p$ is the prior probability that there *are no bugs*, so $1-p$ is the prior probability that there *are bugs*.\n", + "\n", + "Similarly, our posterior is also a probability, with $P(A | X)$ the probability there is no bug *given we saw all tests pass*, hence $1-P(A|X)$ is the probability there is a bug *given all tests passed*. What does our posterior probability look like? Below is a chart of both the prior and the posterior probabilities. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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AviUfHTt2pEuXLixdupSlS5eybNkyVqxYwcSJEyv6VHfCZWwckZijk+Xqtm/X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\nVNMuIiKZQDXtkki1Sdp7AQ+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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "colours = [\"#348ABD\", \"#A60628\"]\n", + "\n", + "prior = [0.20, 0.80]\n", + "posterior = [1./3, 2./3]\n", + "plt.bar([0, .7], prior, alpha=0.70, width=0.25,\n", + " color=colours[0], label=\"prior distribution\",\n", + " lw=\"3\", edgecolor=colours[0])\n", + "\n", + "plt.bar([0+0.25, .7+0.25], posterior, alpha=0.7,\n", + " width=0.25, color=colours[1],\n", + " label=\"posterior distribution\",\n", + " lw=\"3\", edgecolor=colours[1])\n", + "\n", + "plt.xticks([0.20, .95], [\"Bugs Absent\", \"Bugs Present\"])\n", + "plt.title(\"Prior and Posterior probability of bugs present\")\n", + "plt.ylabel(\"Probability\")\n", + "plt.legend(loc=\"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that after we observed $X$ occur, the probability of bugs being absent increased. By increasing the number of tests, we can approach confidence (probability 1) that there are no bugs present.\n", + "\n", + "This was a very simple example of Bayesian inference and Bayes rule. Unfortunately, the mathematics necessary to perform more complicated Bayesian inference only becomes more difficult, except for artificially constructed cases. We will later see that this type of mathematical analysis is actually unnecessary. First we must broaden our modeling tools. The next section deals with *probability distributions*. If you are already familiar, feel free to skip (or at least skim), but for the less familiar the next section is essential." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "_______\n", + "\n", + "## Probability Distributions\n", + "\n", + "\n", + "**Let's quickly recall what a probability distribution is:** Let $Z$ be some random variable. Then associated with $Z$ is a *probability distribution function* that assigns probabilities to the different outcomes $Z$ can take. Graphically, a probability distribution is a curve where the probability of an outcome is proportional to the height of the curve. You can see examples in the first figure of this chapter. \n", + "\n", + "We can divide random variables into three classifications:\n", + "\n", + "- **$Z$ is discrete**: Discrete random variables may only assume values on a specified list. Things like populations, movie ratings, and number of votes are all discrete random variables. Discrete random variables become more clear when we contrast them with...\n", + "\n", + "- **$Z$ is continuous**: Continuous random variable can take on arbitrarily exact values. For example, temperature, speed, time, color are all modeled as continuous variables because you can progressively make the values more and more precise.\n", + "\n", + "- **$Z$ is mixed**: Mixed random variables assign probabilities to both discrete and continuous random variables, i.e. it is a combination of the above two categories. \n", + "\n", + "### Discrete Case\n", + "If $Z$ is discrete, then its distribution is called a *probability mass function*, which measures the probability $Z$ takes on the value $k$, denoted $P(Z=k)$. Note that the probability mass function completely describes the random variable $Z$, that is, if we know the mass function, we know how $Z$ should behave. There are popular probability mass functions that consistently appear: we will introduce them as needed, but let's introduce the first very useful probability mass function. We say $Z$ is *Poisson*-distributed if:\n", + "\n", + "$$P(Z = k) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k=0,1,2, \\dots $$\n", + "\n", + "$\\lambda$ is called a parameter of the distribution, and it controls the distribution's shape. For the Poisson distribution, $\\lambda$ can be any positive number. By increasing $\\lambda$, we add more probability to larger values, and conversely by decreasing $\\lambda$ we add more probability to smaller values. One can describe $\\lambda$ as the *intensity* of the Poisson distribution. \n", + "\n", + "Unlike $\\lambda$, which can be any positive number, the value $k$ in the above formula must be a non-negative integer, i.e., $k$ must take on values 0,1,2, and so on. This is very important, because if you wanted to model a population you could not make sense of populations with 4.25 or 5.612 members. \n", + "\n", + "If a random variable $Z$ has a Poisson mass distribution, we denote this by writing\n", + "\n", + "$$Z \\sim \\text{Poi}(\\lambda) $$\n", + "\n", + "One useful property of the Poisson distribution is that its expected value is equal to its parameter, i.e.:\n", + "\n", + "$$E\\large[ \\;Z\\; | \\; \\lambda \\;\\large] = \\lambda $$\n", + "\n", + "We will use this property often, so it's useful to remember. Below, we plot the probability mass distribution for different $\\lambda$ values. The first thing to notice is that by increasing $\\lambda$, we add more probability of larger values occurring. Second, notice that although the graph ends at 15, the distributions do not. They assign positive probability to every non-negative integer." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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dua5fy1rOY3lQWXpGU287fj+otzw9jZaj/X6I1qvl5Odhw4ZkYktXVxezZs1i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\nWLDAr1i+J8dMn5LjvWmss7uXAyZPYNp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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "import scipy.stats as stats\n", + "a = np.arange(16)\n", + "poi = stats.poisson\n", + "lambda_ = [1.5, 4.25]\n", + "colours = [\"#348ABD\", \"#A60628\"]\n", + "\n", + "plt.bar(a, poi.pmf(a, lambda_[0]), color=colours[0],\n", + " label=\"$\\lambda = %.1f$\" % lambda_[0], alpha=0.60,\n", + " edgecolor=colours[0], lw=\"3\")\n", + "\n", + "plt.bar(a, poi.pmf(a, lambda_[1]), color=colours[1],\n", + " label=\"$\\lambda = %.1f$\" % lambda_[1], alpha=0.60,\n", + " edgecolor=colours[1], lw=\"3\")\n", + "\n", + "plt.xticks(a + 0.4, a)\n", + "plt.legend()\n", + "plt.ylabel(\"probability of $k$\")\n", + "plt.xlabel(\"$k$\")\n", + "plt.title(\"Probability mass function of a Poisson random variable; differing \\\n", + "$\\lambda$ values\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Continuous Case\n", + "Instead of a probability mass function, a continuous random variable has a *probability density function*. This might seem like unnecessary nomenclature, but the density function and the mass function are very different creatures. An example of continuous random variable is a random variable with *exponential density*. The density function for an exponential random variable looks like this:\n", + "\n", + "$$f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0$$\n", + "\n", + "Like a Poisson random variable, an exponential random variable can take on only non-negative values. But unlike a Poisson variable, the exponential can take on *any* non-negative values, including non-integral values such as 4.25 or 5.612401. This property makes it a poor choice for count data, which must be an integer, but a great choice for time data, temperature data (measured in Kelvins, of course), or any other precise *and positive* variable. The graph below shows two probability density functions with different $\\lambda$ values. \n", + "\n", + "When a random variable $Z$ has an exponential distribution with parameter $\\lambda$, we say *$Z$ is exponential* and write\n", + "\n", + "$$Z \\sim \\text{Exp}(\\lambda)$$\n", + "\n", + "Given a specific $\\lambda$, the expected value of an exponential random variable is equal to the inverse of $\\lambda$, that is:\n", + "\n", + "$$E[\\; Z \\;|\\; \\lambda \\;] = \\frac{1}{\\lambda}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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or15PqGcxAK4hzJK7H2bl/3sMF4lkuHUiIiIi0tm0W029mU0B7nfOnR+d/hrg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\nXMeJQGAedxoH/HECEQSpZMAs1befC8JWWxDg3uYynipNtD4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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "a = np.linspace(0, 4, 100)\n", + "expo = stats.expon\n", + "lambda_ = [0.5, 1]\n", + "\n", + "for l, c in zip(lambda_, colours):\n", + " plt.plot(a, expo.pdf(a, scale=1./l), lw=3,\n", + " color=c, label=\"$\\lambda = %.1f$\" % l)\n", + " plt.fill_between(a, expo.pdf(a, scale=1./l), color=c, alpha=.33)\n", + "\n", + "plt.legend()\n", + "plt.ylabel(\"PDF at $z$\")\n", + "plt.xlabel(\"$z$\")\n", + "plt.ylim(0,1.2)\n", + "plt.title(\"Probability density function of an Exponential random variable;\\\n", + " differing $\\lambda$\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### But what is $\\lambda \\;$?\n", + "\n", + "\n", + "**This question is what motivates statistics**. In the real world, $\\lambda$ is hidden from us. We see only $Z$, and must go backwards to try and determine $\\lambda$. The problem is difficult because there is no one-to-one mapping from $Z$ to $\\lambda$. Many different methods have been created to solve the problem of estimating $\\lambda$, but since $\\lambda$ is never actually observed, no one can say for certain which method is best! \n", + "\n", + "Bayesian inference is concerned with *beliefs* about what $\\lambda$ might be. Rather than try to guess $\\lambda$ exactly, we can only talk about what $\\lambda$ is likely to be by assigning a probability distribution to $\\lambda$.\n", + "\n", + "This might seem odd at first. After all, $\\lambda$ is fixed; it is not (necessarily) random! How can we assign probabilities to values of a non-random variable? Ah, we have fallen for our old, frequentist way of thinking. Recall that under Bayesian philosophy, we *can* assign probabilities if we interpret them as beliefs. And it is entirely acceptable to have *beliefs* about the parameter $\\lambda$. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Inferring behaviour from text-message data\n", + "\n", + "Let's try to model a more interesting example, one that concerns the rate at which a user sends and receives text messages:\n", + "\n", + "> You are given a series of daily text-message counts from a user of your system. The data, plotted over time, appears in the chart below. You are curious to know if the user's text-messaging habits have changed over time, either gradually or suddenly. How can you model this? (This is in fact my own text-message data. Judge my popularity as you wish.)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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09CjG7DKsbe1Jpd25Q+PsB0vukCZ7K3fu7X7daub+ypx7mTn3dDox+xkzZtDT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\n8NnFNPba7wBmzl/W523B0hW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 3.5)\n", + "count_data = np.loadtxt(\"data/txtdata.csv\")\n", + "n_count_data = len(count_data)\n", + "plt.bar(np.arange(n_count_data), count_data, color=\"#348ABD\")\n", + "plt.xlabel(\"Time (days)\")\n", + "plt.ylabel(\"count of text-msgs received\")\n", + "plt.title(\"Did the user's texting habits change over time?\")\n", + "plt.xlim(0, n_count_data);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before we start modeling, see what you can figure out just by looking at the chart above. Would you say there was a change in behaviour during this time period? \n", + "\n", + "How can we start to model this? Well, as we have conveniently already seen, a Poisson random variable is a very appropriate model for this type of *count* data. Denoting day $i$'s text-message count by $C_i$, \n", + "\n", + "$$ C_i \\sim \\text{Poisson}(\\lambda) $$\n", + "\n", + "We are not sure what the value of the $\\lambda$ parameter really is, however. Looking at the chart above, it appears that the rate might become higher late in the observation period, which is equivalent to saying that $\\lambda$ increases at some point during the observations. (Recall that a higher value of $\\lambda$ assigns more probability to larger outcomes. That is, there is a higher probability of many text messages having been sent on a given day.)\n", + "\n", + "How can we represent this observation mathematically? Let's assume that on some day during the observation period (call it $\\tau$), the parameter $\\lambda$ suddenly jumps to a higher value. So we really have two $\\lambda$ parameters: one for the period before $\\tau$, and one for the rest of the observation period. In the literature, a sudden transition like this would be called a *switchpoint*:\n", + "\n", + "$$\n", + "\\lambda = \n", + "\\begin{cases}\n", + "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", + "\\lambda_2 & \\text{if } t \\ge \\tau\n", + "\\end{cases}\n", + "$$\n", + "\n", + "\n", + "If, in reality, no sudden change occurred and indeed $\\lambda_1 = \\lambda_2$, then the $\\lambda$s posterior distributions should look about equal.\n", + "\n", + "We are interested in inferring the unknown $\\lambda$s. To use Bayesian inference, we need to assign prior probabilities to the different possible values of $\\lambda$. What would be good prior probability distributions for $\\lambda_1$ and $\\lambda_2$? Recall that $\\lambda$ can be any positive number. As we saw earlier, the *exponential* distribution provides a continuous density function for positive numbers, so it might be a good choice for modeling $\\lambda_i$. But recall that the exponential distribution takes a parameter of its own, so we'll need to include that parameter in our model. Let's call that parameter $\\alpha$.\n", + "\n", + "\\begin{align}\n", + "&\\lambda_1 \\sim \\text{Exp}( \\alpha ) \\\\\\\n", + "&\\lambda_2 \\sim \\text{Exp}( \\alpha )\n", + "\\end{align}\n", + "\n", + "$\\alpha$ is called a *hyper-parameter* or *parent variable*. In literal terms, it is a parameter that influences other parameters. Our initial guess at $\\alpha$ does not influence the model too strongly, so we have some flexibility in our choice. A good rule of thumb is to set the exponential parameter equal to the inverse of the average of the count data. Since we're modeling $\\lambda$ using an exponential distribution, we can use the expected value identity shown earlier to get:\n", + "\n", + "$$\\frac{1}{N}\\sum_{i=0}^N \\;C_i \\approx E[\\; \\lambda \\; |\\; \\alpha ] = \\frac{1}{\\alpha}$$ \n", + "\n", + "An alternative, and something I encourage the reader to try, would be to have two priors: one for each $\\lambda_i$. Creating two exponential distributions with different $\\alpha$ values reflects our prior belief that the rate changed at some point during the observations.\n", + "\n", + "What about $\\tau$? Because of the noisiness of the data, it's difficult to pick out a priori when $\\tau$ might have occurred. Instead, we can assign a *uniform prior belief* to every possible day. This is equivalent to saying\n", + "\n", + "\\begin{align}\n", + "& \\tau \\sim \\text{DiscreteUniform(1,70) }\\\\\\\\\n", + "& \\Rightarrow P( \\tau = k ) = \\frac{1}{70}\n", + "\\end{align}\n", + "\n", + "So after all this, what does our overall prior distribution for the unknown variables look like? Frankly, *it doesn't matter*. What we should understand is that it's an ugly, complicated mess involving symbols only a mathematician could love. And things will only get uglier the more complicated our models become. Regardless, all we really care about is the posterior distribution.\n", + "\n", + "We next turn to PyMC3, a Python library for performing Bayesian analysis that is undaunted by the mathematical monster we have created. \n", + "\n", + "\n", + "Introducing our first hammer: PyMC3\n", + "-----\n", + "\n", + "PyMC3 is a Python library for programming Bayesian analysis [3]. It is a fast, well-maintained library. The only unfortunate part is that its documentation is lacking in certain areas, especially those that bridge the gap between beginner and hacker. One of this book's main goals is to solve that problem, and also to demonstrate why PyMC3 is so cool.\n", + "\n", + "We will model the problem above using PyMC3. This type of programming is called *probabilistic programming*, an unfortunate misnomer that invokes ideas of randomly-generated code and has likely confused and frightened users away from this field. The code is not random; it is probabilistic in the sense that we create probability models using programming variables as the model's components. Model components are first-class primitives within the PyMC3 framework. \n", + "\n", + "B. Cronin [5] has a very motivating description of probabilistic programming:\n", + "\n", + "> Another way of thinking about this: unlike a traditional program, which only runs in the forward directions, a probabilistic program is run in both the forward and backward direction. It runs forward to compute the consequences of the assumptions it contains about the world (i.e., the model space it represents), but it also runs backward from the data to constrain the possible explanations. In practice, many probabilistic programming systems will cleverly interleave these forward and backward operations to efficiently home in on the best explanations.\n", + "\n", + "Because of the confusion engendered by the term *probabilistic programming*, I'll refrain from using it. Instead, I'll simply say *programming*, since that's what it really is. \n", + "\n", + "PyMC3 code is easy to read. The only novel thing should be the syntax. Simply remember that we are representing the model's components ($\\tau, \\lambda_1, \\lambda_2$ ) as variables." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied log-transform to lambda_1 and added transformed lambda_1_log_ to model.\n", + "Applied log-transform to lambda_2 and added transformed lambda_2_log_ to model.\n" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "\n", + "with pm.Model() as model:\n", + " alpha = 1.0/count_data.mean() # Recall count_data is the\n", + " # variable that holds our txt counts\n", + " lambda_1 = pm.Exponential(\"lambda_1\", alpha)\n", + " lambda_2 = pm.Exponential(\"lambda_2\", alpha)\n", + " \n", + " tau = pm.DiscreteUniform(\"tau\", lower=0, upper=n_count_data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the code above, we create the PyMC3 variables corresponding to $\\lambda_1$ and $\\lambda_2$. We assign them to PyMC3's *stochastic variables*, so-called because they are treated by the back end as random number generators." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "with model:\n", + " idx = np.arange(n_count_data) # Index\n", + " lambda_ = pm.switch(tau >= idx, lambda_1, lambda_2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This code creates a new function `lambda_`, but really we can think of it as a random variable: the random variable $\\lambda$ from above. The `switch()` function assigns `lambda_1` or `lambda_2` as the value of `lambda_`, depending on what side of `tau` we are on. The values of `lambda_` up until `tau` are `lambda_1` and the values afterwards are `lambda_2`.\n", + "\n", + "Note that because `lambda_1`, `lambda_2` and `tau` are random, `lambda_` will be random. We are **not** fixing any variables yet." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "with model:\n", + " observation = pm.Poisson(\"obs\", lambda_, observed=count_data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The variable `observation` combines our data, `count_data`, with our proposed data-generation scheme, given by the variable `lambda_`, through the `observed` keyword. \n", + "\n", + "The code below will be explained in Chapter 3, but I show it here so you can see where our results come from. One can think of it as a *learning* step. The machinery being employed is called *Markov Chain Monte Carlo* (MCMC), which I also delay explaining until Chapter 3. This technique returns thousands of random variables from the posterior distributions of $\\lambda_1, \\lambda_2$ and $\\tau$. We can plot a histogram of the random variables to see what the posterior distributions look like. Below, we collect the samples (called *traces* in the MCMC literature) into histograms." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 10000 of 10000 in 2.3 sec. | SPS: 4300.6 | ETA: 0.0" + ] + } + ], + "source": [ + "### Mysterious code to be explained in Chapter 3.\n", + "with model:\n", + " step = pm.Metropolis()\n", + " trace = pm.sample(10000, tune=5000,step=step)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "lambda_1_samples = trace['lambda_1']\n", + "lambda_2_samples = trace['lambda_2']\n", + "tau_samples = trace['tau']" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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M45F5PDKPR+bpQEEPAAAApFhoDz3oRYvizc3a+vY6SdJJRx+74/sWXbofqK7d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\n0/IfUkY2EREREZE+qdcaejN7X/cP8EPgITO7yMxON7PPAL8G7kn6ZO7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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 10)\n", + "#histogram of the samples:\n", + "\n", + "ax = plt.subplot(311)\n", + "ax.set_autoscaley_on(False)\n", + "\n", + "plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of $\\lambda_1$\", color=\"#A60628\", normed=True)\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(r\"\"\"Posterior distributions of the variables\n", + " $\\lambda_1,\\;\\lambda_2,\\;\\tau$\"\"\")\n", + "plt.xlim([15, 30])\n", + "plt.xlabel(\"$\\lambda_1$ value\")\n", + "\n", + "ax = plt.subplot(312)\n", + "ax.set_autoscaley_on(False)\n", + "plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", normed=True)\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim([15, 30])\n", + "plt.xlabel(\"$\\lambda_2$ value\")\n", + "\n", + "plt.subplot(313)\n", + "w = 1.0 / tau_samples.shape[0] * np.ones_like(tau_samples)\n", + "plt.hist(tau_samples, bins=n_count_data, alpha=1,\n", + " label=r\"posterior of $\\tau$\",\n", + " color=\"#467821\", weights=w, rwidth=2.)\n", + "plt.xticks(np.arange(n_count_data))\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.ylim([0, .75])\n", + "plt.xlim([35, len(count_data)-20])\n", + "plt.xlabel(r\"$\\tau$ (in days)\")\n", + "plt.ylabel(\"probability\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Interpretation\n", + "\n", + "Recall that Bayesian methodology returns a *distribution*. Hence we now have distributions to describe the unknown $\\lambda$s and $\\tau$. What have we gained? Immediately, we can see the uncertainty in our estimates: the wider the distribution, the less certain our posterior belief should be. We can also see what the plausible values for the parameters are: $\\lambda_1$ is around 18 and $\\lambda_2$ is around 23. The posterior distributions of the two $\\lambda$s are clearly distinct, indicating that it is indeed likely that there was a change in the user's text-message behaviour.\n", + "\n", + "What other observations can you make? If you look at the original data again, do these results seem reasonable? \n", + "\n", + "Notice also that the posterior distributions for the $\\lambda$s do not look like exponential distributions, even though our priors for these variables were exponential. In fact, the posterior distributions are not really of any form that we recognize from the original model. But that's OK! This is one of the benefits of taking a computational point of view. If we had instead done this analysis using mathematical approaches, we would have been stuck with an analytically intractable (and messy) distribution. Our use of a computational approach makes us indifferent to mathematical tractability.\n", + "\n", + "Our analysis also returned a distribution for $\\tau$. Its posterior distribution looks a little different from the other two because it is a discrete random variable, so it doesn't assign probabilities to intervals. We can see that near day 45, there was a 50% chance that the user's behaviour changed. Had no change occurred, or had the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many days were plausible candidates for $\\tau$. By contrast, in the actual results we see that only three or four days make any sense as potential transition points. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Why would I want samples from the posterior, anyways?\n", + "\n", + "\n", + "We will deal with this question for the remainder of the book, and it is an understatement to say that it will lead us to some amazing results. For now, let's end this chapter with one more example.\n", + "\n", + "We'll use the posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le 70$ ? Recall that the expected value of a Poisson variable is equal to its parameter $\\lambda$. Therefore, the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n", + "\n", + "In the code below, let $i$ index samples from the posterior distributions. Given a day $t$, we average over all possible $\\lambda_i$ for that day $t$, using $\\lambda_i = \\lambda_{1,i}$ if $t \\lt \\tau_i$ (that is, if the behaviour change has not yet occurred), else we use $\\lambda_i = \\lambda_{2,i}$. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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57rvvAOfD+v/+7/+YPn06L7zwAuPGjSMtLS3w+F27dvHyyy9z7Ngx5s2bx/r1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\nlTaJaZ/8HJPelFYN60TorG4M5R4ntezzXvXl6+5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "# tau_samples, lambda_1_samples, lambda_2_samples contain\n", + "# N samples from the corresponding posterior distribution\n", + "N = tau_samples.shape[0]\n", + "expected_texts_per_day = np.zeros(n_count_data)\n", + "for day in range(0, n_count_data):\n", + " # ix is a bool index of all tau samples corresponding to\n", + " # the switchpoint occurring prior to value of 'day'\n", + " ix = day < tau_samples\n", + " # Each posterior sample corresponds to a value for tau.\n", + " # for each day, that value of tau indicates whether we're \"before\"\n", + " # (in the lambda1 \"regime\") or\n", + " # \"after\" (in the lambda2 \"regime\") the switchpoint.\n", + " # by taking the posterior sample of lambda1/2 accordingly, we can average\n", + " # over all samples to get an expected value for lambda on that day.\n", + " # As explained, the \"message count\" random variable is Poisson distributed,\n", + " # and therefore lambda (the poisson parameter) is the expected value of\n", + " # \"message count\".\n", + " expected_texts_per_day[day] = (lambda_1_samples[ix].sum()\n", + " + lambda_2_samples[~ix].sum()) / N\n", + "\n", + "\n", + "plt.plot(range(n_count_data), expected_texts_per_day, lw=4, color=\"#E24A33\",\n", + " label=\"expected number of text-messages received\")\n", + "plt.xlim(0, n_count_data)\n", + "plt.xlabel(\"Day\")\n", + "plt.ylabel(\"Expected # text-messages\")\n", + "plt.title(\"Expected number of text-messages received\")\n", + "plt.ylim(0, 60)\n", + "plt.bar(np.arange(len(count_data)), count_data, color=\"#348ABD\", alpha=0.65,\n", + " label=\"observed texts per day\")\n", + "\n", + "plt.legend(loc=\"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our analysis shows strong support for believing the user's behavior did change ($\\lambda_1$ would have been close in value to $\\lambda_2$ had this not been true), and that the change was sudden rather than gradual (as demonstrated by $\\tau$'s strongly peaked posterior distribution). We can speculate what might have caused this: a cheaper text-message rate, a recent weather-to-text subscription, or perhaps a new relationship. (In fact, the 45th day corresponds to Christmas, and I moved away to Toronto the next month, leaving a girlfriend behind.)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Exercises\n", + "\n", + "1\\. Using `lambda_1_samples` and `lambda_2_samples`, what is the mean of the posterior distributions of $\\lambda_1$ and $\\lambda_2$?" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#type your code here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. What is the expected percentage increase in text-message rates? `hint:` compute the mean of `lambda_1_samples/lambda_2_samples`. Note that this quantity is very different from `lambda_1_samples.mean()/lambda_2_samples.mean()`." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#type your code here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3\\. What is the mean of $\\lambda_1$ **given** that we know $\\tau$ is less than 45. That is, suppose we have been given new information that the change in behaviour occurred prior to day 45. What is the expected value of $\\lambda_1$ now? (You do not need to redo the PyMC3 part. Just consider all instances where `tau_samples < 45`.)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#type your code here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "\n", + "- [1] Gelman, Andrew. N.p.. Web. 22 Jan 2013. [N is never large enough](http://andrewgelman.com/2005/07/n_is_never_large).\n", + "- [2] Norvig, Peter. 2009. [The Unreasonable Effectiveness of Data](http://static.googleusercontent.com/media/research.google.com/en//pubs/archive/35179.pdf).\n", + "- [3] Salvatier, J, Wiecki TV, and Fonnesbeck C. (2016) Probabilistic programming in Python using PyMC3. *PeerJ Computer Science* 2:e55 \n", + "- [4] Jimmy Lin and Alek Kolcz. Large-Scale Machine Learning at Twitter. Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data (SIGMOD 2012), pages 793-804, May 2012, Scottsdale, Arizona.\n", + "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. ." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.core.display import HTML\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter1_Introduction/Chapter1.ipynb b/Chapter1_Introduction/Chapter1.ipynb deleted file mode 100644 index f727404f..00000000 --- a/Chapter1_Introduction/Chapter1.ipynb +++ /dev/null @@ -1,1134 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Probabilistic Programming and Bayesian Methods for Hackers \n", - "========\n", - "\n", - "Welcome to *Bayesian Methods for Hackers*. The full Github repository is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!\n", - "\n", - "#### Looking for a printed version of Bayesian Methods for Hackers?\n", - "\n", - "_Bayesian Methods for Hackers_ is now a published book by Addison-Wesley, available on [Amazon](http://www.amazon.com/Bayesian-Methods-Hackers-Probabilistic-Addison-Wesley/dp/0133902838)! \n", - "\n", - "![BMH](http://www-fp.pearsonhighered.com/assets/hip/images/bigcovers/0133902838.jpg)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Chapter 1\n", - "======\n", - "***" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Philosophy of Bayesian Inference\n", - "------\n", - " \n", - "> You are a skilled programmer, but bugs still slip into your code. After a particularly difficult implementation of an algorithm, you decide to test your code on a trivial example. It passes. You test the code on a harder problem. It passes once again. And it passes the next, *even more difficult*, test too! You are starting to believe that there may be no bugs in this code...\n", - "\n", - "If you think this way, then congratulations, you already are thinking Bayesian! Bayesian inference is simply updating your beliefs after considering new evidence. A Bayesian can rarely be certain about a result, but he or she can be very confident. Just like in the example above, we can never be 100% sure that our code is bug-free unless we test it on every possible problem; something rarely possible in practice. Instead, we can test it on a large number of problems, and if it succeeds we can feel more *confident* about our code, but still not certain. Bayesian inference works identically: we update our beliefs about an outcome; rarely can we be absolutely sure unless we rule out all other alternatives. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "### The Bayesian state of mind\n", - "\n", - "\n", - "Bayesian inference differs from more traditional statistical inference by preserving *uncertainty*. At first, this sounds like a bad statistical technique. Isn't statistics all about deriving *certainty* from randomness? To reconcile this, we need to start thinking like Bayesians. \n", - "\n", - "The Bayesian world-view interprets probability as measure of *believability in an event*, that is, how confident we are in an event occurring. In fact, we will see in a moment that this is the natural interpretation of probability. \n", - "\n", - "For this to be clearer, we consider an alternative interpretation of probability: *Frequentist*, known as the more *classical* version of statistics, assumes that probability is the long-run frequency of events (hence the bestowed title). For example, the *probability of plane accidents* under a frequentist philosophy is interpreted as the *long-term frequency of plane accidents*. This makes logical sense for many probabilities of events, but becomes more difficult to understand when events have no long-term frequency of occurrences. Consider: we often assign probabilities to outcomes of presidential elections, but the election itself only happens once! Frequentists get around this by invoking alternative realities and saying across all these realities, the frequency of occurrences defines the probability. \n", - "\n", - "Bayesians, on the other hand, have a more intuitive approach. Bayesians interpret a probability as measure of *belief*, or confidence, of an event occurring. Simply, a probability is a summary of an opinion. An individual who assigns a belief of 0 to an event has no confidence that the event will occur; conversely, assigning a belief of 1 implies that the individual is absolutely certain of an event occurring. Beliefs between 0 and 1 allow for weightings of other outcomes. This definition agrees with the probability of a plane accident example, for having observed the frequency of plane accidents, an individual's belief should be equal to that frequency, excluding any outside information. Similarly, under this definition of probability being equal to beliefs, it is meaningful to speak about probabilities (beliefs) of presidential election outcomes: how confident are you candidate *A* will win?\n", - "\n", - "Notice in the paragraph above, I assigned the belief (probability) measure to an *individual*, not to Nature. This is very interesting, as this definition leaves room for conflicting beliefs between individuals. Again, this is appropriate for what naturally occurs: different individuals have different beliefs of events occurring, because they possess different *information* about the world. The existence of different beliefs does not imply that anyone is wrong. Consider the following examples demonstrating the relationship between individual beliefs and probabilities:\n", - "\n", - "- I flip a coin, and we both guess the result. We would both agree, assuming the coin is fair, that the probability of Heads is 1/2. Assume, then, that I peek at the coin. Now I know for certain what the result is: I assign probability 1.0 to either Heads or Tails (whichever it is). Now what is *your* belief that the coin is Heads? My knowledge of the outcome has not changed the coin's results. Thus we assign different probabilities to the result. \n", - "\n", - "- Your code either has a bug in it or not, but we do not know for certain which is true, though we have a belief about the presence or absence of a bug. \n", - "\n", - "- A medical patient is exhibiting symptoms $x$, $y$ and $z$. There are a number of diseases that could be causing all of them, but only a single disease is present. A doctor has beliefs about which disease, but a second doctor may have slightly different beliefs. \n", - "\n", - "\n", - "This philosophy of treating beliefs as probability is natural to humans. We employ it constantly as we interact with the world and only see partial truths, but gather evidence to form beliefs. Alternatively, you have to be *trained* to think like a frequentist. \n", - "\n", - "To align ourselves with traditional probability notation, we denote our belief about event $A$ as $P(A)$. We call this quantity the *prior probability*.\n", - "\n", - "John Maynard Keynes, a great economist and thinker, said \"When the facts change, I change my mind. What do you do, sir?\" This quote reflects the way a Bayesian updates his or her beliefs after seeing evidence. Even — especially — if the evidence is counter to what was initially believed, the evidence cannot be ignored. We denote our updated belief as $P(A |X )$, interpreted as the probability of $A$ given the evidence $X$. We call the updated belief the *posterior probability* so as to contrast it with the prior probability. For example, consider the posterior probabilities (read: posterior beliefs) of the above examples, after observing some evidence $X$:\n", - "\n", - "1\\. $P(A): \\;\\;$ the coin has a 50 percent chance of being Heads. $P(A | X):\\;\\;$ You look at the coin, observe a Heads has landed, denote this information $X$, and trivially assign probability 1.0 to Heads and 0.0 to Tails.\n", - "\n", - "2\\. $P(A): \\;\\;$ This big, complex code likely has a bug in it. $P(A | X): \\;\\;$ The code passed all $X$ tests; there still might be a bug, but its presence is less likely now.\n", - "\n", - "3\\. $P(A):\\;\\;$ The patient could have any number of diseases. $P(A | X):\\;\\;$ Performing a blood test generated evidence $X$, ruling out some of the possible diseases from consideration.\n", - "\n", - "\n", - "It's clear that in each example we did not completely discard the prior belief after seeing new evidence $X$, but we *re-weighted the prior* to incorporate the new evidence (i.e. we put more weight, or confidence, on some beliefs versus others). \n", - "\n", - "By introducing prior uncertainty about events, we are already admitting that any guess we make is potentially very wrong. After observing data, evidence, or other information, we update our beliefs, and our guess becomes *less wrong*. This is the alternative side of the prediction coin, where typically we try to be *more right*. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "### Bayesian Inference in Practice\n", - "\n", - " If frequentist and Bayesian inference were programming functions, with inputs being statistical problems, then the two would be different in what they return to the user. The frequentist inference function would return a number, representing an estimate (typically a summary statistic like the sample average etc.), whereas the Bayesian function would return *probabilities*.\n", - "\n", - "For example, in our debugging problem above, calling the frequentist function with the argument \"My code passed all $X$ tests; is my code bug-free?\" would return a *YES*. On the other hand, asking our Bayesian function \"Often my code has bugs. My code passed all $X$ tests; is my code bug-free?\" would return something very different: probabilities of *YES* and *NO*. The function might return:\n", - "\n", - "\n", - "> *YES*, with probability 0.8; *NO*, with probability 0.2\n", - "\n", - "\n", - "\n", - "This is very different from the answer the frequentist function returned. Notice that the Bayesian function accepted an additional argument: *\"Often my code has bugs\"*. This parameter is the *prior*. By including the prior parameter, we are telling the Bayesian function to include our belief about the situation. Technically this parameter in the Bayesian function is optional, but we will see excluding it has its own consequences. \n", - "\n", - "\n", - "#### Incorporating evidence\n", - "\n", - "As we acquire more and more instances of evidence, our prior belief is *washed out* by the new evidence. This is to be expected. For example, if your prior belief is something ridiculous, like \"I expect the sun to explode today\", and each day you are proved wrong, you would hope that any inference would correct you, or at least align your beliefs better. Bayesian inference will correct this belief.\n", - "\n", - "\n", - "Denote $N$ as the number of instances of evidence we possess. As we gather an *infinite* amount of evidence, say as $N \\rightarrow \\infty$, our Bayesian results (often) align with frequentist results. Hence for large $N$, statistical inference is more or less objective. On the other hand, for small $N$, inference is much more *unstable*: frequentist estimates have more variance and larger confidence intervals. This is where Bayesian analysis excels. By introducing a prior, and returning probabilities (instead of a scalar estimate), we *preserve the uncertainty* that reflects the instability of statistical inference of a small $N$ dataset. \n", - "\n", - "One may think that for large $N$, one can be indifferent between the two techniques since they offer similar inference, and might lean towards the computationally-simpler, frequentist methods. An individual in this position should consider the following quote by Andrew Gelman (2005)[1], before making such a decision:\n", - "\n", - "> Sample sizes are never large. If $N$ is too small to get a sufficiently-precise estimate, you need to get more data (or make more assumptions). But once $N$ is \"large enough,\" you can start subdividing the data to learn more (for example, in a public opinion poll, once you have a good estimate for the entire country, you can estimate among men and women, northerners and southerners, different age groups, etc.). $N$ is never enough because if it were \"enough\" you'd already be on to the next problem for which you need more data.\n", - "\n", - "### Are frequentist methods incorrect then? \n", - "\n", - "**No.**\n", - "\n", - "Frequentist methods are still useful or state-of-the-art in many areas. Tools such as least squares linear regression, LASSO regression, and expectation-maximization algorithms are all powerful and fast. Bayesian methods complement these techniques by solving problems that these approaches cannot, or by illuminating the underlying system with more flexible modeling.\n", - "\n", - "\n", - "#### A note on *Big Data*\n", - "Paradoxically, big data's predictive analytic problems are actually solved by relatively simple algorithms [2][4]. Thus we can argue that big data's prediction difficulty does not lie in the algorithm used, but instead on the computational difficulties of storage and execution on big data. (One should also consider Gelman's quote from above and ask \"Do I really have big data?\" )\n", - "\n", - "The much more difficult analytic problems involve *medium data* and, especially troublesome, *really small data*. Using a similar argument as Gelman's above, if big data problems are *big enough* to be readily solved, then we should be more interested in the *not-quite-big enough* datasets. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Our Bayesian framework\n", - "\n", - "We are interested in beliefs, which can be interpreted as probabilities by thinking Bayesian. We have a *prior* belief in event $A$, beliefs formed by previous information, e.g., our prior belief about bugs being in our code before performing tests.\n", - "\n", - "Secondly, we observe our evidence. To continue our buggy-code example: if our code passes $X$ tests, we want to update our belief to incorporate this. We call this new belief the *posterior* probability. Updating our belief is done via the following equation, known as Bayes' Theorem, after its discoverer Thomas Bayes:\n", - "\n", - "\\begin{align}\n", - " P( A | X ) = & \\frac{ P(X | A) P(A) } {P(X) } \\\\\\\\[5pt]\n", - "& \\propto P(X | A) P(A)\\;\\; (\\propto \\text{is proportional to } )\n", - "\\end{align}\n", - "\n", - "The above formula is not unique to Bayesian inference: it is a mathematical fact with uses outside Bayesian inference. Bayesian inference merely uses it to connect prior probabilities $P(A)$ with an updated posterior probabilities $P(A | X )$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Mandatory coin-flip example\n", - "\n", - "Every statistics text must contain a coin-flipping example, I'll use it here to get it out of the way. Suppose, naively, that you are unsure about the probability of heads in a coin flip (spoiler alert: it's 50%). You believe there is some true underlying ratio, call it $p$, but have no prior opinion on what $p$ might be. \n", - "\n", - "We begin to flip a coin, and record the observations: either $H$ or $T$. This is our observed data. An interesting question to ask is how our inference changes as we observe more and more data? More specifically, what do our posterior probabilities look like when we have little data, versus when we have lots of data. \n", - "\n", - "Below we plot a sequence of updating posterior probabilities as we observe increasing amounts of data (coin flips)." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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fSy70ej3OnDmD48ePQ6vVokePHs7/8kiV1HTOUyu15chiscBqtbo7DAdsF5Tb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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\"\"\"\n", - "The book uses a custom matplotlibrc file, which provides the unique styles for\n", - "matplotlib plots. If executing this book, and you wish to use the book's\n", - "styling, provided are two options:\n", - " 1. Overwrite your own matplotlibrc file with the rc-file provided in the\n", - " book's styles/ dir. See http://matplotlib.org/users/customizing.html\n", - " 2. Also in the styles is bmh_matplotlibrc.json file. This can be used to\n", - " update the styles in only this notebook. Try running the following code:\n", - "\n", - " import json, matplotlib\n", - " s = json.load( open(\"../styles/bmh_matplotlibrc.json\") )\n", - " matplotlib.rcParams.update(s)\n", - "\n", - "\"\"\"\n", - "\n", - "# The code below can be passed over, as it is currently not important, plus it\n", - "# uses advanced topics we have not covered yet. LOOK AT PICTURE, MICHAEL!\n", - "%matplotlib inline\n", - "from IPython.core.pylabtools import figsize\n", - "import numpy as np\n", - "from matplotlib import pyplot as plt\n", - "figsize(11, 9)\n", - "\n", - "import scipy.stats as stats\n", - "\n", - "dist = stats.beta\n", - "n_trials = [0, 1, 2, 3, 4, 5, 8, 15, 50, 500]\n", - "data = stats.bernoulli.rvs(0.5, size=n_trials[-1])\n", - "x = np.linspace(0, 1, 100)\n", - "\n", - "# For the already prepared, I'm using Binomial's conj. prior.\n", - "for k, N in enumerate(n_trials):\n", - " sx = plt.subplot(len(n_trials) / 2, 2, k + 1)\n", - " plt.xlabel(\"$p$, probability of heads\") \\\n", - " if k in [0, len(n_trials) - 1] else None\n", - " plt.setp(sx.get_yticklabels(), visible=False)\n", - " heads = data[:N].sum()\n", - " y = dist.pdf(x, 1 + heads, 1 + N - heads)\n", - " plt.plot(x, y, label=\"observe %d tosses,\\n %d heads\" % (N, heads))\n", - " plt.fill_between(x, 0, y, color=\"#348ABD\", alpha=0.4)\n", - " plt.vlines(0.5, 0, 4, color=\"k\", linestyles=\"--\", lw=1)\n", - "\n", - " leg = plt.legend()\n", - " leg.get_frame().set_alpha(0.4)\n", - " plt.autoscale(tight=True)\n", - "\n", - "\n", - "plt.suptitle(\"Bayesian updating of posterior probabilities\",\n", - " y=1.02,\n", - " fontsize=14)\n", - "\n", - "plt.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The posterior probabilities are represented by the curves, and our uncertainty is proportional to the width of the curve. As the plot above shows, as we start to observe data our posterior probabilities start to shift and move around. Eventually, as we observe more and more data (coin-flips), our probabilities will tighten closer and closer around the true value of $p=0.5$ (marked by a dashed line). \n", - "\n", - "Notice that the plots are not always *peaked* at 0.5. There is no reason it should be: recall we assumed we did not have a prior opinion of what $p$ is. In fact, if we observe quite extreme data, say 8 flips and only 1 observed heads, our distribution would look very biased *away* from lumping around 0.5 (with no prior opinion, how confident would you feel betting on a fair coin after observing 8 tails and 1 head). As more data accumulates, we would see more and more probability being assigned at $p=0.5$, though never all of it.\n", - "\n", - "The next example is a simple demonstration of the mathematics of Bayesian inference. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Bug, or just sweet, unintended feature?\n", - "\n", - "\n", - "Let $A$ denote the event that our code has **no bugs** in it. Let $X$ denote the event that the code passes all debugging tests. For now, we will leave the prior probability of no bugs as a variable, i.e. $P(A) = p$. \n", - "\n", - "We are interested in $P(A|X)$, i.e. the probability of no bugs, given our debugging tests $X$. To use the formula above, we need to compute some quantities.\n", - "\n", - "What is $P(X | A)$, i.e., the probability that the code passes $X$ tests *given* there are no bugs? Well, it is equal to 1, for a code with no bugs will pass all tests. \n", - "\n", - "$P(X)$ is a little bit trickier: The event $X$ can be divided into two possibilities, event $X$ occurring even though our code *indeed has* bugs (denoted $\\sim A\\;$, spoken *not $A$*), or event $X$ without bugs ($A$). $P(X)$ can be represented as:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\\begin{align}\n", - "P(X ) & = P(X \\text{ and } A) + P(X \\text{ and } \\sim A) \\\\\\\\[5pt]\n", - " & = P(X|A)P(A) + P(X | \\sim A)P(\\sim A)\\\\\\\\[5pt]\n", - "& = P(X|A)p + P(X | \\sim A)(1-p)\n", - "\\end{align}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have already computed $P(X|A)$ above. On the other hand, $P(X | \\sim A)$ is subjective: our code can pass tests but still have a bug in it, though the probability there is a bug present is reduced. Note this is dependent on the number of tests performed, the degree of complication in the tests, etc. Let's be conservative and assign $P(X|\\sim A) = 0.5$. Then\n", - "\n", - "\\begin{align}\n", - "P(A | X) & = \\frac{1\\cdot p}{ 1\\cdot p +0.5 (1-p) } \\\\\\\\\n", - "& = \\frac{ 2 p}{1+p}\n", - "\\end{align}\n", - "This is the posterior probability. What does it look like as a function of our prior, $p \\in [0,1]$? " - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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mBX11s67X19jLZYj2dsZYv/ZifoyPC1SO7J8fqvizhaytXz8dkpKSEB8fj7ff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\nuNDlDn51dTWCg4MNxsS26ABAdnZ2518IvvjiC7z77rui5hE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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "p = np.linspace(0, 1, 50)\n", - "plt.plot(p, 2 * p / (1 + p), color=\"#348ABD\", lw=3)\n", - "# plt.fill_between(p, 2*p/(1+p), alpha=.5, facecolor=[\"#A60628\"])\n", - "plt.scatter(0.2, 2 * (0.2) / 1.2, s=140, c=\"#348ABD\")\n", - "plt.xlim(0, 1)\n", - "plt.ylim(0, 1)\n", - "plt.xlabel(\"Prior, $P(A) = p$\")\n", - "plt.ylabel(\"Posterior, $P(A|X)$, with $P(A) = p$\")\n", - "plt.title(\"Is my code bug-free?\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can see the biggest gains if we observe the $X$ tests passed when the prior probability, $p$, is low. Let's settle on a specific value for the prior. I'm a strong programmer (I think), so I'm going to give myself a realistic prior of 0.20, that is, there is a 20% chance that I write code bug-free. To be more realistic, this prior should be a function of how complicated and large the code is, but let's pin it at 0.20. Then my updated belief that my code is bug-free is 0.33. \n", - "\n", - "Recall that the prior is a probability: $p$ is the prior probability that there *are no bugs*, so $1-p$ is the prior probability that there *are bugs*.\n", - "\n", - "Similarly, our posterior is also a probability, with $P(A | X)$ the probability there is no bug *given we saw all tests pass*, hence $1-P(A|X)$ is the probability there is a bug *given all tests passed*. What does our posterior probability look like? Below is a chart of both the prior and the posterior probabilities. \n" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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w8EBwcDCWLl2KqqoqHDx4EDt37tTY98qVK/jpp59QVlYGCwsL2NjYwMzMDMDt\nq9UXL15EVdW9Z925uySmduwDBw5g165dGDNmDAAgKCgIP/zwA27evIlz585h48aNats5OzsjJydH\n4xj3e16IiIiImgu9JexKpRL+/v7w8/PDsmXL6qy/evUqhg8fjuDgYHTt2hVffvnlfY1naa6AjYUC\njrYWOvuysVDA0vzep1CSJIwfPx7jxo1DaGgofHx8MG/ePLX1mrYBgBYtWiAuLg67d++Gn58fXn31\nVaxevRq+vr4Nbn+nzz//HEePHkXHjh3x/vvv429/+5vGsWpqavDZZ5+hS5cu6NixIw4ePCjfHDtg\nwAD4+/vD398fnTp10ip2AGjXrh1atWqFwMBAzJgxAx9++KEc+8yZM2FhYYHOnTsjKioKTz31lNq2\n0dHRmD17Nry9vZGQkKB2k+pfOS9N8WAoIiIiTVjDTrokCT1MdK1SqdC5c2fs3r0bbm5u6NGjB+Lj\n4xEQECD3WbRoESoqKrBkyRJcvXoVnTt3RlFRUZ05yRMTExEaGlpnjIsXL6rVUxvTk06Dg4OxcuVK\n9O/fX2exkPG7+zNKREREVCs1NRWDBw/WuE4vD05KSUmBr6+v/MTKiIgIJCQkqCXsLi4uOH78OADg\njz/+gKOj4309QKivV6smfwIpERERkSbJycm8yk46o5eEvaCgQG1mEnd39zqPmH/hhRcwaNAguLq6\n4saNG/juu+/0ERoRET3g9PEfWTJ9l89cAtyv82Ih6YReEnZtaoffe+89BAcHIykpCdnZ2Rg6dCiO\nHTsGe3v7On1nzZoFT09PAICDgwOCgoLkp28ao99//93QIZCRqJ1FoPYqDNtss234dlKFG67drELu\niSMAAGf/22WXl0+nss221u0bFdX4+j+70PcfTwEwns8328bbPnHiBEpLSwHcfvL8tGnTUB+91LAf\nPHgQixYtkh8dv2TJEigUCkRHR8t9RowYgYULF+KRRx4BAAwePBjLli1DWFiY2r60rWEnMjb8jBIZ\np5id2bhaXoXisnvPgkVUH0dbC7S1scDiYR0NHQo1UwavYQ8LC0NmZiZyc3Ph6uqKTZs2IT4+Xq2P\nv78/du/ejUceeQRFRUU4c+aMUV81JyIi09PZycbQIVAzdOZKOS6fTkXb0F6GDoVMlF4SdnNzc8TG\nxmLYsGFQqVSYOnUqAgICsGbNGgBAZGQkFixYgOeffx7dunVDTU0N3n//fbRp00Yf4RERERERGS29\nJOwAEB5lg4qUAAAgAElEQVQejvDwcLVlkZGR8uu2bdviv//9r77CISIiImoytbXsRLrwQDzplIiI\niIioudLbFXZ9K/ppHy5t2wXVrQqdjWFmZQmXJ4ei3YgBOhtDl1asWIHc3Fx8/PHHOtn/qFGj8PTT\nT+O5557D999/j2+//RZbtmxpkn336dMHy5cvR58+fbB06VLk5uZi9erVTbJvXZ8XIiIyPaxhJ10y\n2YT90rZdqLhaguob5Tobw9zeBpe27TJIwj579my4urpi4cKFf3kfc+fObcKI6pIkSZ7S86mnnsJT\nTz11z220Pa7ffvtNbZy/Kjk5GTNmzMDJkyflZbo+L0RERESNYbIJu+pWBapvlKOi8IoOR3GCuZ2t\nDvevOyqVCmZmZn9p2+rq6vt6Cu390DS2HmYmJSIiahBr2EmXHogadoeQwCb/aoxu3brho48+Qu/e\nveHj44OoqChUVPyvVOerr75CWFgYOnbsiGeffRaFhYXyugULFqBz587o0KED+vbti4yMDHz55ZfY\nvHkzVq1aBU9PTzz77LMAgEuXLmHSpEno1KkTQkJC8O9//1vez9KlSzF58mTMmDEDHTp0QFxcHJYu\nXYoZM2bIfXbs2IHevXvD29sbo0ePxtmzZ9WOYeXKlejbty88PT1RU1P3iYB79+5Fr1694OXlhejo\naLVEOi4uDiNGjABwO8FuzHHdPbZKpUK3bt2wf/9+ALevsN+6dQtTp06Fp6cnHn30UZw6dUoe29HR\nEbm5uXJ79uzZePfdd1FeXo6nn34ahYWF8PT0hKenJwoLCxt9XmJjY9GvXz94eXlh6tSpau8tERER\n0f16IBJ2Y7B582Zs2bIFqampyM7OxvLlywEA+/fvxzvvvIP169cjIyMDHh4e8pOuEhMTcfDgQRw+\nfBjnz5/H+vXr0aZNG0yZMgXjx4/HP/7xD+Tl5eGbb75BTU0NJkyYgIceegjp6enYvn07Vq9ejT17\n9sgxKJVKjBkzBufPn8dTTz2lVkqSlZWF6dOnY+nSpcjKysKQIUMwYcIEVFdXy322bt2K7777Djk5\nOVAo1D86xcXFmDx5Mt544w1kZ2fDy8sLhw4d0ngu9uzZo/VxaRrbzMxMLXYhBHbs2IEnnngCOTk5\nGDduHCZOnAiVSlXv+yFJEmxsbPD999+jffv2yMvLQ15eHtq3b9+o8yJJEhISErB582b8/vvvOHXq\nVJ1nDBARkemrffIpkS4wYdcDSZIwbdo0uLq6olWrVnj55ZexdetWAMD333+PiRMnIigoCC1atEBM\nTAwOHz6MCxcuoEWLFvjzzz9x9uxZ1NTUwM/PD+3atZP3e+cV7NTUVBQXF2P+/PkwNzdHhw4d8Nxz\nz8njAEDPnj3lqTWtrKzUtt+2bRsee+wxDBgwAGZmZnjxxRdx8+ZNpKSkyMcwffp0uLq6wtLSss4x\n7tq1CwEBARg1ahTMzMwwc+ZMODs7azwfFhYWWh+XNmMDQHBwsDz27NmzUVFRgcOHD2t+Q+4YQ1M5\nTWPOC3B7etJ27dqhVatWGD58OE6cOFHvuERERESNxYRdT9zc3OTX7u7uctlLUVERPDw85HW2trZo\n06YNLl68iH79+mHatGl49dVX0blzZ8ydOxc3btzQuP/8/HwUFhbC29tb/lqxYgWuXr0q93F1da03\nvsLCQri7u8ttSZLg5uaGS5cuaTwGTdvfvf/6+vfv31/r49JmbED92CRJgqurq1pp0V+lzXm58w8T\nKysrlJWV3fe4RETUvLCGnXSJCbueFBQUyK8vXLgAFxcXAJDLMWqVlZWhpKRETkCnT5+OPXv24MCB\nA8jOzsaqVasA1J0Zxd3dHR06dEBOTo78lZeXh2+//Vbu39BsKi4uLsjPz5fbQggUFBTIcWoa807t\n27dXO8ba7euj7XFpMzagfn5rampw8eJFtG/fHgBgY2OD8vL/zRZUVFQk7+9e+9XmvDQmTiIiIqLG\neiAS9tK09Cb/agwhBNatW4eLFy/i2rVr+PDDD/Hkk08CAMaNG4e4uDicPHkSFRUVWLx4McLCwuDu\n7o60tDQcOXIEVVVVsLa2hqWlpTyzi7OzM86fPy+P0b17d9jZ2WHlypW4efMmVCoV0tPTkZaWJsfQ\nkDFjxmDXrl3Yv38/qqqqEBsbCysrK/Ts2VOrY3zsscdw+vRp/PDDD6iursaaNWtw+fJljX0bc1za\nOnbsmDz2Z599BktLS/To0QMA0LVrV2zevBkqlQq7d+/GgQMH5O2cnJxw7do1/PHHHxr329jzwhlr\niIgeTKxhJ10y2YTdzMoS5vY2sGzvpLMvc3sbmFlprqm+kyRJGD9+PMaNG4fQ0FD4+Phg3rx5AIAB\nAwZgwYIFmDx5MgIDA5GXl4e1a9cCAG7cuIG5c+eiY8eOCA4OhqOjI1588UUAwMSJE3HmzBl4e3tj\n0qRJUCgUiI+Px4kTJxAaGgo/Pz+1UhNNV9jvXObn54fVq1cjOjoafn5+2LVrF+Li4rSevrFNmzZY\nv3493n77bfj6+iInJwcPP/ywxrEac1zakCQJI0aMwLZt2+Dj44PNmzdjw4YN8h8BS5YsgVKphLe3\nN7Zs2YKRI0fK23bq1Aljx46V35fCwsL7Oi/3+k8GERERUWNJopldEkxMTERoaN06sYsXL6rVMRvT\nk06Dg4OxcuVK9O/fX2exkPG7+zNKRMYhZmc2rpZXobisCp2dbAwdDjVDZ66Uw9HWAm1tLLB4WEdD\nh0PNVGpqKgYPHqxxnck+OKndiAEGeQIpEREREVFTMtmSGCIiIiJ9YQ076ZLJXmE3Jr///ruhQyAi\nIiKiZopX2ImIiIjuE+dhJ13SW8KuVCrh7+8PPz8/LFu2rM765cuXIyQkBCEhIQgKCoK5uTmuX7+u\nr/CIiIiIiIySXhJ2lUqFqKgoKJVKpKenIz4+HhkZGWp95s+fj7S0NKSlpWHJkiUYOHAgWrVqpfUY\nZmZmag/HITIWQggUFxfD0vLeU4ASEVHzxBp20iW91LCnpKTA19cXXl5eAICIiAgkJCQgICBAY/+4\nuDj87W9/a9QYzs7OuHz5Mq/KNzOlpaVwcHAwdBg6JYSAg4MD7OzsDB0KERERNUN6SdgLCgrg4eEh\nt93d3XHo0CGNfcvLy7Fz5058+umnjRpDkiS0a9fuvuIk/eO85EREZApYw066pJeEvTFPfvzvf/+L\nvn37NlgOM2vWLHh6egIAHBwcEBQUhL59+wIAkpOTAYBtttlmm222tWoDLgCAksw0FFyxgltgdwBA\nQfpRAGCbba3al0+nosLKHPj/BycZy+ebbeNtnzhxAqWlpQCAvLw8TJs2DfXRy5NODx48iEWLFkGp\nVAK4/ah4hUKB6OjoOn2ffPJJPPPMM4iIiNC4r/qedErNU3JysvzhJSIyBD7plO7XmSvlUOWfQGBo\nLz7plP6yhp50qpebTsPCwpCZmYnc3FxUVlZi06ZNGD16dJ1+paWl2L9/P8aMGaOPsIiIiIiIjJ65\nXgYxN0dsbCyGDRsGlUqFqVOnIiAgAGvWrAEAREZGAgC2b9+OYcOGwdraWh9hkRHg1XUiIjIFrGEn\nXdJLwg4A4eHhCA8PV1tWm6jXmjx5MiZPnqyvkIiIiIiIjB6fdEoG9b+bvoiIiJovzsNOusSEnYiI\niIjIiOmtJIZIE9awExFRc9fhRBr8TxyB9b5kHN1oa+hwqJmS5tb/0FAm7ERERET3wSftMCxv3kCL\nygrcqi43dDjUTDU05QoTdjIozsNORETNnVlVJc5du4jgSgUqyswMHQ41U0zYiYiIiPTAISTQ0CFQ\nM1Salt7get50SgbFq+tERGQKOlm3MXQIZMKYsBMRERERGTEm7GRQnIediIhMwdmbJYYOgUwYE3Yi\nIiIiIiPGhJ0MijXsRERkCljDTrrEhJ2IiIiIyIgxYSeDYg07ERGZAtawky4xYSciIiIiMmJM2Mmg\nWMNORESmgDXspEtM2ImIiIiIjJjeEnalUgl/f3/4+flh2bJlGvskJSUhJCQEXbt2xcCBA/UVGhkQ\na9iJiMgUsIaddMlcH4OoVCpERUVh9+7dcHNzQ48ePTB69GgEBATIfa5fv47Zs2dj586dcHd3x9Wr\nV/URGhERERGRUdPLFfaUlBT4+vrCy8sLFhYWiIiIQEJCglqfuLg4jBs3Du7u7gCAtm3b6iM0MjDW\nsBMRkSlgDTvpkl4S9oKCAnh4eMhtd3d3FBQUqPXJzMxESUkJHn30UYSFheHrr7/WR2hEREREREZN\nLyUxkiTds09VVRVSU1ORmJiI8vJy9O7dGw8//DD8/Pzq9J01axY8PT0BAA4ODggKCpKv1NbWRLPd\nPNqfffYZ3z+22WbboG3ABQBQkpmGgitWcAvsDgAoSD8KAGyzrVU78XoufKsUcMNtx4ovAQC6Obqw\nzbbGdlZpMcqqKwEAedfyEYP6SUII0cD6JnHw4EEsWrQISqUSALBkyRIoFApER0fLfZYtW4abN29i\n0aJFAIBp06Zh+PDhGD9+vNq+EhMTERoaquuQSU+Sk5NZFkNEBhWzMxtXy6tQXFaFzk42hg6HmiGP\npe+j8EoOgisVcOsVZOhwqBkqTUtHqw2LMXjwYI3r9VISExYWhszMTOTm5qKyshKbNm3C6NGj1fqM\nGTMGycnJUKlUKC8vx6FDhxAYGKiP8MiAmKwTEZEpYA076ZJeSmLMzc0RGxuLYcOGQaVSYerUqQgI\nCMCaNWsAAJGRkfD398fw4cPx0EMPQaFQ4IUXXmDCTkREREQPPL0k7AAQHh6O8PBwtWWRkZFq7fnz\n52P+/Pn6ComMAEtiiIjIFJy9WYJgPo+SdISfLCIiIiIiI8aEnQyKV9eJiMgUsIaddIkJOxERERGR\nEdMqYS8uLtZ1HPSA+t88yERERM3X2Zslhg6BTJhWCbunpyfGjBmDzZs3o7KyUtcxERERERHR/9Mq\nYc/JycGgQYOwdOlStGvXDtOnT+eVUWoSrGEnIiJTwBp20iWtEnZnZ2e89NJLOHLkCA4cOAAnJydM\nnDgRPj4+ePPNN3H+/Hldx0lERERE9EBq9E2nhYWFKCoqwh9//AEfHx8UFBQgODgYS5Ys0UV8ZOL4\nnxoiIjIFrGEnXdLqwUknT57Exo0bER8fD2tra0yePBnHjh2Dh4cHACAmJgZBQUF4/fXXdRosERER\nEdGDRquEfcCAAYiIiMB3332HXr161Vnv5eWFOXPmNHlwZPpYw05ERKagk3UboPK6ocMgE6VVwr5t\n2zb079+/zvKUlBT07NkTALB48eKmjYyIiIiIiLSrYX/88cc1Lh82bFiTBkMPHtawExGRKWANO+lS\ng1fYa2pqIISAEAI1NTVq67Kzs2FhYaHT4IiIiIiIHnQNJuzm5uYaXwOAQqHAwoULdRMVPTBYw05E\nRKaANeykSw0m7OfOnQMA9O/fH7/88guEEAAASZLg5OQEGxsb3UdIRERERPQAa7CG3cvLC15eXsjL\ny0OHDh3kdocOHRqdrCuVSvj7+8PPzw/Lli2rsz4pKQkODg4ICQlBSEgI3nnnncYdCTVLrGEnIiJT\nwBp20qV6r7C/8MIL+PzzzwEAzz33nMY+kiRhw4YN9xxEpVIhKioKu3fvhpubG3r06IHRo0cjICBA\nrd+AAQPwn//8pzHxExERERGZtHoTdm9vb/l1x44dIUmSXBJTS5IkrQZJSUmBr68vvLy8AAARERFI\nSEiok7DfvX8yfaxhJyIiU8AadtKlehP2BQsWyK8XLVp0X4MUFBTIT0UFAHd3dxw6dEitjyRJ+O23\n39CtWze4ublh+fLlCAwMvK9xiYiIiIiau3oT9j179mi1g0GDBt2zjzZX4kNDQ5Gfnw8bGxvs2LED\nTzzxBM6ePatVDNR8JScn8yo7ERE1e2dvliBYu8fbEDVavQn73//+d60S7ZycnHv2cXNzQ35+vtzO\nz8+Hu7u7Wh97e3v5dXh4OGbNmoWSkhK0adOmzv5mzZoFT09PAICDgwOCgoLkpK/2Jka2m0f7xIkT\nRhUP22yz/eC1ARcAQElmGgquWMEtsDsAoCD9KACwzbZW7fyKP2BZpYAbbjtWfAkA0M3RhW22Nbaz\nSotRVl0JAMi7lo8Y1E8Seigcr66uRufOnZGYmAhXV1f07NkT8fHxajXsRUVFcHZ2hiRJSElJwdNP\nP43c3Nw6+0pMTERoaKiuQyYiogdEzM5sXC2vQnFZFTo7cbpiajyPpe+j5Z+lsCm9DrdeQYYOh5qh\n0rR0tNqwGIMHD9a4vsF52JuKubk5YmNjMWzYMKhUKkydOhUBAQFYs2YNACAyMhKbN2/GZ599BnNz\nc9jY2ODbb7/VR2hEREREREat3oTd398fp0+fBgC1G0bvJEkS8vLytBooPDwc4eHhassiIyPl17Nn\nz8bs2bO12heZDtawExGRKWANO+lSvQl77RzsAPD111/rJRgiIiIiIlJXb8Ler18/+fXAgQP1EQs9\ngHh1nYiITAHnYSdd0up/NxUVFYiJiYGvry9sbGzg6+uLN954A7du3dJ1fEREREREDzStEvaZM2di\n7969WLVqFQ4fPoxVq1YhKSkJM2fO1HV8ZOL+N60aERFR83X2ZomhQyATptUsMdu3b0d2djZat24N\nAOjSpQt69eqFjh07Yv369ToNkIiIiIjoQabVFXYXFxeUl5erLbt58yZcXV11EhQ9OFjDTkREpqCT\ndd0HPRI1lXqvsCcmJspPOn3uuecQHh6OqKgoeHh4IC8vD5988gkmTZqkt0CJiIiIiB5E9SbsU6dO\nlRN2ABBCYMmSJWrt1atXIzo6WrcRkknjPOxERGQKOA876VK9CXtubq4ewyAiIiIiIk34pyAZFK+u\nExGRKWANO+mSVrPElJaWYtGiRdi3bx+Ki4tRU1MDAJAkCXl5eToNkIiIiIjoQabVFfbZs2cjNTUV\nb775JkpKSrBq1Sp4enpizpw5uo6PTBznYSciIlPAedhJl7S6wr5z505kZGSgbdu2UCgUeOKJJ9Cj\nRw+MGjUKL7/8sq5jJCIiIiJ6YGl1hV0IAQcHBwCAvb09rl+/DhcXF2RmZuo0ODJ9rGEnIiJTwBp2\n0iWtrrA/9NBD2L9/PwYPHoy+ffti9uzZsLW1RefOnXUdHxERERHRA02rK+yff/45vLy8AAAff/wx\nrKysUFpaig0bNugyNnoAsIadiIhMAWvYSZe0Stg7duyIjh07AgDatWuHdevWYdOmTQgMDNR6IKVS\nCX9/f/j5+WHZsmX19jt8+DDMzc2xdetWrfdNRERERGSqtK5hX7duHYYMGYLAwEAMHToUa9eulad3\nvBeVSoWoqCgolUqkp6cjPj4eGRkZGvtFR0dj+PDhEEI07kioWWINOxERmQLWsJMuaVXDHh0djYSE\nBMyZMweenp7Iy8vDBx98gDNnzuBf//rXPbdPSUmBr6+vXFYTERGBhIQEBAQEqPVbtWoVxo8fj8OH\nDzf+SIiIiIiITJBWCfv69euRmpoKDw8Pednjjz+OkJAQrRL2goICtW3d3d1x6NChOn0SEhKwZ88e\nHD58GJIkaXsM1IwlJyfzKjsRETV7Z2+WIJgPkCcd0eqT1bJlS9jb26sts7e3l6d6vBdtku85c+Zg\n6dKlkCQJQgiWxBARERERoYEr7OfOnZNfz5kzB+PGjUN0dDQ8PDyQl5eH5cuXY+7cuVoN4ubmhvz8\nfLmdn58Pd3d3tT5Hjx5FREQEAODq1avYsWMHLCwsMHr06Dr7mzVrFjw9PQEADg4OCAoKkq/S1s46\nwnbzaNcuM5Z42Gab7QevDbgAAEoy01BwxQpugd0BAAXpRwGAbba1agNARuUfcPv/18eKLwEAujm6\nsM22xnZWaTHKqisBAHnX8hGD+kminkvZCoV2/9bR5sbT6upqdO7cGYmJiXB1dUXPnj0RHx9fp4a9\n1vPPP49Ro0Zh7NixddYlJiYiNDRUq9iIiIjuJWZnNq6WV6G4rAqdnWwMHQ41Qx5L30fLP0thU3od\nbr2CDB0ONUOlaelotWExBg8erHF9vVl5TU2NVl/aMDc3R2xsLIYNG4bAwEA888wzCAgIwJo1a7Bm\nzZq/dmRkEjgPOxERmQLOw066pNVNp7Xy8vJQUFAANzc3uSRFW+Hh4QgPD1dbFhkZqbHv+vXrG7Vv\nIiIiIiJTpVXdy6VLlzBgwAD4+vpi7Nix8PX1Rf/+/XHx4kVdx0cmjjPEEBGRKeA87KRLWiXsM2bM\nQLdu3XDt2jVcunQJ165dQ0hICGbMmKHr+IiIiIiIHmhaJezJyclYvnw5bG1tAQC2trZ4//338euv\nv+o0ODJ9rGEnIiJTwBp20iWtEvY2bdogPT1dbdnp06fRunVrnQRFRERERES3aXXT6auvvoqhQ4di\n6tSp6NChA3Jzc7F+/XosXrxY1/GRiWMNOxERmYJO1m2AyuuGDoNMlFYJ+wsvvICOHTvim2++wfHj\nx+Hq6or4+Ph654okIiIiIqKmcc+Evfa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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "colours = [\"#348ABD\", \"#A60628\"]\n", - "\n", - "prior = [0.20, 0.80]\n", - "posterior = [1. / 3, 2. / 3]\n", - "plt.bar([0, .7], prior, alpha=0.70, width=0.25,\n", - " color=colours[0], label=\"prior distribution\",\n", - " lw=\"3\", edgecolor=colours[0])\n", - "\n", - "plt.bar([0 + 0.25, .7 + 0.25], posterior, alpha=0.7,\n", - " width=0.25, color=colours[1],\n", - " label=\"posterior distribution\",\n", - " lw=\"3\", edgecolor=colours[1])\n", - "\n", - "plt.ylim(0,1)\n", - "plt.xticks([0.20, .95], [\"Bugs Absent\", \"Bugs Present\"])\n", - "plt.title(\"Prior and Posterior probability of bugs present\")\n", - "plt.ylabel(\"Probability\")\n", - "plt.legend(loc=\"upper left\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that after we observed $X$ occur, the probability of bugs being absent increased. By increasing the number of tests, we can approach confidence (probability 1) that there are no bugs present.\n", - "\n", - "This was a very simple example of Bayesian inference and Bayes rule. Unfortunately, the mathematics necessary to perform more complicated Bayesian inference only becomes more difficult, except for artificially constructed cases. We will later see that this type of mathematical analysis is actually unnecessary. First we must broaden our modeling tools. The next section deals with *probability distributions*. If you are already familiar, feel free to skip (or at least skim), but for the less familiar the next section is essential." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "_______\n", - "\n", - "## Probability Distributions\n", - "\n", - "\n", - "**Let's quickly recall what a probability distribution is:** Let $Z$ be some random variable. Then associated with $Z$ is a *probability distribution function* that assigns probabilities to the different outcomes $Z$ can take. Graphically, a probability distribution is a curve where the probability of an outcome is proportional to the height of the curve. You can see examples in the first figure of this chapter. \n", - "\n", - "We can divide random variables into three classifications:\n", - "\n", - "- **$Z$ is discrete**: Discrete random variables may only assume values on a specified list. Things like populations, movie ratings, and number of votes are all discrete random variables. Discrete random variables become more clear when we contrast them with...\n", - "\n", - "- **$Z$ is continuous**: Continuous random variable can take on arbitrarily exact values. For example, temperature, speed, time, color are all modeled as continuous variables because you can progressively make the values more and more precise.\n", - "\n", - "- **$Z$ is mixed**: Mixed random variables assign probabilities to both discrete and continuous random variables, i.e. it is a combination of the above two categories. \n", - "\n", - "#### Expected Value\n", - "Expected value (EV) is one of the most important concepts in probability. The EV for a given probability distribution can be described as \"the mean value in the long run for many repeated samples from that distribution.\" To borrow a metaphor from physics, a distribution's EV as like its \"center of mass.\" Imagine repeating the same experiment many times over, and taking the average over each outcome. The more you repeat the experiment, the closer this average will become to the distributions EV. (side note: as the number of repeated experiments goes to infinity, the difference between the average outcome and the EV becomes arbitrarily small.)\n", - "\n", - "### Discrete Case\n", - "If $Z$ is discrete, then its distribution is called a *probability mass function*, which measures the probability $Z$ takes on the value $k$, denoted $P(Z=k)$. Note that the probability mass function completely describes the random variable $Z$, that is, if we know the mass function, we know how $Z$ should behave. There are popular probability mass functions that consistently appear: we will introduce them as needed, but let's introduce the first very useful probability mass function. We say $Z$ is *Poisson*-distributed if:\n", - "\n", - "$$P(Z = k) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k=0,1,2, \\dots $$\n", - "\n", - "$\\lambda$ is called a parameter of the distribution, and it controls the distribution's shape. For the Poisson distribution, $\\lambda$ can be any positive number. By increasing $\\lambda$, we add more probability to larger values, and conversely by decreasing $\\lambda$ we add more probability to smaller values. One can describe $\\lambda$ as the *intensity* of the Poisson distribution. \n", - "\n", - "Unlike $\\lambda$, which can be any positive number, the value $k$ in the above formula must be a non-negative integer, i.e., $k$ must take on values 0,1,2, and so on. This is very important, because if you wanted to model a population you could not make sense of populations with 4.25 or 5.612 members. \n", - "\n", - "If a random variable $Z$ has a Poisson mass distribution, we denote this by writing\n", - "\n", - "$$Z \\sim \\text{Poi}(\\lambda) $$\n", - "\n", - "One useful property of the Poisson distribution is that its expected value is equal to its parameter, i.e.:\n", - "\n", - "$$E\\large[ \\;Z\\; | \\; \\lambda \\;\\large] = \\lambda $$\n", - "\n", - "We will use this property often, so it's useful to remember. Below, we plot the probability mass distribution for different $\\lambda$ values. The first thing to notice is that by increasing $\\lambda$, we add more probability of larger values occurring. Second, notice that although the graph ends at 15, the distributions do not. They assign positive probability to every non-negative integer." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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VuTwxMZFHH300oH385S9/4aabbvK9IV1ddHQ0ffr0AWDZsmVcfPHF9OvXL7jw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\n9i2jw9oQXXiKZi2aUzEsBUbY+QEr4s/hk6XkHy0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PREQzcvbsWfh8PpSVlUHTNHR2duKD\nDz5QnUVENGdxsCciohlpa2vDgw8+CABwOp344YcfkJCQoDaKiGgOCxFe5UREREREdN3jEXsiIiIi\noiDAwZ6IiIiIKAhwsCciIiIiCgIc7ImIiIiIggAHeyIiIiKiIMDBnoiIiIgoCHCwJyIiIiIKAhzs\niYiIiIiCAAd7IiIiIqIg8B+SfpdI3UNe8gAAAABJRU5ErkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "\n", - "import scipy.stats as stats\n", - "a = np.arange(16)\n", - "poi = stats.poisson\n", - "lambda_ = [1.5, 4.25]\n", - "colours = [\"#348ABD\", \"#A60628\"]\n", - "\n", - "plt.bar(a, poi.pmf(a, lambda_[0]), color=colours[0],\n", - " label=\"$\\lambda = %.1f$\" % lambda_[0], alpha=0.60,\n", - " edgecolor=colours[0], lw=\"3\")\n", - "\n", - "plt.bar(a, poi.pmf(a, lambda_[1]), color=colours[1],\n", - " label=\"$\\lambda = %.1f$\" % lambda_[1], alpha=0.60,\n", - " edgecolor=colours[1], lw=\"3\")\n", - "\n", - "plt.xticks(a + 0.4, a)\n", - "plt.legend()\n", - "plt.ylabel(\"probability of $k$\")\n", - "plt.xlabel(\"$k$\")\n", - "plt.title(\"Probability mass function of a Poisson random variable; differing \\\n", - "$\\lambda$ values\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Continuous Case\n", - "Instead of a probability mass function, a continuous random variable has a *probability density function*. This might seem like unnecessary nomenclature, but the density function and the mass function are very different creatures. An example of continuous random variable is a random variable with *exponential density*. The density function for an exponential random variable looks like this:\n", - "\n", - "$$f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0$$\n", - "\n", - "Like a Poisson random variable, an exponential random variable can take on only non-negative values. But unlike a Poisson variable, the exponential can take on *any* non-negative values, including non-integral values such as 4.25 or 5.612401. This property makes it a poor choice for count data, which must be an integer, but a great choice for time data, temperature data (measured in Kelvins, of course), or any other precise *and positive* variable. The graph below shows two probability density functions with different $\\lambda$ values. \n", - "\n", - "When a random variable $Z$ has an exponential distribution with parameter $\\lambda$, we say *$Z$ is exponential* and write\n", - "\n", - "$$Z \\sim \\text{Exp}(\\lambda)$$\n", - "\n", - "Given a specific $\\lambda$, the expected value of an exponential random variable is equal to the inverse of $\\lambda$, that is:\n", - "\n", - "$$E[\\; Z \\;|\\; \\lambda \\;] = \\frac{1}{\\lambda}$$" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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6QRERERERWUiLL+gBQGmnQfjsv8MpMsQw78yy1bi49r9WjKrlYV+cOMytWMyv\nOMytOMytOMytOJW5VSqVKCwstHI0LU9hYSGUAp6fZLFx6EVT2tshfM4EpLy1AQXnLgEATi99CwAQ\nOmOcNUMjIiIialV8fHyQkZGB3NzchlcmA6VSCR8fH7Nvt8X30FenKy5BypsbUHD+kmFexxfnInT6\nWEuER0RERETUaG26h746pb0dwudOgFNEe8O800vexMX3P7diVEREREREYrS6gh6oLOonGhf1i99k\nT30D2HMoDnMrFvMrDnMrDnMrDnMrDnNrm1plQQ9UKeo7VCnql76F5DfXWzEqIiIiIiLzanU99NXp\nioqR8tZGo576Dk9NQsQz0yBJkogQiYiIiIgahT309VA62CN83kQ4dww3zEv+1yc4s3wNWtjfMkRE\nRERENbT6gh74c5x6165RhnkX39uEU8+9AVmvt2JktoV9ceIwt2Ixv+Iwt+Iwt+Iwt+Iwt7apTRT0\nAKDQqBE6czzcenQyzEv95GscX/AqZJ3OipERERERETVdq++hr07W6nDpo83IPZBkmOc/egi6vrUI\nClWrec4WEREREbUg7KFvBEmlRMjUMfDs18Mw79rX23D0seehKy6xYmRERERERI3X5gp6AJAUCgRP\nfABeA3sZ5mX8lICDj8yH9maBFSOzLvbFicPcisX8isPcisPcisPcisPc2qY2WdAD5UV90PiR8Bk6\nwDAvZ+8R7H/wSZRm5lgxMiIiIiIi07W5HvrapMfvxrWvfjJMO0W0R8///hsOQX5mfR8iIiIiotqw\nh76ZfIcNQPCE+4GKB00VnE/FvlGP49a5i9YNjIiIiIioASzoK3gN6InQGWMhqZQAgOKrGdh33xPI\nO3rKypFZDvvixGFuxWJ+xWFuxWFuxWFuxWFubRML+ircb++C8Nl/h8JOAwAoy87F/gdnI2v3QStH\nRkRERERUO/bQ16IgJQ0pb22ArqAIACCpVej65iIEjB4i9H2JiIiIqG1iD72ZOYUHI+IfU6F2dwUA\nyGVa/PHEMlx4+1O0sL9/iIiIiKiVY0FfB4dAX0Q+Nx32AT6GeWdWvI1Ti/4FWaezYmTisC9OHOZW\nLOZXHOZWHOZWHOZWHObWNrGgr4fG0x0Rz0yDU1SoYV7qh5txdPpiPlWWiIiIiGwCe+hNoC8rQ+qH\nXyH30HHDPI8+sbjtk1WGthwiIiIioqZiD71gCrUaIdMfRrtBfQ3zchKPIXHk4yhKu2bFyIiIiIio\nrbNYQR8cUKz1AAAgAElEQVQfH4+OHTsiMjISq1atqrE8MzMTw4YNQ/fu3dGlSxd88sknlgrNJJJC\ngcCxIxAwZphhXsG5i9g7Yhryjpy0YmTmw744cZhbsZhfcZhbcZhbcZhbcZhb22SRgl6n0+HJJ59E\nfHw8Tp48iU2bNuHUKeMHNq1ZswY9evTA0aNHsWvXLixYsABardYS4ZlMkiT4DIlDyNQxkJTlD6Aq\nvZGNfaNn4fr3O60cHRERERG1RRYp6Pfv34+IiAiEhoZCrVZj3Lhx+Oabb4zW8ff3R35+PgAgPz8f\nXl5eUKlUlgiv0Tx6x6LDU5OgdHQAAOiLSnB06gtIWfOfFj2sZVxcnLVDaLWYW7GYX3GYW3GYW3GY\nW3GYW9tkkYL+ypUrCA4ONkwHBQXhypUrRutMmzYNJ06cQEBAAGJjY/Hmm29aIrQmc44OQ+RzM6Dx\n8TLMO/vSOzjx9KvQl9nWvywQERERUetlkUvgkiQ1uM4rr7yC7t27Y9euXUhOTsY999yDY8eOwcXF\npca6z61bjUDv8vHhXRwcERMShl4xXQAA+0+Vj0RjiWl7v3bIe/AOXPvmF4RfvQkA2Lbxv0g8dgQT\nv/oQajcXQ69Z5V+0tjxdtS/OFuJpTdOV82wlntY2XTnPVuJpTdNJSUmYOXOmzcTTmqbfffdddO3a\n1WbiaU3T/H3G821LmE5KSkJeXh4AIDU1FVOnTkVTWWTYysTERCxbtgzx8fEAgJUrV0KhUGDhwoWG\ndUaMGIEXXngB/fv3BwAMGjQIq1atQs+ePY22ZY1hKxuiL9MibcMW5CQeM8xzigzF7f/5PziGBFox\nssZJSEgwHGhkXsytWMyvOMytOMytOMytOMytOM0ZttIiBb1Wq0V0dHR5MR4QgF69emHTpk2IiYkx\nrDN//ny4ublh6dKlSE9Px+23344//vgDnp6eRtuyxYIeAGRZRvoPu3D9m+2GeWoPV3R//2V4xd1u\nxciIiIiIyNbZ/Dj0KpUKa9aswdChQ9GpUyeMHTsWMTExWLt2LdauXQsAeP7553Hw4EHExsZi8ODB\neO2112oU87ZMkiT43XtX+Qg4FTfzluXk4+DYeUj9+CsrR0dERERErRWfFCtAQXIaLrz7KbR5twzz\ngic8gJiXn4JCrbJiZPXjP6OJw9yKxfyKw9yKw9yKw9yKw9yKY/NX6Nsapw7BiHp+JhxCAgzz0jZs\nwYGH56I0y7b/GCEiIiKiloVX6AXSl5Yhdf0W5O7/wzDPIdgft61fBZdOEVaMjIiIiIhsCa/Q2yiF\nRo2QqWPgP/oeoGLozqK0a0i8dwau/7DLusERERERUavAgl4wSZLgO/xOhM36GxR2GgCArrAIRx97\nHmdefheyTmflCP9UdYxZMi/mVizmVxzmVhzmVhzmVhzm1jaxoLcQt9iO5U+W9f5z5J4Lqzfi4CPz\n2VdPRERERE3GHnoL0xYUIfXDL5GfdNYwzz7QFz0+Wgm32I5WjIyIiIiIrIU99C2IyskBYU8+Ct+R\ndxnmFV9Jx75Rj+PyZ99bMTIiIiIiaolY0FuBpFDAf9QghD35KBQO9gAAfUkpjs9/BSeeeQ36klKr\nxMW+OHGYW7GYX3GYW3GYW3GYW3GYW9vEgt6K3GI7InrRTNgH+hrmpW3Yin33zURh6jUrRkZERERE\nLUWjeui3bt2K+++/HwCQmZmJdu3aCQusLi29h742upJSpK3fgtwDSYZ5KjcXdHtrEXyGDrBiZERE\nRERkCRbroY+Pj8e8efMAAOnp6XjppZea9KZkTGmnQci0hxE4dgSgLP9ItHk3cXjiQpxevgb6Mq2V\nIyQiIiIiW9Wogl6v1yMqKgpPP/00OnfujB07doiKq82RJAneg/sh8h/ToPZ0M8y/+O5n2D96Foqu\npAuPgX1x4jC3YjG/4jC34jC34jC34jC3tqlRBX1qaiqeeOIJeHh4YOXKlVi2bJmgsNoupw7BiF48\nC65dow3zcg8k4fd7JuHGjkQrRkZEREREtqhRPfQJCQmIi4sDAKxcuRKxsbEYMWKEsOBq0xp76Gsj\n6/XI2LYH17b8DOj1hvlhs/+OyGemQaFWWTE6IiIiIjIni/XQVxbzAPDcc8/B3d29SW9KDZMUCvgO\nG4CIBVOgdncxzL+wemP5KDiXrloxOiIiIiKyFc0atrJfv37mioPq4BwViqjFs+DSqYNhXt7hE/h9\n8ERc2/qzWd+LfXHiMLdiMb/iMLfiMLfiMLfiMLe2iePQtwBqV2eEz52IgIeG/jkKzs0CHHt8KZLm\nvQxtQZGVIyQiIiIia2lUD70taCs99HUpuHAZl97/HKU3cgzznCLaI/bd5UY30hIRERFRy2GxHnqy\nPqewIEQvngWP3rGGeQXnU7H3r9Nx4b1NkKvcQEtERERErZ9JBf3rr79e6/x//vOfZg2GTKN0sEfI\n1DFoP+VBKOw0AAC5tAxnlq3GgYfnNnnMevbFicPcisX8isPcisPcisPcisPc2iaTCvrly5fXOn/F\nihVmDYYax7NvD0QvfgIOIQGGedkJh7Dn7gm4umWbFSMjIiIiIkupt4d+x44dkGUZI0eOxPfff2+0\nLDk5GS+99BIuXbokPMiq2noPfW30Wi3Sv9uJ9P/9BlT5OP3uH4zOrz4NtburFaMjIiIiooY0p4e+\n3qcTTZkyBZIkoaSkBI899phhviRJ8PX1xerVq5v0pmReCpUK/g/cA5euUUj9cDNKM8tvmL2+9Rfk\n7DuGbm8thteAnlaOkoiIiIhEqLfl5uLFi7hw4QLGjx+PCxcuGH5SUlKwd+9ejBo1ylJxkgmcI0IQ\nvfRJePa/zTCv5NoNHBgzB6cW/avB4S3ZFycOcysW8ysOcysOcysOcysOc2ub6r1CX2njxo1IT0/H\n/v37kZmZiapdOlOmTBEWHDWe0t4O7SeNhmtsR6Rt2ArdrUIAwKUPvsSN7XvR9d8vGI2QQ0REREQt\nm0nj0G/duhWPPvooIiMjcfz4cXTp0gXHjx9HXFwcdu7caYk4DdhDb7qyvJtIW78V+Uln/pwpSQiZ\n/jCiFs6A0tHeesERERERkYHwcehfeOEFfPTRRzhy5AicnZ1x5MgRrFu3DrfddlvDLyarUbu5IGz2\nowie9AAUDnblM2UZl9Z+jj2DJyLnQJJ1AyQiIiKiZjOpoE9LS8PDDz9smJZlGRMmTMCGDRuEBUbm\nIUkSvPrfjo7LZsOlc6RhfmFKGvaNehynl6+BrqgEAPviRGJuxWJ+xWFuxWFuxWFuxWFubZNJBb2P\njw+uX78OAAgNDcXevXuRnJwMfSOeShofH4+OHTsiMjISq1atqnWdXbt2oUePHujSpQsGDhxo8rap\nYRpPd4TPnYDgCfdDYf/n1fqL736GPYMnInvvEesGSERERERNYlIP/auvvoqIiAg89NBD2LBhA6ZP\nnw5JkrBgwQK89NJLDb6JTqdDdHQ0fvnlFwQGBuIvf/kLNm3ahJiYGMM6ubm56N+/P3766ScEBQUh\nMzMT7dq1q7Et9tA3X2lWLlLXb8GtU8lG84MnPIDoxU9A5eJkpciIiIiI2qbm9NCbVNBXd+nSJRQU\nFKBTp04mrb93714sX74c8fHxAMr/QACAZ5991rDOO++8g+vXr+PFF1+sd1ss6M1DlmVk7T6Iq1/G\nQ19cYphv5++Nzqv+AZ8hcVaMjoiIiKhtEX5TbHUhISEmF/MAcOXKFQQHBxumg4KCcOXKFaN1zp07\nh+zsbNx1113o2bMnNm7c2JTQyESSJKHdHX9Bx+Vz4BrbEQBwUl+Akms3cHjCMzg6YzFKbmRbOcrW\ngz2HYjG/4jC34jC34jC34jC3tsmkceibS5KkBtcpKyvD4cOHsX37dhQWFqJv377o06cPIiMja6z7\n3LrVCPT2AQC4ODgiJiQMvWK6AAD2nzoOAJw2cfpoehrku7sjqncszmzYhJOFBeVJ/mY7sn47gPxH\nBqPdXb0xYMAAAH9+kePi4jjdiOlKthJPa5uuZCvxtKbppKQkm4qnNU0nJSXZVDyc5rQp05VsJZ6W\nPJ2UlIS8vDwAQGpqKqZOnYqmalLLTWMlJiZi2bJlhpablStXQqFQYOHChYZ1Vq1ahaKiIixbtgwA\nMHXqVAwbNgwPPfSQ0bbYciOO9lYhrnzxP+RUu0HWo28PdF71DzhHhVonMCIiIqJWzuItN43Vs2dP\nnDt3DhcvXkRpaSk+//xzjBo1ymid++67DwkJCdDpdCgsLMS+ffsa1dZDzadydkTIlAcRPm8iNF7u\nhvk5e49gz6AJOPvqWsMQl0RERERkG+ot6CuHqmwulUqFNWvWYOjQoejUqRPGjh2LmJgYrF27FmvX\nrgUAdOzYEcOGDUO3bt3Qu3dvTJs2jQW9hVW247h2jkT08jnwGToAUJYfInKZFin/Xo+EgX/DjR2J\n1gyzRar+T5VkXsyvOMytOMytOMytOMytbVLVtzAqKgr5+fmG6dGjR+Prr79u0hsNHz4cw4cPN5o3\nY8YMo+mnn34aTz/9dJO2T+altNMg4KGh8OgTi8v/+RYFyakAgKJLV3Fo/Hz4jbwbHV+cC3t/bytH\nSkRERNS21dtD7+Ligps3bxqmPTw8kJOTY5HA6sIeesuT9Xpk7zmMq5t/gq6wyDBf6eSIiAVTEDJ1\nDBQatRUjJCIiImrZbL6Hnlo2SaGA14CeiHlpHjz6djfM1xUU4syLa7Bn0ARk/rrfihESERERtV31\nFvQ6nQ47duzAjh07sH37dmi1WsN05Q+1HpU99HVRuTghZMpD6LBgCuz9fQzzC85dwsGx83DksedR\nlHZNdJgtEnsOxWJ+xWFuxWFuxWFuxWFubVO9PfQ+Pj547LHHDNNeXl5G0wBw4cIFMZGRzXLpGI7o\nJbNwY2cirn+7w/Ck2fQfduHGjr3oMGcCQmeOh9LezsqREhEREbV+FhmH3pzYQ29byvJu4upX22qM\nXe/QPgDRS2bB968DTXqwGBEREVFb1pweepMK+pMnT2L37t3Izs6Gp6cn4uLi0Llz5ya9YXOxoLdN\nt85fwpXPvq/RcuPRpztiVsyFa9doK0VGREREZPuE3RQryzKmTJmCrl274pVXXsG3336Ll156Cd26\ndcOkSZPQwi7uUwMa6qGvj3NECKIWzUTQ30ZC6exomJ+TeBS/D5mCpKdeQUlGljnCbJHYcygW8ysO\ncysOcysOcysOc2ub6i3o161bh127diExMRGXLl3C3r17kZaWhsTERCQkJOC9996zVJzUAkgKBdoN\n7I2Yl56C9+B+hodSQZZxZdP3+K3vWCS/tQG6Yj5tloiIiMhc6m256d+/P5599lmMHDmyxrLvv/8e\nK1euxJ49e4QGWB1bblqO4us3cPXLeOT/ccZovn2gL6KemwH/0UMgKThyKhEREZGwHnoPDw+kpqbC\nxcWlxrL8/Hy0b98eubmWLa5Z0Lc8N0+ex5XPf0Tx1Qyj+a5doxC95El4DehppciIiIiIbIOwHnqd\nTldrMQ8Arq6u0Ov1TXpTsk3N6aGvj0unCEQvmVWjvz4/6SwOjJmDg4/Mx81TyULe21aw51As5lcc\n5lYc5lYc5lYc5tY21TsOfeWDpGojyzK0Wq2QoKj1kZRKtBvYGx69Y5ERvxsZv/wOubQMAJC5MxGZ\nu/YhcOwIRD4zDfYBPg1sjYiIiIgq1dtyExoa2uAY4pZ+sNT27duRmlyAThotXBUcZaelKs3Jx/Vv\ntyN7z2GgyiGosNOg/eQHET7779B4uVsxQiIiIiLLET4OvS3Zvn07nj1c/kdGsEqLThotumjKEK3W\nwp73V7Y4RZev49rX25CfdNZovtLZEWGPP4LQx8dB5exkpeiIiIiILENYD31BQQGee+45jBo1CkuX\nLkVJiW0NN5imVeGnQnu8keuCmTfcsSLbBV/fssfpUhXKWtSfKbZBVA99fRyC/BA+ZwI6zJ8Mh5BA\nw3zdrUKcf/1D/NprDC68t6nFD3XJnkOxmF9xmFtxmFtxmFtxmFvbVG9B/+STT+L7779HdHQ0vvrq\nKyxYsMBScdUrCCVQwLhi10HCuTIVthY44JUcF8zMcMdrOc74rsAOKWVK6Fng2zSXmA6IeuFxhM58\nBHb+3ob5Zdm5OLNsNXb3G4u0jVuhL+N9G0RERERV1dty4+fnh8OHDyMgIABpaWkYMGAALl68aMHw\natq+fTtyj1xBqSwhDXa4CDtcgh0yoKn3dY6SHlFqLWI05T/tVToo6r89gKxE1uuRk3gU177dgbIs\n4yFKHYL90eGpyQgYMwwKdb33dBMRERG1GMJ66F1cXHDz5k3DtIeHB3Jycpr0RuZSWdBXVyArkFpR\n3F+CHXKgrnc7TpIeHTVadNRoEaPWIogFvs3Rl2mRtfsg0n/YBW3+LaNlDiEBiJg/Bf4PDoFCxcKe\niIiIWjZhBb2joyO+//57AOXDVN5///345ptvjNa5++67m/TGTVVXQV9dnqw0FPeXYI9bUNa7Pgv8\n8h76XjFdrB1GDbqSUmTuSETGtgTobhUaLXMMD0bE/Mnwf+AeSMr6P2NrSkhIQFxcnLXDaLWYX3GY\nW3GYW3GYW3GYW3GaU9DXe2nTx8cHjz32mGHay8vLaBqw/LCVpnKTdOiGQnRDIWQZyIEKl2CH1Iqf\ngmoFfoGswKESDQ6VlLfuOEl6RGu06KguL/LZomM9SjsNfIffgXZ39Ubm9r3I2LYHusIiAEBhShr+\nePJFnP/XJ+gwZwL8Rw9hKw4RERG1KS1y2EpTrtDXR5aBLKgMLTppsENhA1fwHSQZUWotOlYMkRmq\n1kHFAt8qdEXFuLF9L278vAe6wmKjZQ7tAxA++1EEPjwCCrv676sgIiIishVtbhz65hb01VUt8Ct/\nGirwNZARodEiWq1FtEaLDmot7FjgW5S2sAiZv+xFxi+/Q19kXNjb+XsjbNbfEDx+FJSO9laKkIiI\niMg0wsahbyskCWgnaXGbVID7pWzMxjVMxXUMQQ5iUAhn6Gq8phQSTpaqsaXAAa/muODxDHcsz3bB\nf2864EiJGrf0La+6t8Y49M2hcnSA36i70enVBfC7fzCUzo6GZSXXbuD0on/j114PImX1RpRVu6nW\n0jhur1jMrzjMrTjMrTjMrTjMrW1is3EtJAloBy3aQYvbUABZBnKhRGpFe04a7JBXLXU6SEguUyG5\nTIUfK+7bDFTqEKXRIkqtRZRGi3YKPaSWV+fbPJWjA/z+OhDeg/oi67cDyPgpwTAqTmlmDs6+/C5S\n3tqA4IkPIHT6WNj5eFk5YiIiIiLzYctNE+XLSqRBg8sVBX5mA8NkAoCHQo/IiuI+Sq1FsEoHJQt8\ns9OXliEr4RAy4n9DWU6+0TKFnQYBDw9H2BN/g1NYkJUiJCIiIjLGHnobUCQrjAr8dKihR/3Vup0k\no4Nai8iKnwi1Fo5sgjIbvVaLnL1HkbEtASXXM40XShL87r0LYU8+CrfYjtYJkIiIiKgCe+htgIOk\nR5RUjLulPEyUMjAPV/EIbmAA8hCGYmigr/GaErm8D/+bAge8nuuCmTfc8UKWCz7Od8TuIg2uaxWw\n5J9bLa2HviEKlQpeA3qi4/I5CJ05Ho5Vr8jLMq5/twN7h07BvgdmIWNbAmR9zc/IXNhzKBbzKw5z\nKw5zKw5zKw5za5vYQy+IRpIRghKEoATATehl4AbUSIMGV2CHK9Agv1r6ZUhI06qQplVhZ5EdAMBF\n0iNCrUWERodItRZhHE2n0SSFAu63dYJbjxjcOnsBGfG7cfP4OcPynL1HkLP3CBw7tEfo9LEIHDOc\nI+MQERFRi2Gxlpv4+HjMmzcPOp0OU6dOxcKFC2td78CBA+jbty+++OILjB49usZyW225aYp8WYnL\n0OBKRatOBtSQG2jTUUBGsEpX0apT/l9fJW+2bayitGvI+CkBOQeTAJ3xlXm1pxvaT3wA7Sc/yBto\niYiIyCJsvodep9MhOjoav/zyCwIDA/GXv/wFmzZtQkxMTI317rnnHjg6OmLy5Ml48MEHa2yrNRX0\n1ZXKEq5Cg6sVRf4V2KHYhK4oZ0mPDmotOlQU+OFqHZwULerWCKspzc5D5o5EZP52oMZY9pJGDf9R\ngxAydQzcusfUsQUiIiKi5rP5Hvr9+/cjIiICoaGhUKvVGDduHL755psa661evRoPPfQQvL29LRGW\nzdFIMkKlEvSTbmKMlIW5uIppuI4RyEYsbqEdygDULNRvyQocK9Xg6wIH/F9FL/7CTFeszXPE9kIN\nLpYpoTWhvm9tPfSm0Hi6IeChoej82j8QOHYENF7uhmVyaRmubo7H3mGPIfHe6bi29Wfoy7RNeh/2\nHIrF/IrD3IrD3IrD3IrD3Nomi/TQX7lyBcHBwYbpoKAg7Nu3r8Y633zzDXbs2IEDBw5AYg8JJAnw\nghZe0KIbyge3L5YlXK+4gl95Jb+4lqfaXtMpcU2nxJ7i8l58NWSEqnUIV2sRriq/iu/DVh0Dpb0d\nvAf3Q7u7eiPv6Clk/LwHhclphuW5B48j9+Bx2PmtRvuJDyDo0ftg5+1pxYiJiIiIylmkoDelOJ83\nbx5effVVSJIEWZZRXyfQ6v+ug49n+VV8R3sHhAWGoEuH8paI48mnAKDVTp9POQkA6F+5/Pwp3IQS\nzh264xo0+CP5NHKhhHOHHgCA/OSjAADXDt1xrkyFQ6ePG6adJD0cLx6Gv0qHQZ07IyqqK/afSgIA\n9IrpAuDPq/ZtZfrA2VOAI9Dr2RkovHgF27/eilunLyBGLr9J9sjVSziy8t/o/K9P4DfyLlztEQ7n\n6DAMGDAAwJ9XLuLi4jjN6VYzXclW4mkt05XzbCWe1jQdFxdnU/FwmtO1TSclJSEvLw8AkJqaiqlT\np6KpLNJDn5iYiGXLliE+Ph4AsHLlSigUCqMbY8PDww1FfGZmJhwdHfH+++9j1KhRRttqzT305lIm\nA+kVV/Arf6qPqFMXT4Ue4RWj6YSrdAhlPz7K8m8h67cDyNy1D9q8WzWWu3SKQPCk0Qh4cAhUTo5W\niJCIiIhaOpu/KVar1SI6Ohrbt29HQEAAevXqVetNsZUmT56MkSNHtvpRbiypQFbgWkVxf63ip/oN\nt/nJR+HaoXuN1/oqdQhT6RCm1iJMrUOISguHNvgEA71Wi7xDJ3BjRyIKU9JqLFc6OyJwzHAET3wA\nLh3DjZZVvQpH5sf8isPcisPcisPcisPcitOcgt60y7bNpFKpsGbNGgwdOhQ6nQ6PPfYYYmJisHbt\nWgDAjBkzLBFGm+Yk6RGBYkSgfCQXWQZyoTQq8AtqueEWANJ1SqTrlEgs0QAAJMjwU+oRptYitOIq\nflso8hUqFTx6x8KjdywKU68ia9d+5Ow7Bn1pGQBAd6sQqR9/hdSPv4L7X7oi+NH74Dfybo5pT0RE\nREJZbBx6c+EVenEqH351HWpDkX8DaugbGBsf+LPID61W5Du28iJfW1iEnL1HkblrH0quZ9ZYrnJ1\nRsCDQxH06Ci4do60QoRERETUEth8y405saC3LG1FkX8NGlyHBtegRqYJD8Cq5KPUIVSlQ0hFoR+i\n1sG1Ffbky7KMW6dTkPnrfuQdPVXjYVUA4NajE4IeHQX/+wZB5exkhSiJiIjIVrGgJ7M4nnzKMJpO\nfcpkCRkVV/KvQ4PrjSzyPRR6hKi0FVfxy4t8L0XrGUKzLP8Wsn8/gqzdB1GakQUAOKkvQCdFeRGv\ndLCH78i7ETTur/Do251DtJoBezrFYW7FYW7FYW7FYW7Fsfkeempd1JKMQJQiEKUACgCUj6yTUVHc\nX4cG6RVFfm3tOjl6BXJKNTha+uc8J0mPELUO7VXlRX57lRb+Kj1ULbDWVbs6w3fYAPgM6Y9bZy8i\n67cDkA4eMDwTTFdUjKtf/IirX/wIx9BABI4dgYCHR8Ah0Ne6gRMREVGLxCv0JIxWBjKrFPjpUCMD\nGmhNvJKvgowgVXmR376i2A9WtcxhNLU3C5CdeBTZCYdQfDWj5gqSBK87/4LAMcPhM+wOqJwcLB8k\nERERWQ1bbqjF0MtAFlRIr1Lkp0ODEph+92w7hQ7BFQV+5Y+3Ug9FC7iaL8syii5eQdbvh5Gz7w/o\ni4prrKN0coTfvQMRMGY4PPv1gKRo5XcWExEREQt6Mg9Te+jNTZaBPCgNV/AzKgp9Ux+GBQB20p9X\n84MrfoJs6Gr+/lPHDU+jraQvLUPekZPI/v0wbp5KKU9ENfaBvgh4cCgCHhoG56hQC0Xb8rCnUxzm\nVhzmVhzmVhzmVhz20FOLJkmAO3Rwhw7R+POKdbEsIb1KgZ9RT19+iSwhuUyF5DLjQ9pLUV7YVxb5\nwWod/JS20Zuv0KgN49qXZuUiJ/EoshOPGg1/WXwlHSlvbUDKWxvg2jUK/g8Mgd99g9hvT0RERAa8\nQk8tik4GsiqK+6o/hVCavA0lZARUXMEv/9EjWGUbI+1UtuRk7z2KnAN/QHersNb1PPp0h//oIfC7\n9y5oPN0sHCURERGZG1tuqM0rkBWG4v5GxX+zoIbOxBtwAcBekhFYtdBX6hCo0sFNIVul0Ndrtbh5\n/Byy9x5F/h9nIGu1NdaRVEq0G9gbfvcNgu+wO6By4fj2RERELRELejILa/XQi6KTgWyocKNKkX+j\nkb35AOAs6RGo0lUU+3oEVfy/SyP682vroW8MXWExco+cRO7+Y3X22yvsNGh3V3lx73NP/zb18Cr2\ndIrD3IrD3IrD3IrD3IrDHnqiWiglwBtaeEMLoMgwv0SWDEX+nz8qFNfRtnNLVuBMmQJnytRG810V\negRWXMUPqCj0A1RinoSrdLSHV//b4NX/NpTl3UTuwePI2XcMhRcuG9bRl5QiI343MuJ3Q2Gvgfeg\nfvAbNQjeg/tC5eRo9piIiIjINvAKPRHKL3gXQIHMKlfyM6FGFlQobcSQmgDgIukRoNIhUFX+3wBl\neaHvIaB1pyQjC7kHjyP34HEUpV2rdR2FvQbtBvaG718HwmdIHNRuLuYNgoiIiJqNLTdEglQOqZkJ\nNckLZlUAACAASURBVDIr2ncqC31tIwt9B0k2KvADVHr4K8vH0FeaodAvvp6J3INJyD14HMVX0mtd\nR1Kr4BXXE773DoTv0AHQtPNo/hsTERFRs7GgJ7NobT30IullIB9K3Ki4+TYTKkOhX1ZLoZ+ffBSu\nHbrXui0VZPip9AhQ6uCv0sFfWV7s+yl1sG/iM6WKr2Ug98Bx5B4+UWdxD4UCHr1j4Tv8DvgMHQDH\nkICmvZkNYE+nOMytOMytOMytOMytOOyhJ7IwRZWx8yOrjJ1feUW/ssjPqijyi1H3381aSLisVeKy\nVgmUGC/zVJS37fgrdfCvKPL9VTp4NtC+Y+/vA79Rd8Nv1N0ovp6JvMMnkHv4JIouVfljWK9Hzt4j\nyNl7BKeXvAmXThHwGXYHfIYNgGvXKEjWHsOTiIiITMIr9EQWIMvALSgMBX7V/95qxBj6lTSQ4afS\nwV+ph79KBz+lDn4VLTwO9VzVL83KQe7hk8g7fAIFyWm1jpYDlD+h1uee/vAeEgfPfj2gtLdrdIxE\nRERkOrbcELVgxbJkKPCzqxT7OVBBbsQ4+pXcFOWFfWWB76vUw0+lg0+1J+SW5d9C/rHTyDtyCjdP\nJdc6zj0AKB3s4XXnX+AzJA7tBvWFvW+7pu4qERER1YEFPZkFe+jFaUpudTKQC1VFoV+14K97iM36\nSJDhrdTDT1neuuOr0sNXqYOfUg/3siIUnjyPvKMnkf/HWegKi+rcjlv3GLQb1Bfeg/rBrXtHSIom\nNvqbEXs6xWFuxWFuxWFuxWFuxWEPPVErpJQAL2jhBS1QpU8fAAplhaG4z4Ya2RVX9HOgqvPpuDIk\nZOiUyNAp8QeMx9RXwhXeId7wDe8FvwfLEHQpBe4nT0Bx/BR0GZlG6+YdPYW8o6eQ/MZHUHu6w/vu\n3mh3d1+0G9gbGk83s+aAiIiIGsYr9EStSOXoO5WtOzkVV/WzoUI+lEATWni8Mq+j69kkhJ45AY8L\nyZD0+tpXVCjg1iMG3nf1gdfAXnDrHgOFitcMiIiITMGWGyJqUFlFC0/51Xy1odDPgQoFJrbw2BUV\nIuT8KYSePYmwcyfgdOtmneuqXJ3hNaAn2t3VG+3u7AWHYH9z7QoREVGrw4KezII99OLYem5LZcnQ\nslO1fScXqrpH4dHr4XP9MsLOnEDouZPwT7sART2nE21QAFS9boNHXE+E3N0TPr4eUJhpaEz2dIrD\n3IrD3IrD3IrD3IrDHnoiahaNJMMXZfBFWY1lpbKEXKiQA6Wh0M+BCrkKFTICgpER0B777hoO+8Jb\naJ98BqHnTiLk/Gm45OcabUd1+Spw+Spyvv4eWZKEjKAQZHfqDG33WDje1gl+Hk7wc7WDv4sGfi52\ncNI0/sZfIiKitohX6ImoybQykFelyM+BCnlQIkdWQpmRieDzpxF6/iSCLpyHSlvzj4VKZWo1rrbv\ngLSwSKSFRyE9MAROjhr4VRT3fs4a+Lr8Oe3rrIGdyvqj6xAREZkLr9ATkVWojEbiqUIC9L7ALd8Y\n5PTvivNleugvXYFdSgrck8/D8+plSFWuJajLyhCSfBohyacBAKUaO1wJ7YC0sCicDY9Cgn8w5GrD\nY3o6qMqLexcNfCsLfufyot/bWQONkgU/ERG1DSzoycDW+7xbsraYW4UEuEIHV+gADYBIn/If9IFc\nWITSlFSUJKdCmXwB6qwso9dqSksQdvYkws6eBACU2Nnjakg4LodG4nJoBNIDQ5BdBGQXaXEyowD5\nyUfh2qG70Ta8HNWGQt/HuaLor/jxcdHAnlf4TcJ+WXGYW3GYW3GYW9vEgp6ILE5ydIBdl2jYdYkG\nAMi5+dBfuAQ55RL0KZeA3Hyj9e1Kio0K/DK1BleDw3AlNAKXQyNwpqzmU26zCsuQVViGkxkFtcbg\nZq+Cj3N50e9T5ady2tVOCclMN+0SERGJxB56IrIpsiwDObnQp6T+WeDfvFXva/RKJfJDQpARGoFL\n7cOR7B+KQieXZsVhp5TgXaXI93bWwMdJXfFfDbyd1NDwKj8REZlJi+mhj4+Px7x586DT6TB16lQs\nXLjQaPmnn36K1157DbIsw8XFBe+++y66detmyRCJyMokSQI8PaD09AB6xpYX+Nm50F9Mg3whFfqL\naUCO8Qg6Cp0O7ikpcE9JQRSAewDogwNR0jEK+RGRuBHaAemePsgt1SOvWIv8Yi30DVzKKNHJuJxX\ngst5JXWu426vgo9zeXFf+V9vZw28nTTwdlbD00ENpYJX+YmI6P/bu9fYOKqDb+D/Mzt79z2O7fiW\nhNywk5C4hboVD48e0lcqpCIgtR9C1RapSYWQWkQ/VXx6W4nSp2ortX1REa/UiyokQOojBGpDpNJC\naQlOGgglEERTSOJLHCdOfN3r7Mx5PpyZ2V17fVv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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "a = np.linspace(0, 4, 100)\n", - "expo = stats.expon\n", - "lambda_ = [0.5, 1]\n", - "\n", - "for l, c in zip(lambda_, colours):\n", - " plt.plot(a, expo.pdf(a, scale=1. / l), lw=3,\n", - " color=c, label=\"$\\lambda = %.1f$\" % l)\n", - " plt.fill_between(a, expo.pdf(a, scale=1. / l), color=c, alpha=.33)\n", - "\n", - "plt.legend()\n", - "plt.ylabel(\"PDF at $z$\")\n", - "plt.xlabel(\"$z$\")\n", - "plt.ylim(0, 1.2)\n", - "plt.title(\"Probability density function of an Exponential random variable;\\\n", - " differing $\\lambda$\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "### But what is $\\lambda \\;$?\n", - "\n", - "\n", - "**This question is what motivates statistics**. In the real world, $\\lambda$ is hidden from us. We see only $Z$, and must go backwards to try and determine $\\lambda$. The problem is difficult because there is no one-to-one mapping from $Z$ to $\\lambda$. Many different methods have been created to solve the problem of estimating $\\lambda$, but since $\\lambda$ is never actually observed, no one can say for certain which method is best! \n", - "\n", - "Bayesian inference is concerned with *beliefs* about what $\\lambda$ might be. Rather than try to guess $\\lambda$ exactly, we can only talk about what $\\lambda$ is likely to be by assigning a probability distribution to $\\lambda$.\n", - "\n", - "This might seem odd at first. After all, $\\lambda$ is fixed; it is not (necessarily) random! How can we assign probabilities to values of a non-random variable? Ah, we have fallen for our old, frequentist way of thinking. Recall that under Bayesian philosophy, we *can* assign probabilities if we interpret them as beliefs. And it is entirely acceptable to have *beliefs* about the parameter $\\lambda$. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "##### Example: Inferring behaviour from text-message data\n", - "\n", - "Let's try to model a more interesting example, one that concerns the rate at which a user sends and receives text messages:\n", - "\n", - "> You are given a series of daily text-message counts from a user of your system. The data, plotted over time, appears in the chart below. You are curious to know if the user's text-messaging habits have changed over time, either gradually or suddenly. How can you model this? (This is in fact my own text-message data. Judge my popularity as you wish.)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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h4eGBPn36QAiBdevW4eTJk6aujyTSWu+WtWDu8jB7OZi7HMxdDuYuj9ayV3V3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\ne1WD9KioKJw/fx5Vq1Z9oo3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WLMC7776rakO7d+/GypUr8eyzz8LX1xcAMHv2bEyePBkD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\nxMXFwd7evlCLBbM3nbt372LDhg149dVXCy3TQu4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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 3.5)\n", - "count_data = np.loadtxt(\"data/txtdata.csv\")\n", - "n_count_data = len(count_data)\n", - "plt.bar(np.arange(n_count_data), count_data, color=\"#348ABD\")\n", - "plt.xlabel(\"Time (days)\")\n", - "plt.ylabel(\"count of text-msgs received\")\n", - "plt.title(\"Did the user's texting habits change over time?\")\n", - "plt.xlim(0, n_count_data);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Before we start modeling, see what you can figure out just by looking at the chart above. Would you say there was a change in behaviour during this time period? \n", - "\n", - "How can we start to model this? Well, as we have conveniently already seen, a Poisson random variable is a very appropriate model for this type of *count* data. Denoting day $i$'s text-message count by $C_i$, \n", - "\n", - "$$ C_i \\sim \\text{Poisson}(\\lambda) $$\n", - "\n", - "We are not sure what the value of the $\\lambda$ parameter really is, however. Looking at the chart above, it appears that the rate might become higher late in the observation period, which is equivalent to saying that $\\lambda$ increases at some point during the observations. (Recall that a higher value of $\\lambda$ assigns more probability to larger outcomes. That is, there is a higher probability of many text messages having been sent on a given day.)\n", - "\n", - "How can we represent this observation mathematically? Let's assume that on some day during the observation period (call it $\\tau$), the parameter $\\lambda$ suddenly jumps to a higher value. So we really have two $\\lambda$ parameters: one for the period before $\\tau$, and one for the rest of the observation period. In the literature, a sudden transition like this would be called a *switchpoint*:\n", - "\n", - "$$\n", - "\\lambda = \n", - "\\begin{cases}\n", - "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", - "\\lambda_2 & \\text{if } t \\ge \\tau\n", - "\\end{cases}\n", - "$$\n", - "\n", - "\n", - "If, in reality, no sudden change occurred and indeed $\\lambda_1 = \\lambda_2$, then the $\\lambda$s posterior distributions should look about equal.\n", - "\n", - "We are interested in inferring the unknown $\\lambda$s. To use Bayesian inference, we need to assign prior probabilities to the different possible values of $\\lambda$. What would be good prior probability distributions for $\\lambda_1$ and $\\lambda_2$? Recall that $\\lambda$ can be any positive number. As we saw earlier, the *exponential* distribution provides a continuous density function for positive numbers, so it might be a good choice for modeling $\\lambda_i$. But recall that the exponential distribution takes a parameter of its own, so we'll need to include that parameter in our model. Let's call that parameter $\\alpha$.\n", - "\n", - "\\begin{align}\n", - "&\\lambda_1 \\sim \\text{Exp}( \\alpha ) \\\\\\\n", - "&\\lambda_2 \\sim \\text{Exp}( \\alpha )\n", - "\\end{align}\n", - "\n", - "$\\alpha$ is called a *hyper-parameter* or *parent variable*. In literal terms, it is a parameter that influences other parameters. Our initial guess at $\\alpha$ does not influence the model too strongly, so we have some flexibility in our choice. A good rule of thumb is to set the exponential parameter equal to the inverse of the average of the count data. Since we're modeling $\\lambda$ using an exponential distribution, we can use the expected value identity shown earlier to get:\n", - "\n", - "$$\\frac{1}{N}\\sum_{i=0}^N \\;C_i \\approx E[\\; \\lambda \\; |\\; \\alpha ] = \\frac{1}{\\alpha}$$ \n", - "\n", - "An alternative, and something I encourage the reader to try, would be to have two priors: one for each $\\lambda_i$. Creating two exponential distributions with different $\\alpha$ values reflects our prior belief that the rate changed at some point during the observations.\n", - "\n", - "What about $\\tau$? Because of the noisiness of the data, it's difficult to pick out a priori when $\\tau$ might have occurred. Instead, we can assign a *uniform prior belief* to every possible day. This is equivalent to saying\n", - "\n", - "\\begin{align}\n", - "& \\tau \\sim \\text{DiscreteUniform(1,70) }\\\\\\\\\n", - "& \\Rightarrow P( \\tau = k ) = \\frac{1}{70}\n", - "\\end{align}\n", - "\n", - "So after all this, what does our overall prior distribution for the unknown variables look like? Frankly, *it doesn't matter*. What we should understand is that it's an ugly, complicated mess involving symbols only a mathematician could love. And things will only get uglier the more complicated our models become. Regardless, all we really care about is the posterior distribution.\n", - "\n", - "We next turn to PyMC, a Python library for performing Bayesian analysis that is undaunted by the mathematical monster we have created. \n", - "\n", - "\n", - "Introducing our first hammer: PyMC\n", - "-----\n", - "\n", - "PyMC is a Python library for programming Bayesian analysis [3]. It is a fast, well-maintained library. The only unfortunate part is that its documentation is lacking in certain areas, especially those that bridge the gap between beginner and hacker. One of this book's main goals is to solve that problem, and also to demonstrate why PyMC is so cool.\n", - "\n", - "We will model the problem above using PyMC. This type of programming is called *probabilistic programming*, an unfortunate misnomer that invokes ideas of randomly-generated code and has likely confused and frightened users away from this field. The code is not random; it is probabilistic in the sense that we create probability models using programming variables as the model's components. Model components are first-class primitives within the PyMC framework. \n", - "\n", - "B. Cronin [5] has a very motivating description of probabilistic programming:\n", - "\n", - "> Another way of thinking about this: unlike a traditional program, which only runs in the forward directions, a probabilistic program is run in both the forward and backward direction. It runs forward to compute the consequences of the assumptions it contains about the world (i.e., the model space it represents), but it also runs backward from the data to constrain the possible explanations. In practice, many probabilistic programming systems will cleverly interleave these forward and backward operations to efficiently home in on the best explanations.\n", - "\n", - "Because of the confusion engendered by the term *probabilistic programming*, I'll refrain from using it. Instead, I'll simply say *programming*, since that's what it really is. \n", - "\n", - "PyMC code is easy to read. The only novel thing should be the syntax, and I will interrupt the code to explain individual sections. Simply remember that we are representing the model's components ($\\tau, \\lambda_1, \\lambda_2$ ) as variables:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import pymc as pm\n", - "\n", - "alpha = 1.0 / count_data.mean() # Recall count_data is the\n", - " # variable that holds our txt counts\n", - "lambda_1 = pm.Exponential(\"lambda_1\", alpha)\n", - "lambda_2 = pm.Exponential(\"lambda_2\", alpha)\n", - "\n", - "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=n_count_data)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the code above, we create the PyMC variables corresponding to $\\lambda_1$ and $\\lambda_2$. We assign them to PyMC's *stochastic variables*, so-called because they are treated by the back end as random number generators. We can demonstrate this fact by calling their built-in `random()` methods." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Random output: 39 10 32\n" - ] - } - ], - "source": [ - "print \"Random output:\", tau.random(), tau.random(), tau.random()" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "@pm.deterministic\n", - "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", - " out = np.zeros(n_count_data)\n", - " out[:tau] = lambda_1 # lambda before tau is lambda1\n", - " out[tau:] = lambda_2 # lambda after (and including) tau is lambda2\n", - " return out" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This code creates a new function `lambda_`, but really we can think of it as a random variable: the random variable $\\lambda$ from above. Note that because `lambda_1`, `lambda_2` and `tau` are random, `lambda_` will be random. We are **not** fixing any variables yet.\n", - "\n", - "`@pm.deterministic` is a decorator that tells PyMC this is a deterministic function. That is, if the arguments were deterministic (which they are not), the output would be deterministic as well. Deterministic functions will be covered in Chapter 2. " - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "observation = pm.Poisson(\"obs\", lambda_, value=count_data, observed=True)\n", - "\n", - "model = pm.Model([observation, lambda_1, lambda_2, tau])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The variable `observation` combines our data, `count_data`, with our proposed data-generation scheme, given by the variable `lambda_`, through the `value` keyword. We also set `observed = True` to tell PyMC that this should stay fixed in our analysis. Finally, PyMC wants us to collect all the variables of interest and create a `Model` instance out of them. This makes our life easier when we retrieve the results.\n", - "\n", - "The code below will be explained in Chapter 3, but I show it here so you can see where our results come from. One can think of it as a *learning* step. The machinery being employed is called *Markov Chain Monte Carlo* (MCMC), which I also delay explaining until Chapter 3. This technique returns thousands of random variables from the posterior distributions of $\\lambda_1, \\lambda_2$ and $\\tau$. We can plot a histogram of the random variables to see what the posterior distributions look like. Below, we collect the samples (called *traces* in the MCMC literature) into histograms." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[****************100%******************] 40000 of 40000 complete\n" - ] - } - ], - "source": [ - "# Mysterious code to be explained in Chapter 3.\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(40000, 10000, 1)" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "lambda_1_samples = mcmc.trace('lambda_1')[:]\n", - "lambda_2_samples = mcmc.trace('lambda_2')[:]\n", - "tau_samples = mcmc.trace('tau')[:]" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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tWyerNCIiIiIi1ZEyRl6n06FLly7YuXMnPDw80LdvX8TGxiIgIEC/zrvvvouK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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 10)\n", - "# histogram of the samples:\n", - "\n", - "ax = plt.subplot(311)\n", - "ax.set_autoscaley_on(False)\n", - "\n", - "plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", - " label=\"posterior of $\\lambda_1$\", color=\"#A60628\", normed=True)\n", - "plt.legend(loc=\"upper left\")\n", - "plt.title(r\"\"\"Posterior distributions of the variables\n", - " $\\lambda_1,\\;\\lambda_2,\\;\\tau$\"\"\")\n", - "plt.xlim([15, 30])\n", - "plt.xlabel(\"$\\lambda_1$ value\")\n", - "\n", - "ax = plt.subplot(312)\n", - "ax.set_autoscaley_on(False)\n", - "plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", - " label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", normed=True)\n", - "plt.legend(loc=\"upper left\")\n", - "plt.xlim([15, 30])\n", - "plt.xlabel(\"$\\lambda_2$ value\")\n", - "\n", - "plt.subplot(313)\n", - "w = 1.0 / tau_samples.shape[0] * np.ones_like(tau_samples)\n", - "plt.hist(tau_samples, bins=n_count_data, alpha=1,\n", - " label=r\"posterior of $\\tau$\",\n", - " color=\"#467821\", weights=w, rwidth=2.)\n", - "plt.xticks(np.arange(n_count_data))\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.ylim([0, .75])\n", - "plt.xlim([35, len(count_data) - 20])\n", - "plt.xlabel(r\"$\\tau$ (in days)\")\n", - "plt.ylabel(\"probability\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Interpretation\n", - "\n", - "Recall that Bayesian methodology returns a *distribution*. Hence we now have distributions to describe the unknown $\\lambda$s and $\\tau$. What have we gained? Immediately, we can see the uncertainty in our estimates: the wider the distribution, the less certain our posterior belief should be. We can also see what the plausible values for the parameters are: $\\lambda_1$ is around 18 and $\\lambda_2$ is around 23. The posterior distributions of the two $\\lambda$s are clearly distinct, indicating that it is indeed likely that there was a change in the user's text-message behaviour.\n", - "\n", - "What other observations can you make? If you look at the original data again, do these results seem reasonable? \n", - "\n", - "Notice also that the posterior distributions for the $\\lambda$s do not look like exponential distributions, even though our priors for these variables were exponential. In fact, the posterior distributions are not really of any form that we recognize from the original model. But that's OK! This is one of the benefits of taking a computational point of view. If we had instead done this analysis using mathematical approaches, we would have been stuck with an analytically intractable (and messy) distribution. Our use of a computational approach makes us indifferent to mathematical tractability.\n", - "\n", - "Our analysis also returned a distribution for $\\tau$. Its posterior distribution looks a little different from the other two because it is a discrete random variable, so it doesn't assign probabilities to intervals. We can see that near day 45, there was a 50% chance that the user's behaviour changed. Had no change occurred, or had the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many days were plausible candidates for $\\tau$. By contrast, in the actual results we see that only three or four days make any sense as potential transition points. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Why would I want samples from the posterior, anyways?\n", - "\n", - "\n", - "We will deal with this question for the remainder of the book, and it is an understatement to say that it will lead us to some amazing results. For now, let's end this chapter with one more example.\n", - "\n", - "We'll use the posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le 70$ ? Recall that the expected value of a Poisson variable is equal to its parameter $\\lambda$. Therefore, the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n", - "\n", - "In the code below, let $i$ index samples from the posterior distributions. Given a day $t$, we average over all possible $\\lambda_i$ for that day $t$, using $\\lambda_i = \\lambda_{1,i}$ if $t \\lt \\tau_i$ (that is, if the behaviour change has not yet occurred), else we use $\\lambda_i = \\lambda_{2,i}$. " - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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h+P3334X1JyQkID09Hb169aryPTpnzhxoaWkhISEB69atw+7du2vFMDJCCCG1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\nvIeuDOYuh9nL0PvMllpVCcfB3ajfXwjH/kKox0vdvjZw4P+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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 5)\n", - "# tau_samples, lambda_1_samples, lambda_2_samples contain\n", - "# N samples from the corresponding posterior distribution\n", - "N = tau_samples.shape[0]\n", - "expected_texts_per_day = np.zeros(n_count_data)\n", - "for day in range(0, n_count_data):\n", - " # ix is a bool index of all tau samples corresponding to\n", - " # the switchpoint occurring prior to value of 'day'\n", - " ix = day < tau_samples\n", - " # Each posterior sample corresponds to a value for tau.\n", - " # for each day, that value of tau indicates whether we're \"before\"\n", - " # (in the lambda1 \"regime\") or\n", - " # \"after\" (in the lambda2 \"regime\") the switchpoint.\n", - " # by taking the posterior sample of lambda1/2 accordingly, we can average\n", - " # over all samples to get an expected value for lambda on that day.\n", - " # As explained, the \"message count\" random variable is Poisson distributed,\n", - " # and therefore lambda (the poisson parameter) is the expected value of\n", - " # \"message count\".\n", - " expected_texts_per_day[day] = (lambda_1_samples[ix].sum()\n", - " + lambda_2_samples[~ix].sum()) / N\n", - "\n", - "\n", - "plt.plot(range(n_count_data), expected_texts_per_day, lw=4, color=\"#E24A33\",\n", - " label=\"expected number of text-messages received\")\n", - "plt.xlim(0, n_count_data)\n", - "plt.xlabel(\"Day\")\n", - "plt.ylabel(\"Expected # text-messages\")\n", - "plt.title(\"Expected number of text-messages received\")\n", - "plt.ylim(0, 60)\n", - "plt.bar(np.arange(len(count_data)), count_data, color=\"#348ABD\", alpha=0.65,\n", - " label=\"observed texts per day\")\n", - "\n", - "plt.legend(loc=\"upper left\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our analysis shows strong support for believing the user's behavior did change ($\\lambda_1$ would have been close in value to $\\lambda_2$ had this not been true), and that the change was sudden rather than gradual (as demonstrated by $\\tau$'s strongly peaked posterior distribution). We can speculate what might have caused this: a cheaper text-message rate, a recent weather-to-text subscription, or perhaps a new relationship. (In fact, the 45th day corresponds to Christmas, and I moved away to Toronto the next month, leaving a girlfriend behind.)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Exercises\n", - "\n", - "1\\. Using `lambda_1_samples` and `lambda_2_samples`, what is the mean of the posterior distributions of $\\lambda_1$ and $\\lambda_2$?" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# type your code here." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\\. What is the expected percentage increase in text-message rates? `hint:` compute the mean of `lambda_1_samples/lambda_2_samples`. Note that this quantity is very different from `lambda_1_samples.mean()/lambda_2_samples.mean()`." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# type your code here." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "3\\. What is the mean of $\\lambda_1$ **given** that we know $\\tau$ is less than 45. That is, suppose we have been given new information that the change in behaviour occurred prior to day 45. What is the expected value of $\\lambda_1$ now? (You do not need to redo the PyMC part. Just consider all instances where `tau_samples < 45`.)" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# type your code here." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "\n", - "\n", - "- [1] Gelman, Andrew. N.p.. Web. 22 Jan 2013. [N is never large enough](http://andrewgelman.com/2005/07/31/n_is_never_larg/).\n", - "- [2] Norvig, Peter. 2009. [The Unreasonable Effectiveness of Data](http://static.googleusercontent.com/media/research.google.com/en//pubs/archive/35179.pdf).\n", - "- [3] Patil, A., D. Huard and C.J. Fonnesbeck. 2010. \n", - "PyMC: Bayesian Stochastic Modelling in Python. Journal of Statistical \n", - "Software, 35(4), pp. 1-81. \n", - "- [4] Jimmy Lin and Alek Kolcz. Large-Scale Machine Learning at Twitter. Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data (SIGMOD 2012), pages 793-804, May 2012, Scottsdale, Arizona.\n", - "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. ." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC2.ipynb b/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC2.ipynb new file mode 100644 index 00000000..943770c6 --- /dev/null +++ b/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC2.ipynb @@ -0,0 +1,2515 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Chapter 2\n", + "======\n", + "______\n", + "\n", + "This chapter introduces more PyMC syntax and design patterns, and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A little more on PyMC\n", + "\n", + "### Parent and Child relationships\n", + "\n", + "To assist with describing Bayesian relationships, and to be consistent with PyMC's documentation, we introduce *parent and child* variables. \n", + "\n", + "* *parent variables* are variables that influence another variable. \n", + "\n", + "* *child variable* are variables that are affected by other variables, i.e. are the subject of parent variables. \n", + "\n", + "A variable can be both a parent and child. For example, consider the PyMC code below." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pymc as pm\n", + "\n", + "\n", + "parameter = pm.Exponential(\"poisson_param\", 1)\n", + "data_generator = pm.Poisson(\"data_generator\", parameter)\n", + "data_plus_one = data_generator + 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`parameter` controls the parameter of `data_generator`, hence influences its values. The former is a parent of the latter. By symmetry, `data_generator` is a child of `parameter`.\n", + "\n", + "Likewise, `data_generator` is a parent to the variable `data_plus_one` (hence making `data_generator` both a parent and child variable). Although it does not look like one, `data_plus_one` should be treated as a PyMC variable as it is a *function* of another PyMC variable, hence is a child variable to `data_generator`.\n", + "\n", + "This nomenclature is introduced to help us describe relationships in PyMC modeling. You can access a variable's children and parent variables using the `children` and `parents` attributes attached to variables." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Children of `parameter`: \n", + "{.new_class 'data_generator' at 0x7f812404a8d0>}\n", + "\n", + "Parents of `data_generator`: \n", + "{'mu': .new_class 'poisson_param' at 0x7f812404a898>}\n", + "\n", + "Children of `data_generator`: \n", + "{}\n" + ] + } + ], + "source": [ + "print(\"Children of `parameter`: \")\n", + "print(parameter.children)\n", + "print(\"\\nParents of `data_generator`: \")\n", + "print(data_generator.parents)\n", + "print(\"\\nChildren of `data_generator`: \")\n", + "print(data_generator.children)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course a child can have more than one parent, and a parent can have many children." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### PyMC Variables\n", + "\n", + "All PyMC variables also expose a `value` attribute. This method produces the *current* (possibly random) internal value of the variable. If the variable is a child variable, its value changes given the variable's parents' values. Using the same variables from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "parameter.value = 0.032177775515776275\n", + "data_generator.value = 0\n", + "data_plus_one.value = 1\n" + ] + } + ], + "source": [ + "print(\"parameter.value =\", parameter.value)\n", + "print(\"data_generator.value =\", data_generator.value)\n", + "print(\"data_plus_one.value =\", data_plus_one.value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "PyMC is concerned with two types of programming variables: `stochastic` and `deterministic`.\n", + "\n", + "* *stochastic variables* are variables that are not deterministic, i.e., even if you knew all the values of the variables' parents (if it even has any parents), it would still be random. Included in this category are instances of classes `Poisson`, `DiscreteUniform`, and `Exponential`.\n", + "\n", + "* *deterministic variables* are variables that are not random if the variables' parents were known. This might be confusing at first: a quick mental check is *if I knew all of variable `foo`'s parent variables, I could determine what `foo`'s value is.* \n", + "\n", + "We will detail each below.\n", + "\n", + "#### Initializing Stochastic variables\n", + "\n", + "Initializing a stochastic variable requires a `name` argument, plus additional parameters that are class specific. For example:\n", + "\n", + "`some_variable = pm.DiscreteUniform(\"discrete_uni_var\", 0, 4)`\n", + "\n", + "where 0, 4 are the `DiscreteUniform`-specific lower and upper bound on the random variable. The [PyMC docs](http://pymc-devs.github.com/pymc/distributions.html) contain the specific parameters for stochastic variables. (Or use `object??`, for example `pm.DiscreteUniform??` if you are using IPython!)\n", + "\n", + "The `name` attribute is used to retrieve the posterior distribution later in the analysis, so it is best to use a descriptive name. Typically, I use the Python variable's name as the `name`.\n", + "\n", + "For multivariable problems, rather than creating a Python array of stochastic variables, addressing the `size` keyword in the call to a `Stochastic` variable creates multivariate array of (independent) stochastic variables. The array behaves like a Numpy array when used like one, and references to its `value` attribute return Numpy arrays. \n", + "\n", + "The `size` argument also solves the annoying case where you may have many variables $\\beta_i, \\; i = 1,...,N$ you wish to model. Instead of creating arbitrary names and variables for each one, like:\n", + "\n", + " beta_1 = pm.Uniform(\"beta_1\", 0, 1)\n", + " beta_2 = pm.Uniform(\"beta_2\", 0, 1)\n", + " ...\n", + "\n", + "we can instead wrap them into a single variable:\n", + "\n", + " betas = pm.Uniform(\"betas\", 0, 1, size=N)\n", + "\n", + "#### Calling `random()`\n", + "We can also call on a stochastic variable's `random()` method, which (given the parent values) will generate a new, random value. Below we demonstrate this using the texting example from the previous chapter." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "lambda_1.value = 4.970\n", + "lambda_2.value = 1.039\n", + "tau.value = 5.000 \n", + "\n", + "After calling random() on the variables...\n", + "lambda_1.value = 1.411\n", + "lambda_2.value = 1.806\n", + "tau.value = 3.000\n" + ] + } + ], + "source": [ + "lambda_1 = pm.Exponential(\"lambda_1\", 1) # prior on first behaviour\n", + "lambda_2 = pm.Exponential(\"lambda_2\", 1) # prior on second behaviour\n", + "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=10) # prior on behaviour change\n", + "\n", + "print(\"lambda_1.value = %.3f\" % lambda_1.value)\n", + "print(\"lambda_2.value = %.3f\" % lambda_2.value)\n", + "print(\"tau.value = %.3f\" % tau.value, \"\\n\")\n", + "\n", + "lambda_1.random(), lambda_2.random(), tau.random()\n", + "\n", + "print(\"After calling random() on the variables...\")\n", + "print(\"lambda_1.value = %.3f\" % lambda_1.value)\n", + "print(\"lambda_2.value = %.3f\" % lambda_2.value)\n", + "print(\"tau.value = %.3f\" % tau.value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The call to `random` stores a new value into the variable's `value` attribute. In fact, this new value is stored in the computer's cache for faster recall and efficiency." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### **Warning**: *Don't update stochastic variables' values in-place.*\n", + "\n", + "\n", + "Straight from the PyMC docs, we quote [4]:\n", + "\n", + "> `Stochastic` objects' values should not be updated in-place. This confuses PyMC's caching scheme... The only way a stochastic variable's value should be updated is using statements of the following form:\n", + "\n", + " A.value = new_value\n", + "\n", + "> The following are in-place updates and should **never** be used:\n", + "\n", + " \n", + " A.value += 3\n", + " A.value[2,1] = 5\n", + " A.value.attribute = new_attribute_value\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Deterministic variables\n", + "\n", + "Since most variables you will be modeling are stochastic, we distinguish deterministic variables with a `pymc.deterministic` wrapper. (If you are unfamiliar with Python wrappers (also called decorators), that's no problem. Just prepend the `pymc.deterministic` decorator before the variable declaration and you're good to go. No need to know more. ) The declaration of a deterministic variable uses a Python function:\n", + "\n", + " @pm.deterministic\n", + " def some_deterministic_var(v1=v1,):\n", + " #jelly goes here.\n", + "\n", + "For all purposes, we can treat the object `some_deterministic_var` as a variable and not a Python function. \n", + "\n", + "Prepending with the wrapper is the easiest way, but not the only way, to create deterministic variables: elementary operations, like addition, exponentials etc. implicitly create deterministic variables. For example, the following returns a deterministic variable:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "pymc.PyMCObjects.Deterministic" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(lambda_1 + lambda_2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The use of the `deterministic` wrapper was seen in the previous chapter's text-message example. Recall the model for $\\lambda$ looked like: \n", + "\n", + "$$\n", + "\\lambda = \n", + "\\begin{cases}\n", + "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", + "\\lambda_2 & \\text{if } t \\ge \\tau\n", + "\\end{cases}\n", + "$$\n", + "\n", + "And in PyMC code:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "n_data_points = 5 # in CH1 we had ~70 data points\n", + "\n", + "\n", + "@pm.deterministic\n", + "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", + " out = np.zeros(n_data_points)\n", + " out[:tau] = lambda_1 # lambda before tau is lambda1\n", + " out[tau:] = lambda_2 # lambda after tau is lambda2\n", + " return out" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. \n", + "\n", + "Inside the deterministic decorator, the `Stochastic` variables passed in behave like scalars or Numpy arrays (if multivariable), and *not* like `Stochastic` variables. For example, running the following:\n", + "\n", + " @pm.deterministic\n", + " def some_deterministic(stoch=some_stochastic_var):\n", + " return stoch.value**2\n", + "\n", + "\n", + "will return an `AttributeError` detailing that `stoch` does not have a `value` attribute. It simply needs to be `stoch**2`. During the learning phase, it's the variable's `value` that is repeatedly passed in, not the actual variable. \n", + "\n", + "Notice in the creation of the deterministic function we added defaults to each variable used in the function. This is a necessary step, and all variables *must* have default values. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Including observations in the Model\n", + "\n", + "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "from IPython.core.pylabtools import figsize\n", + "from matplotlib import pyplot as plt\n", + "figsize(12.5, 4)\n", + "\n", + "\n", + "samples = [lambda_1.random() for i in range(20000)]\n", + "plt.hist(samples, bins=70, normed=True, histtype=\"stepfilled\")\n", + "plt.title(\"Prior distribution for $\\lambda_1$\")\n", + "plt.xlim(0, 8);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n", + "\n", + "PyMC stochastic variables have a keyword argument `observed` which accepts a boolean (`False` by default). The keyword `observed` has a very simple role: fix the variable's current value, i.e. make `value` immutable. We have to specify an initial `value` in the variable's creation, equal to the observations we wish to include, typically an array (and it should be an Numpy array for speed). For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "value: [10 5]\n", + "calling .random()\n", + "value: [10 5]\n" + ] + } + ], + "source": [ + "data = np.array([10, 5])\n", + "fixed_variable = pm.Poisson(\"fxd\", 1, value=data, observed=True)\n", + "print(\"value: \", fixed_variable.value)\n", + "print(\"calling .random()\")\n", + "fixed_variable.random()\n", + "print(\"value: \", fixed_variable.value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is how we include data into our models: initializing a stochastic variable to have a *fixed value*. \n", + "\n", + "To complete our text message example, we fix the PyMC variable `observations` to the observed dataset. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[10 25 15 20 35]\n" + ] + } + ], + "source": [ + "# We're using some fake data here\n", + "data = np.array([10, 25, 15, 20, 35])\n", + "obs = pm.Poisson(\"obs\", lambda_, value=data, observed=True)\n", + "print(obs.value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Finally...\n", + "\n", + "We wrap all the created variables into a `pm.Model` class. With this `Model` class, we can analyze the variables as a single unit. This is an optional step, as the fitting algorithms can be sent an array of the variables rather than a `Model` class. I may or may not use this class in future examples ;)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "model = pm.Model([obs, lambda_, lambda_1, lambda_2, tau])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Modeling approaches\n", + "\n", + "A good starting point in Bayesian modeling is to think about *how your data might have been generated*. Put yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n", + "\n", + "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n", + "\n", + "1. We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n", + "\n", + "2. Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n", + "\n", + "3. Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the latter behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n", + "\n", + "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n", + "\n", + "5. Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n", + "\n", + " What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n", + "\n", + "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n", + "\n", + "\n", + "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n", + "\n", + "\n", + "\n", + "\n", + "PyMC, and other probabilistic programming languages, have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [5]:\n", + "\n", + "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Same story; different ending.\n", + "\n", + "Interestingly, we can create *new datasets* by retelling the story.\n", + "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n", + "\n", + "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "21\n" + ] + } + ], + "source": [ + "tau = pm.rdiscrete_uniform(0, 80)\n", + "print(tau)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from an $\\text{Exp}(\\alpha)$ distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "20.7789591495 62.1938883352\n" + ] + } + ], + "source": [ + "alpha = 1. / 20.\n", + "lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n", + "print(lambda_1, lambda_2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3\\. For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "4\\. Plot the artificial dataset:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Pnz6dz3zmM3zyk58EYMiQIZSWljYsP++88xg2bBi9evXi9NNPb3J85513Hn369GHnnXfm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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.bar(np.arange(80), data, color=\"#348ABD\")\n", + "plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n", + "plt.xlabel(\"Time (days)\")\n", + "plt.ylabel(\"count of text-msgs received\")\n", + "plt.title(\"Artificial dataset\")\n", + "plt.xlim(0, 80)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. PyMC's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability. \n", + "\n", + "\n", + "The ability to generate artificial datasets is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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TO4HZkg6WtAvwQeC6cqplZmZmZtZ/Ople/iVJnwWWkjXivxMR95dWMzMzMzOz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\nXYF3kfWpd7YdiohzIuKgiDiU7DP21oj4MHA9zrY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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_artificial_sms_dataset():\n", + " tau = pm.rdiscrete_uniform(0, 80)\n", + " alpha = 1. / 20.\n", + " lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n", + " data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]\n", + " plt.bar(np.arange(80), data, color=\"#348ABD\")\n", + " plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n", + " plt.xlim(0, 80)\n", + "\n", + "figsize(12.5, 5)\n", + "plt.suptitle(\"More examples of artificial datasets\", fontsize=14)\n", + "for i in range(1, 5):\n", + " plt.subplot(4, 1, i)\n", + " plot_artificial_sms_dataset()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Later we will see how we use this to make predictions and test the appropriateness of our models." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Bayesian A/B testing\n", + "\n", + "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n", + "\n", + "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n", + "\n", + "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n", + "\n", + "### A Simple Case\n", + "\n", + "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n", + "\n", + "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n", + "\n", + "- fraction of users who make purchases, \n", + "- frequency of social attributes, \n", + "- percent of internet users with cats etc. \n", + "\n", + "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n", + "\n", + "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n", + "\n", + "\n", + "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n", + "\n", + "To set up a Bayesian model, we need to assign prior distributions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over [0,1]:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pymc as pm\n", + "\n", + "# The parameters are the bounds of the Uniform.\n", + "p = pm.Uniform('p', lower=0, upper=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Had we had stronger beliefs, we could have expressed them in the prior above.\n", + "\n", + "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if $X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[False False False ..., False False False]\n", + "77\n" + ] + } + ], + "source": [ + "# set constants\n", + "p_true = 0.05 # remember, this is unknown.\n", + "N = 1500\n", + "\n", + "# sample N Bernoulli random variables from Ber(0.05).\n", + "# each random variable has a 0.05 chance of being a 1.\n", + "# this is the data-generation step\n", + "occurrences = pm.rbernoulli(p_true, N)\n", + "\n", + "print(occurrences) # Remember: Python treats True == 1, and False == 0\n", + "print(occurrences.sum())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The observed frequency is:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "What is the observed frequency in Group A? 0.0513\n", + "Does this equal the true frequency? False\n" + ] + } + ], + "source": [ + "# Occurrences.mean is equal to n/N.\n", + "print(\"What is the observed frequency in Group A? %.4f\" % occurrences.mean())\n", + "print(\"Does this equal the true frequency? %s\" % (occurrences.mean() == p_true))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We combine the observations into the PyMC `observed` variable, and run our inference algorithm:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 18000 of 18000 complete in 1.5 sec" + ] + } + ], + "source": [ + "# include the observations, which are Bernoulli\n", + "obs = pm.Bernoulli(\"obs\", p, value=occurrences, observed=True)\n", + "\n", + "# To be explained in chapter 3\n", + "mcmc = pm.MCMC([p, obs])\n", + "mcmc.sample(18000, 1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We plot the posterior distribution of the unknown $p_A$ below:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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NPbtGQwZWxVI/AOBwsQ/GyRlHWOTpIYr+mjO+58BBbWrfG0vdQwdVZuYifQui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\npP9y91OS5TWSznb3VjMbL2m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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n", + "plt.vlines(p_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", + "plt.hist(mcmc.trace(\"p\")[:], bins=25, histtype=\"stepfilled\", normed=True)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n", + "\n", + "### *A* and *B* Together\n", + "\n", + "A similar analysis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using PyMC's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (significantly less than $N_A$) and we will simulate site B's data like we did for site A's data )" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Obs from Site A: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", + "Obs from Site B: [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n" + ] + } + ], + "source": [ + "import pymc as pm\n", + "figsize(12, 4)\n", + "\n", + "# these two quantities are unknown to us.\n", + "true_p_A = 0.05\n", + "true_p_B = 0.04\n", + "\n", + "# notice the unequal sample sizes -- no problem in Bayesian analysis.\n", + "N_A = 1500\n", + "N_B = 750\n", + "\n", + "# generate some observations\n", + "observations_A = pm.rbernoulli(true_p_A, N_A)\n", + "observations_B = pm.rbernoulli(true_p_B, N_B)\n", + "print(\"Obs from Site A: \", observations_A[:30].astype(int), \"...\")\n", + "print(\"Obs from Site B: \", observations_B[:30].astype(int), \"...\")" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.054\n", + "0.0333333333333\n" + ] + } + ], + "source": [ + "print(observations_A.mean())\n", + "print(observations_B.mean())" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 20000 of 20000 complete in 2.6 sec" + ] + } + ], + "source": [ + "# Set up the pymc model. Again assume Uniform priors for p_A and p_B.\n", + "p_A = pm.Uniform(\"p_A\", 0, 1)\n", + "p_B = pm.Uniform(\"p_B\", 0, 1)\n", + "\n", + "\n", + "# Define the deterministic delta function. This is our unknown of interest.\n", + "@pm.deterministic\n", + "def delta(p_A=p_A, p_B=p_B):\n", + " return p_A - p_B\n", + "\n", + "# Set of observations, in this case we have two observation datasets.\n", + "obs_A = pm.Bernoulli(\"obs_A\", p_A, value=observations_A, observed=True)\n", + "obs_B = pm.Bernoulli(\"obs_B\", p_B, value=observations_B, observed=True)\n", + "\n", + "# To be explained in chapter 3.\n", + "mcmc = pm.MCMC([p_A, p_B, delta, obs_A, obs_B])\n", + "mcmc.sample(20000, 1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we plot the posterior distributions for the three unknowns: " + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "p_A_samples = mcmc.trace(\"p_A\")[:]\n", + "p_B_samples = mcmc.trace(\"p_B\")[:]\n", + "delta_samples = mcmc.trace(\"delta\")[:]" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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//OUv9OzZk6VLl/LP//zPVY+dcsopLFq0iNzcXDIyMujTpw/Tp0/n4MGDJ+3n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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 10)\n", + "\n", + "# histogram of posteriors\n", + "\n", + "ax = plt.subplot(311)\n", + "\n", + "plt.xlim(0, .1)\n", + "plt.hist(p_A_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", + " label=\"posterior of $p_A$\", color=\"#A60628\", normed=True)\n", + "plt.vlines(true_p_A, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", + "plt.legend(loc=\"upper right\")\n", + "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n", + "\n", + "ax = plt.subplot(312)\n", + "\n", + "plt.xlim(0, .1)\n", + "plt.hist(p_B_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", + " label=\"posterior of $p_B$\", color=\"#467821\", normed=True)\n", + "plt.vlines(true_p_B, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n", + "plt.legend(loc=\"upper right\")\n", + "\n", + "ax = plt.subplot(313)\n", + "plt.hist(delta_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of delta\", color=\"#7A68A6\", normed=True)\n", + "plt.vlines(true_p_A - true_p_B, 0, 60, linestyle=\"--\",\n", + " label=\"true delta (unknown)\")\n", + "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n", + "plt.legend(loc=\"upper right\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$. \n", + "\n", + "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Probability site A is WORSE than site B: 0.017\n", + "Probability site A is BETTER than site B: 0.983\n" + ] + } + ], + "source": [ + "# Count the number of samples less than 0, i.e. the area under the curve\n", + "# before 0, represent the probability that site A is worse than site B.\n", + "print(\"Probability site A is WORSE than site B: %.3f\" % \\\n", + " (delta_samples < 0).mean())\n", + "\n", + "print(\"Probability site A is BETTER than site B: %.3f\" % \\\n", + " (delta_samples > 0).mean())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n", + "\n", + "Try playing with the parameters `true_p_A`, `true_p_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n", + "\n", + "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## An algorithm for human deceit\n", + "\n", + "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n", + "\n", + "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n", + "\n", + "### The Binomial Distribution\n", + "\n", + "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n", + "\n", + "$$P( X = k ) = {{N}\\choose{k}} p^k(1-p)^{N-k}$$\n", + "\n", + "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$), and $p$ is the probability of a single event. The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Zqf52pJB1vvbaa9TW1nLJJZcA8IEPfIAJEybw8MMP8/Wvf73TfVBdpYQUExJS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\nb8LQoUMZM2ZM6wc1cyON2j2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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "import scipy.stats as stats\n", + "binomial = stats.binom\n", + "\n", + "parameters = [(10, .4), (10, .9)]\n", + "colors = [\"#348ABD\", \"#A60628\"]\n", + "\n", + "for i in range(2):\n", + " N, p = parameters[i]\n", + " _x = np.arange(N + 1)\n", + " plt.bar(_x - 0.5, binomial.pmf(_x, N, p), color=colors[i],\n", + " edgecolor=colors[i],\n", + " alpha=0.6,\n", + " label=\"$N$: %d, $p$: %.1f\" % (N, p),\n", + " linewidth=3)\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim(0, 10.5)\n", + "plt.xlabel(\"$k$\")\n", + "plt.ylabel(\"$P(X = k)$\")\n", + "plt.title(\"Probability mass distributions of binomial random variables\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n", + "\n", + "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Cheating among students\n", + "\n", + "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n", + "\n", + "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n", + "\n", + "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n", + "\n", + "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use PyMC to dig through this noisy model, and find a posterior distribution for the true frequency of liars. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in PyMC. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pymc as pm\n", + "\n", + "N = 100\n", + "p = pm.Uniform(\"freq_cheating\", 0, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. " + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "true_answers = pm.Bernoulli(\"truths\", p, size=N)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ True False True True True False False True False True True False\n", + " True True False True False True True False True False True True\n", + " True True False True True False True False True False True False\n", + " False True True False True True False False True False False False\n", + " True False True True False False False True True False False False\n", + " True True True False False False False False True False False True\n", + " True False False True False False False False True False True False\n", + " False False True True False False True False True True True False\n", + " False False False True]\n" + ] + } + ], + "source": [ + "first_coin_flips = pm.Bernoulli(\"first_flips\", 0.5, size=N)\n", + "print(first_coin_flips.value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "second_coin_flips = pm.Bernoulli(\"second_flips\", 0.5, size=N)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. We do this using a PyMC `deterministic` variable:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@pm.deterministic\n", + "def observed_proportion(t_a=true_answers,\n", + " fc=first_coin_flips,\n", + " sc=second_coin_flips):\n", + "\n", + " observed = fc * t_a + (1 - fc) * sc\n", + " return observed.sum() / float(N)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, produces a proportion. " + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.58999999999999997" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "observed_proportion.value" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expect to see approximately 3/4 of all responses be \"Yes\". \n", + "\n", + "The researchers observe a Binomial random variable, with `N = 100` and `p = observed_proportion` with `value = 35`: " + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "X = 35\n", + "\n", + "observations = pm.Binomial(\"obs\", N, observed_proportion, observed=True,\n", + " value=X)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 40000 of 40000 complete in 10.4 sec" + ] + } + ], + "source": [ + "model = pm.Model([p, true_answers, first_coin_flips,\n", + " second_coin_flips, observed_proportion, observations])\n", + "\n", + "# To be explained in Chapter 3!\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(40000, 15000)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 3)\n", + "p_trace = mcmc.trace(\"freq_cheating\")[:]\n", + "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n", + " label=\"posterior distribution\", color=\"#348ABD\")\n", + "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)\n", + "plt.xlim(0, 1)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.05 to 0.35 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n", + "\n", + "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with a uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n", + "\n", + "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Alternative PyMC Model\n", + "\n", + "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n", + "\n", + "\\begin{align}\n", + "P(\\text{\"Yes\"}) &= P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\\\\\n", + "& = \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\\\\\n", + "& = \\frac{p}{2} + \\frac{1}{4}\n", + "\\end{align}\n", + "\n", + "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In PyMC, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "p = pm.Uniform(\"freq_cheating\", 0, 1)\n", + "\n", + "\n", + "@pm.deterministic\n", + "def p_skewed(p=p):\n", + " return 0.5 * p + 0.25" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I could have typed `p_skewed = 0.5*p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a `deterministic` variable, but I wanted to make the deterministic boilerplate explicit for clarity's sake. \n", + "\n", + "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n", + "\n", + "This is where we include our observed 35 \"Yes\" responses. In the declaration of the `pm.Binomial`, we include `value = 35` and `observed = True`." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "yes_responses = pm.Binomial(\"number_cheaters\", 100, p_skewed,\n", + " value=35, observed=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 25000 of 25000 complete in 1.2 sec" + ] + } + ], + "source": [ + "model = pm.Model([yes_responses, p_skewed, p])\n", + "\n", + "# To Be Explained in Chapter 3!\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(25000, 2500)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 3)\n", + "p_trace = mcmc.trace(\"freq_cheating\")[:]\n", + "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n", + " label=\"posterior distribution\", color=\"#348ABD\")\n", + "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.2)\n", + "plt.xlim(0, 1)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### More PyMC Tricks\n", + "\n", + "#### Protip: *Lighter* deterministic variables with `Lambda` class\n", + "\n", + "Sometimes writing a deterministic function using the `@pm.deterministic` decorator can seem like a chore, especially for a small function. I have already mentioned that elementary math operations *can* produce deterministic variables implicitly, but what about operations like indexing or slicing? Built-in `Lambda` functions can handle this with the elegance and simplicity required. For example, \n", + "\n", + " beta = pm.Normal(\"coefficients\", 0, size=(N, 1))\n", + " x = np.random.randn((N, 1))\n", + " linear_combination = pm.Lambda(lambda x=x, beta=beta: np.dot(x.T, beta))\n", + "\n", + "\n", + "#### Protip: Arrays of PyMC variables\n", + "There is no reason why we cannot store multiple heterogeneous PyMC variables in a Numpy array. Just remember to set the `dtype` of the array to `object` upon initialization. For example:\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "N = 10\n", + "x = np.empty(N, dtype=object)\n", + "for i in range(0, N):\n", + " x[i] = pm.Exponential('x_%i' % i, (i + 1) ** 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The remainder of this chapter examines some practical examples of PyMC and PyMC modeling:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Challenger Space Shuttle Disaster \n", + "\n", + "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Temp (F), O-Ring failure?\n", + "[[ 66. 0.]\n", + " [ 70. 1.]\n", + " [ 69. 0.]\n", + " [ 68. 0.]\n", + " [ 67. 0.]\n", + " [ 72. 0.]\n", + " [ 73. 0.]\n", + " [ 70. 0.]\n", + " [ 57. 1.]\n", + " [ 63. 1.]\n", + " [ 70. 1.]\n", + " [ 78. 0.]\n", + " [ 67. 0.]\n", + " [ 53. 1.]\n", + " [ 67. 0.]\n", + " [ 75. 0.]\n", + " [ 70. 0.]\n", + " [ 81. 0.]\n", + " [ 76. 0.]\n", + " [ 79. 0.]\n", + " [ 75. 1.]\n", + " [ 76. 0.]\n", + " [ 58. 1.]]\n" + ] + }, + { + "data": { + "image/png": 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LcCQwgtCbPgr4aNFFuoiIiIiIBLkvz+juj7j75939aHc/w90f7omA1KOeDvW2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\nct+odaF+gLvvCRwF/KeZHUQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 3.5)\n", + "np.set_printoptions(precision=3, suppress=True)\n", + "challenger_data = np.genfromtxt(\"data/challenger_data.csv\", skip_header=1,\n", + " usecols=[1, 2], missing_values=\"NA\",\n", + " delimiter=\",\")\n", + "# drop the NA values\n", + "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n", + "\n", + "# plot it, as a function of temperature (the first column)\n", + "print(\"Temp (F), O-Ring failure?\")\n", + "print(challenger_data)\n", + "\n", + "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n", + " alpha=0.5)\n", + "plt.yticks([0, 1])\n", + "plt.ylabel(\"Damage Incident?\")\n", + "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n", + "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n", + "\n", + "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n", + "\n", + "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n", + "\n", + "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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6gVJqP65Tq/20rbby8vLYlV7gWWStaOoc+1tM+Ftd9wFWEwEW8/HTVjMB7nkCrWYCWt7b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\nMrIYlp7h9JLeovSSfKZPpuZSJzQ1VXt44/lN+9siLq+kOIP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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12, 3)\n", + "\n", + "\n", + "def logistic(x, beta):\n", + " return 1.0 / (1.0 + np.exp(beta * x))\n", + "\n", + "x = np.linspace(-4, 4, 100)\n", + "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\")\n", + "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\")\n", + "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\")\n", + "plt.title(\"Logistic functon plotted for several value of $\\\\beta$ parameter\", fontsize=14)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n", + "\n", + "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n", + "\n", + "Some plots are below, with differing $\\alpha$." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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sZWth7Yn0AhgQYSI9JoT0WDMZMSFkxIYQH2rst9MOhRj1LezalIhgbVGWb3Mq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\nAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def logistic(x, beta, alpha=0):\n", + " return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n", + "\n", + "x = np.linspace(-4, 4, 100)\n", + "\n", + "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\", ls=\"--\", lw=1)\n", + "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\", ls=\"--\", lw=1)\n", + "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\", ls=\"--\", lw=1)\n", + "\n", + "plt.plot(x, logistic(x, 1, 1), label=r\"$\\beta = 1, \\alpha = 1$\",\n", + " color=\"#348ABD\")\n", + "plt.plot(x, logistic(x, 3, -2), label=r\"$\\beta = 3, \\alpha = -2$\",\n", + " color=\"#A60628\")\n", + "plt.plot(x, logistic(x, -5, 7), label=r\"$\\beta = -5, \\alpha = 7$\",\n", + " color=\"#7A68A6\")\n", + "\n", + "plt.title(\"Logistic functon with bias, plotted for several value of $\\\\alpha$ bias parameter\", fontsize=14)\n", + "plt.legend(loc=\"lower left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n", + "\n", + "Let's start modeling this in PyMC. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Normal distributions\n", + "\n", + "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n", + "\n", + "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n", + "\n", + "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n", + "\n", + "We plot some different density functions below. " + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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A032twBjTBMwBFgMbsWbGN4vIbSJyq11mC/ARsA5YCbxkjNnkWZf6ZDuL+sI5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\ngxH+KSvMVF/89BsbgboT7J3JBHtOuUNRzsDan3xzZpM3fRr+h34Hmyp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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import scipy.stats as stats\n", + "\n", + "nor = stats.norm\n", + "x = np.linspace(-8, 7, 150)\n", + "mu = (-2, 0, 3)\n", + "tau = (.7, 1, 2.8)\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", + "parameters = zip(mu, tau, colors)\n", + "\n", + "for _mu, _tau, _color in parameters:\n", + " plt.plot(x, nor.pdf(x, _mu, scale=1. / np.sqrt(_tau)),\n", + " label=\"$\\mu = %d,\\;\\\\tau = %.1f$\" % (_mu, _tau), color=_color)\n", + " plt.fill_between(x, nor.pdf(x, _mu, scale=1. / np.sqrt(_tau)), color=_color,\n", + " alpha=.33)\n", + "\n", + "plt.legend(loc=\"upper right\")\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"density function at $x$\")\n", + "plt.title(\"Probability distribution of three different Normal random \\\n", + "variables\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n", + "\n", + "$$ E[ X | \\mu, \\tau] = \\mu$$\n", + "\n", + "and its variance is equal to the inverse of $\\tau$:\n", + "\n", + "$$Var( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n", + "\n", + "\n", + "\n", + "Below we continue our modeling of the Challenger space craft:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pymc as pm\n", + "\n", + "temperature = challenger_data[:, 0]\n", + "D = challenger_data[:, 1] # defect or not?\n", + "\n", + "# notice the`value` here. We explain why below.\n", + "beta = pm.Normal(\"beta\", 0, 0.001, value=0)\n", + "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n", + "\n", + "\n", + "@pm.deterministic\n", + "def p(t=temperature, alpha=alpha, beta=beta):\n", + " return 1.0 / (1. + np.exp(beta * t + alpha))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n", + "\n", + "$$ \\text{Defect Incident, $D_i$} \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n", + "\n", + "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the above code we had to set the values of `beta` and `alpha` to 0. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `pm.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in PyMC. " + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n", + " 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n", + " 0.5])" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p.value" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 120000 of 120000 complete in 9.6 sec" + ] + } + ], + "source": [ + "# connect the probabilities in `p` with our observations through a\n", + "# Bernoulli random variable.\n", + "observed = pm.Bernoulli(\"bernoulli_obs\", p, value=D, observed=True)\n", + "\n", + "model = pm.Model([observed, beta, alpha])\n", + "\n", + "# Mysterious code to be explained in Chapter 3\n", + "map_ = pm.MAP(model)\n", + "map_.fit()\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(120000, 100000, 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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lIxzKRfkIZqIuIiIiIiK7BTNR1zrq4dD6q2HROuphUT7CofeqsCgf4VAuyodq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\nIiIiIhIo0UC9HrSPejjtZRpHuYVTZnGUW7ixuLf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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "alpha_samples = mcmc.trace('alpha')[:, None] # best to make them 1d\n", + "beta_samples = mcmc.trace('beta')[:, None]\n", + "\n", + "figsize(12.5, 6)\n", + "\n", + "# histogram of the samples:\n", + "plt.subplot(211)\n", + "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n", + "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", + " label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n", + "plt.legend()\n", + "\n", + "plt.subplot(212)\n", + "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", + " label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n", + "\n", + "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n", + "\n", + "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected). \n", + "\n", + "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50)[:, None]\n", + "p_t = logistic(t.T, beta_samples, alpha_samples)\n", + "\n", + "mean_prob_t = p_t.mean(axis=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Vhxtp9/rhcGOX+ROn5eGJ0DH/9l+2s23nQVI9B0hJi+989NTAV/3XUz57TEoS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\ntLQ0FixYQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n", + "of defect\")\n", + "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n", + "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n", + "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", + "plt.title(\"Posterior expected value of probability of defect; \\\n", + "plus realizations\")\n", + "plt.legend(loc=\"lower left\")\n", + "plt.ylim(-0.1, 1.1)\n", + "plt.xlim(t.min(), t.max())\n", + "plt.ylabel(\"probability\")\n", + "plt.xlabel(\"temperature\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n", + "\n", + "\n", + "An interesting question to ask is for what temperatures are we most uncertain about the defect-probability? Below we plot the expected value line **and** the associated 95% intervals for each temperature. " + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Ez371g/z83m/w8utP0elrT3RofRrNuU52DqdFa4uPLX/bRW11K6A1qHbTfNtL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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from scipy.stats.mstats import mquantiles\n", + "\n", + "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n", + "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n", + "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n", + " color=\"#7A68A6\")\n", + "\n", + "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n", + "\n", + "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n", + " label=\"average posterior \\nprobability of defect\")\n", + "\n", + "plt.xlim(t.min(), t.max())\n", + "plt.ylim(-0.02, 1.02)\n", + "plt.legend(loc=\"lower left\")\n", + "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", + "plt.xlabel(\"temp, $t$\")\n", + "\n", + "plt.ylabel(\"probability estimate\")\n", + "plt.title(\"Posterior probability estimates given temp. $t$\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The *95% credible interval*, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.75.\n", + "\n", + "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over [0,1] quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### What about the day of the Challenger disaster?\n", + "\n", + "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring, given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 2.5)\n", + "\n", + "prob_31 = logistic(31, beta_samples, alpha_samples)\n", + "\n", + "plt.xlim(0.995, 1)\n", + "plt.hist(prob_31, bins=1000, normed=True, histtype='stepfilled')\n", + "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n", + "plt.xlabel(\"probability of defect occurring in O-ring\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Is our model appropriate?\n", + "\n", + "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n", + "\n", + "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data (which if we recall is a *fixed* stochastic variable) with an artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n", + "\n", + "Previously in this Chapter, we simulated artificial datasets for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example, we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to create a new `Stochastic` variable, that is exactly the same as our variable that stored the observations, but minus the observations themselves. If you recall, our `Stochastic` variable that stored our observed data was:\n", + "\n", + " observed = pm.Bernoulli( \"bernoulli_obs\", p, value=D, observed=True)\n", + "\n", + "Hence we create:\n", + " \n", + " simulated_data = pm.Bernoulli(\"simulation_data\", p)\n", + "\n", + "Let's simulate 10 000:" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 10000 of 10000 complete in 1.5 sec" + ] + } + ], + "source": [ + "simulated = pm.Bernoulli(\"bernoulli_sim\", p)\n", + "N = 10000\n", + "\n", + "mcmc = pm.MCMC([simulated, alpha, beta, observed])\n", + "mcmc.sample(N)" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(10000, 23)\n" + ] + }, + { + "data": { + "image/png": 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NpKdlvDVnn5eyPwJzgEHgWnf/fn59mkc9HK2tmn81JMojLMojHMoiLMojHMoi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\n48a66svn8zQ3N9dVX9xCz484hdy2tSCuWV8edPd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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "\n", + "simulations = mcmc.trace(\"bernoulli_sim\")[:]\n", + "print(simulations.shape)\n", + "\n", + "plt.title(\"Simulated dataset using posterior parameters\")\n", + "figsize(12.5, 6)\n", + "for i in range(4):\n", + " ax = plt.subplot(4, 1, i + 1)\n", + " plt.scatter(temperature, simulations[1000 * i, :], color=\"k\",\n", + " s=50, alpha=0.6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n", + "\n", + "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n", + "\n", + "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [7] than p-value tests. We agree.\n", + "\n", + "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[8]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n", + "\n", + "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "posterior prob of defect | realized defect \n", + "0.41 | 0\n", + "0.24 | 1\n", + "0.28 | 0\n", + "0.32 | 0\n", + "0.36 | 0\n", + "0.18 | 0\n", + "0.16 | 0\n", + "0.25 | 0\n", + "0.77 | 1\n", + "0.54 | 1\n", + "0.24 | 1\n", + "0.07 | 0\n", + "0.37 | 0\n", + "0.86 | 1\n", + "0.36 | 0\n", + "0.11 | 0\n", + "0.24 | 0\n", + "0.05 | 0\n", + "0.10 | 0\n", + "0.06 | 0\n", + "0.12 | 1\n", + "0.10 | 0\n", + "0.75 | 1\n" + ] + } + ], + "source": [ + "posterior_probability = simulations.mean(axis=0)\n", + "print(\"posterior prob of defect | realized defect \")\n", + "for i in range(len(D)):\n", + " print(\"%.2f | %d\" % (posterior_probability[i], D[i]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we sort each column by the posterior probabilities:" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "probb | defect \n", + "0.05 | 0\n", + "0.06 | 0\n", + "0.07 | 0\n", + "0.10 | 0\n", + "0.10 | 0\n", + "0.11 | 0\n", + "0.12 | 1\n", + "0.16 | 0\n", + "0.18 | 0\n", + "0.24 | 1\n", + "0.24 | 1\n", + "0.24 | 0\n", + "0.25 | 0\n", + "0.28 | 0\n", + "0.32 | 0\n", + "0.36 | 0\n", + "0.36 | 0\n", + "0.37 | 0\n", + "0.41 | 0\n", + "0.54 | 1\n", + "0.75 | 1\n", + "0.77 | 1\n", + "0.86 | 1\n" + ] + } + ], + "source": [ + "ix = np.argsort(posterior_probability)\n", + "print(\"probb | defect \")\n", + "for i in range(len(D)):\n", + " print(\"%.2f | %d\" % (posterior_probability[ix[i]], D[ix[i]]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can present the above data better in a figure: I've wrapped this up into a `separation_plot` function." + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from separation_plot import separation_plot\n", + "\n", + "\n", + "figsize(11., 1.5)\n", + "separation_plot(posterior_probability, D)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects. As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n", + "\n", + "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n", + "\n", + "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n", + "\n", + "1. the perfect model, which predicts the posterior probability to be equal to 1 if a defect did occur.\n", + "2. a completely random model, which predicts random probabilities regardless of temperature.\n", + "3. a constant model: where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(11., 1.25)\n", + "\n", + "# Our temperature-dependent model\n", + "separation_plot(posterior_probability, D)\n", + "plt.title(\"Temperature-dependent model\")\n", + "\n", + "# Perfect model\n", + "# i.e. the probability of defect is equal to if a defect occurred or not.\n", + "p = D\n", + "separation_plot(p, D)\n", + "plt.title(\"Perfect model\")\n", + "\n", + "# random predictions\n", + "p = np.random.rand(23)\n", + "separation_plot(p, D)\n", + "plt.title(\"Random model\")\n", + "\n", + "# constant model\n", + "constant_prob = 7. / 23 * np.ones(23)\n", + "separation_plot(constant_prob, D)\n", + "plt.title(\"Constant-prediction model\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n", + "\n", + "The perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Exercises\n", + "\n", + "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples. Why might the resulting plot look like this?" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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6565Qq5aTy8H4uFYXtLIAPpWyxa0SCRgYgO7ugJaWiELBFqiKooj+fiWbhe5u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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# type your code here.\n", + "figsize(12.5, 4)\n", + "\n", + "plt.scatter(alpha_samples, beta_samples, alpha=0.1)\n", + "plt.title(\"Why does the plot look like this?\")\n", + "plt.xlabel(r\"$\\alpha$\")\n", + "plt.ylabel(r\"$\\beta$\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "- [1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n", + "- [2] German Rodriguez. Datasets. In WWS509. Retrieved 30/01/2013, from .\n", + "- [3] McLeish, Don, and Cyntha Struthers. STATISTICS 450/850 Estimation and Hypothesis Testing. Winter 2012. Waterloo, Ontario: 2012. Print.\n", + "- [4] Fonnesbeck, Christopher. \"Building Models.\" PyMC-Devs. N.p., n.d. Web. 26 Feb 2013. .\n", + "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. .\n", + "- [6] S.P. Brooks, E.A. Catchpole, and B.J.T. Morgan. Bayesian animal survival estimation. Statistical Science, 15: 357–376, 2000\n", + "- [7] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n", + "- [8] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [conda env:bayes]", + "language": "python", + "name": "conda-env-bayes-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC3.ipynb b/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC3.ipynb new file mode 100644 index 00000000..a3cf2f9b --- /dev/null +++ b/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC3.ipynb @@ -0,0 +1,2580 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Chapter 2\n", + "======\n", + "`Original content created by Cam Davidson-Pilon`\n", + "\n", + "`Ported to Python 3 and PyMC3 by Max Margenot (@clean_utensils) and Thomas Wiecki (@twiecki) at Quantopian (@quantopian)`\n", + "\n", + "___\n", + "\n", + "This chapter introduces more PyMC3 syntax and variables and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A little more on PyMC3\n", + "\n", + "### Model Context\n", + "\n", + "In PyMC3, we typically handle all the variables we want in our model within the context of the `Model` object." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied log-transform to poisson_param and added transformed poisson_param_log_ to model.\n" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "\n", + "with pm.Model() as model:\n", + " parameter = pm.Exponential(\"poisson_param\", 1)\n", + " data_generator = pm.Poisson(\"data_generator\", parameter)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is an extra layer of convenience compared to PyMC. Any variables created within a given `Model`'s context will be automatically assigned to that model. If you try to define a variable outside of the context of a model, you will get an error.\n", + "\n", + "We can continue to work within the context of the same model by using `with` with the name of the model object that we have already created." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "with model:\n", + " data_plus_one = data_generator + 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can examine the same variables outside of the model context once they have been defined, but to define more variables that the model will recognize they have to be within the context." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(0.693147177890573)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "parameter.tag.test_value" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each variable assigned to a model will be defined with its own name, the first string parameter (we will cover this further in the variables section). To create a different model object with the same name as one we have used previously, we need only run the first block of code again." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied log-transform to theta and added transformed theta_log_ to model.\n" + ] + } + ], + "source": [ + "with pm.Model() as model:\n", + " theta = pm.Exponential(\"theta\", 2)\n", + " data_generator = pm.Poisson(\"data_generator\", theta)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also define an entirely separate model. Note that we are free to name our models whatever we like, so if we do not want to overwrite an old model we need only make another." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to P(A) and added transformed P(A)_interval_ to model.\n", + "Applied interval-transform to P(B) and added transformed P(B)_interval_ to model.\n" + ] + } + ], + "source": [ + "with pm.Model() as ab_testing:\n", + " p_A = pm.Uniform(\"P(A)\", 0, 1)\n", + " p_B = pm.Uniform(\"P(B)\", 0, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You probably noticed that PyMC3 will often give you notifications about transformations when you add variables to your model. These transformations are done internally by PyMC3 to modify the space that the variable is sampled in (when we get to actually sampling the model). This is an internal feature which helps with the convergence of our samples to the posterior distribution and serves to improve the results." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### PyMC3 Variables\n", + "\n", + "All PyMC3 variables have an initial value (i.e. test value). Using the same variables from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "parameter.tag.test_value = 0.693147177890573\n", + "data_generator.tag.test_value = 0\n", + "data_plus_one.tag.test_value = 1\n" + ] + } + ], + "source": [ + "print(\"parameter.tag.test_value =\", parameter.tag.test_value)\n", + "print(\"data_generator.tag.test_value =\", data_generator.tag.test_value)\n", + "print(\"data_plus_one.tag.test_value =\", data_plus_one.tag.test_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `test_value` is used only for the model, as the starting point for sampling if no other start is specified. It will not change as a result of sampling. This initial state can be changed at variable creation by specifying a value for the `testval` parameter." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied log-transform to poisson_param and added transformed poisson_param_log_ to model.\n", + "\n", + "parameter.tag.test_value = 0.49999999904767284\n" + ] + } + ], + "source": [ + "with pm.Model() as model:\n", + " parameter = pm.Exponential(\"poisson_param\", 1, testval=0.5)\n", + "\n", + "print(\"\\nparameter.tag.test_value =\", parameter.tag.test_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can be helpful if you are using a more unstable prior that may require a better starting point.\n", + "\n", + "PyMC3 is concerned with two types of programming variables: stochastic and deterministic.\n", + "\n", + "* *stochastic variables* are variables that are not deterministic, i.e., even if you knew all the values of the variables' parameters and components, it would still be random. Included in this category are instances of classes `Poisson`, `DiscreteUniform`, and `Exponential`.\n", + "\n", + "* *deterministic variables* are variables that are not random if the variables' parameters and components were known. This might be confusing at first: a quick mental check is *if I knew all of variable `foo`'s component variables, I could determine what `foo`'s value is.* \n", + "\n", + "We will detail each below.\n", + "\n", + "#### Initializing Stochastic variables\n", + "\n", + "Initializing a stochastic, or random, variable requires a `name` argument, plus additional parameters that are class specific. For example:\n", + "\n", + "`some_variable = pm.DiscreteUniform(\"discrete_uni_var\", 0, 4)`\n", + "\n", + "where 0, 4 are the `DiscreteUniform`-specific lower and upper bound on the random variable. The [PyMC3 docs](http://pymc-devs.github.io/pymc3/api.html) contain the specific parameters for stochastic variables. (Or use `??` if you are using IPython!)\n", + "\n", + "The `name` attribute is used to retrieve the posterior distribution later in the analysis, so it is best to use a descriptive name. Typically, I use the Python variable's name as the `name`.\n", + "\n", + "For multivariable problems, rather than creating a Python array of stochastic variables, addressing the `shape` keyword in the call to a stochastic variable creates multivariate array of (independent) stochastic variables. The array behaves like a NumPy array when used like one, and references to its `tag.test_value` attribute return NumPy arrays. \n", + "\n", + "The `shape` argument also solves the annoying case where you may have many variables $\\beta_i, \\; i = 1,...,N$ you wish to model. Instead of creating arbitrary names and variables for each one, like:\n", + "\n", + " beta_1 = pm.Uniform(\"beta_1\", 0, 1)\n", + " beta_2 = pm.Uniform(\"beta_2\", 0, 1)\n", + " ...\n", + "\n", + "we can instead wrap them into a single variable:\n", + "\n", + " betas = pm.Uniform(\"betas\", 0, 1, shape=N)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Deterministic variables\n", + "\n", + "We can create a deterministic variable similarly to how we create a stochastic variable. We simply call up the `Deterministic` class in PyMC3 and pass in the function that we desire\n", + "\n", + " deterministic_variable = pm.Deterministic(\"deterministic variable\", some_function_of_variables)\n", + "\n", + "For all purposes, we can treat the object `some_deterministic_var` as a variable and not a Python function. \n", + "\n", + "Calling `pymc3.Deterministic` is the most obvious way, but not the only way, to create deterministic variables. Elementary operations, like addition, exponentials etc. implicitly create deterministic variables. For example, the following returns a deterministic variable:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied log-transform to lambda_1 and added transformed lambda_1_log_ to model.\n", + "Applied log-transform to lambda_2 and added transformed lambda_2_log_ to model.\n" + ] + } + ], + "source": [ + "with pm.Model() as model:\n", + " lambda_1 = pm.Exponential(\"lambda_1\", 1)\n", + " lambda_2 = pm.Exponential(\"lambda_2\", 1)\n", + " tau = pm.DiscreteUniform(\"tau\", lower=0, upper=10)\n", + "\n", + "new_deterministic_variable = lambda_1 + lambda_2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we want a `deterministic` variable to actually be tracked by our sampling, however, we need to define it explicitly as a named `deterministic` variable with the constructor.\n", + "\n", + "The use of the `deterministic` variable was seen in the previous chapter's text-message example. Recall the model for $\\lambda$ looked like: \n", + "\n", + "$$\n", + "\\lambda = \n", + "\\cases{\n", + "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", + "\\lambda_2 & \\text{if } t \\ge \\tau\n", + "}\n", + "$$\n", + "\n", + "And in PyMC3 code:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "n_data_points = 5 # in CH1 we had ~70 data points\n", + "idx = np.arange(n_data_points)\n", + "with model:\n", + " lambda_ = pm.switch(tau >= idx, lambda_1, lambda_2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. We use the `switch` function here to change from $\\lambda_1$ to $\\lambda_2$ at the appropriate time. This function is directly from the `theano` package, which we will discuss in the next section.\n", + "\n", + "Inside a `deterministic` variable, the stochastic variables passed in behave like scalars or NumPy arrays (if multivariable). We can do whatever we want with them as long as the dimensions match up in our calculations.\n", + "\n", + "For example, running the following:\n", + "\n", + " def subtract(x, y):\n", + " return x - y\n", + " \n", + " stochastic_1 = pm.Uniform(\"U_1\", 0, 1)\n", + " stochastic_2 = pm.Uniform(\"U_2\", 0, 1)\n", + " \n", + " det_1 = pm.Deterministic(\"Delta\", subtract(stochastic_1, stochastic_2))\n", + " \n", + "Is perfectly valid PyMC3 code. Saying that our expressions behave like NumPy arrays is not exactly honest here, however. The main catch is that the expression that we are making *must* be compatible with `theano` tensors, which we will cover in the next section. Feel free to define whatever functions that you need in order to compose your model. However, if you need to do any array-like calculations that would require NumPy functions, make sure you use their equivalents in `theano`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Theano\n", + "\n", + "The majority of the heavy lifting done by PyMC3 is taken care of with the `theano` package. The notation in `theano` is remarkably similar to NumPy. It also supports many of the familiar computational elements of NumPy. However, while NumPy directly executes computations, e.g. when you run `a + b`, `theano` instead builds up a \"compute graph\" that tracks that you want to perform the `+` operation on the elements `a` and `b`. Only when you `eval()` a `theano` expression does the computation take place (i.e. `theano` is lazy evaluated). Once the compute graph is built, we can perform all kinds of mathematical optimizations (e.g. simplifications), compute gradients via autodiff, compile the entire graph to C to run at machine speed, and also compile it to run on the GPU. PyMC3 is basically a collection of `theano` symbolic expressions for various probability distributions that are combined to one big compute graph making up the whole model log probability, and a collection of inference algorithms that use that graph to compute probabilities and gradients. For practical purposes, what this means is that in order to build certain models we sometimes have to use `theano`.\n", + "\n", + "Let's write some PyMC3 code that involves `theano` calculations." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to p and added transformed p_interval_ to model.\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import theano.tensor as tt\n", + "\n", + "with pm.Model() as theano_test:\n", + " p1 = pm.Uniform(\"p\", 0, 1)\n", + " p2 = 1 - p1\n", + " p = tt.stack([p1, p2])\n", + " \n", + " assignment = pm.Categorical(\"assignment\", p)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we use `theano`'s `stack()` function in the same way we would use one of NumPy's stacking functions: to combine our two separate variables, `p1` and `p2`, into a vector with $2$ elements. The stochastic `categorical` variable does not understand what we mean if we pass a NumPy array of `p1` and `p2` to it because they are both `theano` variables. Stacking them like this combines them into one `theano` variable that we can use as the complementary pair of probabilities for our two categories.\n", + "\n", + "Throughout the course of this book we use several `theano` functions to help construct our models. If you have more interest in looking at `theano` itself, be sure to check out the [documentation](http://deeplearning.net/software/theano/library/).\n", + "\n", + "After these technical considerations, we can get back to defining our model!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Including observations in the Model\n", + "\n", + "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "from IPython.core.pylabtools import figsize\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as stats\n", + "figsize(12.5, 4)\n", + "\n", + "\n", + "samples = [lambda_1.random()[0] for i in range(20000)]\n", + "plt.hist(samples, bins=70, normed=True, histtype=\"stepfilled\")\n", + "plt.title(\"Prior distribution for $\\lambda_1$\")\n", + "plt.xlim(0, 8);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n", + "\n", + "PyMC3 stochastic variables have a keyword argument `observed`. The keyword `observed` has a very simple role: fix the variable's current value to be the given data, typically a NumPy `array` or pandas `DataFrame`. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "value: [10 5]\n" + ] + } + ], + "source": [ + "data = np.array([10, 5])\n", + "with model:\n", + " fixed_variable = pm.Poisson(\"fxd\", 1, observed=data)\n", + "print(\"value: \", fixed_variable.tag.test_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is how we include data into our models: initializing a stochastic variable to have a *fixed value*. \n", + "\n", + "To complete our text message example, we fix the PyMC3 variable `observations` to the observed dataset. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[10 25 15 20 35]\n" + ] + } + ], + "source": [ + "# We're using some fake data here\n", + "data = np.array([10, 25, 15, 20, 35])\n", + "with model:\n", + " obs = pm.Poisson(\"obs\", lambda_, observed=data)\n", + "print(obs.tag.test_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Modeling approaches\n", + "\n", + "A good starting thought to Bayesian modeling is to think about *how your data might have been generated*. Position yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n", + "\n", + "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n", + "\n", + "1. We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n", + "\n", + "2. Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n", + "\n", + "3. Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the latter behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n", + "\n", + "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n", + "\n", + "5. Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n", + "\n", + " What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n", + "\n", + "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n", + "\n", + "\n", + "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n", + "\n", + "\n", + "\n", + "\n", + "PyMC3, and other probabilistic programming languages, have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [5]:\n", + "\n", + "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Same story; different ending.\n", + "\n", + "Interestingly, we can create *new datasets* by retelling the story.\n", + "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n", + "\n", + "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "59\n" + ] + } + ], + "source": [ + "tau = np.random.randint(0, 80)\n", + "print(tau)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from an $\\text{Exp}(\\alpha)$ distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "49.7521280843 10.1226712418\n" + ] + } + ], + "source": [ + "alpha = 1./20.\n", + "lambda_1, lambda_2 = np.random.exponential(scale=1/alpha, size=2)\n", + "print(lambda_1, lambda_2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3\\. For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "data = np.r_[stats.poisson.rvs(mu=lambda_1, size=tau), stats.poisson.rvs(mu=lambda_2, size = 80 - tau)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "4\\. Plot the artificial dataset:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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3/9zjNbZ9VVUVq9ZvZuCwkfXan2nP2/NnsXuXHRvcHqDb4OF5j19bPZe5M95l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\nbZ4kNwEq1TjxxbohUWP7SZNivW/L6TW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.bar(np.arange(80), data, color=\"#348ABD\")\n", + "plt.bar(tau-1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n", + "plt.xlabel(\"Time (days)\")\n", + "plt.ylabel(\"count of text-msgs received\")\n", + "plt.title(\"Artificial dataset\")\n", + "plt.xlim(0, 80)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. PyMC3's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability. \n", + "\n", + "\n", + "The ability to generate artificial dataset is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Y9xKdly2ZMD37+vrYvXs3EL286Oyzz6a7u5vxksjn28zuAHa5+5dKpi0DXnb3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\nzMwq8v9VOpInhJptAAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_artificial_sms_dataset():\n", + " tau = stats.randint.rvs(0, 80)\n", + " alpha = 1./20.\n", + " lambda_1, lambda_2 = stats.expon.rvs(scale=1/alpha, size=2)\n", + " data = np.r_[stats.poisson.rvs(mu=lambda_1, size=tau), stats.poisson.rvs(mu=lambda_2, size=80 - tau)]\n", + " plt.bar(np.arange(80), data, color=\"#348ABD\")\n", + " plt.bar(tau - 1, data[tau-1], color=\"r\", label=\"user behaviour changed\")\n", + " plt.xlim(0, 80);\n", + "\n", + "figsize(12.5, 5)\n", + "plt.title(\"More example of artificial datasets\")\n", + "for i in range(4):\n", + " plt.subplot(4, 1, i+1)\n", + " plot_artificial_sms_dataset()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Later we will see how we use this to make predictions and test the appropriateness of our models." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Bayesian A/B testing\n", + "\n", + "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n", + "\n", + "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n", + "\n", + "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n", + "\n", + "### A Simple Case\n", + "\n", + "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n", + "\n", + "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n", + "\n", + "- fraction of users who make purchases, \n", + "- frequency of social attributes, \n", + "- percent of internet users with cats etc. \n", + "\n", + "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n", + "\n", + "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n", + "\n", + "\n", + "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n", + "\n", + "To setup a Bayesian model, we need to assign prior distrbutions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over [0,1]:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to p and added transformed p_interval_ to model.\n" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "\n", + "# The parameters are the bounds of the Uniform.\n", + "with pm.Model() as model:\n", + " p = pm.Uniform('p', lower=0, upper=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Had we had stronger beliefs, we could have expressed them in the prior above.\n", + "\n", + "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if $ X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 0 1 ..., 0 0 0]\n", + "77\n" + ] + } + ], + "source": [ + "#set constants\n", + "p_true = 0.05 # remember, this is unknown.\n", + "N = 1500\n", + "\n", + "# sample N Bernoulli random variables from Ber(0.05).\n", + "# each random variable has a 0.05 chance of being a 1.\n", + "# this is the data-generation step\n", + "occurrences = stats.bernoulli.rvs(p_true, size=N)\n", + "\n", + "print(occurrences) # Remember: Python treats True == 1, and False == 0\n", + "print(np.sum(occurrences))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The observed frequency is:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "What is the observed frequency in Group A? 0.0513\n", + "Does this equal the true frequency? False\n" + ] + } + ], + "source": [ + "# Occurrences.mean is equal to n/N.\n", + "print(\"What is the observed frequency in Group A? %.4f\" % np.mean(occurrences))\n", + "print(\"Does this equal the true frequency? %s\" % (np.mean(occurrences) == p_true))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We combine the observations into the PyMC3 `observed` variable, and run our inference algorithm:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 18000 of 18000 in 1.7 sec. | SPS: 10329.7 | ETA: 0.0" + ] + } + ], + "source": [ + "#include the observations, which are Bernoulli\n", + "with model:\n", + " obs = pm.Bernoulli(\"obs\", p, observed=occurrences)\n", + " # To be explained in chapter 3\n", + " step = pm.Metropolis()\n", + " trace = pm.sample(18000, step=step)\n", + " burned_trace = trace[1000:]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We plot the posterior distribution of the unknown $p_A$ below:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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PP54JEyZwxx13lLTddXV1TJw4cb/bsrVx/Pjx3HrrrZx11lmMHj2az33uc+zatSu27qVL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\nidYp0teUfDCunPGwKN8tLJn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n", + "plt.vlines(p_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", + "plt.hist(burned_trace[\"p\"], bins=25, histtype=\"stepfilled\", normed=True)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n", + "\n", + "### *A* and *B* Together\n", + "\n", + "A similar anaylsis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using PyMC3's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (signifcantly less than $N_A$) and we will simulate site B's data like we did for site A's data )" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Obs from Site A: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", + "Obs from Site B: [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "figsize(12, 4)\n", + "\n", + "#these two quantities are unknown to us.\n", + "true_p_A = 0.05\n", + "true_p_B = 0.04\n", + "\n", + "#notice the unequal sample sizes -- no problem in Bayesian analysis.\n", + "N_A = 1500\n", + "N_B = 750\n", + "\n", + "#generate some observations\n", + "observations_A = stats.bernoulli.rvs(true_p_A, size=N_A)\n", + "observations_B = stats.bernoulli.rvs(true_p_B, size=N_B)\n", + "print(\"Obs from Site A: \", observations_A[:30], \"...\")\n", + "print(\"Obs from Site B: \", observations_B[:30], \"...\")" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.042\n", + "0.0346666666667\n" + ] + } + ], + "source": [ + "print(np.mean(observations_A))\n", + "print(np.mean(observations_B))" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to p_A and added transformed p_A_interval_ to model.\n", + "Applied interval-transform to p_B and added transformed p_B_interval_ to model.\n", + " [-------100%-------] 20000 of 20000 in 3.2 sec. | SPS: 6201.6 | ETA: 0.0" + ] + } + ], + "source": [ + "# Set up the pymc3 model. Again assume Uniform priors for p_A and p_B.\n", + "with pm.Model() as model:\n", + " p_A = pm.Uniform(\"p_A\", 0, 1)\n", + " p_B = pm.Uniform(\"p_B\", 0, 1)\n", + " \n", + " # Define the deterministic delta function. This is our unknown of interest.\n", + " delta = pm.Deterministic(\"delta\", p_A - p_B)\n", + "\n", + " \n", + " # Set of observations, in this case we have two observation datasets.\n", + " obs_A = pm.Bernoulli(\"obs_A\", p_A, observed=observations_A)\n", + " obs_B = pm.Bernoulli(\"obs_B\", p_B, observed=observations_B)\n", + "\n", + " # To be explained in chapter 3.\n", + " step = pm.Metropolis()\n", + " trace = pm.sample(20000, step=step)\n", + " burned_trace=trace[1000:]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we plot the posterior distributions for the three unknowns: " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "p_A_samples = burned_trace[\"p_A\"]\n", + "p_B_samples = burned_trace[\"p_B\"]\n", + "delta_samples = burned_trace[\"delta\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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C2rVruf/++8PWHzBgAG3btmXWrFkcO3aMzMxMli5dWiXXvHxmvPx9XXjhhaxc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FAAAN\nAUlEQVRaGRcRERERiRPljCcx5YH5o9j6pfj6o5xxSUbKGfdH423i08q4iIiIiEicKGc8iSkPzB/F\n1i/F1x/ljEsyUs64PxpvE1/jeDdAREQk0T0xeqoe+iMiXihnPIkpD8wfxdYvxdcf5Yz7o33G/VHO\nuD8abxOfVsZFREQkrtav2cKXi74BF706O3drS3qb5tGrUMQT75PxYDBIZmam77dpkLKzs/UbryeK\nrV+RxLekpIy9e/ZHtT1lpWVRrS+e1m3I0+q4JytX52p13JNPF35M0aboxvYnnVpHtb5kpZ9nia/O\nybiZPQ/8GCh0zvWpONYGeB3oCqwGrnDOFXtsp4gIALt37uXfb3zB/v2lUauzJIp1iYiIhCOUnPEX\ngB8ecOweYKZz7mRgNnDvoS5Wzrg/+k3XH8XWr0jju2f3fvbuKYnaV2lpFP82HmdaFfdHq+L+KLb+\n6OdZ4qtzMu6cywa2HHD4UmBixfcTgSFRbpeIiEjCGDlmCCPH6EediERffXdTae+cKwRwzhUA7Q91\novYZ90d7h/qj2Pql+PqjfcYlGWnbSH803ia+aN3Aeci/8X744YcsXLiQjIwMANLT0+ndu3fVn00q\nO4nKKidSuVKitCfVypXqc/2unXuBpsB3P8Ar/8Td0MvrNuTx7eZvqBTv9qRaufJYorRH5cOXP1kw\nn6PatIj7eBfvcqVEaU8yl3NzcykuLr9FMj8/n6ysLAKBAJEy5+rOlTSzrsA/qt3AuQQ43zlXaGYd\ngQ+cc6fWdu2sWbOcdlMRkWjZXrybKRM/o6QkdXZAiZbKVXHljUdfZYrKE6OnxrklEqqfXNWfYzoc\nGe9mSArLyckhEAhYpPWEmqZiFV+VpgHXVnw/HHgn0oaIiIiIiDQ0dU7GzexVYB5wkpnlm9l1wGPA\nYDNbBgQqyrVSzrg/ygPzR7H1S/H1RznjkoyUM+6PxtvEV2fOuHNu2CFeGhTltoiIiCSkJ0ZP1YRR\nRLyo724qIdM+4/5o71B/FFu/FF9/lC/uj/bC9kex9UfjbeKL1m4qIiK12rZ1N/v3Re8Jl865Q2/f\nJCIikmS8T8aDwSDaTcWP7Oxs/cbriWIbPd+s2cK8WTXzmKtvDyfRtW5DnlbHPVG/9Uex9Uc/zxKf\n9zQVERERERGpnfeVceWM+6PfdP1RbP3SCpg/WhX3R/3WHx+xbWTGvr0l0avQjCOOSItefTGin2eJ\nTznjIiIiddBDf5LP+1O/JK1x9BIATuzZgX5nZEStPpFK3tNUtM+4P9o71B/F1i9tEeeP9hmXZORj\nTNi5Yy/btu6O2tee3fuj3sZY0M+zxKeVcRGpsnPHXvLzNlNWFr39SvJXbY5aXSIiIqlGOeNJTHlg\n/jTU2JaVOj75aBWlJWVe30e5t/4oZ1ySkcYEfxrqz7Nkot1URERERETiRDnjSUx5YP4otn4pZ9wf\n5YxLMtKY4I9+niU+5YyLiIjU4YnRUzVhFBEvvK+MK2fcH+WB+aPY+qX8UH+UM+6P+q0/iq0/+nmW\n+JQzLiIiIiISJ8oZT2LKA/NHsfVLf+73Rznj/qjf+pMMsXVlsHdPCXt274/aV8n+Uu/t1s+zxKec\ncZEktnHDNjYV7Ihaffv3l1JW6ndbQxGRZLQsd33Un5sQuORUju5wZFTrlOSjfcaTmPLA/EmW2G4u\n3MH8D5JvJVT5of4oZ9wf9Vt/kiG2paWOHdv2RLXO6D1e7dCS5edZQ6aVcZFkZvFugEjDMHLMEKB8\nVxWRaNmwZitbNu2KWn1Htm7KsV2Oilp9EhsRTcbN7ELgKcpzz593zo098JxgMEhmZmYkbyOHkJ2d\nrd94PfER253b95K3pJCyKGaBfLO6KHqVxdDK1blJsRKWjNZtyNPquCSdhjomfJr9dVTr+17/TgdN\nxjVXSHz1noybWSPgf4EAsB741Mzecc4trX5eXl7y/Qk9WeTm5uofmCc+YltaWsai+WsoLY3FHyYT\n2zcFXzfIH7yx8O3mb+LdBJGwaUzwR3MFf4LBIIFAIOJ6ItlN5XRghXNujXNuP/AacOmBJ+3cuTOC\nt5DDKS4ujncTUpaP2JpSSqrs2atxwZe9+6Kb0yoSCxoT/NFcwZ/PP/88KvVEkqbSCVhbrbyO8gm6\nSJ1KSkpxUUzX2Le3hBVfFeKitOhcsK6YRR/nR6eyCiX7Sykr06q4iIj4kfdVIUXf1vzFZsWXhfzr\njS/qXWfv0zrR5Ii0SJtWpUnTxhzdvlXU6ksF3m/gLCgo8P0WMVVSUopFcYnToN5LpmvW5Nc6uXPO\n4aI56TMoi3Jqxa4d+9hUuD1q9ZWVRfczFxSuJ2oz+wqNGzei//e7RrXOZPX+/F1knqlYRFurFTv5\n5Is9iq1Hiq0fGhP82bmniOO6pNf7+s0bo7d9LkD7Y1uzf39pVH/Gljlo2jR59ySJpOXfABnVyp0r\njtXQvXt3brvttqpy3759td1hlAwYkEUwuCjezUgcTaNX1QU/Og/XNLr7ycp3FF8/TuzVgct/fqli\n68HMmTMJBoOKrScaE/xJtNgWFm2mMDn3HiAYDNZITWnZsmVU6jVXz99MzCwNWEb5DZwbgAXAL5xz\nS6LSMhERERGRFFfvlXHnXKmZ/Q6YwXdbG2oiLiIiIiISonqvjIuIiIiISGQi2dqwipm1MbMZZrbM\nzKabWa13CpjZhWa21MyWm9moWl6/08zKzKxtNNqVCiKNrZk9ZGafm9kiM3vPzDrGrvWJLQqxfdzM\nlphZ0MzeMrPWsWt9YotCbC83s8VmVmpmemoYdY+fFedMMLMVFX2yXzjXNmT1iG3/asefN7NCM6v/\ndhUprr5918w6m9lsM/vSzHLN7NbYtjzxRRDbpmb2ScXcINfMHohtyxNfJGNuxWuNzCzHzKbV+WbO\nuYi/gLHA3RXfjwIeq+WcRkAe0BVoAgSBU6q93hl4D/ia/7+9+wmNo4zDOP79qVSqEaWUpsV/tVYE\nQWg8VEFBEQOxQszBg3io1YOeingoSBvEg6A3EUQvIrRKTh5sUAu21IuHlKJNq1QlIFipJF4UEaWI\n/Dy8b+sSZptx33f3ndl9PvDSyeSd3fd9mEzf3Zl5BzbkaNcwlNRsgbGOenuBd0r3qSklQ7aPAFfE\n5deB10r3qSklQ7Z3AncAx4F7SvendFnr+BnrPAp8EpfvBRbqbjvKJSXb+PMDwA7gTOm+NLEk7rub\ngR1xeYxwn5r23QzZxp+vif9eCSwAO0v3qSklNdu47kXgA2B+rffL8s044WE/B+PyQWCmos5aDwl6\nA9iXqT3DJClbd++ck+haIOPs3q2Xmu0x90uzpS8QPlBKkJrt9+6+RJz9U2o9ZO1x4BCAu58Arjez\n8ZrbjrKUbHH3L4BfB9jetuk5X3dfdvfFuP4P4FvCM04kSN13/4x1ribcQ6jrlv+TlK2Z3QTsAt6t\n82a5BuOb3H0lNmgZ2FRRp+ohQTcCmNk08JO7f52pPcMkKVsAM3vVzM4BTwEv97GtbZOcbYdngSPZ\nW9heObOVell1q6OcL6+XbM9X1JFqWfI1s62EMxAnsrewvZKyjZdRnAKWgaPufrKPbW2b1P324hfM\ntT7g1J5NxcyOAuOdq+KbzFZUr/3pyszWA/uByVWvPTL6le2lDdxngdl4zdNe4JUemtlK/c42vscB\n4G93n+tl+7YaRLaSZKSOozK8zGwM+BB4YdXZXkkQz+xOxPudPjKzu9z9bOl2tZ2ZPQasuPuimT1E\njWNx7cG4u092+128eWXc3VfiDYK/VFTr9pCg24GtwGkzs7j+SzPb6e5VrzN0+pjtanPAp4zQYLzf\n2ZrZHsKpqIfztLg9BrjfSr2szgM3V9RZV2PbUZaSrawtKV8zu4owEH/f3Q/3sZ1tlGXfdfffzexz\nYArQYDxIyfYJYNrMdgHrgevM7JC77+72ZrkuU5kH9sTlp4GqP5iTwHYzu9XM1gFPEi5q/8bdN7v7\nNne/jXAqYGJUBuI19JwtgJlt76g3Q7jmToLUbKcIp6Gm3f1C/5vbKknZrqJveOtlNQ/sBjCz+4Df\n4qVCdXMeVSnZXmRoP+0mNd/3gLPu/uagGtwiPWdrZhstznIVr1CYBL4bXNMbr+ds3X2/u9/i7tvi\ndscvNxAHss2msgE4RrjT+TPghrh+C/BxR72pWGcJeKnLa/2AZlPJli3hG4UzhDuBDwNbSvepKSVD\ntkvAj8BXsbxduk9NKRmynSFci/cX4Qm/R0r3qXSpygp4Hniuo85bhBkATtMxC02dY+8ol8Rs54Cf\ngQvAOeCZ0v1pWukh34m47n7gn/j/16l4nJ0q3Z8mlV73XeDumOdiHCMcKN2XppWU40LH7x+kxmwq\neuiPiIiIiEghuS5TERERERGR/0mDcRERERGRQjQYFxEREREpRINxEREREZFCNBgXERERESlEg3ER\nERERkUI0GBcRERERKUSDcRERERGRQv4FzpBgPKO6HzUAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 10)\n", + "\n", + "#histogram of posteriors\n", + "\n", + "ax = plt.subplot(311)\n", + "\n", + "plt.xlim(0, .1)\n", + "plt.hist(p_A_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", + " label=\"posterior of $p_A$\", color=\"#A60628\", normed=True)\n", + "plt.vlines(true_p_A, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", + "plt.legend(loc=\"upper right\")\n", + "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n", + "\n", + "ax = plt.subplot(312)\n", + "\n", + "plt.xlim(0, .1)\n", + "plt.hist(p_B_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", + " label=\"posterior of $p_B$\", color=\"#467821\", normed=True)\n", + "plt.vlines(true_p_B, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n", + "plt.legend(loc=\"upper right\")\n", + "\n", + "ax = plt.subplot(313)\n", + "plt.hist(delta_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of delta\", color=\"#7A68A6\", normed=True)\n", + "plt.vlines(true_p_A - true_p_B, 0, 60, linestyle=\"--\",\n", + " label=\"true delta (unknown)\")\n", + "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n", + "plt.legend(loc=\"upper right\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$. \n", + "\n", + "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Probability site A is WORSE than site B: 0.208\n", + "Probability site A is BETTER than site B: 0.792\n" + ] + } + ], + "source": [ + "# Count the number of samples less than 0, i.e. the area under the curve\n", + "# before 0, represent the probability that site A is worse than site B.\n", + "print(\"Probability site A is WORSE than site B: %.3f\" % \\\n", + " np.mean(delta_samples < 0))\n", + "\n", + "print(\"Probability site A is BETTER than site B: %.3f\" % \\\n", + " np.mean(delta_samples > 0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n", + "\n", + "Try playing with the parameters `true_p_A`, `true_p_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n", + "\n", + "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## An algorithm for human deceit\n", + "\n", + "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n", + "\n", + "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n", + "\n", + "### The Binomial Distribution\n", + "\n", + "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n", + "\n", + "$$P( X = k ) = {{N}\\choose{k}} p^k(1-p)^{N-k}$$\n", + "\n", + "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$). The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Zqf52pJB1vvbaa9TW1nLJJZcA8IEPfIAJEybw8MMP8/Wvf73TfVBdpYQUExJS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\nb8LQoUMZM2ZM6wc1cyON2j2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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "import scipy.stats as stats\n", + "binomial = stats.binom\n", + "\n", + "parameters = [(10, .4), (10, .9)]\n", + "colors = [\"#348ABD\", \"#A60628\"]\n", + "\n", + "for i in range(2):\n", + " N, p = parameters[i]\n", + " _x = np.arange(N + 1)\n", + " plt.bar(_x - 0.5, binomial.pmf(_x, N, p), color=colors[i],\n", + " edgecolor=colors[i],\n", + " alpha=0.6,\n", + " label=\"$N$: %d, $p$: %.1f\" % (N, p),\n", + " linewidth=3)\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim(0, 10.5)\n", + "plt.xlabel(\"$k$\")\n", + "plt.ylabel(\"$P(X = k)$\")\n", + "plt.title(\"Probability mass distributions of binomial random variables\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n", + "\n", + "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Cheating among students\n", + "\n", + "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n", + "\n", + "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n", + "\n", + "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n", + "\n", + "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use PyMC3 to dig through this noisy model, and find a posterior distribution for the true frequency of liars. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in PyMC3. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to freq_cheating and added transformed freq_cheating_interval_ to model.\n" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "\n", + "N = 100\n", + "with pm.Model() as model:\n", + " p = pm.Uniform(\"freq_cheating\", 0, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. " + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "with model:\n", + " true_answers = pm.Bernoulli(\"truths\", p, shape=N, testval=np.random.binomial(1, 0.5, N))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1\n", + " 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1\n", + " 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0]\n" + ] + } + ], + "source": [ + "with model:\n", + " first_coin_flips = pm.Bernoulli(\"first_flips\", 0.5, shape=N, testval=np.random.binomial(1, 0.5, N))\n", + "print(first_coin_flips.tag.test_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "with model:\n", + " second_coin_flips = pm.Bernoulli(\"second_flips\", 0.5, shape=N, testval=np.random.binomial(1, 0.5, N))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. We do this using a PyMC3 `deterministic` variable:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import theano.tensor as tt\n", + "with model:\n", + " val = first_coin_flips*true_answers + (1 - first_coin_flips)*second_coin_flips\n", + " observed_proportion = pm.Deterministic(\"observed_proportion\", tt.sum(val)/float(N))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, produces a proportion. " + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(0.5600000023841858)" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "observed_proportion.tag.test_value" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expected to see approximately 3/4 of all responses be \"Yes\". \n", + "\n", + "The researchers observe a Binomial random variable, with `N = 100` and `p = observed_proportion` with `value = 35`: " + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "X = 35\n", + "\n", + "with model:\n", + " observations = pm.Binomial(\"obs\", N, observed_proportion, observed=X)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Assigned BinaryGibbsMetropolis to truths\n", + "Assigned BinaryGibbsMetropolis to first_flips\n", + "Assigned BinaryGibbsMetropolis to second_flips\n", + " [-------100%-------] 40000 of 40000 in 1891.9 sec. | SPS: 21.1 | ETA: -0.0" + ] + } + ], + "source": [ + "# To be explained in Chapter 3!\n", + "with model:\n", + " step = pm.Metropolis(vars=[p])\n", + " trace = pm.sample(40000, step=step)\n", + " burned_trace = trace[15000:]" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 3)\n", + "p_trace = burned_trace[\"freq_cheating\"][15000:]\n", + "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30, \n", + " label=\"posterior distribution\", color=\"#348ABD\")\n", + "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)\n", + "plt.xlim(0, 1)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.05 to 0.35 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n", + "\n", + "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with an uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n", + "\n", + "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Alternative PyMC3 Model\n", + "\n", + "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n", + "\n", + "\\begin{align}\n", + "P(\\text{\"Yes\"}) = & P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\\\\\n", + "& = \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\\\\\n", + "& = \\frac{p}{2} + \\frac{1}{4}\n", + "\\end{align}\n", + "\n", + "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In PyMC3, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to freq_cheating and added transformed freq_cheating_interval_ to model.\n" + ] + } + ], + "source": [ + "with pm.Model() as model:\n", + " p = pm.Uniform(\"freq_cheating\", 0, 1)\n", + " p_skewed = pm.Deterministic(\"p_skewed\", 0.5*p + 0.25)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I could have typed `p_skewed = 0.5*p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a `deterministic` variable, but I wanted to make the deterministic boilerplate explicit for clarity's sake. \n", + "\n", + "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n", + "\n", + "This is where we include our observed 35 \"Yes\" responses. In the declaration of the `pm.Binomial`, we include `value = 35` and `observed = True`." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "with model:\n", + " yes_responses = pm.Binomial(\"number_cheaters\", 100, p_skewed, observed=35)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 25000 of 25000 in 2.1 sec. | SPS: 12171.2 | ETA: 0.0" + ] + } + ], + "source": [ + "with model:\n", + " # To Be Explained in Chapter 3!\n", + " step = pm.Metropolis()\n", + " trace = pm.sample(25000, step=step)\n", + " burned_trace = trace[2500:]" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 3)\n", + "p_trace = burned_trace[\"freq_cheating\"]\n", + "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30, \n", + " label=\"posterior distribution\", color=\"#348ABD\")\n", + "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.2)\n", + "plt.xlim(0, 1)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### More PyMC3 Tricks\n", + "\n", + "#### Protip: Arrays of PyMC3 variables\n", + "There is no reason why we cannot store multiple heterogeneous PyMC3 variables in a Numpy array. Just remember to set the `dtype` of the array to `object` upon initialization. For example:\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied log-transform to x_0 and added transformed x_0_log_ to model.\n", + "Applied log-transform to x_1 and added transformed x_1_log_ to model.\n", + "Applied log-transform to x_2 and added transformed x_2_log_ to model.\n", + "Applied log-transform to x_3 and added transformed x_3_log_ to model.\n", + "Applied log-transform to x_4 and added transformed x_4_log_ to model.\n", + "Applied log-transform to x_5 and added transformed x_5_log_ to model.\n", + "Applied log-transform to x_6 and added transformed x_6_log_ to model.\n", + "Applied log-transform to x_7 and added transformed x_7_log_ to model.\n", + "Applied log-transform to x_8 and added transformed x_8_log_ to model.\n", + "Applied log-transform to x_9 and added transformed x_9_log_ to model.\n" + ] + } + ], + "source": [ + "N = 10\n", + "x = np.ones(N, dtype=object)\n", + "with pm.Model() as model:\n", + " for i in range(0, N):\n", + " x[i] = pm.Exponential('x_%i' % i, (i+1)**2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The remainder of this chapter examines some practical examples of PyMC3 and PyMC3 modeling:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Challenger Space Shuttle Disaster \n", + "\n", + "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Temp (F), O-Ring failure?\n", + "[[ 66. 0.]\n", + " [ 70. 1.]\n", + " [ 69. 0.]\n", + " [ 68. 0.]\n", + " [ 67. 0.]\n", + " [ 72. 0.]\n", + " [ 73. 0.]\n", + " [ 70. 0.]\n", + " [ 57. 1.]\n", + " [ 63. 1.]\n", + " [ 70. 1.]\n", + " [ 78. 0.]\n", + " [ 67. 0.]\n", + " [ 53. 1.]\n", + " [ 67. 0.]\n", + " [ 75. 0.]\n", + " [ 70. 0.]\n", + " [ 81. 0.]\n", + " [ 76. 0.]\n", + " [ 79. 0.]\n", + " [ 75. 1.]\n", + " [ 76. 0.]\n", + " [ 58. 1.]]\n" + ] + }, + { + "data": { + "image/png": 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LcCQwgtCbPgr4aNFFuoiIiIiIBLkvz+juj7j75939aHc/w90f7omA1KOeDvW2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\nct+odaF+gLvvCRwF/KeZHUQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 3.5)\n", + "np.set_printoptions(precision=3, suppress=True)\n", + "challenger_data = np.genfromtxt(\"data/challenger_data.csv\", skip_header=1,\n", + " usecols=[1, 2], missing_values=\"NA\",\n", + " delimiter=\",\")\n", + "#drop the NA values\n", + "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n", + "\n", + "#plot it, as a function of tempature (the first column)\n", + "print(\"Temp (F), O-Ring failure?\")\n", + "print(challenger_data)\n", + "\n", + "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n", + " alpha=0.5)\n", + "plt.yticks([0, 1])\n", + "plt.ylabel(\"Damage Incident?\")\n", + "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n", + "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n", + "\n", + "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n", + "\n", + "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n", + "\n", + "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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TDXry27i2JJ/OUdExoWbGhJq5ekYM20sa+CavmvUFtaSXNpJe2sgz6/dxwohA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\nB6kodS60TEIppU4jHkvxk4fepPdYmOraAB+7aw2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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12, 3)\n", + "\n", + "def logistic(x, beta):\n", + " return 1.0 / (1.0 + np.exp(beta * x))\n", + "\n", + "x = np.linspace(-4, 4, 100)\n", + "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\")\n", + "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\")\n", + "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\")\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n", + "\n", + "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n", + "\n", + "Some plots are below, with differing $\\alpha$." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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i1x3L1wHThBB3HrVOEPAxMAoIAq4UQnxx7LaO1yZRV1cHQHh4+ID5ZzSYCSGo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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def logistic(x, beta, alpha=0):\n", + " return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n", + "\n", + "x = np.linspace(-4, 4, 100)\n", + "\n", + "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\", ls=\"--\", lw=1)\n", + "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\", ls=\"--\", lw=1)\n", + "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\", ls=\"--\", lw=1)\n", + "\n", + "plt.plot(x, logistic(x, 1, 1), label=r\"$\\beta = 1, \\alpha = 1$\",\n", + " color=\"#348ABD\")\n", + "plt.plot(x, logistic(x, 3, -2), label=r\"$\\beta = 3, \\alpha = -2$\",\n", + " color=\"#A60628\")\n", + "plt.plot(x, logistic(x, -5, 7), label=r\"$\\beta = -5, \\alpha = 7$\",\n", + " color=\"#7A68A6\")\n", + "\n", + "plt.legend(loc=\"lower left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n", + "\n", + "Let's start modeling this in PyMC3. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Normal distributions\n", + "\n", + "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n", + "\n", + "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n", + "\n", + "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n", + "\n", + "We plot some different density functions below. " + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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s0BrZMTFC2kCnhvtAcY312EIV6VwqZUNcpDZsjLk4iGVu6o1YlFJKqb5uf1E1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\nFl/UtqPRON/9+iv09sRYdtNUxlUUpSPkrFRf28bG1w8SCPr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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import scipy.stats as stats\n", + "\n", + "nor = stats.norm\n", + "x = np.linspace(-8, 7, 150)\n", + "mu = (-2, 0, 3)\n", + "tau = (.7, 1, 2.8)\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", + "parameters = zip(mu, tau, colors)\n", + "\n", + "for _mu, _tau, _color in parameters:\n", + " plt.plot(x, nor.pdf(x, _mu, scale=1./_tau),\n", + " label=\"$\\mu = %d,\\;\\\\tau = %.1f$\" % (_mu, _tau), color=_color)\n", + " plt.fill_between(x, nor.pdf(x, _mu, scale=1./_tau), color=_color,\n", + " alpha=.33)\n", + "\n", + "plt.legend(loc=\"upper right\")\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"density function at $x$\")\n", + "plt.title(\"Probability distribution of three different Normal random \\\n", + "variables\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n", + "\n", + "$$ E[ X | \\mu, \\tau] = \\mu$$\n", + "\n", + "and its variance is equal to the inverse of $\\tau$:\n", + "\n", + "$$Var( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n", + "\n", + "\n", + "\n", + "Below we continue our modeling of the Challenger space craft:" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pymc3 as pm\n", + "\n", + "temperature = challenger_data[:, 0]\n", + "D = challenger_data[:, 1] # defect or not?\n", + "\n", + "#notice the`value` here. We explain why below.\n", + "with pm.Model() as model:\n", + " beta = pm.Normal(\"beta\", mu=0, tau=0.001, testval=0)\n", + " alpha = pm.Normal(\"alpha\", mu=0, tau=0.001, testval=0)\n", + " p = pm.Deterministic(\"p\", 1.0/(1. + tt.exp(beta*temperature + alpha)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n", + "\n", + "$$ \\text{Defect Incident, $D_i$} \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n", + "\n", + "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the above code we had to set the values of `beta` and `alpha` to 0. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `pm.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in PyMC3. " + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 120000 of 120000 in 16.5 sec. | SPS: 7283.1 | ETA: 0.0" + ] + } + ], + "source": [ + "# connect the probabilities in `p` with our observations through a\n", + "# Bernoulli random variable.\n", + "with model:\n", + " observed = pm.Bernoulli(\"bernoulli_obs\", p, observed=D)\n", + " \n", + " # Mysterious code to be explained in Chapter 3\n", + " start = pm.find_MAP()\n", + " step = pm.Metropolis()\n", + " trace = pm.sample(120000, step=step, start=start)\n", + " burned_trace = trace[100000::2]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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fzMixhzP80CF5HJ0Ugj5DJSHvibqZnQVcA9SY2RJihcJfd/cn831sERGRvmbX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\nYVE8wlHTtDWSK7/seHM5K+7q9KMyLR/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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "alpha_samples = burned_trace[\"alpha\"][:, None] # best to make them 1d\n", + "beta_samples = burned_trace[\"beta\"][:, None]\n", + "\n", + "figsize(12.5, 6)\n", + "\n", + "#histogram of the samples:\n", + "plt.subplot(211)\n", + "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n", + "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", + " label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n", + "plt.legend()\n", + "\n", + "plt.subplot(212)\n", + "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", + " label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n", + "\n", + "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n", + "\n", + "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected). \n", + "\n", + "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$." + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "t = np.linspace(temperature.min() - 5, temperature.max()+5, 50)[:, None]\n", + "p_t = logistic(t.T, beta_samples, alpha_samples)\n", + "\n", + "mean_prob_t = p_t.mean(axis=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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JAYkTikieNoGkqeP79dArpZRSSg3WsG60n4hun6G+vYf69p5jel6c20VqnJu0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\nO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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n", + "of defect\")\n", + "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n", + "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n", + "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", + "plt.title(\"Posterior expected value of probability of defect; \\\n", + "plus realizations\")\n", + "plt.legend(loc=\"lower left\")\n", + "plt.ylim(-0.1, 1.1)\n", + "plt.xlim(t.min(), t.max())\n", + "plt.ylabel(\"probability\")\n", + "plt.xlabel(\"temperature\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n", + "\n", + "\n", + "An interesting question to ask is for what temperatures are we most uncertain about the defect-probability? Below we plot the expected value line **and** the associated 95% intervals for each temperature. " + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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rAdixY8dp7a63azuxbc235ns4tzXf6dHuuF5cXAzA8uXLWbduHV05WdNuA/uI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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from scipy.stats.mstats import mquantiles\n", + "\n", + "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n", + "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n", + "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n", + " color=\"#7A68A6\")\n", + "\n", + "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n", + "\n", + "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n", + " label=\"average posterior \\nprobability of defect\")\n", + "\n", + "plt.xlim(t.min(), t.max())\n", + "plt.ylim(-0.02, 1.02)\n", + "plt.legend(loc=\"lower left\")\n", + "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", + "plt.xlabel(\"temp, $t$\")\n", + "\n", + "plt.ylabel(\"probability estimate\")\n", + "plt.title(\"Posterior probability estimates given temp. $t$\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The *95% credible interval*, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.75.\n", + "\n", + "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over [0,1] quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### What about the day of the Challenger disaster?\n", + "\n", + "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring, given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 2.5)\n", + "\n", + "prob_31 = logistic(31, beta_samples, alpha_samples)\n", + "\n", + "plt.xlim(0.995, 1)\n", + "plt.hist(prob_31, bins=1000, normed=True, histtype='stepfilled')\n", + "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n", + "plt.xlabel(\"probability of defect occurring in O-ring\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Is our model appropriate?\n", + "\n", + "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n", + "\n", + "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data (which if we recall is a *fixed* stochastic variable) with artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n", + "\n", + "Previously in this Chapter, we simulated artificial dataset for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example, we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to create a new `Stochastic` variable, that is exactly the same as our variable that stored the observations, but minus the observations themselves. If you recall, our `Stochastic` variable that stored our observed data was:\n", + "\n", + " observed = pm.Bernoulli(\"bernoulli_obs\", p, observed=D)\n", + "\n", + "Hence we create:\n", + " \n", + " simulated_data = pm.Bernoulli(\"simulation_data\", p)\n", + "\n", + "Let's simulate 10 000:" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Assigned BinaryGibbsMetropolis to bernoulli_sim\n", + " [-------100%-------] 10000 of 10000 in 27.8 sec. | SPS: 359.1 | ETA: 0.0" + ] + } + ], + "source": [ + "N = 10000\n", + "with pm.Model() as model:\n", + " beta = pm.Normal(\"beta\", mu=0, tau=0.001, testval=0)\n", + " alpha = pm.Normal(\"alpha\", mu=0, tau=0.001, testval=0)\n", + " p = pm.Deterministic(\"p\", 1.0/(1. + tt.exp(beta*temperature + alpha)))\n", + " observed = pm.Bernoulli(\"bernoulli_obs\", p, observed=D)\n", + " \n", + " simulated = pm.Bernoulli(\"bernoulli_sim\", p, shape=p.tag.test_value.shape)\n", + " step = pm.Metropolis(vars=[p])\n", + " trace = pm.sample(N, step=step)" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(10000, 23)\n" + ] + }, + { + "data": { + "image/png": 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E8LfABuAPETyniIiIiEhVK8uCR2Z2NvBxd78XOO7YHM2jHg7dKR4W5REW5REO\nZREW5REOZVH5Sp715SR9Ccgfu170ZF3zqKusssoqq6yyyiqrXOnlUOZRvwj4oruvyJZvJTMt4x15\n+7yU+xE4HRgEbnD37xXWp3nUw9HVpflXQ6I8wqI8wqEswqI8wqEswhLLPOrAFmCBmbWQWfDok8C1\n+Tu4+7tyP5vZw8DjE52ki4iIiIhIRiTzqJvZCuAu3lzw6Pb8BY8K9u0Evu/u352oLs2jLiIiIiLV\nJq4r6jme9wd3vz/3gJmt5M0x6n8EkhE+r4iIiIhI1SnXPOovAR9y90XAWuDBYvVpHvVw5G6MkDAo\nj7Aoj3Aoi7Aoj3Aoi8pXlnnU3f1pdz+QLT5NwfSNIiIiIiJyrChmffk/wOXufkO2/H+BC939s0X2\nvwU4N7d/IY1RFxEREZFqE/cY9RMys0uB6wDNFSQiIiIichxRnKj3A/PyynOz245hZucBDwAr3H1f\nscruuusuGhsbteBRAOX8sW0htKfWy8ojrLLyCKec2xZKe2q9nNsWSntqudzd3c1NN90UTHtqrRzK\ngkfTgBeBZWTmUf8VcK279+TtMw/YBHzK3Z8+Xn1a8CgcXV1aKCEkyiMsyiMcyiIsyiMcyiIsUxn6\nUpZ51M3sQeATQIrM6qSH3f3CierSGHURERERqTaxjVF39x8D7y7Ydn/ez9cD10fxXCIiIiIitSCK\n6RkxsxVm9oKZ/dbMPldkny+bWdLMtpvZ4mJ1aR71cOSPN5T4KY+wKI9wKIuwKI9wKIvKV5YFj8zs\nCiDh7q3AjcB9pT5vpUun0+zYsYN0Oh13U0QkRlF/FoT+2RJ1+zZu3EhnZycbN26MpL6ohZ5H1JLJ\nJD//+c9JJqNZgDyZTPL4449HVl/Uaqn/hty2ahbFzaQXAbe5+xXZ8q1kxqbfkbfPfcBT7r4+W+4B\nLnH3PYX1VfsY9UOHDtHR0UFfXx8jIyNMnz6dRCJBe3s7M2bMiLt5IlImUX8WhP7ZEnX7XnrpJZYt\nW8Ybb7yBu2NmzJo1i02bNvGud73rFLyCyQk9j6jt3buXtrY2UqkUo6Oj1NXV0dLSQmdnJ01NTbHX\nF7Va6r8ht63STGWMehRDX84BXskr72L8yqOF+/RPsE9N6OjoIJVK0dDQwOzZs2loaCCVStHR0RF3\n00SkjKL+LAj9syXq9uVO0qdNm0ZdXR3Tpk3jjTfemPTUZ6dK6HlEra2tjV27dlFfX09jYyP19fXs\n2rWLqc6CJmi2AAAgAElEQVTiFnV9Uaul/hty22pBJGPUo1TNY9TT6TR9fX3U1R17D29dXR19fX3B\nfZ2ksW1hUR5hKSWPqD8LQv9sibp9GzduPHqSDnDkyBGAoyfrcQ+DCT2PqCWTSVKp1NHXe/DgQSDz\nelOp1KSHrRTWlzPV+qJWSf231N8btXYshyiKWV9OZsGjfuCdJ9gHgM2bN7N169aqXPBoz5499Pf3\n09jYyFlnnQXA7t27AZg5cyYDAwP09PQE016VVVb51JSbmpoYGRlh//79AMd8HgwODjIwMEBzc3Ns\n9YX+en/605/i7kdP0HOOHDnCkSNH+NnPfsby5cur5vWGXt63bx+jo6OMjY2R7+DBgwwNDZFMJmlt\nbZ1yfTNnziypvtDzPZXHS3d3d0mv9+WXX2ZkZISGhoaj5yu59vX39/PEE0+wcuXKsr7/lVSupAWP\nPgK0u/tHs2Pav+TuF01UXzWPUU+n06xZs4aGhoZxjw0NDbF27Vqam5tjaJmIlFPUnwWhf7ZE3b6N\nGzdy7bXXHr2inm9sbIxvfvObLF++vKQ2lyL0PKKWTCa5+uqrqa+vH/fY8PAwjzzyCK2trbHVF7Va\n6r8ht60SxTJG3d3HgJuBJ4HngW+5e4+Z3WhmN2T3+SHwOzPrBe4HVpX6vJWoubmZRCLB6OjoMdsP\nHz5MIpHQwS5SI6L+LAj9syXq9i1fvpxZs2aNu4I7NjbGrFmzYj1Jh/DziFpraystLS3jXu/o6Cgt\nLS2TPqmOur6o1VL/DblttSKSMeru/mN3f7e7t7r77dlt97v7A3n73OzuC9x9kbtvK1ZXNY9RB2hv\nb6elpYWhoSFef/11hoaGmD9/Pu3t7XE3bZzc1zgSBuURllLziPqzIPTPlqjbt2nTpqMn64cPHz56\nkr5p06aIWz41oecRtc7OTubOncvw8DB79+5leHiYuXPn0tnZWXJ9g4ODJdcXtUrpv1H83qi1Yzk0\nJQ19MbO3A+uBFuBl4Gp3P1Cwz1xgHXAmcAR40N2/XKzOm266yf/1X/91ym2qFOl0moGBAc4444xg\n/0d67733ctNNN8XdDMlSHmGJKo+oPwtC/2yJun0bN27k7rvv5uabb479SvpEQs8jaslkki9/+ct8\n9rOfjeTKdzKZPDomPe4r6RMJvf9G+Xuj1o7lU6Gzs5N//Md/nNTQl7oSn/NWYKO7/3t2RdLPZ7fl\nGwX+wd23m9ks4Ndm9qS7vzBRhYODgyU2qTI0NzcHf6DnboCQMCiPsESVR9SfBaF/tkTdvuXLl7N1\n69YgT9Ih/Dyi1trayjnnnBPZSXWoJ+g5offfKH9v1NqxfCo8++yzk/43pQ59uRL4WvbnrwEfL9zB\n3Xe7+/bsz28APdToHOoiIiIiIier1BP1d+RWF3X33cA7jrezmc0HFgO/LLZPbvofid/OnTvjboLk\nUR5hUR7hUBZhUR7hUBaV74RDX8zsJ2TGlx/dBDiwZoLdiw54zw572QCszl5Zn1AikWD16tVHy4sW\nLWLx4sUnaqacAueffz7bthW971fKTHmERXmEQ1mERXmEQ1nEa/v27ccMd2lsbJx0HaXeTNoDXOLu\ne8zsLOApd/9fE+xXB3wf+JG73zXlJxQRERERqRGlDn35HvA32Z//GnisyH6dwA6dpIuIiIiInJxS\nr6g3AY8A7wRSZKZn3G9mf0JmGsa/NLMPAD8FuskMjXHgC+7+45JbLyIiIiJSpUo6URcRERERkVMj\nkpVJp8rMXjazZ83sGTP7VXbb283sSTN70cyeMLM5cbaxlhTJ4zYz22Vm27J/VsTdzlpgZnPM7Ntm\n1mNmz5vZ+9U34lMkD/WNGJjZudnPqG3Zvw+Y2WfVP8rvOFmob8TEzP7ezH5jZs+Z2dfNbLr6Rjwm\nyKJ+Kn0j1ivqZvYS8Ofuvi9v2x1AOm8Rpbe7e+EiSnIKFMnjNuCP7v4f8bWs9pjZV4HN7v5w9mbs\nRuALqG/Eokgef4f6RqzM7C3ALuD9wM2of8SmIIs21DfKzszOBrqA97j7iJmtB34IvBf1jbI6Thbz\nmWTfiPWKOpmpHgvbcMJFlOSUmSiP3HYpEzObDXzQ3R8GcPdRdz+A+kYsjpMHqG/EbTnQ5+6voP4R\nt/wsQH0jLtOAxuwFhRlAP+obccnPYiaZLGCSfSOSE3Uz+4qZ7TGz54o8vjI7pOJZM+sys4XZhxz4\niZltMbPPZLedOZlFlCRS+Xlcn7f9ZjPbbmYP6SuzsvhT4DUzezj71dgDZjYT9Y24FMsD1Dfidg3w\njezP6h/xugb4Zl5ZfaPM3P1V4E5gJ5mTwgPuvhH1jbKbIIv92Sxgkn0jqivqDwOXH+fxl4APufsi\nYC3wYHb7B9x9CfARoN3MPsj4RZN0t2v5FOaxFLgHeJe7LwZ2A/oq89SrA5YAHdk8BoFbUd+IS2Ee\nB8nkob4RIzN7K/Ax4NvZTeofMZkgC/WNGJjZ28hcPW8BziZzNfevUN8ouwmymGVmK5lC34jkRN3d\nu4B9x3n86byvip8Gzslu/3327wHgUeBCYI+ZnQlgmUWU/hBFG+XECvL4H+BCdx/wN29keBC4IK72\n1ZBdwCvuvjVb/g6ZE0X1jXgU5rEBeJ/6RuyuAH7t7q9ly+of8cllMQCZ3yHqG7FYDrzk7nvdfYzM\n7/GLUd+IQ2EW3wUunkrfiGOM+meAH5nZTDObBWBmjcBlZOZaP9lFlCRCRfL4TbZT53wC+E0c7asl\n2a8oXzGzc7OblgHPo74RiyJ57FDfiN21HDvUQv0jPsdkob4Rm53ARWbWYGZG9rMK9Y04TJRFz1T6\nRmSzvphZC/C4u593nH0uBe4GlgJvI/O/PSfz1fLX3f32iy++2GfNmsVZZ2VeS2NjIwsWLGDx4sUA\nbN++HUDlMpQ3bNjAggULgmlPrZeVR1hl5RFOube3l6uuuiqY9tR6WXmEU968eTOrV68Opj21Vu7t\n7WVwcBCA3bt3k0gkuO+++7qBI8DLwI25+weKKduJupmdR+Yr/BXu3lesnssuu8zXr18fSZukNKtW\nreKee+6JuxmSpTzCojzCoSzCojzCoSzCsnr1atatW1f+WV+yjCJTzpjZPDIn6Z863kk6cPRKusRv\n3rx5cTdB8iiPsCiPcCiLsCiPcCiLylcXRSVm9g3gEqDZzHYCtwHTAXf3B4B/BpqAe7JjdQ67+4VR\nPLeIiIiISDWK5EQdOERmYvcXJxr64u7Xm9khMneGDwI3FKuosbExoiZJqebM0dS3IVEeYVEe4VAW\nYVEe4VAWYVm0aNGk/01Z5lE3syuAhLu3AjcC9xXbN3dzlsRv4cKFJ94pJul0mh07dpBOp+NuStmE\nnEfUKiHfWsojZOl0mtNOOy3oY6WWJJNJ/vjHP5JMJuNuiqDPqdDkbjSdjLLcTGpm9wFPufv6bLkH\nuGSiO103bdrkS5YsiaRNUn0OHTpER0cHfX19jIyMMH36dBKJBO3t7cyYMSPu5kmJlK+cLB0rYdm7\ndy9tbW2kUilGR0epq6ujpaWFzs5Ompqa4m6eSBC2bdvGsmXLYruZ9HjOAV7JK/dnt4lMSkdHB6lU\nioaGBmbPnk1DQwOpVIqOjo64myYRUL5ysnSshKWtrY1du3ZRX19PY2Mj9fX17Nq1i7a2tribJlLR\n4ljw6Lhy81BK/Lq6uuJuwjHS6TR9fX3U1R17a0VdXR19fX1V/9V3aHlErdLyrfY8QlZ4rOzevRsI\n91ipdslkklQqdTSPgwcPApk8UqmUhsHESJ9TlS+qm0lPpB94Z155bnbbOJs3b2br1q1HpxSaM2cO\nCxcuZOnSpcCbB53KtVfes2cP/f39NDY2Hp3GM/cLeubMmQwMDNDT0xNMe1VWviqfmnJTUxMjIyPs\n37+ffLt372ZwcJCBgQGam5uDaW+1l/ft28fo6ChjY2PkO3jwIENDQySTSVpbW4Npby2Vu7u7g2pP\nrZW7u7s5cOAAADt37uT8889n2bJlTEaUY9TnkxmjPu7OBTP7CNDu7h81s4uAL7n7RRPVozHqUkw6\nnWbNmjU0NDSMe2xoaIi1a9fS3NwcQ8skCspXTpaOlbAkk0muvvpq6uvrxz02PDzMI488Qmtrawwt\nEwlLbGPUs/Oo/xw418x2mtl1Znajmd0A4O4/BH5nZr3A/cCqKJ5XaktzczOJRILR0dFjth8+fJhE\nIqFfzBVO+crJ0rESltbWVlpaWsblMTo6SktLi07SRUoQyYm6u69097Pdvd7d57n7w+5+f3axo9w+\nN7v7Andf5O7bitWlMerhyH2NE5L29nZaWloYGhri9ddfZ2hoiPnz59Pe3h530065EPOIWiXlWwt5\nhCz/WOnr6wv6WKkFnZ2dzJ07l+HhYfbu3cvw8DBz586ls7Mz7qbVNH1OVb66KCoxsxXAl8ic+H/F\n3e8oeHw28N/APDILI93p7l+N4rmltsyYMYNbbrmFdDrNwMAAZ5xxhq6eVRHlKycr/1h54oknuPzy\ny3WsxKipqYlHH32UZDLJY489xpVXXqkr6SIRKHmMupm9BfgtsAx4FdgCfNLdX8jb5/PAbHf/vJmd\nDrwInOnuo4X1aYy6iIiIiFSbuMaoXwgk3T3l7oeBbwFXFuzjwGnZn08D0hOdpIuIiIiISEYUJ+qF\nixntYvxiRncD7zWzV4FngdXFKtMY9XBobFtYlEdYlEc4lEVYlEc4lEXlK9eCR5cDz7j72cD7gA4z\nm1Wm5xYRERERqThR3EzaT+Ym0Zy5jF/M6Drg3wDcvc/Mfge8B9haWFlvby+rVq3SgkcBlJcuXRpU\ne2q9rDzCKisPlVVWuRLKOaG0p5bKQSx4ZGbTyNwcugz4PfAr4Fp378nbpwP4g7v/i5mdSeYEfZG7\n7y2sTzeTioiIiEi1ieVmUncfA24GngSeB77l7j35Cx4Ba4GLzew54CfAP010kg4aox6Swv+NS7yU\nR1iURziURViURziUReWri6ISd/8x8O6Cbffn/fx7MuPURURERETkJJQ89AVOvOBRdp9LgP8E3goM\nuPulE9WloS8iIiIiUm2mMvSl5Cvq2QWP7iZvwSMze6xgwaM5QAdwmbv3Zxc9EhERERGRIsq14NFK\n4Dvu3g/g7q8Vq0xj1MOhsW1hUR5hUR7hUBZhUR7hUBaVr1wLHp0LNJnZU2a2xcw+FcHzioiIiIhU\nrUhuJj3J51kCfBhoBH5hZr9w997CHTWPejhlzRMdVll5hFVWHiqrrHIllHNCaU8tlUOZR/0i4Ivu\nviJbvhXw/BtKzexzQIO7/0u2/BDwI3f/TmF9uplURERERKpNLPOoA1uABWbWYmbTgU8C3yvY5zFg\nqZlNM7OZwPuBHiagMerhKPzfuMRLeYRFeYRDWYRFeYRDWVS+ulIrcPcxM8steJSbnrHHzG7MPOwP\nuPsLZvYE8BwwBjzg7jtKfW4RERERkWpVtnnUs/tdAPwcuMbdvzvRPhr6IiIiIiLVJpahL3nzqF8O\n/BlwrZm9p8h+twNPlPqcIiIiIiLVrlzzqAP8LbAB+MPxKtMY9XBobFtYlEdYlEc4lEVYlEc4lEXl\nK8s86mZ2NvBxd78XmNQlfxERERGRWhTFifrJ+BLwubxy0ZP1xYsXn/rWyEnJzQUqYVAeYVEe4VAW\nYVEe4VAWla/kWV+AfmBeXnludlu+84FvmZkBpwNXmNlhdy+cxpENGzbw0EMPacEjlVVWWWWVVVZZ\nZZUrthzKgkfTgBeBZcDvgV8B17r7hPOkm9nDwOPFZn258847va2traQ2STS6urqOHnASP+URFuUR\nDmURFuURDmURlqnM+lJX6pOezDzqhf+k1OcUEREREal2kcyjHiXNoy4iIiIi1SaWedQhs+CRmb1g\nZr81s89N8PhKM3s2+6fLzBZG8bwiIiIiItWqXAsevQR8yN0XAWuBB4vVp3nUw5G7MULCoDzCojzC\noSzCojzCoSwqX1kWPHL3p939QLb4NAXzrIuIiIiIyLGimPXl/wCXu/sN2fL/BS50988W2f8W4Nzc\n/oU0Rl1EREREqk0ss75MhpldClwHaK4gEREREZHjiOJE/WQWPMLMzgMeAFa4+75ild111100NjZq\nwaMAyvlj20JoT62XlUdYZeURTjm3LZT21Ho5ty2U9tRyubu7m5tuuimY9tRauWIWPDKzecAm4FPu\n/vTx6tOCR+Ho6tJCCSFRHmFRHuFQFmFRHuFQFmGZytCXSOZRN7MVwF28ueDR7fkLHpnZg8AngBRg\nwGF3v3CiujRGXURERESqTWxj1N39x8C7C7bdn/fz9cD1UTyXiIiIiEgtKMuCR9l9vmxmSTPbbmaL\ni9VVK/Oop9NpduzYQTqdjrspReWPN6x2ykMmK6o8oj72tmzZwj333MOWLVsiqS/q9p2K13vLLbdE\n9nqjFvr7dypE+VmVTCZ5/PHHSSaTkdUZpdDzjTKLSjj2qlHJV9TzFjxaBrwKbDGzx9z9hbx9rgAS\n7t5qZu8H7gMuKvW5K9GhQ4fo6Oigr6+PkZERpk+fTiKRoL29nRkzZsTdvJqjPCQuUR97r776Kh/9\n6Ed57bXXGBsbY9q0aZx++un84Ac/4Oyzz469fafy9Y6MjLB+/fqSXm/UQn//Qrd3717a2tpIpVKM\njo5SV1dHS0sLnZ2dNDU1xd28mso35LbVgihuJr0IuM3dr8iWbyUzNv2OvH3uA55y9/XZcg9wibvv\nKayv2seo/7//9/9IpVLU1b35f6TR0VFaWlq45ZZbYmxZbVIeEpeoj733ve99pNNppk2bdnTb2NgY\nzc3NPPPMM7G3L/TXG7XQ37/QffzjH2fXrl3jXu/cuXN59NFHY2xZRi3lG3LbKs1UxqhHMfTlHOCV\nvPIuxq88WrhP/wT7VL10Ok1fX98xBztAXV0dfX19+jqpzJSHxCXqY2/Lli289tprx5y0AkybNo3X\nXntt0sNCom5f6K83aqG/f6FLJpPjTgwh83pTqVTsw2BqKd+Q21YrIrmZNErVPI/6nj176O/vp7Gx\nkbPOOguA3bt3AzBz5kwGBgbo6ekJpr2Fc+LG3Z6oy8pD5bjyaGpqYmRkhP379wMcc/wNDg4yMDBA\nc3PzSdf33HPPMTY2drQ9uV+qo6OjjIyMsG3bNi644ILY2neqX2/uNU/19UZdDv39O9Xl3Lap/vt9\n+/YxOjp6NOOZM2cCcPDgQYaGhkgmk7S2tirfkyiXOo/6yy+/zMjICA0NDUd/P+ba19/fzxNPPMHK\nlSvL+v5XUjmUedQvAr7o7iuy5ZMZ+vIC8BcTDX2p5nnU0+k0a9asoaGhYdxjQ0NDrF27lubm5hha\nNrGuruqef1V5SClKySPqY2/Lli184hOfGHfVCzIn69/97ne54IILYmvfqX69uTHMuZ8n+3qjFvr7\nd6qV+lmVTCa5+uqrqa+vH/fY8PAwjzzyCK2traU0sSSVlG+pWVTasRe6uIa+bAEWmFmLmU0HPgl8\nr2Cf7wGfhqMn9vsnOkkHWLy46IQwFa+5uZlEIsHo6Ogx2w8fPkwikQjuYK/2k0LlIaUoJY+oj70L\nLriA008/fdxV5rGxMU4//fRJn7RG3b5T/XpzJ+lTfb1RC/39O9VK/axqbW2lpaVl3OvNjYuO8yQd\nKivfUrOotGOvGpV8ou7uY8DNwJPA88C33L3HzG40sxuy+/wQ+J2Z9QL3A6tKfd5K1d7eTktLC0ND\nQ7z++usMDQ0xf/582tvb425aTVIeEpeoj70f/OAHNDc3Mzo6yvDwMKOjozQ3N/ODH/wgiPaF/nqj\nFvr7F7rOzk7mzp3L8PAwg4ODDA8PM3fuXDo7O+NuGlBb+YbctlpQ0tAXM3s7sB5oAV4Grnb3AwX7\nzAXWAWcCR4AH3f3Lxeqs5qEv+dLpNAMDA5xxxhnB/o+0loZaKA+ZrKjyiPrY27JlC9u2bWPJkiWR\nXFmOun2n4vVu2LCBq666KvYr6RMJ/f07FaL8rEomk0fHpMd9JX0ioecbZRaVcOyFLo6VSW8FNrr7\nv2cXOvp8dlu+UeAf3H27mc0Cfm1mT+bPs56vt7e3xCZVhubm5uAP9O7u7po5MVQeMllR5RH1sXfB\nBRdEesIadftOxevdunVrkCfpEP77dypE+VkV6gl6Tuj5RplFJRx7odu+ffukbyYtdejLlcDXsj9/\nDfh44Q7uvtvdt2d/fgPo4ThTMw4ODpbYJIlK7k5lCYPyCIvyCIeyCIvyCIeyCMuzzz476X9T6on6\nO3I3hbr7buAdx9vZzOYDi4Fflvi8IiIiIiJV7YRDX8zsJ2TGlx/dBDiwZoLdiw54zw572QCszl5Z\nn1Bunk6J386dO+NuguRRHmFRHuFQFmFRHuFQFpXvhCfq7v6/iz1mZnvM7Ex332NmZwF/KLJfHZmT\n9P/P3R873vMlEglWr159tLxo0aKqnrIxZOeffz7btm2LuxmSpTzCojzCoSzCojzCoSzitX379mOG\nuzQ2Nk66jlJnfbkD2Ovud2RvJn27uxf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lOIK5Sft4jx49yoYNGxgZGWFqaoo9e/bQ1NTE\n/v37ufbaay/BEcxNrb1XnT17ls7OTgYGBhgdHWXHjh20tLSwfft2VqxYUdX+crkc9fX1Ve0vbbWU\nb8x1qwVpzfrygLvfmpQvmvXFzL4C/Je770zKR4Dfcvczpftb6mPUH3nkEQYGBqivf+93pFwuR0tL\nC/fee2/Ami0Oab9+ykNCSfvcu/766xkeHqaurm76scnJSTKZDAcPHkylztVI+3jXrFnDyMjIRcfb\n1NTEG2+8kUqdq1Fr71UbN27kxIkTF9WvubmZ5557Lvj+0lZL+cZct8Um1KwvPwe8WVQ+wcUrj5Zu\nc7LMNkve8PAw/f39M052gPr6evr7+/V10vtI+/VTHhJK2udeT08PQ0NDMzqtAHV1dQwNDQUfBpP2\n8XZ3d1/USYf88Y6MjAQfBlNr71XZbPaijhzk6zcwMDDnYStp7y9ttZRvzHWrFancTJqmxx57jMbG\nxiW54NGZM2c4efIkjY2NXHPNNQCcPn0agIaGBgYHBzly5Eg09S0e2xZDfdJ+/ZSHyqHyWLFiBRMT\nE5w7dw5gxvk3OjrK4OAgmUzmA+/vpZdeYnJycro+hQ/VXC7HxMQEvb29tLe3B3u90j7eF154AXdn\nampq+piXLVvG1NQUU1NTvPjii3R0dCyZ4017f2mX33rrLXK53IxzsKGhgXfeeYexsTGy2SxtbW3z\n3l9DQwPAvPdXy/kePnyYu+66a97He+zYMSYmJli+fPn052OhfidPnmTfvn1s3bp1QV//xVReNAse\nlRn68hrwm+WGvizlBY+Gh4e5//77Wb58+UX/NjY2xoMPPkgmkwlQs/IOHIhroYS0Xz/lIdWoJo+0\nz72enh42bdp00VUvyHfWn332Wdrb2+dV1zSkfbzd3d1s2bJl+or61NQUy5blvyCenJxkx44ddHR0\npFP5eai196psNssdd9zB5ZdfDuQ71IXO9fj4OM888wxtbW3z3l+x+ewvbYsp32o/N2I/9xabaBc8\nSsp/BtMd+3PlOukA69ZVnBBm0ctkMrS2tpLL5WY8fuHCBVpbW6M72WPrFKb9+ikPqUY1eaR97rW3\nt7Ny5coZVzQh32lduXJl0E46pH+8HR0dNDU1TR9vcSe9qakpaCcdau+9qq2tjZaWlun6FTrphXHM\nc+1Ul+6vYL77S9tiyrfaz43Yz71aUHVH3d0ngbuB54FXgG+4+xEz+6yZfSbZ5tvAG2b2OvBV4C+r\nfd7Fqquri5aWFsbGxnj77bcZGxtj9erVdHV1ha7aopD266c8JJS0z729e/eSyWTI5XKMj4+Ty+XI\nZDLs3bs35ZrPT9rHu3///unOemGYRGHWlxjU2nvV9u3baW5uZnx8nNHRUcbHx2lubmb79u1R7C9t\ntZRvzHWrBVUNfTGzK4GdQAtwDLjD3c+XbNMMPA1cDUwBT7r7lyvtcykPfSk2PDzM4OAgV111VbS/\nkcY81CLt1095yFyllUfa515PTw+9vb2sX78++JX0ctI+3u7ubnbu3MnmzZuDX0kvp9beq7LZLLt3\n7+b2229P5cp3NpudHpMe+kp6ObHnm+bnRuzn3mIQYmXS+4Bud384Wejob5PHiuWAz7t7n5k1AT8w\ns+eL51kv9vrrr1dZpcUhk8lEf6IfPnw42o5h2q+f8pC5SiuPtM+99vb2KDvoBWkfb0dHB9lsNspO\nOtTee1VbWxuNjY2pdapj7aAXxJ5vmp8bsZ97i0FfX9+cbyatdujL7cDXkp+/Bmws3cDdT7t7X/Lz\nCHCEWaZmHB0drbJKkpbCncoSB+URF+URD2URF+URD2URl0OHDs35/1TbUf9I4aZQdz8NfGS2jc1s\nNbAO+J8qn1dEREREZEl736EvZvZd8uPLpx8CHLi/zOYVB7wnw152AfckV9bLKszTKeEdP348dBWk\niPKIi/KIh7KIi/KIh7JY/N63o+7uv1Pp38zsjJld7e5nzOwa4McVtqsn30n/N3ffPdvztba2cs89\n90yX165du6SnbIzZDTfcQG9vb+hqSEJ5xEV5xENZxEV5xENZhNXX1zdjuEtjY+Oc91HtrC8PAWfd\n/aHkZtIr3b30ZlLM7GlgyN0/P+8nExERERGpIdV21FcAzwA/DwyQn57xnJn9LPlpGP/AzD4OvAAc\nJj80xoEvuvt3qq69iIiIiMgSVVVHXURERERELo2qVyathpkdM7NDZnbQzL6fPHalmT1vZj80s31m\n9uGQdawlFfJ4wMxOmFlv8ueW0PWsBWb2YTP7ppkdMbNXzOwmtY1wKuShthGAmV2XvEf1Jn+fN7PP\nqX0svFmyUNsIxMz+xsxeNrOXzOzrZnaZ2kYYZbK4fD5tI+gVdTM7Cvyau79V9NhDwHDRIkplx71L\n+irk8QDwE3f/+3A1qz1m9q/Af7v7U8nN2I3AF1HbCKJCHn+N2kZQZrYMOAHcBNyN2kcwJVl0orax\n4MxsFXAA+CV3nzCzncC3gV9GbWNBzZLFaubYNoJeUSc/1WNpHd53ESW5ZMrlUXhcFoiZ/TTwCXd/\nCsDdc+5+HrWNIGbJA9Q2QusA+t39TdQ+QivOAtQ2QqkDGpMLClcAJ1HbCKU4iwbyWcAc20bojroD\n3zWzHjP7dPLY1XNZRElSVZzHnUWP321mfWa2TV+ZLYg1wJCZPZV8NfbPZtaA2kYolfIAtY3QNgP/\nnvys9hHWZmBHUVltY4G5+yngUeA4+U7heXfvRm1jwZXJ4lySBcyxbYTuqH/c3dcDvw90mdknuHjR\nJN3tunBK8/h14AngWndfB5wG9FXmpVcPrAceT/IYBe5DbSOU0jzeIZ+H2kZAZvYh4A+BbyYPqX0E\nUiYLtY0AzOxnyF89bwFWkb+a+8eobSy4Mlk0mdlW5tE2gnbU3f1Hyd+DwHPAjcAZM7sawGZZREnS\nV5LHfwA3uvugv3cjw5NAe6j61ZATwJvu/r9J+VvkO4pqG2GU5rELuF5tI7hbgR+4+1BSVvsIp5DF\nIOQ/Q9Q2gugAjrr7WXefJP85/jHUNkIozeJZ4GPzaRvBOupm1mBmTcnPjcDvkp9r/T+Bv0g2+3Ng\n1pVMJR0V8ng5adQFm4CXQ9SvliRfUb5pZtclD20AXkFtI4gKebyqthHcFmYOtVD7CGdGFmobwRwH\nbjaz5WZmJO9VqG2EUC6LI/NpG8FmfTGzNeR/23PyXy1/3d2/ZBUWUQpSyRoySx5PA+uAKeAY8NnC\nWDe5dMxsLbAN+BBwFPgU+RtT1DYCqJDHP6K2EURyj8AA+a+Qf5I8ps+OACpkoc+NQJKZ2j4JXAAO\nAp8Gfgq1jQVXkkUvcCfwL8yxbWjBIxERERGRCIW+mVRERERERMpQR11EREREJELqqIuIiIiIREgd\ndRERERGRCKmjLiIiIiISIXXURUREREQipI66iIiIiEiE1FEXEREREYnQ/wPklfSww+5wPAAAAABJ\nRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "\n", + "simulations = trace[\"bernoulli_sim\"]\n", + "print(simulations.shape)\n", + "\n", + "plt.title(\"Simulated dataset using posterior parameters\")\n", + "figsize(12.5, 6)\n", + "for i in range(4):\n", + " ax = plt.subplot(4, 1, i+1)\n", + " plt.scatter(temperature, simulations[1000*i, :], color=\"k\",\n", + " s=50, alpha=0.6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n", + "\n", + "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n", + "\n", + "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [7] than p-value tests. We agree.\n", + "\n", + "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[8]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n", + "\n", + "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "posterior prob of defect | realized defect \n", + "0.40 | 0\n", + "0.25 | 1\n", + "0.28 | 0\n", + "0.32 | 0\n", + "0.36 | 0\n", + "0.19 | 0\n", + "0.17 | 0\n", + "0.25 | 0\n", + "0.73 | 1\n", + "0.53 | 1\n", + "0.25 | 1\n", + "0.10 | 0\n", + "0.36 | 0\n", + "0.80 | 1\n", + "0.36 | 0\n", + "0.13 | 0\n", + "0.25 | 0\n", + "0.07 | 0\n", + "0.12 | 0\n", + "0.09 | 0\n", + "0.13 | 1\n", + "0.12 | 0\n", + "0.71 | 1\n" + ] + } + ], + "source": [ + "posterior_probability = simulations.mean(axis=0)\n", + "print(\"posterior prob of defect | realized defect \")\n", + "for i in range(len(D)):\n", + " print(\"%.2f | %d\" % (posterior_probability[i], D[i]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we sort each column by the posterior probabilities:" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "probb | defect \n", + "0.07 | 0\n", + "0.09 | 0\n", + "0.10 | 0\n", + "0.12 | 0\n", + "0.12 | 0\n", + "0.13 | 1\n", + "0.13 | 0\n", + "0.17 | 0\n", + "0.19 | 0\n", + "0.25 | 1\n", + "0.25 | 0\n", + "0.25 | 1\n", + "0.25 | 0\n", + "0.28 | 0\n", + "0.32 | 0\n", + "0.36 | 0\n", + "0.36 | 0\n", + "0.36 | 0\n", + "0.40 | 0\n", + "0.53 | 1\n", + "0.71 | 1\n", + "0.73 | 1\n", + "0.80 | 1\n" + ] + } + ], + "source": [ + "ix = np.argsort(posterior_probability)\n", + "print(\"probb | defect \")\n", + "for i in range(len(D)):\n", + " print(\"%.2f | %d\" % (posterior_probability[ix[i]], D[ix[i]]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can present the above data better in a figure: I've wrapped this up into a `separation_plot` function." + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from separation_plot import separation_plot\n", + "\n", + "\n", + "figsize(11., 1.5)\n", + "separation_plot(posterior_probability, D)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects. As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n", + "\n", + "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n", + "\n", + "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n", + "\n", + "1. the perfect model, which predicts the posterior probability to be equal 1 if a defect did occur.\n", + "2. a completely random model, which predicts random probabilities regardless of temperature.\n", + "3. a constant model: where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(11., 1.25)\n", + "\n", + "# Our temperature-dependent model\n", + "separation_plot(posterior_probability, D)\n", + "plt.title(\"Temperature-dependent model\")\n", + "\n", + "# Perfect model\n", + "# i.e. the probability of defect is equal to if a defect occurred or not.\n", + "p = D\n", + "separation_plot(p, D)\n", + "plt.title(\"Perfect model\")\n", + "\n", + "# random predictions\n", + "p = np.random.rand(23)\n", + "separation_plot(p, D)\n", + "plt.title(\"Random model\")\n", + "\n", + "# constant model\n", + "constant_prob = 7./23*np.ones(23)\n", + "separation_plot(constant_prob, D)\n", + "plt.title(\"Constant-prediction model\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n", + "\n", + "The perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Exercises\n", + "\n", + "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples. Why might the resulting plot look like this?" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Iw8OOYhF8X/3mIxEtigWV3HQtMItFtc4UUR3/ygo0Go6lJc32Z7Oa8W+11O7S\n99XSstn0aTSETschorKaXE5lQr1ddE0zbxiGYRhGvyLO9afE4KmnnnKPPPLIrR7GbcWNBLblMpw5\nA2fPQqPh0WppJn98XAP6YlELX2dmHC+9JHiesLGhQX6hIBQKftDdVTXrsZgG80tL2lXW83zicWi1\nBBFHs6mfs7zsMTLSplBQeUw+v62n73SE/fu1UZbngXPqgtOV8eRyehchEtEMve/rnQbYXkSk0/po\ntbYfsN20yoJ/wzAMwzBebb785S/z5JNPyrWOs4y8scWNBKbZbDdjL4HERdjY0I6v8TgMDelv78AB\nzYK3Wqp7z2aFRMKnVlN9/MYGNJse8bg2kUokPFIpHxGV4pRKep56XYjHCZpPCevrWmirTak0KK/V\nhGZTG2INDOj+dFplOtqtVrP1nqeSnnh829JydVXPe+mSeuxnsyoHarf1PevrKgWKRLQot1tU29uV\n1jAMwzAMYy8xjbzxiikUYGJCA+fZ2WcZGIBUKkKtBl3P+vFxOH5cH699rXrPHzoEIyNadNtuR+h0\nVMozPAyZTIdCQbPoi4uwvKyNoXzfZ2ZGZTUbG45GA+bm4MIFmJ31qFYF52BtLUqrpXcKLlyI8sUv\nemxswEsvwcWLwsmTwuwsNJuOSsXbKsSNRvX53JzH/LzH2ppQqQhzc8JLL8HXvw6zs/remRmVFs3P\nC0tL25aYV6Nc1uD/eo79RjGdY7iw+QgXNh/hweYiXNh89CeWkTdeMd1M9MiII532gwLSDiMj3W6y\n20WlCwv6r9pZalb76FFYWurgnLre7N+vUphi0ZFMqp/95qZPLqfuNNUqOOcxM+MzOak2mVNTWpQ7\nNQXj446BAZ9GA5yLUCw6olGPxUUf5zToz2RUilOrObJZx4EDao155oxm51OpbdecUomtDrblsmbn\nYzFIJByVipDNamFuIuGu6mdfLt851peGYRiGYewdppE3bgoXL24XlB45cvlrs7OwsqISmXLZbWnT\nOx1tQFWvq3b+8GE9fmEB5uf130RCSKVUA/+Vrwhzc1FKpTb33+9YXYXpaY/hYfW8P3RIz+EcfO5z\n4Psx6vU2R486LlyAYjFKNtthYsKRTguxmAbyL76oxbRLS8LEhEpxWi1HoaABeToN9bpHLqeSHed8\nVlaEZNIjmfS56y7HsWMEdpzbC5WuK9D6ukqDunS9+w3DMAzDMHbDNPLGnrIzeO/SzUarXl2z7Nks\nDA9r4yj127W5AAAgAElEQVTPc4yMXJ6hnpjQQFjdb1yQ3ddFgOe1qde1odTYGKyu+sTjet5OR7Pr\nIvDAAzA/3yIW0/2TkzA318bzoFgUCgVHsRil2VTXnaUlod2OkEq12NhwZDLC5qbj8GEN5H3fp9nU\nbrOFgt41qFZ9ajXH2JjeEVhdVR1+MqmLY/W63/bur9X0e0Qir+5cGIZhGIZxZ2AaeeOmsJu2rhvE\nx+MQjTp83zEw4MjltCFVKsXLgnjQbbWy1IC+0dDzZLNw113C5KTq84eG1Nc+k3GkUsL6useFCx7L\ny3D+PJw9G+GrX/U4c0YD7Y0NPV8qpTKdTqdNLAalksP3O+TzTapVoVSCl16KcOFCdKtgtt3WYtrT\np7etN5tNj3JZmJlR3Xy97lEuq63m2tq24w3oQmZzU5tZdTqXa+VvVD/fPX5paff3mc4xXNh8hAub\nj/BgcxEubD76E8vIG68aGsiqNGZ4eDv7rq+5q1o4lssaDDcaHqWSOtRks4Lvg+dp99lsVr3lBwc9\n5udhfd0xNCRsbgqplBCNqtZ+cTHKyIiP7wv5fIf1df1c51TCUyho99pGQ510Wi0YGnJUq0KhoNKf\nqakI6+vdbrMdMhlot/1AE68uOomEHzjdwOtep3cCLl7UYHt9XahUdHFSqwmNxrakbWlJzxGLXVs/\n310cqaOPav4zGdPdG4ZhGMadSN8G8sePH7/VQzB6eOKJJ162rysp6QbzvZ1kr0WrBdGoBryxGLTb\nKqfpZtQjkW1/+EhEZS/JpKNc1gLX9XWfVApaLY9IxCcaFcCnXgfP0+LZUglKJY9aDQ4e9KlUIiQS\nQqfjEYs5jhzxyWQc8/MwM+PY2IiQzbYBDfoXFhylkrC8LORybHWfjcU8PM+n3dbi3fl5WFrS10ol\nYWBA9fyJhGbqy2WhWwhbq6lGP51+eUOuclkbYrXbmtUHod3W69tqbS8MdpsL49Zh8xEubD7Cg81F\nuLD56E/6NpA3wk83aL9W9n03YjGCTLN2gx0f10VBo6GvtVqa2S6XNSjO5x0LC13vd0cyqUG07/tc\nugSrq7qQSCRU4iIixOOOkRGf1VUPEahUfCKRCLmcz9Gj3aJX9a4fGPCJxRzttuPiRS3WFdGsfjwO\nGxsezvkMDGhh6/S0RyLhk0jAyZPQaESBNpmM2nWWyzA83BuAa7faUkkbZmWzur8bzHcz8b4PlYoL\ndPYuWKBsuwMZhmEYhnHnsOcaeRF5u4i8ICIvicj/epXj3iQiLRH5vt1eN418uLiSti6b1aD3RmUf\n2ay6vgwPOyYntZh2clID20hEM9gjI3DkiGrmH3sMHn1UfetTKWFszOPQIQ3GwaPRiOJ5QrOpfvWT\nk459+6BS8YhEoNmE48cdR450GB/XjPv8vFAs6mvNpkc06shmhVhM/eWXl4Vi0bGy4tNqucDv3tFo\n+Pi+dq6dmYGVlWjg1uMxN6dZ9dlZbT4F4PuOtTXN3K+tsaW5P3NG9fhdS8tuXUH3zsa+fXoXwPcv\nv3amcwwXNh/hwuYjPNhchAubj/5kTzPyIuIBvw48CcwBXxCRTznnXtjluPcDf7mX4zPCxW5FsKCB\nbySi+nDYluwUCvr64qJmqPN5ldBMTGin2HrdIULQuEqPTaX0HK2WZuhbLUetpl7zAwOOVqtrIdnt\nNqtymulpj/HxDskk7N8vW11gwXHwoKPT0Qx6IgHOtRkY0CD97rs1q95oOGZntalVOg3Vqkp9pqZA\nxKNQ6ACa7V9a0sx/MqnZ/Laqe6jX2bLyVJ9608kbhmEYxp3EnvrIi8g3Ab/knHtHsP2zgHPO/eqO\n434KaAJvAv7UOfeHO89lPvJ3Nrs1XtKiUtWhg+D7Pp2O+tEvLup7IhEN8GMxoV73mZ0VNjaEfF41\n9aurmmkXEcbGOuTzQrOpspfFRY9EwjE87FhfFxoNIZtVff7581FyOZ/77usQiWih6+Ym5PP6uHQJ\notEInU6Hhx5iyy4zGtVAfWJCWFx0bGx41OvC4cM+Dz2kuvqNDV20pFLaeCoa1WJX1eI79u1zDA7K\ny/zpe68RXH69ymUdH+gCyBYAhmEYhhEewuojfwCY7tmeAR7tPUBE9gPf65x7q4hc9pphdNkt8Ow2\nYtIMuwa16bQGqseOsWULmUgIyaR2e83nHfPz6qZTLGpwnc+rXn5ggCADLgwOqla/0RCGhhyRiDap\nKhT0DsHGhk8222FqCiIR1csPD2smfWEBlpc9fN+xb1+EjY1OoN/X8ZRKETY3fSIR9biPRDQ7v7Sk\nxbALC15QhOtz+LDeVQCPgwchmRSWlhwbG3pnohu0dxcuvq9BfyIB+/drFl8LbLsLHr3LMDFxeSfa\nnYskwzAMwzDCRxiLXT8I9Grnd12NfOhDHyKTyXDo0CEACoUCDz300FbVdVfrZdt7s/3hD384FNf/\n+PEnSCbhi188wfKyvn7PPduvP/LIE1SrPqdOnSCZhDe84QnW1+FznztBswmvf/0TLC3Bl770DBsb\nsG/fWyiXYX7+GeJxeOihx3EOXnjhBM2m0Ok8zsgItFpP02iAyFtot2Fj41k2Nx2ZzFvIZBy+/zTO\nCfX648TjMDNzgmIRRL6ZCxc8ksmnyeUchw8/QSIhzM8/Q7Gon1+vw+nTzwZNqd5MoSBcvPg0588L\n4+OPUyjA2bMnyGTg8cef4Pz5E2xuqpXm5OTjpFI63qEheOyxJxCB558/AQjHj+t4n3nmGXI5vX6l\nEnz+888CjieffIJs9tb/vvp5u1d3Gobx3OnbNh/h2e7uC8t47vTt7r6wjOdO2+4+n5qaAuCNb3wj\nTz75JNfiVkhrftk59/Zg+2XSGhE5330KjAAV4Medc3/ce64PfOAD7r3vfe/eDNy4JidOnNj6UfYT\nXTcY0My1c6pTn5vT1zQbrp71+bxHPO6zsABf/WoM0Ez8oUM+q6va3Gp2Fjod1cqPjMDFi2p/qVp2\nYXRU5TKplGa85+agVIrRbrfZv1+1/76vXWFzOX0+N6c2mtmsT6Oh0qBczgWSG5UT7duntpbxuLC+\nfoLJybdsWVvmcj6NhtYARKPaSAv0s1IpLZo9cqRbC6CuO112ynWMG6df/zZuV2w+woPNRbiw+QgX\nYZXWfAE4JiKHgXngB4Ef6j3AOXd397mIfAz4k51BPJiPfNjo1z/+bYtMLvO5r1RUA59OqwXm4KDq\n4SORruWkj3M+0aijXBYiEY94vEOzqRr2zU1Ip4XNTY8jR1R77/uOr39dOHjQUas5Dhzo6tU7TE46\nhoa0kLXR0IC6VhM8T/c3m2plubQE2axjeloYGXE884zgeXEuXmzxTd+khbwTE49TLPpUq8LKik+z\nqd+pUBA8TyiXfRYWhHhcGB52DA3pYr5cVtlNrea2Col3s7U06c2N0a9/G7crNh/hweYiXNh89Cd7\nGsg75zoi8pPAX6HWl7/tnDstIj+hL7uP7HzLXo7PuDPZGYyOj2swm0w6xsY0651IaDY7kVDdPHTY\n3ATfFxIJmJvzGR0VikVhdFSdZ9LpDgcPdkgk1BWn3YaREXXC2djwiMX8oLGVTzSqlpPdbrWjo1rk\n2mrBuXP6uZOT+jhzRjP0Cwsd9u93dDoNDh7UBcbKij5mZjTzXqno+H3fsbionW5F9PPzeXXtmZnx\nqde1e24+3601cJcVwXaD91aLrWZU2uzr6t15LeA3DMMwjFePvc7I45z7C+C+Hft+8wrHXlE7c/Lk\nScy1JjzcTrfkslmVmhw4sB2IxmKarZ6f10BfRLdHR7VodGQECgWflRUNdIeGVI6TSDg8T4tqUyl9\nz+amBPaUwtKSEI97nDrVIRbzEPEZHXV8/esezaZHrdbhwQcdFy96NJsQizkaDY9WCyYmIoyPd6hU\n4Nw5od1W+Qw8w+DgW5ibExqNOJ7XYGREbSp9X6U9rVaHpSWPctlRqagrz+qqFuoeO+bzaFBmvr6+\nHbxXKsL6uiOTgcHBl3eU7WVbsnTtgP9253b627gdsPkIDzYX4cLmoz/Z80DeMPqB3YLO7r5qtetW\nA/v3ayAsogFvNOqoVNTmslrVgH9xsatfVxedSkXYt0+D40LB0W77lMsRYjFHIuFRqfikUupeAxGa\nTT/oaOuRz/s0Gg7fj3LpUpPBQZibixCLgXPCyorKfOp1YWBAZTuVilpXDg5qHUC9rtl753zqdQ24\n5+fVtafV0jsCvg8TE/o9YzFoNgXfh3bbY2PDJ5nUrP2VOspubupCJRpV68wrBfyGYRiGYbxy9rTY\n9WZiPvLGrabXiz0W0+cLCxoYt1paSNrpaFCsxwnOOVZWVDNfqTjm5zXoX1+HbNYjlVKf+osXwfO0\nwPXAAXj+edjYiDAy0uHuuzWr37XArFSgXPaIRiEW8xkZ0UVHN8jO5XQsi4tQKnlUqz75PCwteQwP\nq5f+0BCsrOidBRE4csTn7rt1bImEavfHxoTBQS2SzWbZ+pyd16Ne39b4R6MwOnq5vaVhGIZhGFcn\nrMWuhnHbkM1eHpyOjWkGe21Ng+jxcd2/uanOMxsbGtgfOQKXLjkWFrQwdn4ejh7VAtpkUotd77sP\najUNuBcWNBgXcYyPa+Y8ndb9yaR+XqEAmYzP2JguJCoVDch9XygWHceOwdqaUC5v+8un0z7Fogbk\n7bZKfyIRiMddYJG5fZ7hYVhbc9x/v+r05+bU3Sefh8OHdeFSLG7Lb6pV1eY7p++3IN4wDMMwbj7e\nrR7AK+XkyZO3eghGD70+qHcyY2Nw//0amPcG+vG4kM0KkYiQyWiDqmy227FVZTCRCDQawvq6R7ut\nTaDabc2IN5tCKqW6+WQyQjQK4+MSSFwiTE9HmJmJUC5Dsfgs+bxHuewxP++xvBzj5EmYnvZYWwPP\n08B8dRWiUY+VFbXKPHrUIaKFuSdPCmfOCFNTHktLMDMjrK56TE3BqVPw+c/D3/+98PTT8LWvCbOz\nGvh3NfWtlgQ++7d2PsKA/W2EC5uP8GBzES5sPvoTy8gbxh6RTutjZESz6KmUMDQkZLOOREKz+AsL\njmZTi1Y9TzPj0Sh4nkPEBxz1uk8ioZn2gQHodHzSaWFoSDP47bZjYMBneloQidBotBkZ8Rgf96lU\n1IKyWHQUi7HAQlNoNrsZeQ8R9cL3fUc6rd1sV1ZAxCceh0uXNFNfqzmcE1IpGB2V4Dvp3YN43G3V\nDDQaehdArTa33W+6RcQ7s/XmdmMYhmEY14dp5A3jVaZcVv/3VkuIxdTScnMTTp4UikWPeNyRz/uU\nSqpTr1YdyaRqzZtNIZPRAlrf99jcVM381JR6xk9NqYSl2VQde6Gg/vKJhGbI5+ZURqNadS1kFVH5\nzuamRzwO2awfuO/A/LxHNKpBfSqlrjuZDMzOCvv3O154QSgUhLU1n7vu0jEeOKCPfF6LaWMxtb7s\nNr3KZHQB02rp52YyKjGKRNhqUDU2ptdqaUkXOdGofu9eb3/DMAzDuFMwjbxhhITtplPusizzXXdp\nZ9hYTB1lukGuZrJV+pJIONJpyOWE6WnH2prQbmsH13PnHM5FSafbjI6qHn5wUDu/1mrdLrHqNjM8\n7LYKUT1PNfWtlk80qo436TScOiWMjanW/ehR7RxbKGj2XQtzPTY2tNPt2bMJEokO5XKHAwcci4sa\nnE9PeySTwspKJxiLLihaLXXVcU5lPAMDEgT5wvq6TzqtLj9TU+qR323ElUz2Z6LBMAzDMPYC08gb\nNwXT1l2dbFZ93LtBfDYLhw7B4cOO/fvV6vHwYQ2gh4dVR3///fDYY/DGN8KxY46DByESceTzWvg6\nMhIlFvPJZtWxJp+HREI4deoZslnd9v0IznnMzXksLkaYn49SrQqViur2R0Z8xscl0NZHWFjwKJfV\n335zU5tPqTVlhIEB7WZbq0Eq5eN5Pp2OR7GoWf+VFSiXhY0NYWHBY3paZThTU/Dccx4vvijMz6tM\nZ3ra0Wg4mk2f5WX46lf1s0olgmJZXbBcyd6yn7C/jXBh8xEebC7Chc1Hf2IZecO4Rex0vQEN6FMp\nzULv7Kx68KA2l2o29bi1tTYiaieZSEAup91bQbPbIyPw2td2aDSE+XkNugcGhHLZMTmprjfqEa9a\n/JERH+f033hc7SPrdZXWpFI+a2vw2GPqaT8w4FMqeWQyHRoNmJ9Xrf/CQodOx2PfPp9mU73kfV8D\n9s1ND3D4PhQKHo2Gz9AQFItCq6V1ALmc3oXodFRe1Gpt6+sNwzAMw7gc08gbRp/Q2y0VVCrTtZLs\nNqSam1NpjHNCNKpaeRBOn9bjGw2VwHievm9wUPA8x/Kyauw7HaFQUH97LaRVrbvvb+ve19dVojM3\np/vabV1YdDqqb08khE7HUa8LL70kjI/D2Jh2uh0YIHDOieKcz4EDPtlshJUVwbkOk5OOkRFhctIx\nNKR1BaWSCxpLwb59Vy6ahasXyVoRrWEYhtEvmEbeMG4zdmrt9+3bbsLUaOhrGxswNye0WhHy+Xbg\nO6+Z/EbDIxr1GR9XWc3aGoyNaVfa5WUtdI1EHJubWjCbTm8XxjqnwXuxqNp951RXH4/re+NxOHtW\nqFajxOM+hw93qNUgHvcYHOxQrYLnaYBfLkO97gPdwtcOGxtRfN+RzRLUAOjnVSoa+CeTQj4P9bpm\n7dfXYXlZawEmJtRP3/PUCajddpcV0MLli6B63W1dz53BvQX7hmEYRj9hGnnjpmDaur1hN639gQMa\ntA4OaiOpZvMEBw92OHhQOHJE9faRiEehECGX04LWZFKD+5UVoVRSGc/oKORy+p8Ez9MAfXExyuJi\nhI0NbSi1sqLHLixEmJuLsLqq79NOsh7ttgb1g4NdiZDP+rreIeh0YGNDKBRU+pPLOVZXNZOfSLQZ\nHFRN/blzwpe+BBcueFy4AIuLwvKy49Ilx1e+Ak8/DZ//vMeXvgQXLwonT8LUlHDunDA31/Xi16C8\nS6sFeidD/+1KdkolqNf1GiwtXb7d+/5vBPvbCBc2H+HB5iJc2Hz0J5aRN4zbgG5gH4vBoUOO++7T\n7WjUcfQoFIs+s7MaZKdSmu3OZqMUix3273dBh1j1fI9GVRdfq2lgXip5jI35DA46VlbUNjKfd0Qi\nQrstQRMpaLc7HDyowXkkojaaDzzgb8l5mk09tt3W7PzysjA66lMsqgSoXNY7CiCBl75PKqVB/Oam\nLgKGh9Uas9Px6XR0UZHPw/y83qWoVPQOxeRkN3jX866twcqKfs9cTh+9wX2lotn9VEoXPhrs96fs\n0DAMw7hz6NtA/vjx47d6CEYPTzzxxK0egoEG9O985xNsbl5eMJtMwtycTySiwXKjITinnV337dNG\nUvG4o1gUmk3NqDvn02wKzaZPNuvodDTz3z2H+uLD/v0QiwmHDjnqdce+fZrZrlY1GC6XNbDe3FTr\nSd+HRqOD5yUoFhuk03D2rEc26yiXHcmkz8qKkM3qmIBgXKqVn51Vn/lWSxcUMzNqZ5nJOJxTKVC7\nrUXB4+PbPv4bGyrRGRhQCU86rVKdSkWoVLoLAbW9zGRunmOO/W2EC5uP8GBzES5sPvqTvg3kDcPY\nnd3ccI4c0QfAxYtQLjs8r8PQkM+xYyqPicWEqSmCjrDaNVakQzKpC4JyWZ1polHYv9/h+z6bm8Lq\nqh6rRa7qgnPunMfdd/tUKlCtRvjiF33GxlTOk06rBGhhocHkpGbL77pL7xgcPqxBt+ep/WUi4ahW\n1Q8ftDFWpwNDQ45mU7Pqqr/XwD0S0aZUa2ts2WcmEiDiUSo5FhYkKPD1efBBzcw3Gqq7T6X0vV33\nHNPIG4ZhGGHHNPLGTcG0deHhWnMxMqKZ9dFRtaHM51WSMzDgGBpy7N+vXvXZrGbFPQ+KRQ8RDZRT\nKfWxTySgUNAgfnwcBgcd7bYLzqeZ7XLZCxx04lQqEdbXI8zNeZw/rwH5Zz+rMpynnoKFhRjnzmnQ\nvrAgTE97zM1pMP788xEuXvS29PinTwsvvhjh+ec1aD992uPFF/W8MzPCF78oXLjgcfas6uZnZnym\nptRyc2PDcfYsPPfctk1nKqXymmZTFxo3M4i3v41wYfMRHmwuwoXNR39iGXnDuMNotWB0VMjnha4W\nPBZzHDig2eiBAZWvNBpCLqdZdOc0az82pq4w2SzMz/u0WprpTyYdpZJmuOfn4d571Xmm2XSICEtL\nTYaGNHDOZFQKU6kIuZywseHI5WKkUj7JpEc06hgYUNvJjQ1otyNkMuBchJUVP+hE6wUad49mU//1\nvA6JhEqG2m2P1VWVzYjoXQTtEquZ/NlZtd6cn1cpUCQCnY6OudMx73rDMAyjPzAfecO4wyiXNTNd\nqWihZy7nGBvbtl/c3NQs9/q6Bt5rayq7yWS0KdXQkB6ztKSvFwqqqV9dhQsXhLU1LU6t1SAa1YWD\n7+t5QEgkHLOzGtCvrMDEhMdzz/k88IDq4O++W49tNNQLf2MDZmZiiLR5wxtUu37mjOrgx8ZUOpNI\nqB9+Mqn75+ehUvHIZn1yOQI5kNpn5vO6MBkbg1RKJUCve52+p1rdvuuQy2171HctKXt963ubdW1u\n6vPeJl7XMw9mdWkYhmHshvnIG4axK9msNnDaWRDbfa1raVkua6BdKmm22jlhaEiP9zwN3ms1AokN\nHDqk8pzFRX3f2ppQr2uA73ma+W40NEDO5zWQVw97n3e8A1ZXtaB2fV2D/eFhdbgpFCCVagf2ldqE\n6oEHVBNfLGoTq/V19cMvlTyGh3327+864KjffCqlkp9GQ98josF3JqP2mJuber7NTV1M5POase8+\nF1H5UKul7jvgGB1VWY7aVup/a7u+9tcKzK/ka28YhmEYN0LfBvInT57EMvLh4cSJE1bxHhKuZy52\nK4jd7RhgqzssXF4E2mrxsqLQhx7Sfe22ZvQXFlRzDpDPC4kEwWJAWF2FhQXH4qJQqUQolRzptFpA\ngk86rXIdLVZ1FIse4+PqglOpqCRoZsYjGvVot7UQt9HwWFxss7AgtFod7rlHHXsSCc22T015ZLPg\n+z5DQ/DSS8KxY46FBZXUtFoeiUSHfF5dceJx4e67HbGYh3M+lYqwsaHjb7VccLdB6NpYttu8zLZy\nt/m43NdeFxKWnd8b7L9V4cHmIlzYfPQnfRvIG4bx6rOzm2xv5v5KFApw7Jg643Q6EQYG1A8+mVQd\nfleP3vVyHxwUcrnOVqfYctlRKDgyGQn848H3HYODPqmULhCyWdWzx2I+4NHptOh0IjSbHRIJn0wm\nEnSWhQMHVCNfqahcp1z2GBlRy82BAb2roDIhj0RCpUNTU45GI0Iy2WFoCAYHfUolOHfOUal4xGJ+\n0HwLVJ6otQSdji4YupKjndepK6fRQF4Lgmu1riVn93pc3pXWMAzDMK6EaeQNw7ipdGUjMzPCxYuO\nXE4D36NHVYrSamkGenERLlyAU6e0m2q5rDKWrvY9Hoe5OY+NDUeppBnwgQFHraa+8vG4I53WjH80\nqkFzs6mynpkZIZfT5ljlshbODg6qvSZ4HDjQoVqFYjFCtep48EGfs2c90mkYGfEBlQ/F4zpmLQTW\n8a6uavY/mYS77up65Ot3jkRUKjM8rPuPHdsOynvlNCsrKiPK5fSOQaOx3VXW8xyHD788mDdNvWEY\nxp2DaeQNw7gldIPMY8e6WXctOO362IMGvt3mTMeOqZa+XteAFoTJSQ10RXwiESES8YlGt4PYYtEL\n/OV94nFHLCYsLWlg7xwMDXlkMh06HWFxETzPA3xGR1VPX61CoxEhnQbf99jc9MlkfMbGtOPsxoYG\n1JOTarN56pSe99y5KK2WMDra4eBBmJ52VKs61nrdY2PDJx6H2VldPHSz74WCfufuomJpSZtalUrq\nEuT7+v3LZXXkWV/3L7PBNE29YRiGsRt9G8ibRj5cmLYuPIRhLrpB5uDg7q+n01psq69rAN5ogIgQ\niTgyGZXCFArafbVQ0ILTTEblK6WSZuV9X/B93d9uq5Wl72un1oEBgs6yMRIJn9VVzX7X68LoKBSL\nPiIR4vHOVvEt6HmGhhybmx6+3+HsWS3Ozechl/ODDrNCuezTbnc7xnabbAkvvKBOPNq9Fp577lm+\n7dsep9PRgP3MGR374KBjbQ2WloR0Wm0x43HwPD/Q629fr8s19fIyHb5x/YTh78NQbC7Chc1Hf9K3\ngbxhGP1LVzZSraobTDdj3Q3q02ktlI3FhNe/XqUzzaZ2dlUbyA6Li+puUy5DJiPMzIBzwsyMx/79\nmhkfHYWNjRapFCwve0xMOCoV/YyHH3asrrYpl+G55zxGR33uv9+xtORYXIxRKvmBFEiD/RdfVHea\n4WHHyIhPJqNBfLMJU1Owb58uQIaHhVbLB4TpaXXeOXNGC2c3N+HSJdmyyaxUhIEBXZjUavodDxwg\nkPjoNSqX9TrValo3AFqvYBiGYRh9G8gfP378Vg/B6MFW8eGhX+aiVwNeLm+743Q6mm2emIBUSjXx\n3cLXUglaLWFiwnHpksP3NYu9vOxYXYXFxSjZrDrS5HLqB1+va4faVkuLXlMpn8lJPZcIrKx4JBLa\nYGp93Q/08B0OHNDmU8PDPr6v8pzBQe142+mo000m47G5qQuRWs3hnC42UintblurQT7/OF/7mjak\nmpryaDaFsbEOQ0Mq32k2YW5Os+6RiDawikQ0mG+19E5F14e/WNRuvCareeX0y9/HnYDNRbiw+ehP\n+jaQNwzj9mE36YgGzd0iTw1u4/Ftrfijj2pgvrGhTjirq7Cy0uHuu7XB1V13aSb7rru2O9aOjekC\nYW5Og3jfV7eaVkt1+MkknD8PhYIG8YODGpA3Gup3H4sJ1arbaoJVr/vs26dFsAcOaJZ9eNixsqLn\nn5/X8SeTsG8f1Go+nqca/K5zz8WL0Ol4tNtaJDs15eH7PpGIZulVf68NrjIZddvp1c8bhmEYdy59\nG8ibRj5cmLYuPPTjXMRiBEWcL5eO9Aas6TQkEpc3slpf1+B+dVUlOJGIOsYcOKDOOPfc42i1NABP\np6brjL0AACAASURBVGFmBiDCwkKHgQG45542zabHwIDq8kdGVEJTLKpsJpNRP/uhIY9Wy+feezXA\nPnFCyGYj5PNt3vhGLYidnY0wNuaTSjnW1iK02x0qlRPAW5ibc8GiQ0gmfYaHdaHRbHqABuzLy6qf\nb7WERsMFhbLC8rK+3mjoYqZW0zsO6fTldzYuXtRrsbO42NimH/8+bldsLsKFzUd/sueBvIi8Hfgg\n4AG/7Zz71R2vvwv4t4APtIB/6Zx7dq/HaRjG3nElv/rdjtv5WiymGe+REY9kUj3pY7Ft60jfVzlO\nva7Zdec8Ll3yGR/XrHgsJltuN+PjGsznco5qNQL4+L4QiwmLi0IkEmV5uU277SESo153OBdletqn\nVtMFRCqlBbsiPu22EItpwJ7JQLUq5HKO9XVh3z6V3oj4eJ5+r3odhoY6lErqbZ/JwNqauuJEIi7o\nmKvfbf9+tcEEDeYvXoRz57SpVbvts7EBhw+bXaVhGMbtzJ76yIuIB7wEPAnMAV8AftA590LPMWnn\nXDV4/hDw+8651+w8l/nIG4bR5eJFfdTrmtEHGB/X5+pmo1nsWk2z3NWqFtNOTmoAH42qLGZzUzP6\nzz0HtVoUz+tw6JBjeRnK5Qibmz6vf71jfR2+8IUIzkWYnGzyyCP6HtAmUiMj8NnPRhkehmi0zeCg\nh+f5NJuwuqrNql7zmg6plPreN5tabOv7wrlzQr0e4ciRFvv2aRAuouPa3IT9+/XfyUltaHXwIDz4\nIHzta7CyItRqQrstxOMdHn5Yr08isXuDKsMwDCOc3DQfeRH5aeCdwCng/cB7gSLwO8650g2O61Hg\njHPuUnDuTwDvBrYC+W4QH5BFM/OGYRhX5MgRlZmsralHfD4vZDLbTjDJpLCw4BgfV+mJSmW0sLRQ\ngMlJ4dIlRzotLC2pw0w67VMuqzXk3XfD9HSH/ftVwpPJwMMPd2i31SO/a22ZSDhGRzU4TyY9qtUO\nw8Me0ag2kGo2hUJBi2KrVW12FY0KxWKERELPMTwM5XIH31cry0OHBFBfeYDTp9WDfm3NceTI9kKk\nWIT5ea0b6HQcqZSwuuooFvX77NvnmJi4cjDf23U2FrNMvmEYRj/gXccx551zbwP+K/CbwBpwD/Bp\nETl4g593AJju2Z4J9l2GiHyviJwG/gRdOLyMkydP3uBHG68mJ06cuNVDMALu1LkYG4P774d771Vd\nO6h7jDrYOI4ehUOHVHM+Pu5xzz1qFRmNapfYe+6BiQnH8LA+kklNhLTbqpUvFLb15xsbun9xUYP4\n5WXY3Ixw4YLHxYt67NBQi7ExWPr/2XuzGMnS687v990b+5KR+1qVte9d3dVkNUmxqzny9EiiZAMa\njAbG0BtgwbAgjGw96GHGBgyPDT94ZMiQDGHk0UAwYL8IBsagPYAtiOBAYie3ZpNdZDera+uqzMo9\nMzIjY9/u/T4/nIjM7OoqdjVZnXWz6vyARMWNuBHxRRxG83zn/s//bHyL0VG5AjA46CiX+xNuxV2n\n0XAkk+HucKty2fX88EUS5BysrXkkErKO5WWf7W3D4qLHgweG27fhRz8SC8xqVTYzsZhjbc3x7rtw\n/76hWJSJtGLx+XFqNZHyzM8bFhb2+g5qtQMK3gHyov4+oojGIlpoPA4nT6yRd879yBhzxzn3ZwDG\nmFHgHwP/3dNelHPu68DXjTHXgP8B+JWHz/nbv/1b3nnnHWZnZwEoFApcvnx5t1Gj/z9IPT6Y4/fe\ney9S69HjF/c4l4PvfneOIIA33pDjb3xjjkYDvvCFNwDHO++8he8bTp16nWTS8NZb3yaddvzyL1/j\n7FnY3HyLlRXD8eOvE4vB4uK3qVYdvv/LlEoh7fZbhCGMjr5BrQbt9rep1RxDQ18hkYBvfevbDA6K\n9eSFC3D79ltYC7duXSMeh7W1t5iehoGBa73nv0W1ChcvXmNgAO7dk/WG4Ru8/74hFnuLn/7UcerU\nNXZ2HLXaWwCcOnWNrS3DzZtv0e3C2Ng1jh6Fv/7rOdptw8DA64yOQqUyx8iI4+///WsUCvL91Ovw\n2mvX6Hbhm9+co9uF06evUakYvv/9txgfh1/5lb3vt9mEq1dl/devRyfeenx4j/tEZT0v+nGfqKzn\nRTvu337w4AEAV69e5c033+ST+ESNvDHmVaDgnPsbY8xl59x7+x77B865/+sT32Xv/C8B/8w599Xe\n8T8F3MMNrw8950PgNefc9v77VSOvKMqnoVYTbXm7LU2lm5uQyRiGhqS6ns/LMCaA5WWo1Qz37ztW\nVuTxWs1w967pTV8VeU2r5XqVcrGOLJWgVDKUyx6dDsRijlxOGmF93/Dhhz6JhDS3Hjtme/aShtu3\nfQYHHdlsSKEAW1se8bh42m9teYyPW5pNQ6fjqFZjbG87xsbELnNwUGws33vPcPKkI5mE+fkYxnjU\nao5z57oYI1cmjh6VqxJBIN+B74skJx73aLUcvu9oNAzj4/JdnDghVzpqtT3bT5D3U9mNoijKZ8dT\n08g75941xlwxxvyHwIIxxnfOhb2HM59yXT8AThtjjgGrwD8Cvrb/BGPMKefch73bnwMSDyfxiqIo\nnxYZCgWeZ0inZUBTp7M3LTWf3zu3UBDv+dOn+5p1WFuTRLdaNQwNiRa+VhPZSi4nMp4gkIba9XWx\numw0LLkcvP224bXXHImEZXZWBlgNDop/fLPpCAKfbDYAfMCRzcrj8bhsEmQglWNgABqNkLExx/S0\nWFJms7Ip8TyPtbWQs2chnw+Ix6Fc9tjZMcTjUrCp1/vNtexaco6Pi7PO9rZhZMSQTjs8Txx2trdF\nChSG4pSTTotFaLcrr9fX1aueXlEU5dnwiYk8gHPuOnC9p4n/B8aYFHAN0bA/Mc650Bjze8Bfs2c/\n+YEx5nfkYffnwG8ZY/4ToAM0gX//Ua+lPvLRYm5O/Wejgsbi8ez3q0+nJfmMxz9uedm/nUrRS56l\nmXZqSiwys1mxqlxZcRQK4vve6YjGfmgIBgelR18S5zlefvkrGOMYHLS9jYRYT9ZqlnPnoFJpMzHh\n84MfhBw9GuPOHcdv/VbIe+/B0JDH4mLIhQuwuCiuNaursLpqSKWkAu95hkIh5PRp0e/XapKcT09L\ng+/77xvyeYPnWYyRIVgrK+J6IwOuRItvjKXVEj3/+rok8cawa485OAiZjAzIajTYnbor3+nTSeYf\ntTl4mhsG/X1EB41FtNB4HE6eKJHv45xbZK9Z9f/oVeq/BoTOuf/zCV/jr4BzD933L/fd/kPgDz/N\nuhRFUZ6EJ/Wr338uSCJprQyKAmmmnZigV8WXKv36ulSyMxnTm+IqSX2lAkNDlm7XkEw6hodlwJTI\nayRRvnwZgiDkS1+CWi3gwgVpbi2VfFIpuHkzTjJpWV11HD3q8H2PSsUDAkolWFw0gGF42LK97SF1\nkoB222N52ZBIWGIxx8ZGjGQyoNVybG/HabW6nDsHqZSlUOgPqBLZTbdruHNHPkMyaTh+3NHpiNtP\nreZotcBaw7FjIiuS6by/GPslPP3NAXz8Pq3+K4qiCJ8qkX+YfqX+Ka3lU3HlypVn8bbKY9BdfHTQ\nWPxsfp4ksP+ch6fK5nKS/N69K8mstRAEhqkpSzxuqFYN2ew1kkkIArGGdA5u3pRzNzdhddXD9yGT\nscRikEx6DA5aEgkoFEJiMZ9EQgZdVasx2u2QWMz2JsHGcS5gYMAjCNyu28zSkuPKFSgURI/fasHK\nCqTTIUEAMzMO6DAwIOsJAnlcBk/Bzo7pyW9krUePGjY3HRcvQqkkG5EwlGr+1pbh5ZdF6vOLIpuB\nviR0T8Lz6Pt+PvT3ER00FtFC43E4+YUSeUVRlBeFR02VBfGw73Zhbc30EnnR3TvXt7IU/fzoKD3d\nPExOil1kPG6Yn4dm09BsilwnDC3j42JtefIkxGIho6MhngeLiwE7Ox4bG47ZWUux6BgcdCwuWpJJ\nSzYL1jrOnXOMjrIrjbFWrDnv3JEpsQ8ewOnTcPcupFKGd991u02/exp+QzIpE2TX12UglvjiSyW+\n0ZBG26Ul2dh0uzJ1tt9r0Peij8fl+HHSmP2ymf3SJ3C7z33UfYqiKMohTuRVIx8tVFsXHTQWB8/U\nFBjjCAJJhoeG9hLTd96Z4403PhqPMJQqebUqOnTn3O7k1lTKZ33dsrnp0WgYEomAsTEQXb9HuQyx\nmE+z6XBOZD6XLjlyOZkuu7UVp9WyjI8HtNtw82aMZtNw8mSXiQnxiu92RXcfj0sSvbLi02oZVlbA\nuaBnZSmOPLdvOyoVD2tDhodFg59ISCW+1RIt/q1bfXmP48gRGVCVy4njTSpFr1lX3mtoaM8Jp+8i\nlE7vuehYC+A+Non2SeRQT4L+PqKDxiJaaDwOJ4c2kVcURYkKuZxU2R9VdU6nP37+xIS4x6yuwtCQ\nNM+22/RsKkM8z+D7UiVvtcTJJpl0xOOWZNJgrVTfRXcP16+LXWQYej2HGq+3qTCAJOkDAyHVqqXV\nEnlOGMp7VCowOWl71XeR+WxuygTanR1DoQADAyETE7LedFquIGxuwuys9AVsbsp7tdsyVTYMDUND\nhjC0DAxIpb5alX6BTEY+f38TkUrJMfQHb8mG4OHvV1EURfk4n+gjH1XUR15RlMPM8jJcvy7a9I0N\nkarEYm5XqiMTYyWpbbXEmWZgQG4DfPihVLYzmb2q982bBs/zqVYtL70kmvvvftcQi/lkMgHnzsEH\nHxiGh0Xvb4xIb1ZXRR6zvi5XF+p1w8SESGpu3IgxOmo5fjzg/Hm4d0+capaXYWxMNiDSECuynUJB\nrkoMD0tlvt9EOz9vWF83TE7aXvLukU478nm3+zmSScPoqHy+VEo2Mp+EWmAqivI88tR85BVFUZSn\nTzwuHvWVigyLisXEm35sTJLaSgXKZamY1+si3TFGEucPPzScOSMuOL7vWF6WZP6llxzWhrsyH4BX\nXnEEgVTGKxUYGXE0mx6FgjTFBgGk0x7JpOPcObGXXF0Vj/2dHZ+REUMsJtr3uTmxsVxYsExOGlZX\nxe++XJbE3/OkEbZWEw/6dls2G/k8vc9hqNWkH6DdhslJaV6t1ei5AIkWfnTU0e3CnTsiQ0qlZEPw\ncLL+KJcbTeYVRXmROLSJvGrko4Vq66KDxiJaPCoetZokqOPj/SmrlokJ8bZPpyVphb0ktVh0u7r6\nnR2DtWI3mUhYfB+OHDG7g6OWlkT6Uqk4Uim4ccMwOGgolyVZ3tnx2Nmhp2U3jI4a3nsPXnoJbt1y\nHD26J3/xvJD19ZCBAal6j456WGs5c8aQybhdTXutJhX0VEqSb2s9BgZkOJVsVMSX3jmLc6J1N8ax\nsyOvG4v5FIshZ87I5qXZlOdtbEiCns3KBkfsPfeuREjj66dztNHfR3TQWEQLjcfh5NAm8oqiKIeV\nvs1iOg2nTkkCnsk8upmz23WcOCH3b2zIEKp02vX075IkDw0Z5uelAp7JiOwml/PwPMuJE5IYZzIy\nBTYIHNVqgvn5DtPTUnl/+WXZQFy5wm7T7f37BmMcn/sc/PSn8vybN0NeftljYcFy7pzZTd4XFuRc\n5+D+/QSJhCGbDdnZgVLJwzm5IrCzY1hclM8DMmAqlYIgsOzs+Ny6Ffb880Xms70NYWhIJKRSPzUl\nTbfnzslnGRiQabP9PoSHHW1UdqMoyvOOauQVRVEOmP2SEHDk80+eaPbdXvo0m4YgoCdpkQbVlRVH\nJiP69zt3oNPxyGZl2uz8vCTInucxOSlNs8vLUv0ulz3GxkKmpw2VCszPexw96iiVDJlMyNiYoVaD\njY0ElUqXV15xeJ5jc1Om1Z44AX/zNx6+H+PYsS7r64aNjQRTUx2mphwLCwmc63L2rGVry2d42DIz\n42g25YpBIiFOOYmEWFxubxt83xIEMuTq9GlLPu8xNWUZHna7SbxzstEYHpZq/S/6HSuKojxrVCOv\nKIoSUT7NhNlHPbd/fq0GnifV6kJBKvLFogxnymTEKtL3pQpfLotWvV6HsTGPSkWmuVYq0Gp5GOMR\ni3l4HpTLls1NQxjGGBxsU697WOtTq4Xk87C0ZBkYiNHpdGg0DNWqz9ZWyMmTjhMnLEEQkMs5Hjzw\nSCZFflMoOGZmusRidndN2axU30slaeStVkWrv71tmJpyBIH0BQwNWWo1SxgaKpWAiQmptAcBrK31\nm3Q9RkYsjcaet/+jZDf7N0IPW1wqiqIcNrxnvYCfl+vXn8lAWeUxzM3NPeslKD00FtHicfHI5cTt\n5RdJJHM5Sc5TKak4Hz8ug59mZ2F01DA+DufPm979HhcuGH71Vw2XLlkuXhRXmakpOHnSksuFWOt6\nfvGSkA8NdWm14MIFy/HjIRcvSkU/DD1arQ5TU+K0E4s5ZmYMpRIkkxCLWUZHIZcLGR4OOHnSsrIC\ni4vergVlLCa6eZkua6nXpSk3lXKAyHTSaUn2fV8ag5tNsbtcWhK3n+VlWFiArS3Du+/Cd74D77wj\na2w0ZAptpeJoNmXDVKvB178+x8KCeOavrcl9yrNB/1sVLTQehxOtyCuKohxiHt4I7K/2+z4MDDjq\ndUO9LpXw4WHxvF9eNqTTBrDMzMDMjGNjo0s8Lo4yqRSMjopVZL3OrnvO+LjH8HCXXE60754n72Gt\npVj0WFrymJkJKZdFX9/piH1OqeTTH2q1tGRpt8UDv1iUpttSCSYmxKUnm5UrCPW6JP0y9dZQr8ug\nqP4U3ERCNg6Li45Wy9Dtip4+CODSJUOtJtIb35fvpFyGatXQbHq95N72KveKoiiHk0ObyF+5cuVZ\nL0HZh3a6RweNRbR4FvF42KIxlZLKd3/abLncl7uIPKUvf1lakkq274vufGtLEvjNzb3nFouORMKj\n2w1xDrpdD+ccU1OGUskxMuLodmXzsLUlE2eTSajVQrpdj1ZLJDKrq3F2djxOnQoIQ49m02BtyPy8\nodGIk0p1mZwUe82REbBWGmvX16HTMaysGLJZR6HgqFYNYSgbl6UlkdW0Wo5k0uP8edcbnuVoNODs\n2ddZWwupVAwTEzA9vfc9aWPswaL/rYoWGo/DyaFN5BVFUZRP5nFJabstiXE/cQ1DkeOsrTmSSbG6\nzGalCu6cJPrxOFy86AjDkHZbmklTKcvkpCTQx48b7t8PSac9Njctg4MiodnagmPHYHJS9O1LS45U\nKiSTCXHO0W6Lb3yt5jh2zGFtm2bTMDzsepsAuUqwswOplKFeNySTBmOgUnGUSqLtLxRCmk24cUOm\nxNZqlloNZmbkKoRzsim5fZtdT/4bN+T7CENQP3pFUQ4bhzaRVx/5aKH+s9FBYxEtohiPRzXb9iv3\nsZgk8bGYYWBAbB6vXIHFRbm/X72v1eSv2YTFRUMYSlJ9+TLcvm0ZHBRLykwGikWZEruyYmg2xZnm\nyJGQdFqkOQCTk+Fuk+q9ex7GODY2oNn0iMVEd5/JGOJxubpQr0tSnstBLBZijPzf2daWPOfePcvR\no33XHjk/FoOf/OTbxGJvANBu+ywvB0xOyuftu9zUarJu2PP012r90yeKv40XGY3H4eTQJvKKoijK\nz8/jtPVDQ31nF/Gfz2ZFwjI0BJ5nqNelSTWZNMzOOmo1g7UejQbE45Zq1REEHo2GYXQ0BMQjv1z2\niMelii6DnaRxdXtbKuXVqsfx45aFBdHTd7shx47J/d2uZWjIY3vbcvYshKHreeJLcl2tekBILObh\n+46VFdlwLCxI8t634gSx6vR9ucrQbgc0m9Ig23/NblfWk83C6Kh8H4mEfA/9aj1oYq8oSjRQH3lF\nURTlkezXjcOeL3u97uh05LH792F+3lAu+3Q6ASdOSAW+0TB0u5ZORxLuWg3u3YN2O0YiEXDliujx\nl5cNo6My6Or8efjwQ59q1WCMYWJCEu0ggOFhaXTd2JCk3DlDEDguXhSpTCpl2NiQ40pF3HwGBuC9\n9ySRT6elQbbdloZY5yTZ394Wz/pUyjE4KBX4tTWYmPBIJCzT0zK4amhIXrP/nFZLntMf1qUoivI0\nUR95RVEU5RfiUQlqtytWl3Jb7CuPHHHs7ATkcpL0Ly46traket9oiDPN4CBcvQobGyEjI/LcfnId\nizkmJvrPDTl+3KfbDTh3TiQ9QSAuOvPzYq3ZbovDTd+CcnPTkM/LY5mMnHvrFhSLHqdOWYyRqvp7\n78HQkBSvJicl4W80oNFwlMuGI0dEpx+GsLJi8X3xn19fl+9iYICezz7E43JFoV6Hl17SZF5RlGfD\noU3kVSMfLVRbFx00FtHieYrH45LV/jRVkMS6b3vZ6YiGfnJSKvI7O1Aue3Q64HmWahUaDUOrZcjn\nLTs78Nprkkxns4a7dx0rKx6ZjMHzQo4cEdeayUlDsegIQ4NzUkmv1w337hmWlhyJhOPUKbh712dn\nB6wVX/tGw6fT+VvGx69x+7bpVdfl+c5Jtb/V8vB9SeITCcfoqFxJSKXkCsDIiFyZsFZkO52OfO6x\nMdmUgMpunpTn6bfxPKDxOJwc2kReURRFiR6FglStczmpVlsryfzAgAxxGh0NCQJDteqo1z2KRYPv\nOyYnpdI9Py+VfOdkWuvsrMPzHM2mIRZz+L7H6irs7BgGBiwgFftKxSedlmm1YWgIAksuFzA6KhNv\nPc+QSoVsbxsqFZ92O87Zs21GRw2ZjLjjdLvS8GutVPPjccfgoGV9XSbRdjoepZKjXhcLTt93pFKG\nWEwq+NmsbGomJ6XpNp3+2dNj+9Kl/qTZTOajmyJFUZRPQjXyiqIoylOln6B2uyJdCQJDNise9Gtr\nYIzBWtezsBQnm36Fe31d3GjAADIYKp83LC46Ll2CmzcN1arH6qrj8mVHNusAw8aGVOWLRY+ZGcvM\njN2VvtTr0ryaShkWFgzOyUZgbEwGQs3MOIpF2QxkMpaREcfGhjTnTkyEJJMiw1laMuTz0sh79myA\nczEmJiyFgqNWg0zGMD1te1p8sbTMZiWxP3/+o9/R/Lx8zlbL0Ok4BgbkCsDUlCbziqKoRl5RFEV5\nRjw8kKpalWR7dJSevl7sHTMZccfZ3JREuVKBsTHDzo4k8A8eyMCpYhGmp8W2cnbWUalY4nGR4AwM\nwMaGIx43ZDKSlGezIpEBS6kExniUy5ZcThL/IDAcPWpJp6VyvrUlzbNTU65XZZerCLUa5HKGdlt0\n84UCDA2FjI31G18DPA8qFfHft9axuiqJeCwGpZI8f2JC7p+aksm629ui4bfW603g9QFHImFIJi3j\n4zqgSlGUJ+PQJvKqkY8Wqq2LDhqLaPGix+Nhz/qpqY8/XiiI7rxYFIvH06fh5k3H2ppPuw2xmE8i\n0WV8XCrWm5sixelLd0ZGAByNhmN5Wary4+Mh1kIiIRNnL18WCU8QzOF54iNfqUC97jE5aWm1RL7j\nnDjUHDniqFZFttPpGI4dc3zvexCGYofpeYZKBbJZx/CwY3ER6vUYQRBy/rz0CNTrsLYmSfzW1p6X\nvVhuGioVkfR0OiHZrBTerBWtfhjKFYYgcAwPP59V+hf9txE1NB6Hk0ObyCuKoiiHg0+qKPcfT6Xc\nRyrQlUpIPm8olSQ5Hh0VyYrvGzY3HbmcJL5bW6LLn5+XRtj1dcfsLHz4IXQ6breqHo+Lw41zPvm8\nJR53FApS6TdG/OW3tsR+cmtLXiMeF9eanR3xkk8kYGDAo9MRb/ytLUezaXHOI522JBIy1bbRMGxt\niVvP8rIMx/J917PyFDlRLCbrnpqSzy7yH0n0m01DpyNyoFJJrmBoZV5RlIdRjbyiKIoSSebnxX7S\nmD1HmGLRUKtJ82k8LhXzjQ2R4aytiVyl3Zam19VV0aevrEChIMl8oQB378rUWnBMT4sEptUy1GqG\n7W2PWCxkaMhjaiokkZDEemREXq9el43D+Ljhzp04p051+PznZQ3ZrPzb7cp0WGsN7bY0zY6POwYG\nxAVnZ8eQSoG1jmPHJHnP5WB6mt1NRbMpFfl4XK5CTE3JlYI++/sQ4vE9r3+V4yjK84Fq5BVFUZRD\nzfHj8tenVgNjHEND4hTTd7pZWJAkemQEWi3LwIAk554nSXe5HCORcNy/b7lwQZLqkRFJmMNQXjeR\ncMzMOKy1OBdndbXL0aOGRkMaYUEq7WNjckVgdNTheV1efhm++U2oVlP4fps33xSJTywmibrnhTgn\n/QDJpDTz1mo+1loyGdHjr6wYTp40NBqWkRHR3zebMiTL82Sdo6N738PGhmwuul1pGs7n5cqE50E6\nvTeBVpN5RXn+8Z71An5erl+//qyXoOxjbm7uWS9B6aGxiBYaj6dHLifJ+8SEaOT7+vrJSRkGdeEC\nfPnL8Mu/DF/8Ily8CGfPwqlTIYODcOaMwbk5cjkPz/Mol0Uyk0gYRkZkM3DunGF4uMvnPy/NtJ4H\nKytS7o7FPBIJQxiKHCeddhSLhk4nSbkM29tJVlY8EgnZHDSbcP++6WndJSFPJg21Wki3aygWRSrU\nbBp2diwLC/CTn8APfwjf/a40xN6/D2+/LcOsQF5XhmB5rK05KhXY3ja7FXrB7LsdXfS3ES00HocT\nrcgriqIoh4aHq8z942RS/i0U5N9MRuQod+9K4h8EFs9zLC1Jwt5ui7NNvQ5BEMOYDtvbhp0dj3LZ\n4ZwlkxGXmenpkGxWhlgVi9KAa23IpUvgeY7r19u02yni8YCREcvysjTRptOOIPCp1RytliWddiws\nOIaHDRsbITMzsr7tbahUPAYHLc5BKuXRaMDIiOWDD3wKBWg25fx4XK5CtFrSjFuvy1WLZFJkOc2m\no9uVzwcqs1GU550DT+SNMV8F/hi5GvAXzrl//tDj/wHwT3qHVeB3nXPvPfw6V65c+ayXqnwKtNM9\nOmgsooXG47Mnl3t0sppKySCqM2fENQeg1brGxoalXBaf+vV1GBwMyGalMg6GTscnmQxoNMAYy/Cw\nJZ8Xycvduz6djmN21rGxYZmchN/4DdjYaDEyIpNeNzdlWFUYQjxuSSQk0d7ZkcfTaUcy6REEKddS\nmgAAIABJREFUFms9xsYkmR8eFinQ8DAUi7L+1VVDOg2bmz4/+EHIyAi9jYJYYg4NQRhKQ288LtN0\nu12R11grQ6n631HU0N9GtNB4HE4ONJE3xnjAnwJvAivAD4wx/7dz7ua+0+4BX3HOlXtJ/78CvnSQ\n61QURVEON/sT14etG2s18a8fHoalJQgCizGQzVpyOUgmQ3I5x+CgJOAXLog9Joh9pDSk2t2BTsWi\nY2TEcPeu2EkuLkqCffq0JPJB4FMsWnxfZDZgaTTkqkGhYAkCj+FhSyolSXwQWMbHxSEnmw1ZXvbZ\n3jZMT0vjbrEokp3hYcjlRP4TBNK4C2ZX059KOdLpvU2MoijPHwddkf8CcMc5twBgjPlL4DeB3UTe\nOfe9fed/D5h51Aupj3y0UP/Z6KCxiBYaj2jRj0dfX18oiBOO54ndZLdrWVuTc3M5carpV9ITCXjp\npS6JhGj0FxYMGxsetZpPKhUAcn4sFqPTCSmVLKWSRywmQ59KJcfQEDgHFy9a2m15zYUFeX3Pk0S+\n2YRKRSQy5845nAuJxRytlmwS1tcNGxsxEokumYw00OZyItNZW3N0OgbPsz39P4yNyWamWpWNQDL5\n8UbiZ4H+NqKFxuNwctCJ/AywuO94CUnuH8d/Bvx/n+mKFEVRlBeSXE509Lkcu57unicV+HIZwCOf\nt2xsyP2pFFSrhlOnHL4P8/MiZwnDgGTS0W6LG876OsRiUp2PxWSqbSwmQ5/yeXGquX7d9LTwjtFR\nj81ND8+zLCx4WOsoFCznz4sOfnnZ0Gp5TE+HDA6angQnJAg8FhZs7/VFH7+9LQOshodFWuMc3L4t\njbCJhAzBslYGXF29CidOyOf/tJNkdfKsokSDA/WRN8b8FvBrzrn/vHf8HwFfcM79l484999BZDjX\nnHOlhx//3d/9Xbezs8Ps7CwAhUKBy5cv7+4m+93XeqzHeqzHeqzHjzuu1eCb35wDDF/4wuvk83D9\n+hylEly+fI1MBr71rTkWF2Fs7A26XUe1OkezCQMD19jchAcP5rAWzpy5xsoKbGzM0W5DNnsNa6HV\nmiORAN+/Rj4Pq6tzbGzEyOWuEQSGavVv8TzHqVOvU6n4NJvfolKBL3zhdW7cMLTb36HbdVy79mXS\nabh799s45xgcvEYYwubmt8nn4cSJaxSLjrW1OWIxeOWVaz3f+zkaDTh6VI43N+cwBr70pTc4dsyx\nvCzn/+qvvkG16vjpT+fI5eDv/T25cvFv/o18nq985Rrj4/CNb8jrfeELbwCO99+fI52ORjz1WI8P\n63H/9oMHDwC4evUqf/AHf/CJPvIHnch/Cfhnzrmv9o7/KeAe0fD6MvCvga865z581GvpQChFURTl\nafAk1eW+d3u1Cvm8DHwKQ5G5LC/LYKd4XGQya2tS/V5dNVhr6HTEH36xdz06mZRq/vZ2nOPHO5w6\nJZVyz4N334Xjx8XicmYGvv1tn7W1ONY6/uE/bO/aTW5uwvnzYj/54Yc+4+MwOBhy9KhcETBGvPSb\nTZ9USlx36nV575ERuH8/xpEjFmsdV644ksm+5t6ws+NIJmV41cRE3wHHAyxTU/I5W629/CKVch8Z\nVqUoyi/Okw6EOmgf+R8Ap40xx4wxCeAfAf/P/hOMMbNIEv8fPy6JB/WRjxr7d5TKs0VjES00HtHi\nUfHI5aQ59WdJRMbH4fx5kd1MTDjOnxdZyssvO3791+HVV+Gll+Dv/l346lflvJdflgbUqSlDudwf\nUOVx7x4cOeI4fbrL6dMG58Rdp1iEmRmPQkGGPJVKYkF55kzIF7/YZnsbVld97txJUCjE2doyJJNw\n5IilVjPs7MRZXJTXcs5jeBgSiZAw9Gi1PEZGRGrTaHhUKpKgLy/7rK3B5qbj3j3DvXvi5LO0BO++\na3jnHekRAAeILaZMke0XAWXCbq0m663VfrFYKM8OjcfhJHaQb+acC40xvwf8NXv2kx8YY35HHnZ/\nDvw3wDDwL4wxBug6536Wjl5RFEVRDoT9yf7+2/2qfj4PJ09KBf/uXRgaksr9xobhxg3odCz1eoxK\nxTI2Ji45AwPSJFssxqnXPSqVNi+9JK954oRjbS0gHpcqezzuSKcdsViH2VkIAlhZ8bhzJ8bYmFTM\nNzcN1apMe81mDdvbjmbTw1ppfI3FLK++Kp71Y2Nik1kqyf3NpjTeNhryecplQ6XiOHnS9foBJJGv\nVsUNp2/LWa1Kk263K5uih52CFEX5bDhQac3TRKU1iqIoSpTpy3G6XUMQOO7ehQ8+MLse8YWCY2Bg\nr9n2xz82NJuG7W3LzIwk94OD8nirJUny/fse9brH9HTA8eNyf7ttuHnTkMlIlT0e92g2LWfPOqx1\nLC/HKJUM09MB2aw02374IQwM+GxvW86ckSr8qVOyWchkYHMTPM/Q6cDJk2KZKdackMkYNjcdR46I\nxebwsDyvWpVGW2PEAUiTeUX5+XlSac2BVuQVRVEU5UVhfFyS4m5X5CdnzsDnPucoFvcPh5KqubWO\nIHBsbHik05Ic12ricvP22wAeZ85Y0mnI5x1rax5B4Gg0HMPDjnPnoFbbk+QsLXlsbwecOAHr6yED\nAx7ttmjZOx0D+DQa4Fycej2g2YR6XbzxZ2Y85ufF177b9YjHba+HwFCtGqanLZ4nG41GAy5flisD\nm5v01iObj0xGHW0U5bPmoDXyTw3VyEcL1dZFB41FtNB4RIuDjsd+/X0uJ1XvL34RXn9ddPRHjhjG\nxhzHj0tCfPq05dVXxeP9lVdkAzA1FWNszCORgETCEgSGQsHieY4g8PE8mRbbT66NsXzlKwEXLshG\nIQikMg/g+zAw4KhWAzzP0Wh08X1LJmN71XyfrS3H+DhcuuSYnJThWPm8yHr6Pvu3b0vF/u5deP99\nuH4dvv99uHEDPvhAmn67XfkOHqef/7Sx+Hl0+MqTo/+tOpxoRV5RFEVRDphcDiYn96r1IM2wyaRI\ncqQaLud0OgGVSpx2WzYBm5sBYSjDnUZGLENDUuFfXEyQy4UkEpZcznHjBj23Gh/nDJ4nSX48Dl/+\nMnS7IefOSTUdIAzBmBCIkc2G3L/vsFaGZZVKUC7HaLcDXn0VwLC6KlcNOh1Huy0yn9u340xPQ7fb\n3XXyWVuDIDDEYjJI69NU6fu9B92urA8MrZbb/Q4V5UXn0CbyV65cedZLUPbR90NVnj0ai2ih8YgW\nUYrHoxLRVEqq3yDSlHgcpqfhzp0u5bI0sA4MiAXlqVOOfF4aUMPQw9ou6TS02w5jJAmOx+kNqzIk\nEtLYOj8v5ycSIsvZ2oJqNYZzIsXpdEIGBmBhwScIRALknMh9FhZi3L9vefDA8frr0lgbBDJ1tlw2\nhKFHEAS02x6Li5ZyWaw1Uymxyrx9G44eFVvLS5eu7VbXH2X/WauJ7h5kc2OtIZ8XKVK3ezj7+6JM\nlH4bypNzaBN5RVEURXme6Cex+z3ZazWYnZW/u3dhcdEwMCA+9ZmMYXRUJrh6nrjZLC2J9eSDB3b3\ndaamLGEomvdKRRJhqfp7bG6GjI1BsWiZnZWqdzLpKJUMxoTkctJMW6uB5/mkUpLsDw7KhmJwUBLq\nVAoyGUer1aHbNTSblkpFpD5bW+Jo027Lmj/4QHT+x49DoSANwek0jI6KpAgksW805CpF30mn1ZJj\n2NvsKMqLjmrklaeCauuig8YiWmg8osVhi0cuJ/aOqRScOwfnzok85dIluHLFcfKkWEpOTkI6bTh+\n3JBOQzLpMTMjle9UynDqlDjjHDkiWvehIbGbLBTE477R8Fhf98hm4cEDiMUkWS4U5PyrVx2XL1te\ne00GS3U6hsVFKJU87tzxqNUk2U6lHEePWjoddpt69xJ6w9IS3LhhuHXL4+tfn+Pf/lt4+22P69fh\n1i344Q9lw9JP/vuWltZCIiGblnRaZTWfBYftt6EIWpFXFEVRlAizP2nNZGByUqrghYIkuVtb4lDX\nbsPWliOVkmmyhYJU2Ot1x9iYVO+Nkfvu3rXUah5ra47BQRgasiQSkkAHgdy/seExNibe8svL4oE/\nOyuJfCJhKJUkyY/HfVotx8qKw/fF0vLYMahWHSMjMsU2n3eUy45EwtBuW2Kxvqbeo1TyGBkxdDoh\n5bJ8zrExGbg1NCSynmYTYjGZLtvvKejzJJN5FeV5RX3kFUVRFOWQ0teRl8uGtTVHtyuVcWMk4QaP\nTscyOCiVfeekOr6yAvW6R7Xq2NwEaV51XLniuHNHqviLizI51jnD1JTF96Wp9ebNJIVCQK1mGRnx\n8DzL6dOul/AbOh0fay3nzjlWVw0PHsRJJjucP+/wfRkw1enIVYSNDUO5HCMWC/jyl0Wvb4xo4M+d\ng6tXRXKzsCAblWQSjh0TvX61Kn+xWN/mU4dRKc8P6iOvKIqiKM85/Qq0tY5EQmQnzaZIUUolQ60m\n016PHBH3mHrdkMk4MhlYWZFq/Oiow/NEStNoyGTaTscRi8G9ex6eZyiVHJ7nkclYRke7ZLOSMOdy\nIYWCIZGQRtahIXj//ZCTJz2KRUsqZchkQuJxn2YzJJ+HSsXvXR0Qd51sNiCXk4bZRsNQr0uB8cYN\naXI9eVI86kdH5YrB9etydaFQgFZLmm0HByGb9Wg07CP967VqrzyvHNpE/vr162hFPjrMzc1px3tE\n0FhEC41HtHge49H3qO8nq/1G0JER95HEdXISymVJkoeH4dgxqbCLtaQ0sBaLUvn2PJiZcQwNhbTb\nUuUfHbVsbQGIVt33HUFATzIDMzPQbDpeew0gZGICbt60ZLOGMAyZnobbt2WoVBiG1GpzDAxc4+5d\nn8nJgFYLmk1DqWSwlt0G3Z/8RJp7i0V6en5x6hGffPkMOzuyvkZDJsuKBaZ87ni8/90Y4nG1rnwc\nz+Nv40Xg0CbyiqIoiqLs8UnJaT/hB0lsMxm5ncmIZGVgQJL97W2pzJdKUmHf3oaRETm32xWnmk5H\nnrO8LHr5QsGxsSGbgVu3PC5edCwsiDxmfd2RTsP6uvjOj42FpFKyWfA8mJoKOXNGmlxjMQOEnD0r\nVxViMdlEtNsio9nakisBzsHiojw/k5HzlpcBHPfuicZ+dlb6CDoded9YzBCLiSuPJvLK84Jq5BVF\nURTlBWS/3KTREO18p8Ou1n17WyQ41orzTLcLKyuGTMawvi7J9MKC4cgRS6MhCf3yMtTrCWZn2zjn\nsNbnxg04dy5kaMhQLMoGoFBwnD4tyXurJe/reYZy2WCtY2TEMDhouX0b2u0Y9brltdcs9bok57Wa\nrHN8HKpVw/i4+NRXq5DLGVIpmYx78aLc12yKq0+3K1KidFo2AdPTe/p6ld0oUUI18oqiKIqiPJb9\nSWsuJwltsShTWNNpSebzecPoqKVaFfnKmTPiV7+4KOdmMuIzb60jCByxWIJWS+Q4uRxMT4ckEh5H\nj8LmpmNiwvDggVTEf/xjWF2N4ZxUydNp6HY9stku8bjrJfcx8nlDsxmjWg3Y3paBV84ZfF8cbLpd\naaCtVsEYj1u3vJ5jj8h1BgcN1aojl5Nm21JJNiGeJw3Cs7Ny5aEvMSoUNKFXDg+HNpFXjXy0UG1d\ndNBYRAuNR7TQeDyefvJarTqyWUMq5YjHHcPD8Mor8litJsnuxIT4zQ8NQavlWFiQ27lch1dfpZdA\nw/e/D2trPrWa5ehRacAFj1rNUip9m273GoWCT6sVMjMD6+visLO8LO40zWZALucTBJZk0mGtYWjI\n0WiIfObWLUOn41EsOs6dc1Srdrd5Nx6XKbZBAMmkYXLSEYuJpr7d9kgmDbVaSCxGT5NvepuHF1NH\nr7+Nw8mhTeQVRVEURXm69JPXbtdx4sTHk9n+cbMJ584ZslnHzo5UuJ2ThD+RENnK2hrMzPjMzFis\n9TEm7CXRhjAE5ywnTji2twOGhx3lsrjryCAon83NkCtXwPdDLl2S5H5szPHggWwSlpag2YyxswPT\n0x5BEDI0JBuMbNajVLIkk7Cx4VMsBrz+OlgrnvY7O7JJqdXExafblSFYk5OiZFhf37vi0Lez/FnO\nN+qKozwrVCOvKIqiKMoTUyqJ7WOfctmxvW1oNCTxHRsTb/qFBbGQ3N6OAQHT01IdbzQgm5Wkt69r\nbzQADOm0OOGsrXkkEo5mUxxomk2pmAeB5CzxuCEMHcvLhlYrxsmTXcbGYG3NUCyKC87Ro/K6/YbZ\nREIm5I6NydrW1z06Hbh40XLkiDT65vOGWs3hHIyOShOvc+LJ32qJBWY+37feFHvM7W162nsDiI1n\nP5nf2GD3e1F/e+XToBp5RVEURVGeOvG4yGlAEtfhYWle7R/n86Izz2YloV1dDRgakiZX3zdMTIh9\n5caGVL2/9z0oFmOk0wH5PHzwgaHTEW3+5z8v2vxkUiQ/hQLcvGkYGREHm/PnHc1ml4sX4f59ANHK\nnzolsp5mM04QhHzlK1Kdn5+XybYyEdej1fL54IM28bgk+eWyJO3JpKFelw1Du+1ot6VR98gRuVKR\nTO41CNfrHs2mbDDSacP6uiOVku+q3QbwKJctoMm88vQ5tIm8auSjhWrrooPGIlpoPKKFxuMXZ7/8\npi8lEWnJ3nH/HOfk9vCwodNxpFL9xB86nTleffUahQLcuRPQaEiFfnDQ601p9djasrRaMmV2ctKx\nuuoYH5cBWK+8IhKYqSlJ0JtNaXp96aUAYzyGhgxbWx7Fos/mZodk0jI5KZX5QgESCUsqZXFOBk41\nm1LlHx2FUsnh+5KIDw7Sm4Arm4JsVl4nDKFS8bBWNjGrq44wFA1+Pi9ricU8Rkchk5FhVY+S4ERF\nlqO/jcPJoU3kFUVRFEV5NjxOO7+f8fF+cmoIAnGJSSQk0V1eFonOlStw+bI4y9y543rOMR6djiTM\niYTIZYaGDK2WI5UyrK0ZUimPtbWQjQ2fatUyNmbwPEc67bGwYDh+PGRjQzYD7bYhn7e023IFYHAQ\n3n5bpuB2OpYzZ2Bry3D3rjTslsuQSsmE2YEB0dzncoZut0ssJhX7zU2R7GxtWWIxg+dZfF8kQLWa\nodUyiHTZksl4gKVQEBkRmN4VDeHh+1Rjr3waVCOvKIqiKMpnQq22l6iWyyKp6XYNYEgmRZsOIlGZ\nnxd5zMICGCOVc5GvePi+I5l03LkDxvgMD4ecPAn370vzarMpr7u1Jb7z8XiXl18WbXzfB99aSdQ7\nHVhailEuG5wznDjRpVRyGOMzMhJSqxmyWdHjnzkjTbh9jf3YGIyMGHzfMTm51y+QSLjdTcDt21Ao\nGGZn5epBImEYHRWt//7eglRK8q+H7xsaOrDwKBFGNfKKoiiKojxT9stwfF8SX0nkHbGYoduVxPXM\nGZGqlEoAkkTncqJFn5yUynypBNmsodm0TEyI1j6ddr1GWVhclOT6/n1LEMRYXw96PvMe3a40rc7P\nG6amLLVaSKeTIJHo9uwmDcaIjr5YhHv3PLa3fXZ2Ohw75vA8ePDAo912FIuQSPgsL4c0GnK1wfc9\nBgZEOlOpmF03nKEhelIgaYp1Tqw9QTYIrZbIhPrJezx+4CFSDjmHNpFXjXy0UG1ddNBYRAuNR7TQ\neBw8D0tFtrdFjvLTn77Fm2/uxWJiAq5eZbcCbgwMDIilpSTIsLLiCAKPZNIyMQEXL4r0ZXNTEvAH\nD8Tu0vNEi3/rllTEm01DLAaplCTbv/IrjgcP2gwMwMqKOO2MjMhmYmAAikWfM2cc2axHKhWytQWe\nZ+l0DK0WpFIhYQjNpmxIajVDGBq2t+V9ul3ZeMzPS9PsxITpaenBGNnUlMsAop1PJuXzq0Ze+bQc\n2kReURRFUZTDxfi4WDF2u45M5qOJazwuuvV0Wo4ftnHc3pYku9ORoVFDQ+D7cs7WFgwPw/37IdaK\n002nA+fPSwIeBKLN73ZlDWtr8lp370qSXauJl7wxMD3tKJc71Os+zWaI78uawhAGB6Wyv7goWvkw\nlEbelRXH2bOObteRz4vTTRjC6qpYcy4vO44dE2mOtfI+W1sexjjSabky0e3KhkU18sqnQTXyiqIo\niqJEgicZutR/vH9OP8mPxUSPv7QECwse9brtTXXd86zf2hJveN8Xi8vNTcPYmCOTceTzknyvrMgm\noFyWxLtWkwFX773nceQIGGNpt0VfD67npmOYnnZsb4uTTaMBR49axsagXjcMDIg85/RpdmU0QQCd\njocxllOn5L3EreejNpUPe9FHxeVG+WxRjbyiKIqiKIeKn5WYPu6xvSq/DHWamYHRUcvqqmjap6ak\n6VSccqR4ub7uSKehUBC9/fCwyF3u3ZMk/u5dw/x8gtnZDtY6xscNznkkEpbtbY/tbfA8j1RKPPJ3\ndsQGs932qFbFPnN9vT/sypHJGGIxw9KS5aWXZPOQzUpVv1AQadDqqlT++xuTVEoq/hsbYl9ZLlsa\nDdmYlEqS3I+OwvHjTz8OyuHh0CbyqpGPFqqtiw4ai2ih8YgWGo/o8DRjsT/J798eGrLE46I9B0m0\nu11JkldXRd8+OgrJpMhuNjag2/XxPMvUFEBAOi0Ntvm8Ix4P6HQkmc9mTc9tRjTwg4OOWAzA4Xni\nT5/Pw5EjsLTkUa2KNr5UijM0FBKPQ73uSCY9dnYsm5uyCSiXHTs7jtOn4dgx2aB4ntf7ZB7Npnym\nnR3TOw7JZPY2Mr9IlV5/G4eTQ5vIK4qiKIqiPIrx8cdPUc1kxEpye9sQhnJ7eVmaVPN5x4kThp0d\ny8iIJQxFAhOPw4ULEIvJhNYf/lCaYD1PPORnZ+G99yTp933LL/2SONJsbcHYmMUYed+f/jTA9w3W\nSuW/2w1JJg2djqzh9m1DPg87O5Z6HWZmHL5vSSQ8wlAafItFsazM5SyZjGF7WyRB6kX/YqIaeUVR\nFEVRXihqNdHAN5sAhvV1x/q6DKNyzu5uAqyVZLzVMty65SgURIv/4YdgjCTOIyMidbl9O0GxaBgZ\ncfzSL3U4eVKaYtfWoNWSRHxqSjzmYzHxvg+CvkYfvv99j0oljrVdBgcNxjiuXpXNRDJpGBwU+c/K\nimw+cjkYGZHK/czM473oP0lTr5r7aBJZjbwx5qvAHwMe8BfOuX/+0OPngP8N+BzwXzvn/ueDXqOi\nKIqiKM8vuZz8SRIrE1yzWSgWLem0PGatJNwnT4oGXgY+GVIpRzIpOnvn+k44htXVLkGQZGioTS4n\nEp4PP/QolTx8H06eFLkNOEoleR1j3K5//sSEJRZrMzgo02xnZjyWlyWJt9awtOTodg31uk8mE3Lk\niNtt9l1ZcQwNSbJ/4sTe59w/kOtR1fpPelyJPt4nn/L0MMZ4wJ8CvwZcAr5mjDn/0GlbwH8B/E8/\n67WuX7/+maxR+fmYm5t71ktQemgsooXGI1poPKJDFGKRy+25xJw+DSdPQi4n2vd83jExIVXvyUmp\nfF+4IEOnLlyAo0cNxaJPPG7Y2nJ85Svwyist/s7fkSbVdLqvv/fY2RHLyU4HqlXDxoZUwItFqfhX\nqyLFSSSkAfbMGXrSGQCxptza8mm1pFJvjN9L6qVB98MPYXnZUamwOyCrVpPXl6sOMvSq2/3o55dj\nKfq+/fa3P/a4En0OuiL/BeCOc24BwBjzl8BvAjf7JzjnikDRGPPvHfDaFEVRFEV5QelXopNJqUwX\nCntV+1RKqvYyKVYcaTodSCQsqZTred87XnlF/O/rdbh/HyYnHUNDHeJxmJ6WJtVOBy5dEqeanZ0Y\nKyuQTEq1PgwtJ06IFWWz6QgC2RBUq46JCUuzKRX6bNaRSom15f37hrExj/V1x8hIyMqKXA3odiGd\nNtTr8nnSafexybHxOL1KvFhp6mTZw8dBJ/IzwOK+4yUkuf/UXLly5aksSHk6aKd7dNBYRAuNR7TQ\neESHKMaiL7l5+L6H6VfKJydlsNToqAyn6jedbmw4ymWptDtnmJlxzMyILn9hwdBqWfJ5Qz5v2N72\nSSa7dLuQychwqp0dQ7ksmvhaTTYEY2Oijwepyg8OGjxPrDE9zxKLiUSn04FUygPEdjOblfP2D9h6\n+LN1u44337ymsppDiLrWKIqiKIqifApyObh8+eONon3NvTjgwNiYRxhCoSANrSMjjkLB0enI1Nd0\nOiCRCMnlHNZKk+r2tmFlxWN1NcbFix06nTjGBDQajiAwPYlOjM3NgNlZsdmMxaSinkxKEt/tyrmt\nlmN09NFJ/P7PohxeDjqRXwZm9x0f6d33qfmTP/kTstkss7PycoVCgcuXL+/u8PvaOz0+mOM/+7M/\n0+8/Isf7dadRWM+LfqzxiNaxxiM6x/37orKen+c4l3v0cbEI+fwbOAc3b75FIuF49dVr+D6src2R\nTsPLL18jlXJ0Om8RhnDxorz+d74zR7NpyGTeoNUyVCp/g3OOqalrrK/D4uJ3MCbgS1+6Rr1u2NmZ\nY3AQPve5a3ie43vfewuAl156ncFBeP99eb/HfZ5vfGOOIBCbzWvXrvHOOz/7fD3+7H4Pc3NzPHjw\nAICrV6/y5ptv8kkcqP2kMcYHbgFvAqvA28DXnHMfPOLc/xaoOef+6FGv9Ud/9Efut3/7tz/L5Sqf\ngrk5HSQRFTQW0ULjES00HtHheY5FrSYa+XLZEI+LLGZ8/KPV7+VlaXztV/R9Xyr1d+7A8rJHsWiZ\nnhYZz/i4JNq3bhlu3jQUCpZKBc6e9Rgft5w6ZRgddezs9OU80rj7SVNf+641zSa89dYcr7/+Btns\nz67gKwfDk9pPHriPfM9+8k/Ys5/8H40xvwM459yfG2MmgHeAPGCBGnDROVfb/zrqI68oiqIoSlTp\ne9XDXuPsw4/3rR9hL3menxe3Gd8Xt5xSSRxtjJHNwY0bPt1uyNaWx5kzhokJy/i4bBYqFfG3j8cd\nx449fihWH3ltQ6Ui/yaT4pX/sBe9cvBE1kfeOfdXwLmH7vuX+26vA0cPel2KoiiKoihPi0c1zj78\nOIimfv8wpuPH5a+vv5+dlX9bLbGWbDQc1kIm40inDfG46PFbLUOrZRgYcCQSHo2G3X1xsPW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#type your code here.\n", + "figsize(12.5, 4)\n", + "\n", + "plt.scatter(alpha_samples, beta_samples, alpha=0.1)\n", + "plt.title(\"Why does the plot look like this?\")\n", + "plt.xlabel(r\"$\\alpha$\")\n", + "plt.ylabel(r\"$\\beta$\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "- [1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n", + "- [2] German Rodriguez. Datasets. In WWS509. Retrieved 30/01/2013, from .\n", + "- [3] McLeish, Don, and Cyntha Struthers. STATISTICS 450/850 Estimation and Hypothesis Testing. Winter 2012. Waterloo, Ontario: 2012. Print.\n", + "- [4] Fonnesbeck, Christopher. \"Building Models.\" PyMC-Devs. N.p., n.d. Web. 26 Feb 2013. .\n", + "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. .\n", + "- [6] S.P. Brooks, E.A. Catchpole, and B.J.T. Morgan. Bayesian animal survival estimation. Statistical Science, 15: 357–376, 2000\n", + "- [7] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n", + "- [8] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [conda env:bayes]", + "language": "python", + "name": "conda-env-bayes-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter2_MorePyMC/Chapter2.ipynb b/Chapter2_MorePyMC/Chapter2.ipynb deleted file mode 100644 index 745d8caf..00000000 --- a/Chapter2_MorePyMC/Chapter2.ipynb +++ /dev/null @@ -1,2643 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Chapter 2\n", - "======\n", - "______\n", - "\n", - "This chapter introduces more PyMC syntax and design patterns, and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## A little more on PyMC\n", - "\n", - "### Parent and Child relationships\n", - "\n", - "To assist with describing Bayesian relationships, and to be consistent with PyMC's documentation, we introduce *parent and child* variables. \n", - "\n", - "* *parent variables* are variables that influence another variable. \n", - "\n", - "* *child variable* are variables that are affected by other variables, i.e. are the subject of parent variables. \n", - "\n", - "A variable can be both a parent and child. For example, consider the PyMC code below." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import pymc as pm\n", - "\n", - "\n", - "parameter = pm.Exponential(\"poisson_param\", 1)\n", - "data_generator = pm.Poisson(\"data_generator\", parameter)\n", - "data_plus_one = data_generator + 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`parameter` controls the parameter of `data_generator`, hence influences its values. The former is a parent of the latter. By symmetry, `data_generator` is a child of `parameter`.\n", - "\n", - "Likewise, `data_generator` is a parent to the variable `data_plus_one` (hence making `data_generator` both a parent and child variable). Although it does not look like one, `data_plus_one` should be treated as a PyMC variable as it is a *function* of another PyMC variable, hence is a child variable to `data_generator`.\n", - "\n", - "This nomenclature is introduced to help us describe relationships in PyMC modeling. You can access a variable's children and parent variables using the `children` and `parents` attributes attached to variables." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Children of `parameter`: \n", - "set([])\n", - "\n", - "Parents of `data_generator`: \n", - "{'mu': }\n", - "\n", - "Children of `data_generator`: \n", - "set([])\n" - ] - } - ], - "source": [ - "print \"Children of `parameter`: \"\n", - "print parameter.children\n", - "print \"\\nParents of `data_generator`: \"\n", - "print data_generator.parents\n", - "print \"\\nChildren of `data_generator`: \"\n", - "print data_generator.children" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Of course a child can have more than one parent, and a parent can have many children." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### PyMC Variables\n", - "\n", - "All PyMC variables also expose a `value` attribute. This method produces the *current* (possibly random) internal value of the variable. If the variable is a child variable, its value changes given the variable's parents' values. Using the same variables from before:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "parameter.value = 0.984449056031\n", - "data_generator.value = 0\n", - "data_plus_one.value = 1\n" - ] - } - ], - "source": [ - "print \"parameter.value =\", parameter.value\n", - "print \"data_generator.value =\", data_generator.value\n", - "print \"data_plus_one.value =\", data_plus_one.value" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "PyMC is concerned with two types of programming variables: `stochastic` and `deterministic`.\n", - "\n", - "* *stochastic variables* are variables that are not deterministic, i.e., even if you knew all the values of the variables' parents (if it even has any parents), it would still be random. Included in this category are instances of classes `Poisson`, `DiscreteUniform`, and `Exponential`.\n", - "\n", - "* *deterministic variables* are variables that are not random if the variables' parents were known. This might be confusing at first: a quick mental check is *if I knew all of variable `foo`'s parent variables, I could determine what `foo`'s value is.* \n", - "\n", - "We will detail each below.\n", - "\n", - "#### Initializing Stochastic variables\n", - "\n", - "Initializing a stochastic variable requires a `name` argument, plus additional parameters that are class specific. For example:\n", - "\n", - "`some_variable = pm.DiscreteUniform(\"discrete_uni_var\", 0, 4)`\n", - "\n", - "where 0, 4 are the `DiscreteUniform`-specific lower and upper bound on the random variable. The [PyMC docs](http://pymc-devs.github.com/pymc/distributions.html) contain the specific parameters for stochastic variables. (Or use `object??`, for example `pm.DiscreteUniform??` if you are using IPython!)\n", - "\n", - "The `name` attribute is used to retrieve the posterior distribution later in the analysis, so it is best to use a descriptive name. Typically, I use the Python variable's name as the `name`.\n", - "\n", - "For multivariable problems, rather than creating a Python array of stochastic variables, addressing the `size` keyword in the call to a `Stochastic` variable creates multivariate array of (independent) stochastic variables. The array behaves like a Numpy array when used like one, and references to its `value` attribute return Numpy arrays. \n", - "\n", - "The `size` argument also solves the annoying case where you may have many variables $\\beta_i, \\; i = 1,...,N$ you wish to model. Instead of creating arbitrary names and variables for each one, like:\n", - "\n", - " beta_1 = pm.Uniform(\"beta_1\", 0, 1)\n", - " beta_2 = pm.Uniform(\"beta_2\", 0, 1)\n", - " ...\n", - "\n", - "we can instead wrap them into a single variable:\n", - "\n", - " betas = pm.Uniform(\"betas\", 0, 1, size=N)\n", - "\n", - "#### Calling `random()`\n", - "We can also call on a stochastic variable's `random()` method, which (given the parent values) will generate a new, random value. Below we demonstrate this using the texting example from the previous chapter." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "lambda_1.value = 0.666\n", - "lambda_2.value = 1.741\n", - "tau.value = 3.000\n", - "\n", - "After calling random() on the variables...\n", - "lambda_1.value = 1.800\n", - "lambda_2.value = 0.190\n", - "tau.value = 2.000\n" - ] - } - ], - "source": [ - "lambda_1 = pm.Exponential(\"lambda_1\", 1) # prior on first behaviour\n", - "lambda_2 = pm.Exponential(\"lambda_2\", 1) # prior on second behaviour\n", - "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=10) # prior on behaviour change\n", - "\n", - "print \"lambda_1.value = %.3f\" % lambda_1.value\n", - "print \"lambda_2.value = %.3f\" % lambda_2.value\n", - "print \"tau.value = %.3f\" % tau.value\n", - "print\n", - "\n", - "lambda_1.random(), lambda_2.random(), tau.random()\n", - "\n", - "print \"After calling random() on the variables...\"\n", - "print \"lambda_1.value = %.3f\" % lambda_1.value\n", - "print \"lambda_2.value = %.3f\" % lambda_2.value\n", - "print \"tau.value = %.3f\" % tau.value" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The call to `random` stores a new value into the variable's `value` attribute. In fact, this new value is stored in the computer's cache for faster recall and efficiency." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### **Warning**: *Don't update stochastic variables' values in-place.*\n", - "\n", - "\n", - "Straight from the PyMC docs, we quote [4]:\n", - "\n", - "> `Stochastic` objects' values should not be updated in-place. This confuses PyMC's caching scheme... The only way a stochastic variable's value should be updated is using statements of the following form:\n", - "\n", - " A.value = new_value\n", - "\n", - "> The following are in-place updates and should **never** be used:\n", - "\n", - " \n", - " A.value += 3\n", - " A.value[2,1] = 5\n", - " A.value.attribute = new_attribute_value\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Deterministic variables\n", - "\n", - "Since most variables you will be modeling are stochastic, we distinguish deterministic variables with a `pymc.deterministic` wrapper. (If you are unfamiliar with Python wrappers (also called decorators), that's no problem. Just prepend the `pymc.deterministic` decorator before the variable declaration and you're good to go. No need to know more. ) The declaration of a deterministic variable uses a Python function:\n", - "\n", - " @pm.deterministic\n", - " def some_deterministic_var(v1=v1,):\n", - " #jelly goes here.\n", - "\n", - "For all purposes, we can treat the object `some_deterministic_var` as a variable and not a Python function. \n", - "\n", - "Prepending with the wrapper is the easiest way, but not the only way, to create deterministic variables: elementary operations, like addition, exponentials etc. implicitly create deterministic variables. For example, the following returns a deterministic variable:" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "pymc.PyMCObjects.Deterministic" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "type(lambda_1 + lambda_2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The use of the `deterministic` wrapper was seen in the previous chapter's text-message example. Recall the model for $\\lambda$ looked like: \n", - "\n", - "$$\n", - "\\lambda = \n", - "\\begin{cases}\n", - "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", - "\\lambda_2 & \\text{if } t \\ge \\tau\n", - "\\end{cases}\n", - "$$\n", - "\n", - "And in PyMC code:" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "n_data_points = 5 # in CH1 we had ~70 data points\n", - "\n", - "\n", - "@pm.deterministic\n", - "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", - " out = np.zeros(n_data_points)\n", - " out[:tau] = lambda_1 # lambda before tau is lambda1\n", - " out[tau:] = lambda_2 # lambda after tau is lambda2\n", - " return out" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. \n", - "\n", - "Inside the deterministic decorator, the `Stochastic` variables passed in behave like scalars or Numpy arrays (if multivariable), and *not* like `Stochastic` variables. For example, running the following:\n", - "\n", - " @pm.deterministic\n", - " def some_deterministic(stoch=some_stochastic_var):\n", - " return stoch.value**2\n", - "\n", - "\n", - "will return an `AttributeError` detailing that `stoch` does not have a `value` attribute. It simply needs to be `stoch**2`. During the learning phase, it's the variable's `value` that is repeatedly passed in, not the actual variable. \n", - "\n", - "Notice in the creation of the deterministic function we added defaults to each variable used in the function. This is a necessary step, and all variables *must* have default values. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Including observations in the Model\n", - "\n", - "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" " - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%matplotlib inline\n", - "from IPython.core.pylabtools import figsize\n", - "from matplotlib import pyplot as plt\n", - "figsize(12.5, 4)\n", - "\n", - "\n", - "samples = [lambda_1.random() for i in range(20000)]\n", - "plt.hist(samples, bins=70, normed=True, histtype=\"stepfilled\")\n", - "plt.title(\"Prior distribution for $\\lambda_1$\")\n", - "plt.xlim(0, 8);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n", - "\n", - "PyMC stochastic variables have a keyword argument `observed` which accepts a boolean (`False` by default). The keyword `observed` has a very simple role: fix the variable's current value, i.e. make `value` immutable. We have to specify an initial `value` in the variable's creation, equal to the observations we wish to include, typically an array (and it should be an Numpy array for speed). For example:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "value: [10 5]\n", - "calling .random()\n", - "value: [10 5]\n" - ] - } - ], - "source": [ - "data = np.array([10, 5])\n", - "fixed_variable = pm.Poisson(\"fxd\", 1, value=data, observed=True)\n", - "print \"value: \", fixed_variable.value\n", - "print \"calling .random()\"\n", - "fixed_variable.random()\n", - "print \"value: \", fixed_variable.value" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is how we include data into our models: initializing a stochastic variable to have a *fixed value*. \n", - "\n", - "To complete our text message example, we fix the PyMC variable `observations` to the observed dataset. " - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[10 25 15 20 35]\n" - ] - } - ], - "source": [ - "# We're using some fake data here\n", - "data = np.array([10, 25, 15, 20, 35])\n", - "obs = pm.Poisson(\"obs\", lambda_, value=data, observed=True)\n", - "print obs.value" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Finally...\n", - "\n", - "We wrap all the created variables into a `pm.Model` class. With this `Model` class, we can analyze the variables as a single unit. This is an optional step, as the fitting algorithms can be sent an array of the variables rather than a `Model` class. I may or may not use this class in future examples ;)" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "model = pm.Model([obs, lambda_, lambda_1, lambda_2, tau])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Modeling approaches\n", - "\n", - "A good starting point in Bayesian modeling is to think about *how your data might have been generated*. Put yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n", - "\n", - "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n", - "\n", - "1. We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n", - "\n", - "2. Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n", - "\n", - "3. Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the latter behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n", - "\n", - "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n", - "\n", - "5. Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n", - "\n", - " What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n", - "\n", - "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n", - "\n", - "\n", - "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n", - "\n", - "\n", - "\n", - "\n", - "PyMC, and other probabilistic programming languages, have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [5]:\n", - "\n", - "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Same story; different ending.\n", - "\n", - "Interestingly, we can create *new datasets* by retelling the story.\n", - "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n", - "\n", - "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "53\n" - ] - } - ], - "source": [ - "tau = pm.rdiscrete_uniform(0, 80)\n", - "print tau" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from an $\\text{Exp}(\\alpha)$ distribution:" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "22.3473316377 22.00741773\n" - ] - } - ], - "source": [ - "alpha = 1. / 20.\n", - "lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n", - "print lambda_1, lambda_2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "3\\. For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "4\\. Plot the artificial dataset:" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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ERETqFnXUmkqCi1s/8zCzMjP7yMzuNLOCuhY2s4PNbKqZLTSz+WZ2ZVjexcxe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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.bar(np.arange(80), data, color=\"#348ABD\")\n", - "plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n", - "plt.xlabel(\"Time (days)\")\n", - "plt.ylabel(\"count of text-msgs received\")\n", - "plt.title(\"Artificial dataset\")\n", - "plt.xlim(0, 80)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. PyMC's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability. \n", - "\n", - "\n", - "The ability to generate artificial datasets is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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7IHBRRJxM0R1lPfAHbSmhpJ421oM5vHhKkqa3Ks5ydvL3SDN3R/kOEA0meU9w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\nlXc8vbY93WY6xn86bnMzxov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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def plot_artificial_sms_dataset():\n", - " tau = pm.rdiscrete_uniform(0, 80)\n", - " alpha = 1. / 20.\n", - " lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n", - " data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]\n", - " plt.bar(np.arange(80), data, color=\"#348ABD\")\n", - " plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n", - " plt.xlim(0, 80)\n", - "\n", - "figsize(12.5, 5)\n", - "plt.suptitle(\"More examples of artificial datasets\", fontsize=14)\n", - "for i in range(1, 5):\n", - " plt.subplot(4, 1, i)\n", - " plot_artificial_sms_dataset()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Later we will see how we use this to make predictions and test the appropriateness of our models." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Bayesian A/B testing\n", - "\n", - "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n", - "\n", - "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n", - "\n", - "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n", - "\n", - "### A Simple Case\n", - "\n", - "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n", - "\n", - "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n", - "\n", - "- fraction of users who make purchases, \n", - "- frequency of social attributes, \n", - "- percent of internet users with cats etc. \n", - "\n", - "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n", - "\n", - "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n", - "\n", - "\n", - "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n", - "\n", - "To set up a Bayesian model, we need to assign prior distributions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over [0,1]:" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import pymc as pm\n", - "\n", - "# The parameters are the bounds of the Uniform.\n", - "p = pm.Uniform('p', lower=0, upper=1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Had we had stronger beliefs, we could have expressed them in the prior above.\n", - "\n", - "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if $X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data." - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[False False False False ..., False False False False]\n", - "86\n" - ] - } - ], - "source": [ - "# set constants\n", - "p_true = 0.05 # remember, this is unknown.\n", - "N = 1500\n", - "\n", - "# sample N Bernoulli random variables from Ber(0.05).\n", - "# each random variable has a 0.05 chance of being a 1.\n", - "# this is the data-generation step\n", - "occurrences = pm.rbernoulli(p_true, N)\n", - "\n", - "print occurrences # Remember: Python treats True == 1, and False == 0\n", - "print occurrences.sum()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The observed frequency is:" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "What is the observed frequency in Group A? 0.0573\n", - "Does this equal the true frequency? False\n" - ] - } - ], - "source": [ - "# Occurrences.mean is equal to n/N.\n", - "print \"What is the observed frequency in Group A? %.4f\" % occurrences.mean()\n", - "print \"Does this equal the true frequency? %s\" % (occurrences.mean() == p_true)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We combine the observations into the PyMC `observed` variable, and run our inference algorithm:" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 18000 of 18000 complete in 1.0 sec" - ] - } - ], - "source": [ - "# include the observations, which are Bernoulli\n", - "obs = pm.Bernoulli(\"obs\", p, value=occurrences, observed=True)\n", - "\n", - "# To be explained in chapter 3\n", - "mcmc = pm.MCMC([p, obs])\n", - "mcmc.sample(18000, 1000)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We plot the posterior distribution of the unknown $p_A$ below:" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n", - "plt.vlines(p_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", - "plt.hist(mcmc.trace(\"p\")[:], bins=25, histtype=\"stepfilled\", normed=True)\n", - "plt.legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n", - "\n", - "### *A* and *B* Together\n", - "\n", - "A similar analysis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using PyMC's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (significantly less than $N_A$) and we will simulate site B's data like we did for site A's data )" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Obs from Site A: [0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] ...\n", - "Obs from Site B: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n" - ] - } - ], - "source": [ - "import pymc as pm\n", - "figsize(12, 4)\n", - "\n", - "# these two quantities are unknown to us.\n", - "true_p_A = 0.05\n", - "true_p_B = 0.04\n", - "\n", - "# notice the unequal sample sizes -- no problem in Bayesian analysis.\n", - "N_A = 1500\n", - "N_B = 750\n", - "\n", - "# generate some observations\n", - "observations_A = pm.rbernoulli(true_p_A, N_A)\n", - "observations_B = pm.rbernoulli(true_p_B, N_B)\n", - "print \"Obs from Site A: \", observations_A[:30].astype(int), \"...\"\n", - "print \"Obs from Site B: \", observations_B[:30].astype(int), \"...\"" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0533333333333\n", - "0.04\n" - ] - } - ], - "source": [ - "print observations_A.mean()\n", - "print observations_B.mean()" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 20000 of 20000 complete in 1.9 sec" - ] - } - ], - "source": [ - "# Set up the pymc model. Again assume Uniform priors for p_A and p_B.\n", - "p_A = pm.Uniform(\"p_A\", 0, 1)\n", - "p_B = pm.Uniform(\"p_B\", 0, 1)\n", - "\n", - "\n", - "# Define the deterministic delta function. This is our unknown of interest.\n", - "@pm.deterministic\n", - "def delta(p_A=p_A, p_B=p_B):\n", - " return p_A - p_B\n", - "\n", - "# Set of observations, in this case we have two observation datasets.\n", - "obs_A = pm.Bernoulli(\"obs_A\", p_A, value=observations_A, observed=True)\n", - "obs_B = pm.Bernoulli(\"obs_B\", p_B, value=observations_B, observed=True)\n", - "\n", - "# To be explained in chapter 3.\n", - "mcmc = pm.MCMC([p_A, p_B, delta, obs_A, obs_B])\n", - "mcmc.sample(20000, 1000)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we plot the posterior distributions for the three unknowns: " - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "p_A_samples = mcmc.trace(\"p_A\")[:]\n", - "p_B_samples = mcmc.trace(\"p_B\")[:]\n", - "delta_samples = mcmc.trace(\"delta\")[:]" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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95eGiGkmN75sbdHjFB2d9cvdjr3iNpXTnnmSvbatLy13F/s+u3Pyfr4z10j61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\nKtV4vLQZrvwJAInt/O3bt/sdAxDL3hMTjW1i6dKlnGPRStGsYw4AAAD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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 10)\n", - "\n", - "# histogram of posteriors\n", - "\n", - "ax = plt.subplot(311)\n", - "\n", - "plt.xlim(0, .1)\n", - "plt.hist(p_A_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", - " label=\"posterior of $p_A$\", color=\"#A60628\", normed=True)\n", - "plt.vlines(true_p_A, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", - "plt.legend(loc=\"upper right\")\n", - "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n", - "\n", - "ax = plt.subplot(312)\n", - "\n", - "plt.xlim(0, .1)\n", - "plt.hist(p_B_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", - " label=\"posterior of $p_B$\", color=\"#467821\", normed=True)\n", - "plt.vlines(true_p_B, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n", - "plt.legend(loc=\"upper right\")\n", - "\n", - "ax = plt.subplot(313)\n", - "plt.hist(delta_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", - " label=\"posterior of delta\", color=\"#7A68A6\", normed=True)\n", - "plt.vlines(true_p_A - true_p_B, 0, 60, linestyle=\"--\",\n", - " label=\"true delta (unknown)\")\n", - "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n", - "plt.legend(loc=\"upper right\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$. \n", - "\n", - "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Probability site A is WORSE than site B: 0.088\n", - "Probability site A is BETTER than site B: 0.912\n" - ] - } - ], - "source": [ - "# Count the number of samples less than 0, i.e. the area under the curve\n", - "# before 0, represent the probability that site A is worse than site B.\n", - "print \"Probability site A is WORSE than site B: %.3f\" % \\\n", - " (delta_samples < 0).mean()\n", - "\n", - "print \"Probability site A is BETTER than site B: %.3f\" % \\\n", - " (delta_samples > 0).mean()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n", - "\n", - "Try playing with the parameters `true_p_A`, `true_p_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n", - "\n", - "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## An algorithm for human deceit\n", - "\n", - "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n", - "\n", - "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n", - "\n", - "### The Binomial Distribution\n", - "\n", - "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n", - "\n", - "$$P( X = k ) = {{N}\\choose{k}} p^k(1-p)^{N-k}$$\n", - "\n", - "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$), and $p$ is the probability of a single event. The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. " - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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W6zj+EXFXRBwcEQdGxNfSeV9Ok34i4pKIODQi3h0RH4iIpen8X6Tzj4iIoyLi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\nWZKbeB+PiGgtI6kfyfCeE0l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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "\n", - "import scipy.stats as stats\n", - "binomial = stats.binom\n", - "\n", - "parameters = [(10, .4), (10, .9)]\n", - "colors = [\"#348ABD\", \"#A60628\"]\n", - "\n", - "for i in range(2):\n", - " N, p = parameters[i]\n", - " _x = np.arange(N + 1)\n", - " plt.bar(_x - 0.5, binomial.pmf(_x, N, p), color=colors[i],\n", - " edgecolor=colors[i],\n", - " alpha=0.6,\n", - " label=\"$N$: %d, $p$: %.1f\" % (N, p),\n", - " linewidth=3)\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.xlim(0, 10.5)\n", - "plt.xlabel(\"$k$\")\n", - "plt.ylabel(\"$P(X = k)$\")\n", - "plt.title(\"Probability mass distributions of binomial random variables\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n", - "\n", - "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Cheating among students\n", - "\n", - "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n", - "\n", - "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n", - "\n", - "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n", - "\n", - "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use PyMC to dig through this noisy model, and find a posterior distribution for the true frequency of liars. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in PyMC. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior." - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import pymc as pm\n", - "\n", - "N = 100\n", - "p = pm.Uniform(\"freq_cheating\", 0, 1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. " - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "true_answers = pm.Bernoulli(\"truths\", p, size=N)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*." - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[False False False True False False False True False True True True\n", - " False False True True True True False False True False False False\n", - " False False False True False True True True False True True True\n", - " True True False False True True True True False True False False\n", - " True False False False True True True True True False True False\n", - " False False True False False True True False True True True False\n", - " False True True True False True False True False False True False\n", - " False True True False False True False True True True True True\n", - " True False False True]\n" - ] - } - ], - "source": [ - "first_coin_flips = pm.Bernoulli(\"first_flips\", 0.5, size=N)\n", - "print first_coin_flips.value" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "second_coin_flips = pm.Bernoulli(\"second_flips\", 0.5, size=N)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. We do this using a PyMC `deterministic` variable:" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "@pm.deterministic\n", - "def observed_proportion(t_a=true_answers,\n", - " fc=first_coin_flips,\n", - " sc=second_coin_flips):\n", - "\n", - " observed = fc * t_a + (1 - fc) * sc\n", - " return observed.sum() / float(N)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, produces a proportion. " - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.29999999999999999" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "observed_proportion.value" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expect to see approximately 3/4 of all responses be \"Yes\". \n", - "\n", - "The researchers observe a Binomial random variable, with `N = 100` and `p = observed_proportion` with `value = 35`: " - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "X = 35\n", - "\n", - "observations = pm.Binomial(\"obs\", N, observed_proportion, observed=True,\n", - " value=X)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 40000 of 40000 complete in 10.4 sec" - ] - } - ], - "source": [ - "model = pm.Model([p, true_answers, first_coin_flips,\n", - " second_coin_flips, observed_proportion, observations])\n", - "\n", - "# To be explained in Chapter 3!\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(40000, 15000)" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 3)\n", - "p_trace = mcmc.trace(\"freq_cheating\")[:]\n", - "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n", - " label=\"posterior distribution\", color=\"#348ABD\")\n", - "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)\n", - "plt.xlim(0, 1)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.05 to 0.35 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n", - "\n", - "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with a uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n", - "\n", - "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Alternative PyMC Model\n", - "\n", - "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n", - "\n", - "\\begin{align}\n", - "P(\\text{\"Yes\"}) &= P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\\\\\n", - "& = \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\\\\\n", - "& = \\frac{p}{2} + \\frac{1}{4}\n", - "\\end{align}\n", - "\n", - "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In PyMC, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "p = pm.Uniform(\"freq_cheating\", 0, 1)\n", - "\n", - "\n", - "@pm.deterministic\n", - "def p_skewed(p=p):\n", - " return 0.5 * p + 0.25" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I could have typed `p_skewed = 0.5*p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a `deterministic` variable, but I wanted to make the deterministic boilerplate explicit for clarity's sake. \n", - "\n", - "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n", - "\n", - "This is where we include our observed 35 \"Yes\" responses. In the declaration of the `pm.Binomial`, we include `value = 35` and `observed = True`." - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "yes_responses = pm.Binomial(\"number_cheaters\", 100, p_skewed,\n", - " value=35, observed=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 25000 of 25000 complete in 1.3 sec" - ] - } - ], - "source": [ - "model = pm.Model([yes_responses, p_skewed, p])\n", - "\n", - "# To Be Explained in Chapter 3!\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(25000, 2500)" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 3)\n", - "p_trace = mcmc.trace(\"freq_cheating\")[:]\n", - "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n", - " label=\"posterior distribution\", color=\"#348ABD\")\n", - "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.2)\n", - "plt.xlim(0, 1)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### More PyMC Tricks\n", - "\n", - "#### Protip: *Lighter* deterministic variables with `Lambda` class\n", - "\n", - "Sometimes writing a deterministic function using the `@pm.deterministic` decorator can seem like a chore, especially for a small function. I have already mentioned that elementary math operations *can* produce deterministic variables implicitly, but what about operations like indexing or slicing? Built-in `Lambda` functions can handle this with the elegance and simplicity required. For example, \n", - "\n", - " beta = pm.Normal(\"coefficients\", 0, size=(N, 1))\n", - " x = np.random.randn((N, 1))\n", - " linear_combination = pm.Lambda(lambda x=x, beta=beta: np.dot(x.T, beta))\n", - "\n", - "\n", - "#### Protip: Arrays of PyMC variables\n", - "There is no reason why we cannot store multiple heterogeneous PyMC variables in a Numpy array. Just remember to set the `dtype` of the array to `object` upon initialization. For example:\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "N = 10\n", - "x = np.empty(N, dtype=object)\n", - "for i in range(0, N):\n", - " x[i] = pm.Exponential('x_%i' % i, (i + 1) ** 2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The remainder of this chapter examines some practical examples of PyMC and PyMC modeling:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "##### Example: Challenger Space Shuttle Disaster \n", - "\n", - "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Temp (F), O-Ring failure?\n", - "[[ 66. 0.]\n", - " [ 70. 1.]\n", - " [ 69. 0.]\n", - " [ 68. 0.]\n", - " [ 67. 0.]\n", - " [ 72. 0.]\n", - " [ 73. 0.]\n", - " [ 70. 0.]\n", - " [ 57. 1.]\n", - " [ 63. 1.]\n", - " [ 70. 1.]\n", - " [ 78. 0.]\n", - " [ 67. 0.]\n", - " [ 53. 1.]\n", - " [ 67. 0.]\n", - " [ 75. 0.]\n", - " [ 70. 0.]\n", - " [ 81. 0.]\n", - " [ 76. 0.]\n", - " [ 79. 0.]\n", - " [ 75. 1.]\n", - " [ 76. 0.]\n", - " [ 58. 1.]]\n" - ] - }, - { - "data": { - "text/plain": [ - "Text(0.5,1,u'Defects of the Space Shuttle O-Rings vs temperature')" - ] - }, - "execution_count": 53, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 3.5)\n", - "np.set_printoptions(precision=3, suppress=True)\n", - "challenger_data = np.genfromtxt(\"data/challenger_data.csv\", skip_header=1,\n", - " usecols=[1, 2], missing_values=\"NA\",\n", - " delimiter=\",\")\n", - "# drop the NA values\n", - "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n", - "\n", - "# plot it, as a function of temperature (the first column)\n", - "print \"Temp (F), O-Ring failure?\"\n", - "print challenger_data\n", - "\n", - "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n", - " alpha=0.5)\n", - "plt.yticks([0, 1])\n", - "plt.ylabel(\"Damage Incident?\")\n", - "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n", - "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n", - "\n", - "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n", - "\n", - "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n", - "\n", - "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$." - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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84FvAiVHZD9MP1QFWW17wd8DHJMnpmELuEk469YmfSB4BvIT5x+E5P5H8rpNO\n1cYcWrtFF9zdihmB488ba1IshBD5anO4Nq11PXA+psUkhRl94l2l1G+VUsdFq10K/FwpNRvzx/JM\n3VZTtBCiqIWuPSd07RtD1x4BfBPTB/kNoB9wCuaCvYWWF/zF8oKjLC8oizHcTuWkUwswk6p8DFjA\nFD+RHBBvVB3yA+B7wJeYUYWEEEKQ4wQfWuspmCHYMh+7JuP+e8BBhQ1NCFEsQtf+GHOR1s2WF+wI\nnIw5e7QPcGZUllheMBEzUcZrG9v01E46Nd9PJG1My/FBwN/9RHK0k04VrFtJV6go9xOsn8jj2soq\nR2ZIFEKISE4TfAghRJPQteeFrn1T6Nr7YvrdXgu8D2yBmVL4VWCO5QW/sbxglxhDLTgnnZqH6Tb2\nBWZ67if9RLJPnDG1w0XATpghN6tijkUIIYqKJMZCiHYLXfuD0LV/CwzHtB7fjBnH/JvANcAHlhe8\nbnnB+ZYXbB5jqAXjpFMfYpLjxZjuCBP9RLJbdCOpKPeHsr7rxEWVVc66OOMRQohiI4mxEKLDQtfW\noWvPCl3bBbbHjGX+V8xoFvtjZpL7wvKCxy0v+EF374/spFMpzDEuw/TXvaubTB99IzAAqK6scl6I\nOxghhCg2khgLIQoqdO2G0LWnhq59JrAVZiSLZzEjIJwATAbmW15wi+UFe7a8peLmpFNvYWYTrAN+\nDlwWb0Stqyj3D8DMcrcWc8G0EEKIZiQxFkJ0mtC1V4eu/Wjo2sdgWpIvx4xusyVwCfDWPfP67WZ5\nwbmWFwxqbVvFyEmnXgNOjxZv8hPJE+OMpyXR8GxNM9z9obLKmRtnPEIIUawkMRZCdInQtT8LXfv3\nwO6YaeWrgJpFa0v7A3/GdLX4i+UFB0eTjXQLTjr1OCbhB3jQTyQPiDOeFhwKHAwsB25oY10hhOix\nJDEWQnSpqD/yG6FrnwcMPXrLuo+BFzHjI58J/BtIWV5wSTe6YO8m4D7M5EaT/URyx3jD+ZqmC+5u\nr6xyuu3EJEII0dkkMRZCxCZ07TUjNlm3LHTtI4CdMa2ZXwC7ArcAn1le8JDlBYcUcyuyk05pzFB1\n/8R0E/mHn0huEm9URkW5vz/mQsEVmIsghRBCtEASYyFEUYhm2rsS0xf5eMwFe72BH2Mm1XjH8oJf\nWl5QFAlnc046tQ4zffZ7mOHrHi+SYdwqotu7K6ucZbFGIoQQRS6nme+EEKKrhK5dD1QD1dEsez8H\nzsYkm7eya67uAAAgAElEQVQDN1he8DBwd+jas2ILNAsnnarxE8nRwGuYsY5vBi6MK56Kcn8v4Dhg\nDetnuxNCbBy+A1wPDI47kFwdccQRSWBGJ+6iBrgaM9FUu0iLsRCiaEWz7FVgWpFPwHRV6IdJlmda\nXvCq5QU/trwgEWecmaLZ8Y4H1gG/9BNJJ8Zwroxu762schbFGIcQovC6VVLcRQZj6qXdJDEWQhS9\n0LXXha79t9C1j8RMQ307pmVgJPAQ8KnlBZWWF2wXZ5xNomHcLooW7/MTyT26OoaKcn9X4GRMgu51\n9f6FEJ1OkuLsOlQvkhgLIbqVaBrqi4BtMS3Hs4AhmNbReZYXTCySId+qgAcxLdxP+IlkV/8RuxxQ\nwITKKmd+F+9bCCG6JUmMhRDdUujaq0LXvg/YFzNG72PRUydhhnz7j+UFZ1le0CeO+KKRKv4PeAvY\nBfhLV00bXVHu74iZeKQBMw20EEKIHEhiLITo1qJxkV8JXftUYEegElgMfBsYD3xiecFvLS/Yuqtj\nc9Kp1Zi+0TXADwG3i3b9K8wU3H5llfNRF+1TCCG6PUmMhRAbjdC154eufRXmYr0zgZmYbhZXA/+z\nvGCC5QXf7sqYnHRqDuunjb7BTyTtztxfRbm/DfAzQCOz3Akhusi0adP6TZw4cdD06dP75vO6hoYG\nfvazn32js+LKlyTGQoiNTujadaFr/xXYDzgMeBIoA36KGc1imuUFx1le0CW/gU469XdMS3YJ8Kif\nSHbmRYKXYsZ//ltllfNeJ+5HCCEAmDx58sChQ4fWn3zyybV33nnnkFxft3DhwtLrr79+q+nTpw/o\nzPjyIYmxEGKjFXWzeCl07R8B38KMZrESOBwzVnLK8oKxlhfk1cLRTtcCL2BasB/xE8nSQu+gotwf\nDIyNFscVevtCCNFcXV2dWrlyZcluu+22ds2aNWrZsmU5z5Gx1VZbNVx33XULBwwY0NiZMeZDJvgQ\nQvQIoWt/BFxkecG1mAlDLsJcFPcn4HeWF9wN3BW6dqeM9+ukUw1+IvljYDZwCGZGut8WeDdnAf2B\noLLK+U+Bty2EKFKWF+zXGdsNXfvNttZ5/vnnB4wePXrFI488MvjBBx/c/LLLLlvYGbF0FUmMhRA9\nSujaNcCtlhfcgZnC+VJgBHAN8GvLCx4Abgld+4NC79tJpxb7ieTpmJbja/1EMnDSqZcLse2Kcr8U\nuCBa/GMhtimEEG1ZuXJlyeDBgxvT6XTJ6tWrS5YsWdILYMaMGX2mTJkyKHPd0tLSXg0NDVuWl5cv\nHTJkSEM8EbdOEmMhRI8UTT39qOUFj2FacC8FfoAZG/kcywuqAS907XZPLZqNk05N9RPJ32PGGX7Y\nTyS/7aRTywuw6WOAbwLzgKcLsD0hRDeRS8tuZzvrrLOW9+vXr3HWrFl9TznllJoRI0bUjRgxoi5z\nndra2s0HDRpU1LNw5pQYK6WOxvTNKwXu01p/bVxMpdTJwHWYK6Fna61PK2CcQgjRKULX1sBLwEuW\nF+wKXIK5SO944HjLC14BbgKeDl27UP3grgFsYH/gXj+RPCka97gjfhnd3lVZ5RRlS4wQYuPS0NBA\nbW3tV9dLzJ49u+8+++yzGlpvMR47duzSrbbaqih/p9pMjJVSpcBdwJHAfCBUSk3WWr+Xsc7OwBXA\nQVrr5UqpLTsrYCGE6CxR94mxUT/kC4DzgIMwF+q9b3nBTcDDoWuv7ch+nHRqnZ9InoYZTu4E4Bzg\n3vZur6LcT2J+o1cD93ckNiGEyNXMmTP7zJs3rzfA4sWLS+fOnZsYN27cAoBcWoxrampKbrvtti3m\nzp3b57rrrtvq4osvXjx48OBYL8TLZVSK/YE5WuuPtNZrgUeBMc3W+Tlwl9Z6OYDWuqibyYUQojWh\nay8IXbsCMx7yxcCnwG6YCUM+srzgYssLOjS8kJNOzcXMjAdwu59IDu/A5s6Pbh+srHIK0S1DCCHa\n9P777/c544wzlo0fP37TSZMmDZ4wYcIn+bx+8ODBjddee+2ipUuXzr7uuusWxp0UAyitWz97p5Q6\nEThaa31OtHw6cIDW+vyMdZ4C/otpWSkFrtNaP5tlW+cC5wJMmjRp97KysncLdSB5SgKpmPbdHUl9\n5UfqKz9FX1/1GjWrpmzT15f3Hrp8XUkfgESJbth70LpFIzdbu2hgL13f3m2nb35wx4Y33t1cDd1i\nTZ+bfplSid5tdanYoL7WrdWls19cs1djIyW7j0y8239waV0rr+2Jiv7zVWSkvvITW30dccQRyTj2\nm+kf//hH6ejRo3PuEtHY2NinpKSk03+jpk2b9rX3ZMCAAYwaNWpEW6/NJTE+CTiqWWK8v9b6gox1\nngbWAScD2wH/BvbQWn/Z0nanTp06I5cAO0N1dfWMMWPGxLLv7kjqKz9SX/npTvUVTQhyLObCuYOi\nh9dgukHcHLr2p/lu008kBwJvAjsDdzjp1C9bW795fVWU+xcDfwCmVlY53813/xu77vT5KgZSX/mJ\nub5mxLTfr0yfPr3vyJEj1+S6fm1tbXLQoEFd8Y/E196TXPPOXLpSzAcyp+rbDvg8yzrVWut1WuuP\ngQ8wP/JCCLHRCF27MXTtp0PXPhgzksU/gL6YC98+srxgfHQBX86cdGoF4AD1wAV+Ivm9XF8bDdHW\ndPbujnz2K4QQHZVPUtxd5JIYh8DOSqlhSqnewKnA5GbrPAUcAaCU2gIzaP5HhQxUCCGKSejaL4eu\n/X1gb8DH/J6ehZlNb5LlBfvmui0nnXoTMzMewF/8RHKzHF8qQ7QJIUQBtZkYa63rMS0Sz2H60UzU\nWr+rlPqtUuq4aLXngKVKqfeAaYCrtV7aWUELIUSxCF37rdC1TwN2Be7BdCs7EXjT8oJnLC84OMdN\n3QS8CmwDVPmJpMrhNU3dLu6UIdqEEKLjcmkxRms9RWu9i9Z6J611ZfTYNVrrydF9rbW+RGs9XGu9\np9b60c4MWgghik3o2nNC1x6LacH9A7AKOBr4t+UF/7K84HuWF7SY7DrpVD1wRvS6kzHdK1pUUe4P\nZ/0QbeMLcxRCCNGz5ZQYCyGEyE3o2p+Frn0psANwPfAlcCjmzNoblhccH13E9zXREG4XRYt3+4nk\nN7KtF2nqW/yADNEmhBCFIYmxEEJ0gtC1l4aufQ0mQb4CWIy5UvpJ4C3LCxzLC0qzvPR+4O/AYGCC\nn0h+7Xe6otwfjGldBrizM+IXQoieSBJjIYToRKFr14aufSOwI6ZP8Hxgd+ARzIV6Z1leUNa0fjQ1\n9M8xibTN+n7Emc4A+gPTKqucuMaDF0KIjY4kxkII0QVC114duvYdwE6YxPcjzLCW44E5lhecZ3lB\nHwAnnVoYrQNwo59I7t60nWjs+fJo8e4uCl8IIXoESYyFEKILha69NnTt+zCjWJyOGe1ne+Au1k83\n3d9Jp6ox3SoSwEN+ItkboGZx40DMbFtfANVxHIMQQjQ3bdq0fhMnThw0ffr0vrm+Zs2aNerOO+/c\nfMKECZuceOKJO9bU1MSel8YegBBC9ESha9eHrv0QsAdmeLdZwFDMiBYfW15w+av26GuAj4FvA1cD\nLPxk3ZBoE/dWVjnruj5yIYTY0OTJkwcOHTq0/uSTT6698847h7T9CuOll17q/8ILLww688wzv1yx\nYkXp008/PbAz48yFJMZCCBGjaDa9J4B9gR8AbwBDgBtes4995/njT3tRgwau/NOuJxxbs7RxE6AB\nMw21EELEqq6uTq1cubJkt912W7tmzRq1bNmyXrm+9sgjj1x53333fQKwZMmSXgcffPDqzos0NzkH\nL4QQovOErq2Bpy0v+AfwXeAq4NB3Rhx01uYLv1i73/RpvddsvvWDaBQwubLKmR9rwEKIouEnkvt1\nxnajWTlb9fzzzw8YPXr0ikceeWTwgw8+uPlll122MNftl5SUsG7dOnXttddudfrppy/ZYYcdYj8L\nJomxEEIUkShBfgF4wfKCQ4GrXv7emCO3/+h9anbaczOAmkSvx2INUgghIitXriwZPHhwYzqdLlm9\nenXJkiVLegHMmDGjz5QpUwZlrltaWtqroaFhy/Ly8qVDhgxpANhmm23qf/Ob3yw86qijdtp1113T\nxxxzzMo4jqOJJMZCCFGkQtd+Cfie5QUHzjz2tPu3Uf2H965ZyhcDSx6Mppq+KXTtT+OOUwgRr1xa\ndjvbWWedtbxfv36Ns2bN6nvKKafUjBgxom7EiBF1mevU1tZuPmjQoEWZjzU2NlJSUsIuu+xS99BD\nD20mibEQQohWha79WkX5wk+B4Zu9/ybfm/9B2QMXVJy/tk/fsZYXTABuDF37o5jDFEL0MA0NDdTW\n1n41UdHs2bP77rPPPquh9RbjsWPHLt1qq60aLr/88q3T6XTJrbfe+vmiRYt67bHHHmu6+hiak8RY\nCCGKXEW5/y3gKLSu23TN542lNcv7jX5s/MdP/vQXO2LGOz7b8oKHgRtC134/1mCFED3GzJkz+8yb\nN683wOLFi0vnzp2bGDdu3AKAXFqMf/KTnyx/6aWX+t92222b9+7dW19xxRWLiJkkxkIIUfzGAqDU\no/3HjrHqfn3HTsM+fG/Yifffdt7jP7voAOAnmNnwTre8YCJQGbr22zHGK4ToAd5///0+Z5xxxrLx\n48dvWldXpyZMmPBJPq/fY4890nvssUc6WlzaCSHmTYZrE0KIIlZR7vcFzo4W7y4Ztm0dcAXA9h9/\n+JtLrvrFr4BdgHuAeuAU4C3LC56yvMCKI2YhRM9QUlKihw8fvvbss89eft555y3r27evjjumjpLE\nWAghittJwGbAm5VVThg99kdgGma843svueoXH4euPRYz3fQdQB0wBnjD8oJnowv1hBCioIYNG7Y2\n7hgKTRJjIYQobudFt3c3PeCkU43AmUAtcBxwFkDo2p+Grv1LYEfgJmAVcBTwb8sLXrS84EjLC1TX\nhS6E2JiNHDky9ovlCk0SYyGEKFIV5f6+wAHAl8Cjmc856dQnwC+ixdv9RPKbTc+Frr0wdO1fAzsA\nvwVqgMOA54HXLC8YY3mB/P4LIUQz8sMohBDF64Lo9i+VVU62qVIfBiYBA4AH/ESyNPPJ0LWXhq59\nLSZBrgCWAPsDTwGzLS84zfICuQhbCCEikhgLIUQRqij3twROAzRwV7Z1nHRKA+XAF8BBgJttvdC1\na0LXHodJkC8CPgP2wCTW71tecI7lBYmCH4QQQnQzkhgLIURx+jnQG3i6ssqZ29JKTjq1lKiPMfBb\nP5Hcp6V1Q9deHbr27ZiL9M4FPoru3wvMtbzgIssL+hfqAIQQoruRxFgIIYpMRblfxvqL7v7Y1vpO\nOvUcplW5DHjITyT7tLZ+6Nrp0LXvBXYFfgy8A2wL3Ar8z/KCqy0v2LQDhyCEEN1STomxUupopdQH\nSqk5SqnLW1nvRKWUVkqNKFyIQgjR4/wI2AZIAVNzfM2vgP8Cw4FxubwgdO360LUfAfbGDO/2OrA5\n5oK9TywvuMnygqF5xi6EEN1Wm4mxUqoU0xJxDOYH11FKDc+y3kDgl5gfViGEEO3XdNHdHZVVTk4D\n5jvp1GrMDHgNwMV+InlUrjsLXbsxdO3JwEjABl7AXNDnAvMsL/iz5QU753MAQgjRHeXSYrw/MEdr\n/ZHWei1myKAxWda7HjNuZl2W54QQQuSgotzfD3MhXQ3wYD6vddKpELg2Wvyrn0hulc/rQ9fWoWtP\nC137e5jf/r9humecC3xgecFEywv2y2ebQoieYdq0af0mTpw4aPr06X07cz+vv/5638bGRt55553E\nypUrCz4uu9K69cYIpdSJwNFa63Oi5dOBA7TW52essw9wldb6BKXUi8BlWusZWbZ1LuYHlkmTJu1e\nVlb2bsGOJD9JzClKkRupr/xIfeVH6ivDhzPTOy5f2LD5kO1KFw7bIzE/yyqt1pduaCR9ddUujXM+\nHViS3LE2ce25H6qS9l9OsjBdknh5ae+tP1jZa/NGlALYrk9D7cjN1i7YpX/9ClX804XI5ys/Ul/5\nia2+jjjiiGQc+81m2rRpJTvuuKMeNmyYvvDCC3vffvvtWWfEa2xs7FNSUtKhBtQddtihX+/evfX5\n55+/7sILL6xvIZ6vvScDBgxg1KhRbXb1zWX8ymw/e19l00qpEswFG2e2tSGt9T3APQBTp06dkUuA\nnaG6unrGmDFjpB90jqS+8iP1lR+pr/WiIdo+BfTi+Q3fuahizEfN18mlvnznym2BtxpT8zZbc+qV\njzjp1B86Ete5gOUF2wIXA2Pn15UOmvR530HATMyZwsdD1876Bypu8vnKj9RXfmKur681QMahrq5O\nrVq1atDee+9ds2bNGrVgwYJhgwYN+tpvF0BtbW1y0KBBHfpHorKycrPzzjtvWWvrZHtPpk6dmlN9\n5dKMMB/4RsbydsDnGcsDMeNhvqiUmgccCEyWC/CEECJv57J+iLasf1hy4aRTn7F+CLcb/USyw90f\nQtf+LHTty4DtgauARcA+gA98aHnBBTLUmxA9z/PPPz9g9OjRKx555JHBP/rRj4ZddtllCztzfzNm\nzOj/6KOPDr7mmmvy6iqWq1xajENgZ6XUMMyg8KdiBp0HQGtdA2zRtNxaVwohhBDZRUO0lUeLbQ7R\n1hYnnZrsJ5J3AucDj/qJ5L5OOrWio9sNXXs5UGl5wS3AGcBlwM6YmK+zvOBu4M7QtTv1j6MQYr3o\n2oSCq6xy3mxrnZUrV5YMHjy4MZ1Ol6xevbpkyZIlvQBmzJjRZ8qUKYMy1y0tLe3V0NCwZXl5+dIh\nQ4Y0tCeme+6559NevXoxbty43k888cSgE044obY922lJm4mx1rpeKXU+8BxQCozXWr+rlPotMENr\nPbmQAQkhRA/VniHa2uIChwF7AneQQ5e3XIWuXQfcY3nB/cBxmOHiDsS0Jv/K8oKHgD+Erh3XtSRC\niC501llnLe/Xr1/jrFmz+p5yyik1I0aMqBsxYsQG/Ylra2s3HzRo0KLmr62trS3561//umnz694G\nDBjQePbZZy9vWr799ts3r6+vV5deeumSvn376lmzZvXt8sQYQGs9BZjS7LFrWlj38I6HJYQQPc4v\no9s/5jpEW1ucdKrOTyRPxfRF/KmfSL7gpFMPF2LbTULXbgCetLzgKcxoGpdiRi46Gzjb8oJngFuA\nIHTtghyXEGJDubTsdoaGhgZqa2tLm5Znz57dd5999lkNrbcYjx07dulWW231VYvxoEGDGi+44IKl\nbe1viy22qD/kkENWAcybN6/34YcfvrJwR2PklBgLIYToPBXl/gjgO7RjiLa2OOnUe34ieSHmwucq\nP5F8w0mnPizkPsAM9Qa8DLwcjXl8MaaF+piozLa84DbAD107Xej9CyG63syZM/vMmzevN8DixYtL\n586dmxg3btwCgHxajHN16qmn1owbN27LgQMHNmy77bbrfvjDHxa0tRgkMRZCiGLQNKPovZVVzqpO\n2P59wJHAScATfiI50kmnOmM/AISu/SFwnuUF1wD/h+nnvDfwF+D3UT/kqtC12/0HUggRv/fff7/P\nGWecsWz8+PGb1tXVqQkTJnzSmfsrLS3l6quv7tTfjfYPbimEEKLDKsr94cAJQBro0LBqLXHSKQ2c\ng5kyek/gT34i2ekjEIeuvSR07d8BO2BGyXgL2BK4DjPl9P2WF+zV2XEIITpHSUmJHj58+Nqzzz57\n+Xnnnbesb9++3b67lCTGQggRryui2/srq5wvOmsnTjpVi7nAr2nq6PM6a1/Nha6dDl17AvBtzJTT\nf8cMS3c2povFNMsLfmh5gZzFFKIbGTZsWNaJPLozSYyFECImFeX+TpjhL+sxE2V0Kiedehf4WbR4\nq59IjuzsfWbKmHL6OGBX4E5gJXA4ZvrpuZYX/Mrygs26Mi4hRPuMHDlyTdwxFJokxkIIEZ9fY36H\nH6qscv7XFTt00qlHgduBMmCSn0hu2RX7bS507Q9D174AM2nURcAczOQhvwfmW15wr+UF344jNiFE\nzyWJsRBCxKCi3P8GZtQGDdzQxbt3gVeAbTGTf8TWhSF07ZrQtW/HtCCPxoyZ3xfTJ3qm5QWvWF7w\nY8sLEnHFKIToOSQxFkKIeFyGabWdWFnl/Lcrd+ykU+swI1QsBI4AKrty/9mErt0YuvaU0LWPBnbD\nzKRXixnG7iHgU8sLbrC8YIc44xRCbNwkMRZCiC5WUe5vBZwbLY6LIwYnnfoCOBloAH7lJ5KnxBFH\nNqFrfxC69oWYmQDHYkazGIIZ1u5jywv+YXnBD+RiPdHD1cQdQJHqUL1IYiyEEF3vYqAPMLmyynkr\nriCcdOolTLcKgL929cV4bQlde1Xo2vdgRrM4CHgYWAccC0zGJMnXWl6wXYxhChGXq5HkuLkaTL20\nm/y3LYQQXaii3N8M+EW0GHsXBuA2TP/escBkP5E8wEmnPoo5pg1Es+q9CrxqecHFwE8xLe47Y8ZE\nvsbygqeBe4FnQ9eujytWIbrQq8CouIP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Y5KuBq7Op9CHAEkaGWhxT7B8A+E+AbCqdA/43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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12, 3)\n", - "\n", - "\n", - "def logistic(x, beta):\n", - " return 1.0 / (1.0 + np.exp(beta * x))\n", - "\n", - "x = np.linspace(-4, 4, 100)\n", - "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\")\n", - "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\")\n", - "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\")\n", - "plt.title(\"Logistic functon plotted for several value of $\\\\beta$ parameter\", fontsize=14)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n", - "\n", - "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n", - "\n", - "Some plots are below, with differing $\\alpha$." - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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ot4udIHofnbELeB+YFvvuog47kQIS+24mnW+mfhjIS4e22IfI5L8RThD1Qazu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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def logistic(x, beta, alpha=0):\n", - " return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n", - "\n", - "x = np.linspace(-4, 4, 100)\n", - "\n", - "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\", ls=\"--\", lw=1)\n", - "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\", ls=\"--\", lw=1)\n", - "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\", ls=\"--\", lw=1)\n", - "\n", - "plt.plot(x, logistic(x, 1, 1), label=r\"$\\beta = 1, \\alpha = 1$\",\n", - " color=\"#348ABD\")\n", - "plt.plot(x, logistic(x, 3, -2), label=r\"$\\beta = 3, \\alpha = -2$\",\n", - " color=\"#A60628\")\n", - "plt.plot(x, logistic(x, -5, 7), label=r\"$\\beta = -5, \\alpha = 7$\",\n", - " color=\"#7A68A6\")\n", - "\n", - "plt.title(\"Logistic functon with bias, plotted for several value of $\\\\alpha$ bias parameter\", fontsize=14)\n", - "plt.legend(loc=\"lower left\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n", - "\n", - "Let's start modeling this in PyMC. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Normal distributions\n", - "\n", - "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n", - "\n", - "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n", - "\n", - "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n", - "\n", - "We plot some different density functions below. " - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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dJjyZ+Dze0+Nx3KGly2tsIlRUVJS+cePGtHPPPffA7Nmzm/bs2bOkZcuWlZGm\nsXXr1vRA4bdZs2aVmzdvrrZ8uWLFioy77rqr3bp16zzHHntseVpampk6derazMzMOl8P0caSCBEF\nICIXOE9TRaQftoNDwEnA3lgHppRSSqm46QdkAauBzQlM90tgD/AjoDt2/G3lskmTJrXo3bt3McCE\nCRNaT506dS3AwoULG82cOTOtsrLy2NB9cnNzd2RnZ1cC+P1+UlNTAaisrJTA86oUFRVlzJgxY+0j\njzySfffdd28LrF+4cGGjGTNmhK2JDk6vOtHGkgiRlvYnOX8bAZOD1hvsh/S2WAallFJKqbgKNCFZ\nkOB0K7Ftt/sBl6CF7R9EUgMdL4WFhU1Gjhy5paSkRPx+P4Ea5l69epV06dKlIisra2t1+7dq1aqi\nuLg4BWD37t2p2dnZ1U6ONHDgwGKATZs2pQev79WrV0mvXr1K6nIu0caSCBEVto0xHQBE5CVjzC/j\nG5JSSiml4iUv15cCDHEWE9mEJCBQ2L4UGO9C+ipIeXk5W7duTU9PT+fVV19tnpOTs2/JkiWeHj16\nlFZXs33LLbfsaNWqVSVAnz599n722WdNr7766t2fffZZ0wsvvHCP3+/n66+/zujatWvZ4anCsmXL\nMpo0aXJIu+vqaraD0wtn5cqVGV27di0LF0t0ORJ7UbVj0YK2UkopVe+dBbQGvgOKXEh/MXaCm7Py\ncn0txz09dLsLMSjHvHnzmmZnZ1dMmTKlefPmzf2tW7cu9/ttGTjSmu1LL7107/Tp05tPnjz5aIDL\nL798z7p169IHDBjQZf369WHvXnzwwQeZZ5555r7gdZHUbO/evTvl8ccfb7lmzZpGo0aNanXnnXdu\nKysrk6uuuuqkwsLCFeFiiSI74iLqRuMi0go4A2hJUNttY8zkKndSSimlVLIINCH51KX0S4Bl2Onb\nBwKvuBSHAmbPnt1sxIgRm/v27bu/tsdITU1l4sSJGwCGDRv2PUCHDh3Kn3zyyXVV7ZObm7uzNmk1\nb97c/+CDD2598MEHD/kBUFhYuKKqWNwWVWFbRC7Dfii+xnZsWAr0wPYu1sK2UkoplcTycn3CwcJ2\noYuhfIEtbF+CFrZdtXbtWs9ZZ511IB7HDrSdPtJFmwljgV8bY04F9jl/byYxM08ppZRSqm56AB2B\nncBKF+MIlBsG5eX60qvdUsXVa6+9ts7j8cR8CEa/38/gwYNdb8KRDKItbJ9gjHkjZN2LgLblVkop\npZJfoGNfEBvrAAAgAElEQVTkp0DYSUESZAuwETv84DkuxqHiJCUlhViMm90QRFvY3uq02QYoEpGz\nsb+Qox7EUEQGishKEVktIveGef0GEdkmIoXO46Zo01BKKaXUIQY6f5NhyL1A7fYlrkahVJxFW9h+\nDjjPef4XYC62V/HfozmIiKQCTwGDgG7AUBHpFmbT14wxPZ3HxChjVUoppZQjL9fXHDsSSSXJVdge\n7GoUSsVZVIVtY8wEY8y/nOcvAV2A040xD0SZ7hnAamPMWmNMGTCFg7e2lFJKKRV7F2DvRC8B4tIh\nLkorgX1Al7xcXye3g1EqXsSYxDenEZErgIHGmJuc5euBM40xtwZtcwPwMLANWAXcaYz5NsyxbsZ2\n0uSNN97onp6evjT+ZxCWF1juUtoNheZh3Wke1p3mYd1pHtZdzPNwzeLSE3ZsqsxudWLajjYd03fH\n8ti1tfbL0mN3b/dntu2U/m3bTunVjuVcC0l/Hfbr18/rdgw18fv9jVJSUuo0q2NDMHfu3MOupczM\nTPr379+rpn2jHmc7RiTMutBS/38AnzGmVET+D9sR84LDdjLmWeBZgDlz5iyM5KTjYdq0aQuHDBni\nStoNheZh3Wke1p3mYd1pHtZdrPPQGfJvDZC9ZV3Fo1vWVayO1bHrqDdw+8bV5at++4crLozlgevJ\ndbjQ7QBqsmfPHm9WVlZS/2hJhHDX0pw5cyJ6/9wa/3ADcHzQcjvsTFY/MMbsMMaUOovPAacnKDal\nlFKqoekIdAB2A2tdjiXYIuyoKH3ycn3N3A5GqXhwq2Z7AdBZRDpgh/65GrgmeAMROc4Ys8lZHEyS\n3wpSSimlkthFzt9A4TZZFGObiv4IuBCY6m44qjYOHDggkyZNapGZmVk5ffr0oyZNmrS+efPmcbnO\nSkpK5LHHHmtZUlKSsmvXrtS//vWvh1TWVlRU8Oyzz7Zo0qSJf9OmTen33HPPtpQUd+fWiSp1EckQ\nkZtF5O8i8lLwI5rjGGMqgFuBmdhC9OvGmKUiMlpEAr2SbxeRpSKyGLgduCGaNJRSSin1g0Bhe5mr\nUYQXmMnyJ65GoWpt3rx5TWfNmpV1ww037Nq7d2/q9OnT43aX4oUXXjh62LBhO0ePHr1l1apVjebM\nmdM0+PU333yzec+ePQ/ccMMNu4477rjyjz/+uEm8YolUtEX9F4HfA3uxbb+CH1ExxswwxnQxxnQ0\nxoxz1o00xrztPL/PGNPdGHOKMaafMWZFtGkopZRSR7q8XF8G0M9ZXOxmLFUIxDTIaVuu6pkBAwYU\nT5w4cT3A9u3b084777z98Upr5cqVjV544YUWAO3bty9bv359RvDrzZs3rxw5cmSb3bt3p2zcuDGj\na9eupeGPlDjRNiMZCHQwxuyKRzBKKaWUirmzgUxsW+2dLscSzlpsc5ITsW3Lk6XzZkLl5fri0jdt\n3NNDv6hpm6KiovSNGzemnXvuuQdmz57dtGfPniUtW7asjDSNlJQUysvL5cEHH2x1/fXXbz/xxBPL\nq9t+xYoVGXfddVe7devWeY499tjytLQ0M3Xq1LWRzDg5evTozYGR9JYsWdJ4+PDhW4JfHzRoUPGk\nSZNaer3e7nffffd32dnZEZ9HvERb2F4PeOIRiFJKKaXiItA840tXo6iaHxvbOdjmLkdkYdtNkyZN\natG7d+9igAkTJrSeOnXqWoCFCxc2mjlzZlplZeWxofvk5ubuCC7ItmnTpuJPf/rTlosuuqhj165d\nSwcNGlRcVXpFRUUZM2bMWPvII49k33333dsC6xcuXNhoxowZWeH2CaTXrFkzP8B7772X2bdv372d\nOnU6pGC/bt269LPPPrv43HPPLX744YfbXnLJJXtCt0m0aAvbLwHTROQJ4JBfEsaYgphFpZRSSqlY\nCbTXdmseikgUcrCw/ZTLsbgikhroeCksLGwycuTILSUlJeL3+wnUMPfq1aukS5cuFVlZWTWOge73\n+0lJSaFLly4lr7zySovqCtsDBw4sBti0aVN68PpevXqV9OrVq8Yxvbdt25b6/vvvZ44fP35z6Gt/\n+9vfWo4bN26zx+MxHTt2LH3ppZdajB49eku44yRKtIXtwKQzD4WsN8BJdQ9HKaWUUrGSl+vLBk4D\nykjOzpEBgXbbF+Tl+jLGPT20zNVojiDl5eVs3bo1PT09nVdffbV5Tk7OviVLlnh69OhRWl3N9i23\n3LKjVatWlQD33ntv69LS0pS//OUv323dujWtR48eB/x+P19//XVG165dw76Xy5Yty2jSpMkhI5ZU\nV7MdnN7kyZNbjB07dnN5eTnvvPNOs8suu2zvypUrM7p27VpmjKG0tFQ8Ho/Jyck5EFqgd0NUhW1j\nTId4BaKUUkqpmLsQO5Hcl9gCd7LaiZ2Dox1wFjDP3XCOHPPmzWuanZ1dMWXKlObNmzf3t27dutzv\nt2XgSGu2r7vuuu/nzZvX9PHHHz8mIyPD3HfffVvXrVuXPmDAgC7r169fEm6fDz74IPPMM8/cF7wu\nkprtRx99tOXYsWPbjh8/vo3f75dZs2at3LZtW+pVV111UmFh4Yp777136yOPPJJ93HHHlQPk5ua6\n3k/BrXG2lVJKKRV/gfbayVyrHVCILWxfhBa2E2b27NnNRowYsblv3761HkGkR48epT169AiM+rED\noEOHDuVPPvnkuqr2qW0hePjw4duHDx++PXR9YWHhCoDs7OzKsWPHutpsJFTUo3yLSGcRGSkizzh/\nu8QjMKWUUkrVnjOMXqCwnYxD/oUKxDjQ1SiOMGvXrvWcddZZB+Jx7OLiYndnk0kS0U5qcynwBXam\np51AV2BB0EQ0SimllEoOPYA2wHbsaGLJbhlQDpzqtDVXCfDaa6+t83g8NQ65Fy2/38/gwYP3xPq4\n9VG0zUgeAoYYY+YGVojI+cCTwNsxjEsppZRSdROo1S6sdqvkUYadVfpkbFtzn7vhqLpISUkhknGz\njwTRVu+3A+aHrPvQWa+UUkqp5FEfhvwLpVO3qwYn2sJ2IfCHkHV3UX9+NSullFINXl6urzHQx1lM\n1slswgm0275Ip25XDUW0zUh+C7wtIncA3wInYKdY1TbbSimlVPLog53xeSVQn9rNrgd2AccB3YGw\nw8Y1ILuB5m4HoWq0uy47R1WzbYxZDniBXwB/Bq4EujnrlVJKKZUcAs0wvnI1itr5oXbb1SgS4wHq\nWJBTcbcb+z7VWo012yLSxxgzz3l+QdBL24EMoLeIRD1du4gMBJ4AUoGJxpjxVWx3BfAGkGOMWRhN\nGkoppdQRKlBQrY81w4VAX+w5/NnlWOLtY6C/20FUZ+7cuQuHDBnSy+046rNImpH8HTt8EMCkKraJ\narp2EUkFngIGYGeMWiAibxtjloVs1wy4Hfgs0mMrpZRSR7K8XF9bbBOM/dhmJPVNoI1577xcX+Nx\nTw+NyxjQSiVKjYVtY0yPoOexmq79DGC1MWYtgIhMAYZw+AxXY4BHgOExSlcppVQc+DzeY4D2gPGM\nyW3s83hPxhb21g4tXe53NbgjT/CQfxVuBlJLe4C12Eq8PsBMd8NRqm7EmMiHQBSR4caYR8Osv8sY\n81gUx7kCGGiMuclZvh440xhza9A2pwJ/NMb8XETeB4aHa0YiIjcDNwO88cYb3dPT090a4siLHR9U\n1Z7mYd1pHtad5mEE/Os3eyo/X9rcv2ZDU3/Rd03Njt2esBs29lSmtD9uX0qn44tTvB2KU0/90V5J\n1UnlIlDr63DlFyUn7d7mP7pNx7TtrU5Mr0+dI3+w4euyFtu+rTwqu13qlg49PBtqeRj9LMeG5mMV\nMjMz6d+/f41NbKItbO8xxmSFWb/TGNMiiuNcCVwUUtg+wxhzm7OcAhQANxhjiqorbAebM2fOwkhO\nOh6mTZumbZrqSPOw7jQP607zsGo+jzcF+ClwK4d3XivFjiRhpE32iea7bd9iR1kInQnwG+CvwOSh\npcvrZUEwEWp7Hebl+lKBrUALbDPMTbGOLUG6A6OAZeOeHtq9NgfQz3JsaD5WLdJyZ0RD/wV1jEwV\nkX5A8NiXJwF7o4xvA3B80HI74Lug5WbYduLviwhAa+yQg4O1k6RSSiWWz+NNxd5BHM7B/jkl2EnO\n1jiPb4FKgEaj/2/CgZvG3OdsdwzQBegKnA50AP4CjPZ5vJOB8UNLl29O0KkcCU7DFrQ3Un8L2mDb\nmpcA3fJyfW3HPT10o9sBKVVbkY6zHegY2QiYHLTeAFuA26JMdwHQWUQ6YL8Qrgau+eGgxuwGWgaW\nI63ZVkopFVs+j/dU4FkgUHuzEduGdj52noWa7AA+cR4vYQvcP8VWqNwB/Mrn8Y4AJg0tXa5TO9dd\nfZuivSoV2JkvT8ee0/PuhqNU7UVU2A50jBSRl4wxv6xrosaYChG5FfuFnQpMNsYsFZHRwEJjzNt1\nTUMppVTt+TzeTGA0tkCcAmwGXgYWArXt8OjHVrYswHamvAY4FXgOuM7n8d48tHT5qrpFfsQLNO9p\nCG1sC9HCtmoAou2lsktEzgleISLniMjj0SZsjJlhjOlijOlojBnnrBsZrqBtjDlfa7WVUioxfB7v\nKdjh1+50Vv0LGAF8Tu0L2qGKgIeAx7GTRvQFvvR5vLf6PF6dprsW8nJ9WcDZ2OY89XEym1CB2vmf\nOG3RlaqXoi1sD8XWagT7gqAmIEoppeovn8d7FbbJRwds7eg9wBRs+9l4+Aj4PTAXO73434DnfB5v\n+NFNVHX6Ye9YL8UOu1jfbeZgZ89TXY5FqVqLtrBtwuyTWovjKKWUSiI+jzfV5/GOxxasGwPvYec6\nKEpA8sXYCdSeAMqAG4ECn8fbKgFpNySB9tr1cdbIqhxJU7erBiraQvJ8YKwzNF9giL5RznqllFL1\nkM/jbQr8B1uLXQn8A9sxvjzBoXwIPADsBM4BFvo83p4JjqE+q89TtFdFC9uq3ou2sH0HcCGwSUQ+\nxw7XN4DoRyNRSimVBHwebxbwLjAIW8gdBcxxMaS12EL/KuywsO/7PN4zXYynXsjL9XUEOmJnX1zj\ncjix9BW2n8DZTpt0peqdqArbxpgN2DE8LwPynb+nO+uVUkrVIz6P92hgFtAbOybzKGCFmzE5dgEP\nAp9iJ8aZ7fN4z3M3pKQXaELyP2LXiTUZ7Ae+xrZF7+dyLErVStRtrY0xfmPMJ8aYN4wxnxpjGtKH\nWimljgg+jzcbO1PvGdiJxsaSXJOgVGAnv/kIyARm+jxeLWxVLdDMYpmrUcTHD6OSuBqFUrUU6aQ2\nAIhIBnAD0BP75feDWIy/rZRSKv58Hm9L7Ogf3bEdIB/GNiFJNn7s1O4V2KEBZ/g83iFDS5f/192w\nkkteri8dCMz03BCG/Au1GLgKGOh2IErVRrQ12y9ih2jay8EpegMPpZRSSc6ZrGYGtqC9BhhHcha0\nA/zAU9h25I2AqT6P9yx3Q0o6ZwHNgG+A7S7HEg9rsCPWnOS0TVeqXomqZhv7q7KDMWZXPIJRSql4\ny8kvSAG6AJ2BTs7fE7FjPKe19jTpOja/4EPs+L7fAuudRyGwesGIC+rtlOI+jzcD+DeQg206Mh7b\nPjrZGeAZbAVRP+Adn8d73tDS5Q1hlsRYCDSvWFztVvWXH1tjfzb2XJ92NxylohNtYXs99h+SUkrV\nGzn5Be2xIykNwN5ub1nVtptLUwHOrerlnPyCecA84N0FIy5YG9tI48fn8aYAL2HzYDswgfpR0A4I\nFLizsFN4z/R5vOcMLV2uHfQbdnvtgMVoYVvVU9EWtl8CponIE8CW4BeMMQUxi0oppeooJ7+gOXbW\n2xuBXiEvbwbWYWuvtzt/SwH/z487cPO/NjV+GjgaWyg/xvnbFWgN/MJ5kJNf8BHwCvD6ghEXJG1T\nDGf68yew7V6LsQXtza4GVTuVwGPYkUq6AO/5PN7eQ0uXf+9uWO7Jy/Udg72+y2j4hW2A/nm5vvRx\nTw9N9BjwStVatIXtW52/D4WsN8BJdQ9HKaXqJie/IAe4HbgC28YXbAHzC+ywdkuopqB5YpPKEqoe\n/q4N0A3b3rkXtgb8XOCJnPyCfwPjF4y4IBlv5d+F/f4uAx4hMbNCxksZtkPnGOz7MM3n8Q4YWrq8\n1N2wXHMhIMCX2B+MDdV2YCPQFttGXSfTU/VGVIVtY0yHeAWilFJ1kZNfcCa2xnNQ0OqF2H/KC7GF\ntLr6znnMxhbkzwD6AD8GrgauzskveAd4eMGICz6KQXp15vN4L8HOiwDwONAQ2jkXY4cqfAg7RvjT\nPo/3xqGly+tte/o6OBKakAQUYgvbP0EL26oeiXbov9FVvWaMGRnlsQZib2umAhONMeNDXv8/4HfY\n24bFwM3GmCPhy0QpFYWc/ILTsQWvwLBg+4F3gPexzUPipQTbdnsetqnJpdhaxouBi3PyCwqAOxeM\nuODLOMZQLZ/H2wPwYWs+XwIWuBVLHOzAdvAcC/wae8fiMVcjSrC8XJ9w8LpviEP+hVqM/XwNBB5w\nORalIhbt0H/HhzxygOHYKWIjJiKp2KGcBmFvyQ4VkW4hm/3TGPNjY0xP7G3PI+pLVClVvZz8gmNy\n8gv+gS1ADgT2Aa9hm0u8TnwL2qF2AC8AvwX+5cRyAbAoJ7/g6Zz8gio7ZMaLM2nNf7BzIsxxnjc0\n3wB/c57n+zzen7oZjAtOBY7D9qEqcjeUhFiGHXP9dKetulL1QrTTtf865DEIuBx78UfjDGC1MWat\nMaYMmAIMCUlrT9BiU2y7cKXUES4nvyA1J7/gZmAVcAv27tebwG3O370uhrcH+312K3Ysa4D/A77O\nyS+41Rl2MO58Hq8HO8Rfe2ApMDkR6brkU+yPrBRgis/j7e5yPIl0sfN3oatRJE4pthmUYO8iKVUv\nxOKL/7/AZVHu0xY7fm3ABmfdIUTkdyKyBluzfXutI1RKNQg5+QWdsW01nwFaYAsZI7CFLTcL2aGK\ngeeBP2BvfR+FrYF9Pye/oFMC0n8COA/bEfRxYtNePZm9iZ3WvRnwts/jPcrleBLlEufvElejSKxA\nB2Sdul3VG2JM5BXGIhI64kgT4BpgsDGmRxTHuRK4yBhzk7N8PXCGMea2Kra/xtn+V2Feuxm4GeCN\nN97onp6evjTSOGLMS8PoeOQmzcO6a5B5aAx8/H1G9vwdGe0qjKQ0SfVX9G5RuqNbs8p9IrFNq1GK\naVvil42xOp4xsLI4renc7RktD/hTUtPE+M9rUbbhnBZl21JiHDtA+TsfHlP+4vT2pKWajBHXb0zt\neHziC9pNG7dl34GY5WEkTGmZlD70fFuzcWtGSveOuz0P3LhaUhJyIyFeqv0sl5X40wrfLzlFBPPj\n3o2KUtPkiLj7u2+PP2PVwtJ2aRmUn9qv8ZdS/RdAg/w+dIHmYxUyMzPp379/6NCyh4m2sO3HNucI\nXN37gUXA740xX0RxnLOBUcaYi5zl+wCMMQ9XsX0K8L0xpnl1x50zZ87CSE46HqZNm7ZwyJAhrqTd\nUGge1l1DzMOc/IK22GYQgZqs/wL/xLaLjrm7OhZPeGxN5j1xOHQmMAw7egbAXOD6BSMuiFmh1Ofx\n9gI+xE4+9oTzPOEaT3xgwoGbxsQjD2tyLHYM8UzgvqGly8fXsH3SqumznJfruwF79+RT4M+JiisJ\nCPAs9m5R93FPD61y4ISG+H3oBs3HqkVa7oy2zXaKMSbV+ZtijMk0xvSOpqDtWAB0FpEOIpKBHTLr\n7eANRKRz0OLFwNdRpqGUqudy8gsGYccP/gnwPbZJ2XPEqaAdZ8XAX4FHgd3YaccLc/ILLqp2rwj5\nPN6W2M6ZHuz3qSsFbZdtxeYxwDifx3uBm8HEWaC99pEwCkkww8GmJAOr21CpZFFjYVtEbg16HpO2\nhsaYCmwHopnYWxOvG2OWishoERnsbHariCwVkULshAyHNSFRSjVMTifIMdhOhi2Aj4G7aRhD132G\n/U5bjJ2Z8r2c/IJxOfkF0U4y9gOfx5uG7Zh5AvbHiS8WgdZTi7A/OgIdJg/rD1Tf5eX6Mjh4p6fQ\nzVhcssj5O6TarZRKEpHUbI8Lev6/WCVsjJlhjOlijOlojBnnrBtpjHnbeX6HMaa7MaanMaafMcat\ntthKqQTKyS9ohW0q8kfAj71V/jiwy824YmwPdkKWKdhzvB+Y45x7bfwJ6I+dZe8poh8hqqF5Hfuj\nIxt4w+fxZrgcT6ydB2QBa0nsEJfJYhF2FKLzdAhAVR9EUtheIyJ/FpFhQLqIDAv3iHegSqmGLye/\noBf2R/0F2ILjKGztdkPs/OXH1sCOxjaR6QMsdCbpiZjP4x2ELaz7se20d8Y4zvookBc7gLOxzY8a\nkkATkphVgNUz+7FDWqZwMC+USlqRFLavBpoDQ4F04Powj+viFaBS6siQk19wNXZYvzbYW+P3c2T0\ngF+KbSKzCmgHfJiTXzA0kh19Hu8JwCvO4ovAirhEWD/twXYcrADu8Hm8V7kcTywFCpiuzU6aBAJN\nyrQpiUp6NRa2jTGrjDE3GWMGAB84TTpCHw25E4pSKo5y8gtScvILxmLbGTfCTrU+AVvbe6TYBTwI\nFGDz4J85+QXjc/ILUqvawWka8Rq2TfsnwLuJCLSe+Ro7syfAJJ/H63UxlpjIy/V1Arpif0ysdDkc\nNwUm8hmYl+tr5GokStUg2tFI+scrEKXUkScnv6ApdkKSPOyt/2ewhaMjsc1xBfA0dphDP3AP8FpO\nfkHjKrYfD5wFbMIOhdYQm9rEwkzsHZOmwL99Hm8zl+Opq+BZI/1uBuKy7cA32Pk+tMJPJbV6PeK/\nUqr+cjoDzgV+hh0KbzQw29WgksO7wFhsu9SfA7Ny8gsO6QTm83h/BtyJLaD/DTusoKraM9hZi38E\nPOfzeOMwnVDCHImzRlZFm5KoekEL20qphMvJL+iKbfqQA2wARmLbLivrK+ABbAe/c4GPcvILOgD4\nPN6OHGwaMRmdgyASpdjxzUuAq4DfuRtO7eTl+loA52NH4jgSh/wL9UNhOy/Xp+UZlbT04lRKJVRO\nfkFvbEG7A7aAPQr4zs2YktR6bCfR9dg2up9ceO9rZwNvYId9mwfMci+8euc74O/O88d8Hm+Om8HU\n0mAgDTsKyV6XY0kGRcA2oBX2h7tSSSmqwraIPCYiPeMVjFKqYcvJL7gc21TkaOwMhw9jm5Co8HZi\na7i/AlrlzJ81DzgV2yRikpuB1VOBjqTp2PG3W7gcT7SudP4urHarI0sgL7QpiUpa0dZspwMzRWSJ\niNwjIu3iEZRSquHJyS/4DbZWNgOYhm1rXOpqUPXDfuChUz79YMXJCz9Kq0hL4/PeAz5x1qvovQSs\nBk4EXvR5vPXiDm9eru8oYAC2U6QWtg8KNCW5zNUolKpGtKOR3IYdA/deoCewXERmi8gvRSQzHgEq\npeq3nPwCyckvuA87YkYK8DJ2bOgjeSSFqHgLPz+234w32wPM/ekVfHjRZb94/cbf/8Iv9bmfn2sq\ngMeAfdjOhsPdDSdig7EVXouww/4paxn2vfQ6wyIqlXSi/kVvjKk0xkw3xgzFDjuVje2ss1lEJopI\n2xjHqJSqp3LyC1KwE4s8hB2a7u/A264GVc9k7dzeqN/010ek+P2N9mYd9eWuFi1nY4zZ0KHzla/8\n7r5bKtLS60XNbJLZhr2zAvCQz+Pt7WYwEbrC+au12oeq5OBMmlq7rZJS1F/SIpIlIjeKyFxsB53P\ngN6AFzv8lE6soJQiJ78gHXgeO0RdOXY0iLmuBlXPiN/P5S8+dUujkgPtyjI8W9af1OX9rksXLe68\ndNE08fsrtrdue+GLt+XdeaBJ0zS3Y62HvsA2Z0oFpvg83mNdjqdKebm+LOAi7A9WLWwf7nPnb0Oa\nJVQ1INF2kHwT2AhcDvwDaGOMudkY85Ex5lvgLuwIA0qpI1hOfkET4N/AL3HaHHPwH6KK0KX/fG5g\nix1bz/OnpJR+26HzjMr09HKAE9esWNNt0advplRWlO4+Jvusl269//5dLVrqLHrR82GnuG8DvOrz\neKucsdNll2L7OhRiZxtVh/ofcADolZfr6+x2MEqFirZm+3OgszHmYmPMa8aYUgARuQvAGOPHDsFT\nIxEZKCIrRWS1iNwb5vW7RGSZiHwpInNE5MQoY1VKuSAnv+Ao7Kx9l2ALBmPQCTiiljPvv106rvzq\nVwCb257w7r6s5juDXz9uQ9HGkz+fPyW1vHzfvqyjfvzPW0b86bvjO2S5E229VQn8BdsG+kLgj+6G\nUyVtQlK9MuxddoBr3AxEqXCiLWz/0RizOdz6wBNjTI095EUkFXgKGAR0A4aKSLeQzRYBvYwxJ2On\nc34kyliVUgmWk19wHPABcB6wGTuG9mo3Y6qPjlu/NuusuTP+IMak7WrR8tPtrduuCbddy62btp/2\nSYEvvbRkV0nTzJP+/avfjVnbtUfLRMdbz+0EnsA20XjQ5/EOcDmeQ+Tl+pph/1fCwZE31OE+dP5e\nm5fr057DKqlEVNgWkQtE5AIgTUT6BZadx01EP7j+GcBqY8xaY0wZMIWQMTKNMXODCu6fAjrMoFJJ\nLCe/oCP2H97JwDfAn7DNzlQUUsvLUi71Tfx9enl5iwONm3zzbYdOn1S3ffPvd+zu9eFsn+fAvm1l\njRq3mX71jeOWnHaWfl9G50tspY5gm5MkU/5dDHiAxcD3LseSzL7CjtnfGTjN5ViUOkSkNduTnIcH\nOz1wYHkiMAy4Lcp022InZQjY4Kyryo1ox0ulklZOfkFP4CPgJOxQXGOB7a4GVU9d8fzfrsrcu/vH\nFalpe9ef1GWmSUmtcYjEpsV79p8x779TmhTv2VCRntFi9uChYz7vPaBLIuJtQN7EFrqzsRPeeFyO\nJ0CbkETGD3zsPNemJCqpiDEm8o1FXjLG/LLOiYpcCVxkjLnJWb4eOMMZxzt02+uAW4G+gTbiIa/f\nDNwM8MYbb3RPT09fWtf4askLLHcp7YZC87DuEp6Hq/elZv7ru8adyo2ktm1Usf+y1iVbPKlE/sWS\nZL9cRG0AACAASURBVBqlmLYlfnGnRv7TL5vwxKutESHl99fulG4nlUeze7mBabuOOuqbMo8nDWMu\nO2rX5q6NSg/EK9wqNW3cln0H6t1dDbO7OKVkzHPt2FWclnpez22e269e72I43ooys2rR+wdOMX6k\n29medZ7GKZUuxpP0indVer7+X1nbtHTKT+3X+EtJEf2fEhuaj1XIzMykf//+vWraLqrCdqyIyNnA\nKGPMRc7yfQDGmIdDtrsQOxZqX2PM1pqOO2fOnIWRnHQ8TJs2beGQIUNcSbuh0Dysu0TnYU5+waXA\n60Aj7LB+z2InDam37upYPOGxNZn3JDrdTksLj734tcn5qf7KJtuOPW7OphNPKqzNcfwpKbLorH4/\n+T67VQ+Mqey26NMnB/77lQ9r3jN2Gk98YMKBm8YkPA9j5CTsnZl0YNjQ0uXPuxHEtGnTFn7+3v6J\nwNPYWu0JbsRRDz2JHaih/xkDmzyi/1PqTv83Vy3ScmeNzUhEpE/Q8wuqekQZ3wKgs4h0EJEM4GpC\nJroQkVOBZ4DBkRS0lVKJlZNfcAMwFVvQ/g92ONB6XdB2S9M9uzMGvPXqiFR/ZZPizKxlm07oUKuC\nNkCK329O+3jOzOzvvl2ASOqy086+461rbxlU857KsRbbRBLgaZ/He7qLsQxz/ib0x1I9F8grbUqi\nkkYkbbb/HvR8UhWPiWH2q5IxpgLbNGQm9tbE68aYpSIyWkQGO5vlA5nAGyJSKCI665xSSSInv2A4\ndsKaVOBV4CV0+vVaEb+fK57/628aH9jfviw9Y9v6jl3mUMdp2AU4ZcH8eW2KVs8DWOs9edhrN915\nlU7vHrECYBa2n9K/fB5vwkd4Kd5V2RjIwQ5AoKOQRG6+8/dKf6XRC14lhRpnHTPG9Ah6HrMJa4wx\nM4AZIetGBj2/MFZpKaViIye/QICHgUATgWeA2e5FVP8NeeUfFx+zbfP5fpGyDe07zajI8JTF6tjd\nFn++IKOsdH9R524XbWzf6YpXf3tv1tBnHp2UVlGuP4xqNhk7SVsnbIfJnwwtXR5VG/q62PptRaCA\nPxc7jrSKzEagCGi/c3Nlc5djUQqIfgbJfiLSwXneWkReFJFJItI6PuEppZKFM/36ZGxBuwJ4DC1o\n10nv96ae0mHV0l8CbG534ozio46O+QgunZYvXupM71657bh2P3nptvt/r9O7R6QCe4f1e+B84G8+\njzchNaV5uT7P91sqWziLHyUizQZmHsD27yqOcTsQpSD6SW3+jp1xC+w/2nTn+bMxi0gplXRy8gua\nAdOBG7DTrz8MVDv+s6rejxYvaHPax3PvEkjZ0bLVvKomromFE9esWOMt/OzNlMrKsl3HHHv2y7+7\n7z6d3j0iO7ETqpUDtwC/TVC6l1ZWkAaswrYhV9GZD1Tu2eE/Ki/Xd7zbwSgVbWG7rTFmvYikARdh\nh9zLBc6JeWRKqaSQk1/QBltT9BNgB3aymi9dDaqea7l5Y9P+b0+5J9Vf2aS4WdbSje07xr1Nbptv\nv9nw4wXzp6SWl+8vbn70yb5bhj+4ue0JzeKdbgOwGjsiCMATPo+3fwLSDHSM/CABaTVEu7CT4YH9\nkaSUq6ItbO8RkVZAX2CZMabYWZ9ezT5KqXoqJ7+gG7YGuye2HeSDaE1bnWSUHEj92Ut/v9NTWtKm\n1NPou3UdfzS7rh0iI5W95bttp34615deWrr7QNNmnd789e1jV3Xr2Sohiddv87Ej76Ri2293jldC\nebm+dsBFIhgOTtKiovee8/eWvFxfskxQpI5Q0Ra2/4btFf0q8JSz7lxgRSyDUkq5Lye/oA+2vegJ\n2Jrs0cAWV4Oq58Tv5+pn/3xzsz27TqlITd27vmPXdyrT0xM6XOJRO7fvOv2jWT9M7/7uL254aOF5\n/TslMoZ6yocd7/po4F2fx5sdp3R+BaRkHZNSDBTXtLGq0gpPEykDWnJwFk6lXBFVYdsYMwG4EDjX\nGDPFWb0BO526UqqByMkvuAo79NlR2FvZE7BDkKk6+Pnzf/t5y62bLvCLlG3o0HnagaaZe9yII3Pv\nnn1nfDBzStM9u4oq09Kz5v/ksj8VXHJljhux1CMGeAJ7Z6cj8B+fx9sklgnk5fpScJqQtDguTQva\nddSybdpu5+nvXA1EHfGiHY0kA9sr+w8i8pKIvAQ8ANwdh9iUUgmWk18gOfkFfwCmABnYW+d/R4ce\nq7NBb7zQ94RvVl1twGw6vsP0PUcf4+pdAk9pSdkZH8ycevS2zV+ZlJSMwjP/v707j4+juvIF/jtV\n1ZvU2jfLkmzLu7xhY8sLBhwwix0H/EkCCU7IQh4howEGMlmAKBBCYhJGM/OSl8x4wmMLS0QwJGBW\nG1sBHDbbWN53eZMtWfvae3Wd+aPasbAto6VbpZbO9/OpT1d3V1efvmp1n75169xFP3r5699bKrW4\nL8gP8+TgBgDzAPyp3FGkRnH/18OcwbImJVPxRXG/w1JGrtoJ84TuBaUl5RdbHY8Yvno7jOSPAO6G\n2cNVddYihIhjxWUVGsyhYv8euen/A/gTZLKaflv49prpk7dvLgGAhhF565pyco9YHRMAqEbYuPiD\ninW5xw+/DyI6XDTjO8/98z23BhzOaCaQQ00rgJUAPACWA/hNNEoClpaUE4B7I1dfI/nR02+qRgyz\nTjkgvdvCQr1NtpcAuISZ72Hmn3ddYhGcEGJgFJdVpMM8oeh2mL3YZQDWWRrUEHHx+xvGzdn49o8I\nUFvSMz84VTBml9UxdUUAplZ+9NHYvTteN2txF1z7x3+5v7R+RJ7b6tgGsZMwh1adng353gtv3iOX\nw+wtb0GkTrSIitMnSn6ttKQ8/YJbChEjvU22j8OcvlYIMUQUl1VMBvAxgMUAGgE8CGCTlTENFdO2\nfFBw2bpXfqoahqsjKWVn9diJg7Y2+dgDu/ZN++SDSGnA1Okv3Pr9h/dNn51rdVyD2F6YR4IYwMPl\njqI7+rm/07Oyvg4g0M99iTNOAdgOwAngFotjEcNUb5PtpwG8QkQriOjKrkssghNCxFZxWcVSmIn2\neJhVhe4HcNDSoIaICbu2jrjytRceUMNht8edtO/oxKIBK/HXVzk1x0/Nfn/9s5FKJblv3fDNX7+z\n9Msy1rV7H+DMpG6/K3cUfbsvOyktKb8IwFIAPgAbohOa6OLNyOXdpSXlMpmTGHC9TbbvAJAD4GEA\nj3dZHotyXEKIGCouq1CKyyruh9mLlgzgHQC/hNmzLfpp9ME9Gde+9MwDmh5K9SYkVh2ZOOUtVtS4\nGPue3NbSMe+dt8qTWpoOGqqWsPWSK+594Tt33RBW1cH9S8E662GezwQAj5c7ir7Sh32cLjLwJqTc\nXyxsBXAMQD5kkhthgd6W/ivsZhkbqwCFENFVXFaRBmANzLrZgHnE6r8hh66jYlTVvvQvPP/4A/ZQ\nMMvvdB07MnHq64aqha2OqzfswUBo7sZ1a3KPV20EQCfGTvzqk3f/7J7G7NyolrobQl4D8GeY36nP\nlTuKru/pA0tLygsB3ARz/PfbsQlv2GOYFZYA4CelJeWJVgYjhp/e9mwLIeJYcVnFTJgTcyyDWVXh\nFwBehfllJPqpcN/OzOufe/Sh07NDHpk49dWwzRayOq6+IGZMrfx406QdW15SdN3fnpYxu/x7P3yk\ncv6iQqtjG6ReBPAKAA3AS+WOoht7+LgfwPwu3gA5shRLWwAcApAN4E6LYxHDTK+TbSK6moieIKJX\nI9fn9GXMNhEtIaL9RHSIiM45k5uILieirUSkE5HM/iREP0TqZ98O4COYdXz3AigFsNPSwIaQCbu2\njvjCn5/4hT0YyPE7XdWHJ039a8jhiPujBQVHDx6d/f6GZxxeT33I4RzxzudveFjqcXfrWZxJuJ8v\ndxR980Ibl5aU5+HMpHBvXWhbERXlkcsfl5aUp1gaiRhWejupzZ0AVgE4ALNMEWCe0PHLXu5HhTnd\n+1IAUwCsIKIpZ212HMC3Ydb5FUL0UXFZRQbMyWl+D7Oa0Gsw/2frrYxrKCmq/DhvyYtPP2QLBTP9\nroSjhydNfTnkcPqtjitaUlqb2hf87Y0/ZdTVbGNF0Q4XzfjOk99/8EdSHvC8ngXwAszv1z+WO4ou\nNEb4EZhVMt6FORuziK0dAPYASAPwfYtjEcNIb3u27wZwFTP/GmcmutgHYFIv9zMXwCFmPszMQZhj\nqZZ33YCZjzLzDsiEGkL0WXFZxSKYZa+WA2iHWT/7j5AZIaNm9sb1469++U8P2fRQmi8hsapq0rQ1\nut0x5NpX00PhWR+9s2Hcnm2vKuFwsC09c+7zt/2g7P3Fy6ZaHdsgtBrAM5H1/yl3FP347IlvSkvK\nLwXwdZizUr4wwPENZ6d7t/+1tKQ8w9JIxLBBzD0fqklE9QBymTlMRM3MnE5ETgBHmLnH9Vgjw0KW\nMPOtkevfADCPmc+pU0pETwF4jZlf7GZftwG4DQBWr1491Waz7e7xC4quIpiH5kXfSRv2XxGAvUED\ntK7ekbet3ZYDELLtYd+yEf6GNBvrVgc42DkVzvMbdLJHG79fmYg/vJiNkE6YMtav3P7VNrLbYhyh\n9Vp0VX21LSWlTrfZAGCWy9t2dXJ7s40iY/8TXXnw+HrWhkNYaO2Hyfrq9ZkAoF46s8H+zzceJ00F\nG4yd7/un+D3syh6lNeeNt7We/VhNQ56uY9i3YX9014YHtwZyO1sNV1aBVlc41S5HFD6bfDd3w+12\nY/HixXM+azutl/t9D+ZMWSu73PYvODMdak+db7Bfn07QYuZHEalzumHDhi09edGx8Morr2xZvny5\nJc89VEgb9t8rr7yy5ZcHkm6H2XudAyAM4M/1QXXNk8cT46oihlX+dVznI/9Z5b7nQtuQYWD5s/+z\nrPDA7m8RQO0paVuPubLf5afeGzZH4qYoqkIz5847lT9mQaUvIWV3C3UuqHjjd7M/qKhyPXb/I75b\nf3HBNhxGFgC4M/z3bVm+v2/bAuCru77zwNcA/A+A2vrj+g/rj+vnHAmZdaXrkcoKn7RhP1ygDccB\n+HVDtZ7eUK1fvXLVCjl35QLku7l7GzZs2NKT7XqbbN8J4FUi+i6AJCLaD/PQ9HW93M8JAAVdrucD\nqOnlPoQQXRSXVbhmpzjyYE60oQA4DOAPkUsRJXa/T73x8d9+K6e2eikANGaPqKgZNbZysE9YE22q\nETambf3ww+za6sP7ZhQvDTpdee8u/dLD+6df/NrNcvZkVx8CaII5Q+RS3ZnwIdgYCVIAc3z3kBty\nFAeqAKwDcA2AJ0tLyuevXLVCjvqJmOltne1aAMUAvgLgawC+BXP4x6lePu9mABOIqJCI7DBrjK7p\n5T6EEBGRmSB3f9JmHwHzyNELAH4KSbSjKv/IwdRbfvPQz3Jqq5cykV6bP3pNzehxwy7R7iq79kTd\ngg2vPZtZe2ILADpVUHj9HxozC95d8sVZVsc2iBwA8BMANfUzL58KUtJUv+cAgE0WxzWcPQOz1OJs\nAD+yOBYxxH1mzzYRPXSBu6cD+DwRgZkf6OmTMrNORHcAWAtABfAEM++OPNcWZl5DRMUwKyikAbiO\niH7OzHIijhBdFJdV5AH4DYAbACDdFg40h9SfQ6Zcj7oFG16bWrzx7bs1XU/VNa3t5Khxr7dlZNZa\nHddgYNND+sxN771bn1uwf/+0i6/uSEjM/uTSq35SNXnG+4vXPP/06MP7m62OcRCoa5wy78nmojml\nMAyMeePpCWFX4pePXfP1v7CqSp37geeHWV3tfgAPlpaUr1m5aoVV53yJIa4nPdsFXZYJMMdsLwYw\nHsCVkesTevvEzPwGM09k5nHMvDJy2wPMvCayvpmZ85k5kZkzJNEW4ozisgpXcVlFKcxqQDfALMH5\n2DcKfCchiXZUKbpOX3rqd8vn/+3NBzRdT/UlJFZVTZ7+J0m0z5VdW31q4YZXn73M3dFBRjjUmpm9\n8C/fvv3/rf7Ov3y5MynZbnV8VvJm5SfXzbmyBKQg+di+amdrA7lrj9404cXf3edqqEmyOr5hagfM\nyYTsAJ4oLSnv7dBaIXrkM5NtZr7l9ALz8PQKZl7IzF9j5kthDgERQgyA4rIKpbis4mYA+2HWynYD\n2AjgXwGsVYfvaIaYGLdne/at/3H/g2MO7buZAKU5I/vvh4pmvBJwJXitjm2wUgyD5yd6vXM2vv1U\nckvTAVZUR/XYSTc98f0Hf7v2i19fOByHcxuqphy/8oa7WLOlqwHfUSXof7Ft7LSXDEX12T3tswrf\neOo/Rny0drbVcQ5TT8McUz8X5myeQkRdb3/FLYVZF7SrVwA8GZ1whBDnU1xWQQCuhTm9+umzwvfB\nrBm7x6q4hioyDHzh+cevHrdvxzcVw3CGVbXzVN7otU05uUetji1epLQ2t899b+2rNQVjC6qKpl8R\ncCVm7Z59yd1VRTOun1K56c+Xv/WXrUovSs/Gs6PXfv0GPTF5BoX1joSaI2uJ2fCMGH00mJT6TPr+\nrcs0vzcvc8/H97pPVr1bfcWXnwyk53isjnkY8cKsDFMK4JelJeWVK1etWGdxTGKI6e2kNocA3H7W\nbf8M88xeIUSURaZZvxZmhZE3YSba9QB+C+BnkEQ7+mrqtVv//f6fTtiz7TbFMJydSSm7Dk656GlJ\ntPtmZPXh6oVvr3lm9ME969RQsNOf4B67deGV9/3hnl+t/PtV100f6j3dp4qvmunNGXUDmNlVf+IN\nLeDrPH1fKDGlo27moj97cka9w0S6s61x0bhXH//P3A/flDJrA2sbzI5DDcCLpSXlF1kcjxhietuz\nfSuAvxLRjwGcBJAHQAfwpWgHJsRwVlxWocAsqfljAJdEbm4G8DKACgABi0IbspKbG52fX/3Ul1Bz\nfFRSODwqrKqeutyC9Y25eYesji3eKcw8Yc+2nWMO7N57aMrMi04VjJnrcydN3PS5JQ/snLPwwITd\nlWs+9+ZfNmt6aEjVKW8tnJrbNGXuXSAiR0vDO462pnMnUFEUbh03/RNv5sjDaVU7lmh+78iMvZvv\n0R9u8qVmTM9rnXCRTGwzMJ4DkAlgIYA3IuUAqy2OSQwRvUq2mbmSiCYAmA9gJIBaAB8ycygWwQkx\n3BSXVSTALKn5fZw58bgFZmWev8E8g15EkaLrdM3Lz102YVflzTY9lAYA7Smp22oLCj+UsdnRZdND\netGOzZ+M27djx8GpM2fVjRw9x+dOmrhj3uU/3HdRce3oQ3vXXPH66vfcHe1xX3u6ZcJF+TULPv8z\nVjW36vPsd9Ud/+RC2wdTMlrqZi56PuXI7lmJ9ScuwZ7Drjw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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import scipy.stats as stats\n", - "\n", - "nor = stats.norm\n", - "x = np.linspace(-8, 7, 150)\n", - "mu = (-2, 0, 3)\n", - "tau = (.7, 1, 2.8)\n", - "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", - "parameters = zip(mu, tau, colors)\n", - "\n", - "for _mu, _tau, _color in parameters:\n", - " plt.plot(x, nor.pdf(x, _mu, scale=1. / np.sqrt(_tau)),\n", - " label=\"$\\mu = %d,\\;\\\\tau = %.1f$\" % (_mu, _tau), color=_color)\n", - " plt.fill_between(x, nor.pdf(x, _mu, scale=1. / np.sqrt(_tau)), color=_color,\n", - " alpha=.33)\n", - "\n", - "plt.legend(loc=\"upper right\")\n", - "plt.xlabel(\"$x$\")\n", - "plt.ylabel(\"density function at $x$\")\n", - "plt.title(\"Probability distribution of three different Normal random \\\n", - "variables\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n", - "\n", - "$$ E[ X | \\mu, \\tau] = \\mu$$\n", - "\n", - "and its variance is equal to the inverse of $\\tau$:\n", - "\n", - "$$Var( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n", - "\n", - "\n", - "\n", - "Below we continue our modeling of the Challenger space craft:" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import pymc as pm\n", - "\n", - "temperature = challenger_data[:, 0]\n", - "D = challenger_data[:, 1] # defect or not?\n", - "\n", - "# notice the`value` here. We explain why below.\n", - "beta = pm.Normal(\"beta\", 0, 0.001, value=0)\n", - "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n", - "\n", - "\n", - "@pm.deterministic\n", - "def p(t=temperature, alpha=alpha, beta=beta):\n", - " return 1.0 / (1. + np.exp(beta * t + alpha))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n", - "\n", - "$$ \\text{Defect Incident, $D_i$} \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n", - "\n", - "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the above code we had to set the values of `beta` and `alpha` to 0. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `pm.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in PyMC. " - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n", - " 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n", - " 0.5])" - ] - }, - "execution_count": 58, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "p.value" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 120000 of 120000 complete in 8.9 sec" - ] - } - ], - "source": [ - "# connect the probabilities in `p` with our observations through a\n", - "# Bernoulli random variable.\n", - "observed = pm.Bernoulli(\"bernoulli_obs\", p, value=D, observed=True)\n", - "\n", - "model = pm.Model([observed, beta, alpha])\n", - "\n", - "# Mysterious code to be explained in Chapter 3\n", - "map_ = pm.MAP(model)\n", - "map_.fit()\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(120000, 100000, 2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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o65ORU6bNnj17YXl5OfVXilVUVCyMZ7usKNCRequWb7o+3BgenGicnNxAwh9o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\ntDdO73NODZ7ys++skPR20pPMsA1/fum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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "alpha_samples = mcmc.trace('alpha')[:, None] # best to make them 1d\n", - "beta_samples = mcmc.trace('beta')[:, None]\n", - "\n", - "figsize(12.5, 6)\n", - "\n", - "# histogram of the samples:\n", - "plt.subplot(211)\n", - "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n", - "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", - " label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n", - "plt.legend()\n", - "\n", - "plt.subplot(212)\n", - "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", - " label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n", - "\n", - "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n", - "\n", - "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected). \n", - "\n", - "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$." - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50)[:, None]\n", - "p_t = logistic(t.T, beta_samples, alpha_samples)\n", - "\n", - "mean_prob_t = p_t.mean(axis=0)" - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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yaREt3mheqkp7DhjihfKNaRGsn/FZVqNF2N/Eh33QSa8A+wMPe0F/fCTcFZRL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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "\n", - "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n", - "of defect\")\n", - "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n", - "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n", - "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", - "plt.title(\"Posterior expected value of probability of defect; \\\n", - "plus realizations\")\n", - "plt.legend(loc=\"lower left\")\n", - "plt.ylim(-0.1, 1.1)\n", - "plt.xlim(t.min(), t.max())\n", - "plt.ylabel(\"probability\")\n", - "plt.xlabel(\"temperature\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n", - "\n", - "\n", - "An interesting question to ask is for what temperatures are we most uncertain about the defect-probability? Below we plot the expected value line **and** the associated 95% intervals for each temperature. " - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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rbGENMFREBopIDPA5YEmtYw4A8wBEZCT2j57Wa1adlogwMDMn78q5X9k2e/J1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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from scipy.stats.mstats import mquantiles\n", - "\n", - "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n", - "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n", - "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n", - " color=\"#7A68A6\")\n", - "\n", - "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n", - "\n", - "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n", - " label=\"average posterior \\nprobability of defect\")\n", - "\n", - "plt.xlim(t.min(), t.max())\n", - "plt.ylim(-0.02, 1.02)\n", - "plt.legend(loc=\"lower left\")\n", - "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", - "plt.xlabel(\"temp, $t$\")\n", - "\n", - "plt.ylabel(\"probability estimate\")\n", - "plt.title(\"Posterior probability estimates given temp. $t$\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The *95% credible interval*, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.75.\n", - "\n", - "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over [0,1] quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### What about the day of the Challenger disaster?\n", - "\n", - "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring, given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings." - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 2.5)\n", - "\n", - "prob_31 = logistic(31, beta_samples, alpha_samples)\n", - "\n", - "plt.xlim(0.995, 1)\n", - "plt.hist(prob_31, bins=1000, normed=True, histtype='stepfilled')\n", - "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n", - "plt.xlabel(\"probability of defect occurring in O-ring\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Is our model appropriate?\n", - "\n", - "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n", - "\n", - "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data (which if we recall is a *fixed* stochastic variable) with an artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n", - "\n", - "Previously in this Chapter, we simulated artificial datasets for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example, we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to create a new `Stochastic` variable, that is exactly the same as our variable that stored the observations, but minus the observations themselves. If you recall, our `Stochastic` variable that stored our observed data was:\n", - "\n", - " observed = pm.Bernoulli( \"bernoulli_obs\", p, value=D, observed=True)\n", - "\n", - "Hence we create:\n", - " \n", - " simulated_data = pm.Bernoulli(\"simulation_data\", p)\n", - "\n", - "Let's simulate 10 000:" - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 10000 of 10000 complete in 1.4 sec" - ] - } - ], - "source": [ - "simulated = pm.Bernoulli(\"bernoulli_sim\", p)\n", - "N = 10000\n", - "\n", - "mcmc = pm.MCMC([simulated, alpha, beta, observed])\n", - "mcmc.sample(N)" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(10000, 23)\n" - ] - }, - { - "data": { - "image/png": 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Ys4KRQ8n2PZp66W66kxHxuaWOZ75KyWG1P3X1JZ46HRE3LHLubDnMNXe15/oK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\n7ba/a/shXtJsa1dJOiXp72w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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 5)\n", - "\n", - "simulations = mcmc.trace(\"bernoulli_sim\")[:]\n", - "print simulations.shape\n", - "\n", - "plt.title(\"Simulated dataset using posterior parameters\")\n", - "figsize(12.5, 6)\n", - "for i in range(4):\n", - " ax = plt.subplot(4, 1, i + 1)\n", - " plt.scatter(temperature, simulations[1000 * i, :], color=\"k\",\n", - " s=50, alpha=0.6)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n", - "\n", - "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n", - "\n", - "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [7] than p-value tests. We agree.\n", - "\n", - "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[8]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n", - "\n", - "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "posterior prob of defect | realized defect \n", - "0.40 | 0\n", - "0.24 | 1\n", - "0.28 | 0\n", - "0.32 | 0\n", - "0.36 | 0\n", - "0.18 | 0\n", - "0.15 | 0\n", - "0.24 | 0\n", - "0.77 | 1\n", - "0.55 | 1\n", - "0.24 | 1\n", - "0.07 | 0\n", - "0.37 | 0\n", - "0.87 | 1\n", - "0.36 | 0\n", - "0.11 | 0\n", - "0.24 | 0\n", - "0.04 | 0\n", - "0.10 | 0\n", - "0.06 | 0\n", - "0.11 | 1\n", - "0.10 | 0\n", - "0.75 | 1\n" - ] - } - ], - "source": [ - "posterior_probability = simulations.mean(axis=0)\n", - "print \"posterior prob of defect | realized defect \"\n", - "for i in range(len(D)):\n", - " print \"%.2f | %d\" % (posterior_probability[i], D[i])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we sort each column by the posterior probabilities:" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "probb | defect \n", - "0.04 | 0\n", - "0.06 | 0\n", - "0.07 | 0\n", - "0.10 | 0\n", - "0.10 | 0\n", - "0.11 | 1\n", - "0.11 | 0\n", - "0.15 | 0\n", - "0.18 | 0\n", - "0.24 | 1\n", - "0.24 | 1\n", - "0.24 | 0\n", - "0.24 | 0\n", - "0.28 | 0\n", - "0.32 | 0\n", - "0.36 | 0\n", - "0.36 | 0\n", - "0.37 | 0\n", - "0.40 | 0\n", - "0.55 | 1\n", - "0.75 | 1\n", - "0.77 | 1\n", - "0.87 | 1\n" - ] - } - ], - "source": [ - "ix = np.argsort(posterior_probability)\n", - "print \"probb | defect \"\n", - "for i in range(len(D)):\n", - " print \"%.2f | %d\" % (posterior_probability[ix[i]], D[ix[i]])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can present the above data better in a figure: I've wrapped this up into a `separation_plot` function." - ] - }, - { - "cell_type": "code", - "execution_count": 69, - 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"text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from separation_plot import separation_plot\n", - "\n", - "\n", - "figsize(11., 1.5)\n", - "separation_plot(posterior_probability, D)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects. As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n", - "\n", - "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n", - "\n", - "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n", - "\n", - "1. the perfect model, which predicts the posterior probability to be equal to 1 if a defect did occur.\n", - "2. a completely random model, which predicts random probabilities regardless of temperature.\n", - "3. a constant model: where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23. \n" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5,1,u'Constant-prediction model')" - ] - }, - "execution_count": 70, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(11., 1.25)\n", - "\n", - "# Our temperature-dependent model\n", - "separation_plot(posterior_probability, D)\n", - "plt.title(\"Temperature-dependent model\")\n", - "\n", - "# Perfect model\n", - "# i.e. the probability of defect is equal to if a defect occurred or not.\n", - "p = D\n", - "separation_plot(p, D)\n", - "plt.title(\"Perfect model\")\n", - "\n", - "# random predictions\n", - "p = np.random.rand(23)\n", - "separation_plot(p, D)\n", - "plt.title(\"Random model\")\n", - "\n", - "# constant model\n", - "constant_prob = 7. / 23 * np.ones(23)\n", - "separation_plot(constant_prob, D)\n", - "plt.title(\"Constant-prediction model\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n", - "\n", - "The perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Exercises\n", - "\n", - "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples. Why might the resulting plot look like this?" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0,0.5,u'$\\\\beta$')" - ] - }, - "execution_count": 71, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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Uz1yI9sMUi2CdwUX+PfjTiIHodx9uy5nErTxVPKcgnxd84nDNCfqyNeg99232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\naq36r8u/HxTap9GFR+n1T+iThtdR+L8t3wZdEKR6o/k1t+J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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# type your code here.\n", - "figsize(12.5, 4)\n", - "\n", - "plt.scatter(alpha_samples, beta_samples, alpha=0.1)\n", - "plt.title(\"Why does the plot look like this?\")\n", - "plt.xlabel(r\"$\\alpha$\")\n", - "plt.ylabel(r\"$\\beta$\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "\n", - "- [1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n", - "- [2] German Rodriguez. Datasets. In WWS509. Retrieved 30/01/2013, from .\n", - "- [3] McLeish, Don, and Cyntha Struthers. STATISTICS 450/850 Estimation and Hypothesis Testing. Winter 2012. Waterloo, Ontario: 2012. Print.\n", - "- [4] Fonnesbeck, Christopher. \"Building Models.\" PyMC-Devs. N.p., n.d. Web. 26 Feb 2013. .\n", - "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. .\n", - "- [6] S.P. Brooks, E.A. Catchpole, and B.J.T. Morgan. Bayesian animal survival estimation. Statistical Science, 15: 357–376, 2000\n", - "- [7] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n", - "- [8] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013." - ] - }, - { - "cell_type": "code", - "execution_count": 72, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 72, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.11" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/Chapter2_MorePyMC/separation_plot.py b/Chapter2_MorePyMC/separation_plot.py index cbb68ed5..a5316bed 100644 --- a/Chapter2_MorePyMC/separation_plot.py +++ b/Chapter2_MorePyMC/separation_plot.py @@ -26,11 +26,10 @@ def separation_plot( p, y, **kwargs ): p = p.reshape( n, 1 ) M = p.shape[1] - #colors = np.array( ["#fdf2db", "#e44a32"] ) colors_bmh = np.array( ["#eeeeee", "#348ABD"] ) - fig = plt.figure( )#figsize = (8, 1.3*M) ) + fig = plt.figure( ) for i in range(M): ax = fig.add_subplot(M, 1, i+1) @@ -43,8 +42,6 @@ def separation_plot( p, y, **kwargs ): linewidth = 1.,drawstyle="steps-post" ) #create expected value bar. ax.vlines( [(1-p[ix,i]).sum()], [0], [1] ) - #ax.grid(False) - #ax.axis('off') plt.xlim( 0, n) plt.tight_layout() diff --git a/Chapter3_MCMC/Ch3_IntroMCMC_PyMC2.ipynb b/Chapter3_MCMC/Ch3_IntroMCMC_PyMC2.ipynb new file mode 100644 index 00000000..a7fdb028 --- /dev/null +++ b/Chapter3_MCMC/Ch3_IntroMCMC_PyMC2.ipynb @@ -0,0 +1,1413 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3\n", + "\n", + "\n", + "_______\n", + "\n", + "## Opening the black box of MCMC" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The previous two chapters hid the inner-mechanics of PyMC, and more generally Markov Chain Monte Carlo (MCMC), from the reader. The reason for including this chapter is three-fold. The first is that any book on Bayesian inference must discuss MCMC. I cannot fight this. Blame the statisticians. Secondly, knowing the process of MCMC gives you insight into whether your algorithm has converged. (Converged to what? We will get to that) Thirdly, we'll understand *why* we are returned thousands of samples from the posterior as a solution, which at first thought can be odd. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Bayesian landscape\n", + "\n", + "When we setup a Bayesian inference problem with $N$ unknowns, we are implicitly creating an $N$ dimensional space for the prior distributions to exist in. Associated with the space is an additional dimension, which we can describe as the *surface*, or *curve*, that sits on top of the space, that reflects the *prior probability* of a particular point. The surface on the space is defined by our prior distributions. For example, if we have two unknowns $p_1$ and $p_2$, and priors for both are $\\text{Uniform}(0,5)$, the space created is a square of length 5 and the surface is a flat plane that sits on top of the square (representing that every point is equally likely). " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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1lixZwoUXXsiTTz7JU089FVEsjhkzhnfffZeuXbsGzpXfS2232/n6669p06YN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\nR45k06ZNT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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import scipy.stats as stats\n", + "from IPython.core.pylabtools import figsize\n", + "import numpy as np\n", + "figsize(12.5, 4)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "jet = plt.cm.jet\n", + "fig = plt.figure()\n", + "x = y = np.linspace(0, 5, 100)\n", + "X, Y = np.meshgrid(x, y)\n", + "\n", + "plt.subplot(121)\n", + "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", + "uni_y = stats.uniform.pdf(y, loc=0, scale=5)\n", + "M = np.dot(uni_y[:, None], uni_x[None, :])\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", + "\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "plt.title(\"Landscape formed by Uniform priors.\")\n", + "\n", + "ax = fig.add_subplot(122, projection='3d')\n", + "ax.plot_surface(X, Y, M, cmap=plt.cm.jet, vmax=1, vmin=-.15)\n", + "ax.view_init(azim=390)\n", + "plt.title(\"Uniform prior landscape; alternate view\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, if the two priors are $\\text{Exp}(3)$ and $\\text{Exp}(10)$, then the space is all positive numbers on the 2-D plane, and the surface induced by the priors looks like a water fall that starts at the point (0,0) and flows over the positive numbers. \n", + "\n", + "The plots below visualize this. The more dark red the color, the more prior probability is assigned to that location. Conversely, areas with darker blue represent that our priors assign very low probability to that location. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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75rFq0DnQE6gxfmN+oS/b2woM7682fjWaRuLII49k5MiRXHHFFWywwQZEIhEO\nOOCAvMfVK7lcjj333JMrrrgCKQvj1oYMGZJ/HQwGiUQixc1ty4B8X3/605+47rrrmDp1Kttssw3t\n7e38+c9/ZubMmSXnJaVk6NChPPnkk/3mFQ476Z/D0KFD2W+//bjnnns48MADuffee9l///0L1qKS\ny+UQQjBjxgxaWgqdcEL0bWbZfffd+c9//sPuu+/ORhttxKhRo9h99915+umnkVIyceJEx3uhaT6q\nrPZQGEbQQyvDWMUQm9CHvglk823Vfpz6N37aKzk4l/cfw24OUKgYYen9RkUKS7XCETX0wdohG1Lq\nV0PBoFZqD251rXLV+A251C01Nzdli6onuWhk3BJeeFmUWwIKp7pDMIzfHmBtD+N4pZoJL/QjB82a\nx/Lly/nggw+46KKL2GuvvQD45JNP+PLLL0u2C4fDZLOFn3MTJkzg7rvvZr311iMSieQNTdXwq4Tn\nn3+eyZMnF4QdzJs3r6BOJBKxndfKlSuJx+NsueWWvsY86qijOP7445k3bx4zZ87kzjvvdKxrbcZf\nvHgx3/zmNx3rTZo0iUsvvZSHHnqIPffcEzAM4iuvvBIpJd/5znd8zVHT2NRE59dCzfYWbELLJEeA\nnBQknnqRUBPO3zOfdHmrp6Y6bqqNb10DPYEa41fn16IN419AAi0/ptE0DsOGDWPttdfmjjvu4MMP\nP+TFF1/kxz/+Ma2trSXbbbTRRrz44ossXrw4v5ntpJNOIpvNcvTRR/Pss8+ycOFCnnvuOS6++GJe\nfPFFstlsP8+rG2r9TTfdlGeeeYbZs2fz4YcfcvHFF/dTpRgzZgxz587lvffeY9myZaRSKfbYYw/2\n2GMPjj/+eB5++GE++ugjXn/9dW666aaSxizA5MmTGTp0KD/60Y8YPnw4kydPdqw7duxYjj76aH7x\ni19w7733smDBAt5++23+/ve/88c//jFfb4cddqC1tZX77rsvv7Ft0qRJvPPOO7z99tt6s9sgo6pu\nFXUDW5AMASBODAEMY2W/TW6Fntr+m+CMo/TmOBWn8lJ9lSpHCDLCsPhaggmCwcJNbsFQJn+IUDZ/\nEMqYB5UfTlRzw5tXrD1KYMjDum1o8zMfp+t+5unULkAD7KlSN3mpm+PK3fBVvGms1E1y2phml+3N\ny2a0emxWU+eh0axZCCG4/fbbWbhwIXvssQennXYap5xyCqNGjepXT+W8885j5cqV7LTTTmy++eYs\nXryYkSN42QTqAAAgAElEQVRHMmPGDNZaay1OOOEEdtttN37605+yePFiRowYQTqdLujPi0dYrXPW\nWWex6667cuyxx7L//vuzatUqfvKTnxTU//73v892223H/vvvz+abb879998PGBJr3/72t/n1r3/N\nzjvvzFFHHcXMmTMdVRssgsEghx12GG+99RaHH344gUChKVO8huuuu46TTz6Zq6++ml133ZVDDjmE\ne+65h4033jhfJxQKseOOO5LL5fKG7tChQxk/fjxtbW1sv/32rvdF0zwIv9/4nHjiiSckk39Dr7Kx\nLU4rw1jBSJaynKEswgiAL64DkCSaL7O7btSJ9CvrVV6nlOQYvTbtUg5jqOVJpY84rYTI0EqCtAyy\ngmGkkn3Xk4m+16lEXx/SKk8oj7ETlH7tdr34daaMumq5XZmXdkmM0Idiu8RtbhmH13Z1/NT10k59\nbRv5Ih1eqw3TJcpKlVuv1YGlQ10/47n153QDiusuBz7FMII3LFHXrj+36051nK73/+WcdNI2HHlk\nG5MnT9ZWcIUsX768qZ7XaKpDLpcjm82Sy+UcPbyhUIhwOFxgNKp1q2UnaDT1ZPjw4Y6fGzVTe7Do\noZWRLC3I9tZMZAgipX22tzWSAIaNYv0vbK5fp6YfxdneNBrNYEBKmQ9pKGX4gqF8kMlkEEIQCAQI\nBAIEg8G8J1gI0a+9Nog1zUxVY37tdHlzBPOqCR2s9qTd66bHGywqdzvcQiScNH+Nshyrul4DIEai\nfG1fP5QbDuGlrl2ZGvPr1s7pSXS5oRXVCGtwQ3a5VLDT+/WiXetFH7jS8Aan8dT++sfbe19HiL5s\nb70l6tr153e8cjSBNRqNX3K5HJlMJm/8FhuqkUiElpaWvKfX+mkZzOl0mkQiQTweJ5FIkEql8hvW\nLGM4EAgUGMcaTTNRl0+fXlqJmJJnvfkYw+Yhbd6m8GDe9OYHQd+mN/0/bxDQAcQx4n7bB3guGo2m\nXHK5XN7Lqx4qqsFqeXQjkQiBQCBv/Kr9WK/V9to7rGl2qub5teRE7OjNpzpeXa3h6kqwc1fAMH5F\nc8kceGODTn/11XdNM9wO0TnQM6gxzn973lCzvTXDL1Sj0ahYRqt12BmsblhGbTgcJhqN0tLSQktL\nC5FIhFAolN9Upr3DmsFAVT2/lnJC37nxOk2IrJntrYXego1pdtq92Fw3Jmu8ViW+ndv1L/eiJWyn\n+SuJ5LO9RUSKpDQ2t4WU0Ies8jpjvQ4pt9dJ8zdkU+ZH59aPfq5ax24OxX04tZMuc7Ta+dEBLq7j\nVrca7XzhLLpuUG2pMOv94vQn6jSe1c6Lvq5VN4axvjTGrsJ6ZmN00gTW8fUajRfsvL0qlgHqFvdr\nhxAinwUNyPdfrncYIB6PI4QgFovl+9Ro6k1NdX77EHSb4Q7t9FRryLqR6nqelGmEREVygGdTAxZ3\n+atvhZw2C64xv81Oqb89L1jZ3oAm/PvUaNZEvHh7LcPXCTXW1wuVeoctWTUppfYOawaUuu046aaN\noaymPa8n2lykCQNJb9ne1gSsbG/6VgwSOjBkz7qpbrY3jUZTbSz5MqCft7fehmS53uF4PK5jhzUD\nRtWM3wkTJhDizqLQgr7HrQli+WxvYVLkTNehVSfkEJJQnAij+LpTO7tyLyESQRuXZuteEwFJDkFQ\n5IgGU2QIFSg+BEN9fWRDRh++/lydwhC8hCf4qWsXkrBhp/926m0KepiPUwgEDnXc+nCjYIzOvpcN\n9zTdLqWvipdwiu1s+vAbhmFle0uabcM4hyRYvwgvaYz9pF7WaDSlUI1Iy5BUDUM3T69KNpVyr1QG\nqkfXQjWGM5lMQZnlIQYKjGF1LcUGsTaGNZVSN89vjiBxYrSSYAirWcGweg1dJQQZgkTIEMEwftdo\nLNUqiZaHHRRY2d5WY3h/hw/sdDQaTQHV9vZ+8vzziFCI4ePHQyTi3qACLO+wlDJv/MZiMUfvsFVH\nK0toakXVdX7t9HUtLd24uZFmqJLq2E5rt7Turn165MLr9u2c6rqlRU53PWdqFhu3K0qy39i25NMc\ne0h17AU/fbjVUcs+63Lvw67MeveUSnVcqi+nOm7X/d67XFff61pm5LXFLqVxJW+C4n4F8AbeF1VK\nj9dSfehxuF4t/GgpazRrNlJKkslkXk2hOHzAMg79GL7ZdJo3brmFfx54IK9ffz2rP/mk7sZjpcoS\n1j3QscOacqia8esFS/KsvUkllbIEkBJCIofQ7s6+d4+l+atpcnS2N42mkchms2QyGdtH/l42tDmx\n+uOPWfDooyAlL11xBQ8edBCLn3mGdDxetbn7xfIORyIRYrEYLS0txGIxwuFw3usLfQk8kskk8Xic\neDxOMpkknU7b3hshhO191KzZ1EXn1yJN2Mz2lqOV3moNXXNinTuar0Q+4UWk6tJWA8jozvLaOWV7\nazQCnQM8gVqznXsVT4QwZM8kWvVBoxk4LAPPSZ6sHG+vyor588km+5SLVi5cyD+//W2ev/RSVixY\n0BBGYjV0hy3vcDqdJpPJ9PMOaw/xmkuVdX6zthvU1NdxWoiwmqGsIknUdhOb2oed7q6fzXFquV1f\ndmsoHlvdFpAiTIQMYTIFG97sNH8zagpkN83fcje5qfjR0vWjCezULoThIMxQqPpQ7hher5eq76ed\nLU7/DCv9U6nGlyWnzXFufftp146h9Vsq25udBnHa5rqX8ez6hb4QDv3hpFlzcNvQVg2jTeZyzP/3\nv22vvXLddbz/j3+wz/XXs/6OOxJpa6yMrHbKEur9coodtshkMv10h4tpBMNfU3vqpPPbRxxD2LqZ\nJM8SXS/mXxemOh4kfyQfd5XfVg0zbdTbocb8Dkpeq2JflsHbnKFJGk2zYm1oK5WwohLD12rX+9ln\nfPDAA471uj/5hAcPOYRZF1zAsnnzGtoYFEIQDAZdvcMW5cQOa+/w4KSuMb8ASaJmtrc0EWojtVJL\nJAEyMogQmJq/azh1fwdpaksUw1ubxfAAazSaWlKN1MR+WLVgAelud+fTm7fcwn377ceHjzxCYuXK\nqs6hltjFDlt4iR1WY4OLjWBtDA8eqqrzGyTTTzGhP6Ig4UW3ucnGKdTBLg2xlzTFbu2c++uvBdzW\nuT2WQGxIZMkQJESWWCCRlzxTQyBqhp+0yH5CJ8Z2uvdhlxY5Q1+2tyyGIRwsUdcOPyEQKn5CQFSd\n36aRmLX+wTqlVVYXYhfz60WD165+iL6EFz30pTp20+v1o/nrZz76g0YzePEqX2bVqQYfPf6457rx\npUv599FHs9mhh7LTWWcxYqutms74U+cbiUTyMmnqFw3L2259AbHwqjsMOlyi2RgQv10zpzoGyJgf\n3obnWr/h87aMFggYJFiqD80TmqTRNBOqoVUc4wuVb2hzIv7ZZ7x3992+2829/37u2Xdf3rvvPnq/\n+qrpDT0773A0GvWsLKG9w81P3WN+wTB+rWxvTt7YRiKuxPwC5AiY2d6kB093E7Coq7L2lvHbqJJn\n2a6BnkGNqWbML/TP9qbRaKqFZVBls9l+sb1u8mWVGp2rPvqIZJkhDOnubmb8+Md8Pns2vW+9VWCs\nNzt2scOxWMxRWSKVSrnGDksp89e0Qdx4VFXtoX+SCPtwggCRfLa3DjPbm7OCg10f9qmJndQcrPKs\nozKEfXIAa+yAomJh1c0SIEDWNtublerYSnMMIJX0x4SUR9mVqj34VYawG8+pPy9qDxYJ+rK9udUt\nV4nCyzz9tLOo+/cXt5TGKl4Wp2rO+UmRbDePNPXN9uZ0L5omPkWj8YRlOFlqBFaZRSmj1+4xezks\nevLJivvoaGtj7uTJrP+HPzDsO98hvN56g9Kws7zvFl6VJYq/wEgptbJEA1JXnV+VHjP0YQirqjWF\nmtHaObFfWbYg9KHJGdNZeR9qtrdGI9g50DOoMdXS+VVRs71pNJpKsJIs2Ck5VJKswitSSno++4x3\npk2rqJ+29dYjt3AhMpXik3PP5cMjjqD7hRfIKZrBjUZxHHW5+PUOW8aw6gHWyhKNw4Dt1e8xs711\nNKmkkpXtLSyyBAZD6EOl6Gxvgwyd7U2jqZRMJpNPS2wZvPWI7bVQPZOrFiwguWJFRf3tcvbZLLvt\ntvx54u23mXfAAXx26aUkGiQ5Rj0JBAKOscOq11jHDjceVY35NZJc2B8h5QiSJUfQzPaWpYPVBX0V\nts3kD7W9U7/WYdefitrOqdxq19v1ks2K+7K9xUgQDGXzR8g81DJfhHwcfvuw45Mu++t27Zz6CtN/\nY75TXbe5VWOtKmXH/AqbQx0krBxu5U51y0Wd0xs++nNaSzFqtrdeh7pe+rKro9EMbpw2tNXb26uO\nueiJJyruc9To0STeead4IL645hrmHnAAK2fOJLOq8Z/m1grVO2wl4wgEAhXFDmvvcG0YUJXWXtP7\nO6TI+G0WUqYMVVjHJxqoG980gwA14YVGo/FCcbKKYurp7bWIL1lSlZCH7MKFjtczn3/Ogu9+l4/P\nPJOed95Z47zATtRCWaLYINb4p6o6v+A13bDxOkEUgA5WO6o+2G2E86vXa21Sc9rk5qYbPKTzG1i7\notRNc/2zvZV4E7qlOq7GBq5yN7xt1Oneh5dNbKrGb9Clbqm5lasJ7FS3KXV+LdT3lJPm7zd89OGm\nsavWHQp8hRH36/L+9oVfDWKNpvGxS02sUg9jpTiswhpv1fz5Zas8WOx6zjks++tfXeutuO8+Vj38\nMOtfdhlte+9NeOTIfpvH1mQs73Aw2Pe/r3gjXSndYUtz2El3WI0p1/fcmQF9Bqlme4uSIGmmPm4W\nJAGyMkBQ5IiKFEkZHegpDSzq35n+0j8IiGIY3GkMOY+W0tU1mjWUUskqLGppiNilQ84bR1Ky4NFH\nKx5j1OjRfPzuu57q5np6WPyzn9E6cSLrXXwxoS23hKJ0w6VUENY0/CpLWFheYDUJhxCCRMLIzqlm\nt9Oe+EIGROe3D5FPeDG0gVUferpedrxmeX+jonF3u7ryUVd1+rGyvUFjGb+ZroGeQY15tUb9CvpC\nH7Tqg0ZTjJQyr9nr5vWt5RxKxRN3f/JJWYktVDpGjyYzb57vdr0vvcSH++/PihtuIPfpp4WhGEWP\n9p3CRJoV9ffhl0p0h5NFyhs6dtieqnp+rQ1qfZ276fVCLy0MZTXDWMlSRvS7Xqjpm+133alfdexU\nibL+/QX7lQfJ2Y6NiOSzvUVFkmDQyPdrbXALKtq+rpq/XnR+7V57CRFwCxcIOvRXTiiGlepY1fv1\n26+fEAkVv/rAdgyocIdbiIOfsAAn/Vw3zd/iulaq425g7aK6bmmMS9XRaJoby9urPm62UBMd1Mqg\nK+ntVVg5fz6p1ZXtq5l03nksu/ba8hrnciy57DKW3XknWz14P5m1RpBtNZxedo/21cf6td4U2Ez4\n8Q5bxONxR+8w9NePHkxfPtyoesyvX3ppRQJt9BAwVSAajbbO7R2vFWR7k9l+CS+ago07q9dXsee3\nEf5vhToHegY1xi3mtxKKs705xR1rNGsGdoaGkwFaS8PXLra32FCU2SxzH3yw4vFGrLMOH8+dW1Ef\nrTvsQOsdNyJWraD3J2fAVlsXGHCWAWwX52od6gaxNZ3i2GHri1A2myWd7nNylBs7rLYfjAy4pZYj\nmM/2NsTM9tZcCDIEiZCxzfa2xmGpWg3Ov5c1kHpme9NoGhfVUCvl7a1niAOUzgzXvXgxH/zznxWN\nOXzzzUm//XZFfQCsf/yxRM/4IaKnm8gTj9J7/lQye+9PYNS6BV5y1RguFeeqGsOl7nkl4QfNhHof\n0uk0QghisZjn2OFiY3iwe4errPPbp8VbrLtbSps3bm6kGcoqT9q9frR9vRxumr/xrpdKjpEzb2OU\npKFJXI62r1+qqf+7sMv+ult7p3I14YWfdn7Gc6urHlWJ+XXT/HVr56QDrB5B5fCDGvNrjeelL68a\nvGq2N6e6fjR//WgC693KmoGnWL6s3skqVPxoBS97/32y5uanctn9nHNYevPNFfUBEEvFET2GbKJI\nxGn7zRm0/fAwgi89h1Qez1uyYC0tLXlZMLs413Q63U8jVw1DGWgGah7Fsmhq7HAsFnOMHbYSsqj3\nNJ1O5z3Ggy122LObUggRAF4GFkspp1RzEr20MoLltLOaZnQZWtneQiKHkDobFgH6YmerqZClGSCK\ns73pX6hmzcBOvmwgvL3FhpQXQzubTPLuXXdVPP6Q9nZWLl5cUR9rff9YYk883K889P47tB/1LZLH\n/4TkMSciN9msYF2lHu3beTKtlMKqJ3OgaSTjUDVgLfwoS7h5h602xWM0In5m93PgHaeL5cb8AqQJ\nkyRCiByt9JbdT61o73TXUbVUHyKOG4oamGrG/EKf865R0DG/FaJme9OqD5o1Aztvb3G4Qb2ytKl4\nHXP1okUsfOyxisZfb6edSL5kl+HUZz+HHUrkP/axxwKI/e1GOg7/JqF//RP51ZeOXlPLqFJVEFpa\nWkp6MlOpVL7M8mQ2ine4Eaimd1i9x43uFfbk+RVCbAh8C7gY+KVTveLQAD8JL7ppI0qKoaxihRJX\naN9HfwUIYzFuag4RmzLn/uwSXqhjZAvGCxMhU5DtLaSEPmSV1xm7hBch5U3iRe3BT5KHctUV3NQl\nSrXLmWV2nl8/iTSc2qn4Snjho50v3DaCVftLkZOag9t45Sa8GIKh9dtDn/xZLRFFPzWa+mB5EC1j\ntzjmsZ7e3mIjzc+4IhVHZisLv9v19NNZevrpFfVBKER09QpEqrQcaGDVStrP+BHp7Xci/quLyW21\nDSLqrp1vZVCzKPZkqhu91I1gg3UjXaUxzl68w9Y9dZL2awbZOq+e32uAsykRk1Cezm8fq0293/YG\nTKXa3eWuo6pmexPNFrqxoKv6fap21UDfjnTXAE+g1rxShzGs0IduBv4XqtHUBrvUxJV4e8tRfbDT\n7fVLINnNBgse5qdPPcQm++/nu71FC5BdurTs9gDr/PQUYv93r+f64VdeoOOIfYlefwUs/NC3EVXs\nyYwqBrRdOuFUKjXoNYcrxavusIWUkkQiQTKZbNj76Gr8CiEOBJZIKedQwwfacVqUbG/NlzBCEiAj\ngwgBEZFybzDYaexwH41vrGxvGQwPsEYzeChOVlFMPbyDdnGW5YZWhL5aSMuj17D2nw/j0KO35/iH\n/0HrqFG++tjs4IPpmTnTVxs7Ru2zF+Gn/PUjcjla/nwlHUfsS2jG/yGXLS3biFLjUtVQCaeNdE6P\n9f2OP5hVJoo3J8ZiMVpaWvKx2eo9b9T1ewl72A2YIoT4FsYXwQ4hxB1SyuPUSvPmzePsE1ay7sbG\nB2PHMMEmEzLs0NkKwBtdRl7xb3S2EyTLHPN8804j5OD9ri/4ggx7dgYYxnJmdxlvnDGdGwHwQdfn\nJImyaecGBMmyoOtjANbvHAfAR10fkSTG6M6xAHze9T4AG3RuSogsn3XNJUGUUZ1bArC86y0ARnZu\nRZAsS81zK753edebJIkytHMCQzu/zuouI+4p2rkzAD1dr5AgSkvnjgBkn3qW1aQZ3jmBWCBBb9dL\nyHSY0B67AiCe7wIgMGkS2VAQ+ezTxo37+v7Gz5eM60zsNH6+Yp6PN89f6zI2kU0wz98xr29unr/V\nZcR6fE05B9jSPP/APN/EPLeyuo3rhLGdfd7f0eb1hWZ/Y8zzxeb1dc3zT8zr65nnXynXM8CX5vW1\nOg1D+Avz+giz/jLzfIh5vtysP7TTeFeuMq+3mtdXm9fbzPNe5XoIiJvXo+b1lHk90gnhzj7vrzCv\nZ7pMUQTzPGdez5rnmOcUn++pnEvl+lNF183fL7uaP58xf+5m/nzW/DnR/Pkcxo3b2Tx/wfxpaUy/\naI63o3luxeFNNOtY3t9tzZ+vmT+3w1jonKLrc8zxrPM3zJ9bmT/fxHjDbW2evwN8hZHoogdYYF63\n6n+gtM8A75nnm5o/3zfnv4V53aq/iflzrnl9M/O1sf5XXtmcLbb4BpMnT0ajqQWlklWA9xjbSnDT\n7fWbMCP84YuGlyqXoe1fU2kZMoqT7riUDz5YxiOnnempj+2PPZbPv/99v0spIDBkCJElnyHKDL8I\nLFtK+6nH033NjeS23orc6C0R4Yh7Qxf8bqQrbqeGTDQaA2V0q+/XUChEKBRqWK8vgPAzOSHEnsCZ\ndmoPTzzxhNxi8nfppTVf1ktfXul4QXn/OnFaaWc16/EFq2ljvvmhaNeH2j6pxOs6jZEy69iVeelP\nLUsRtW2XIkKALO3EyUrBMoaTSvbVTSaUPhJ95bLb7COhvFFVx5r6OmNT7lTXrQ8/Y6ivna7blafM\nckFh5rSMw2u7MbyMZ7cmpz7sXqtlrg8dpMNrtZO0TbldWXG5XR21brnjqTdf7cPPPCWG1u8iDC/w\nxh7nZlfH7XrfnE86aSuOPDLC5MmTG9N90EQsX768cT+JBgDVyHGKsa3U8FWNWsvQKr7uJUubWz8q\nwe6lDLt8X4LL+is0pLbai5X7/IInrr2d9+9/wLGPQCjE0TfeyMcnnlhyLDdGX3IxYx5/gPCclyvq\nZ/U9/6T9su+SOOxMUnt+D7nuWM+/l1wuRyKRQAhBS0uLewOlXfFRjKo5XOylTyaTZLPZfGhAvUin\n06TT6bxXtp6kUikymQzhcJhwOFzTDIdeGD58uOObpMo6v0Z6Y+vwo/kbJEuSKBJop4cwqZKav+7a\nvn3zsLvu1M6uvLfrZVsdYHWMIFkEMp/tLYLH0IdQxjwoX7s335ePPtSyRV3uGrx+NHqtMuttJ+lL\noexFg9jL+tyuq4efmN9ypXbLRtW2VTV//bwB7GJ+1X79LKqUXq+a7S3jcW4aTWOhZrxSPXz19pjZ\njVsNL3Poiw9tDV+AyLv/Ze0bDmXKtzfhh4/dz5CNNrKtt8Npp7HinnsqmgfA8K22IFSh4ZvdYDSB\nzz5A5LK03Hc5Hb/al9BzDyFXflVTw8rusX40GiUcDttqDieTyQLN4Ub2etaKZgr18GX8SimfqrbG\nr0qOIAmiCKCjATe+uSPImre0KSXPqk2jSZ5pKsTK9gY05d+nZk3Ha7KKWlLN2F6bzom88WjJKiKX\npfWRq9jgrhP54Q3ncfDt/0ugyDO52e67s/rxxyuaSmTsWKLz51b8ERA/59fEHrkxfx5Y9RXtV51A\n2xXHEZj7CjJd+nFdtQwyddOXZQxbm77sNtJZv99UKlXXjXTNZIAOJFX7K69E51fFCiXoYHVV+qsG\nQzq381w3a3rXws1k/G7SWbu+7bK91Ztw5wAOXg+2d69SNVTVB42mOVC9vcVxnVA9r6uXedRy3PDy\nxcRm/c1T3UDPcob+7RS+9vZN/PTxe9jhpycD0DpqFHLRIrB5zO+HMRf8mtjf/lJRHwBynWEElyzs\nVx5+91k6zt+X6PSp8Mncunta1U1fdprDKsUb6ZLJ5KDUHG4mw7uqzytL6/yW1vy1fibMmNoOugmS\nJmijwau2d9LdDdmM7aw17N6fXTs7XWE121s4lCJnGsOumr/qH4sfzV8/2r9qfS9auuVqAmeUMrts\nb+WO4beOXV2VsnR+nf6oq/GnVI0vTNb81Pl46ddru+Jsb3bfn500iNMer2s01cMutlelXmmJi71+\ntRg3+Pn7iKS/L6bhha+w1g2HMXn3H7B91/+x5JPVfPWHP1Q8l/ah7QQXL6qoj/T2OxGa55xkQ+Ry\ntDx0HdEn/kbviZeT3WZP5LB1Bsz4UjWHrfddOBzOn1v6uNaXMIvBqjncyFQ15rcaZAiTJEyQHK3E\nq9Jnpazqes29Up6+bG/RZpE8m99Vu74DDHzog6X8MGiph86vhc72pmkOnLy9FvXw9qrGbq29zIF0\ngtjTt5fVVgCxWbcx6qbvMWbbDdj4qgsIDBtW9lza99qL6AvPuFd0IfGzXxCdcYtrvUD3Ctqv+zFt\nU48k8O7zyETjZIotzkin6uO6aQ6n02nfoRID6X1tJi924+l0AN1mBqn2Jv1wTZnZvqKi+fSKa4K1\nz6p5/i40JbEyvDXn36dm8KPGXQ5kamI7L3Otxg1+tZDw25XF6WZGb0Ns0X8Y+cH/MOHRPzHm6qll\n9bPhqScTu/u2iuaSA0Q4S6B7uec2oflz6PjNAcT+dj7io3eQFYZuVJtifVw3zeF0Ol2gOZxKpZoi\nVKIZPNdVC3uYMGFCXuHBwktogR3dtDGC5bTTbduH0xgqbmmKvbSzGN75dbAJnXBKi5wWfZ7fYNDQ\n+gqGSq+5KvhJi6yWWVrB6nWnvr2mN1bLgg6vS/Xh9XpxHbu6kc7y2jU06j+XnW2ue1mIXapjp3Zq\n3aEYmr9WtrfinY1OaZOFx+tqncb/J6ppHCyjQd3IVk5qYlVX1+8H+UCEV0gpCc9/CVGhUZSYcgZt\ns04mkFzBkMe+T2yjbzL8pYf46PK/seK++711EgjQkowjuivbt5M68jjCL/yf73YCiD12G9Gn7qH3\nuN+T2v4AaBte0VzKwasH1q/mcCaTKWinfqFqBqOzUWhIz2+vku0t0qTZ3rIEjGxvOo6x8F3W2F9Y\nNZ6wsr1l0dneNI1COp0u8IypBqiqx1qPLG12nrlajGuNF+z+ipbH/lhRX7lAABFMEUiuyJdFPprJ\nsEcPYYvjNmTrWQ8S3XJL135G/exntPhIZ+xE6uCDiTznrEXshkj20nLTWYRWvE/b4tkEUqsb3mMK\nfe9VNVRC3UineoetUAl1I52dHnG9aKYNbw0X82sg6DYllYawqor9lsfKLv9rs+J+Pev9DiQfdtW2\nf8HAqj4M+phf5w0htUGgQx80jYLlDVON3prIiJXAKRtYvQzt8BfzCC6tbHNZcvIpRObd169cyBwt\nr/2RtZ45jm1uPJnNH7iDQHu7TQ8G6+yzF+EnS8utuZFrH0KgewkiU5nzKDX5WCJv3cOQe77L0P+c\nRuCzOchs8zmkrI10dprDatITNSTCMoqtxBPNYPjXk6qqPYSyWYJBf6EOTgoOvbQwlNUMZTVfMbKg\nD7sQv0sAACAASURBVC8qEoUhCf3DJZyUIbI2/QXJuYZOFCpJBJHm41rD+C180wVDfXWzIfNRh1JG\nKKy8pvRrv2EBftQe3MIlvKg9WAQwgrhyHvqopcKDG07t6hC1Uoid+kKlfZXqz+4DoZQqQwewHCP0\nYe2KZmePKPqp0RSiGpxOntZ6PAouNrahL8RB9T6XE0LhNF6BV1vmiL7yUMX9Zr4xmdgjhzteD6RW\n0f7UL4gN24y2J27iy6fmsvicCwrqhNZfn+jHCxAVeh/jvzyP6GPuG93cSO11CB0PHAVAZN6jhD+c\nSWK3X5La5kjkiHFN4aG0wylUIpfLkUr1OdycNnla4RLV/PsoDi8qLms0Gk7n16KXViTQRg+B+lse\nBQzt3NZ3mxyCrAwQFNI1xnnAGddZ+zHUbG/1/ntwivkdNEwcgDHbMH6pSbREmabe2CWrUBlIb686\nbi3GL9YJji7/mOizd1XW57D1CfQsQEh3ozW0Yi5DZxzFmHWfZdsXH2T4d/sM5jG/vYDYbX+uaC4A\nua9tTmhuZZnhcq1DCCS/QGT7jEEhs7TMvoKO2/Yh9Oa9sOqzhjbQvKJupLPec9Fo1HEjnRoqkUgk\nBqXmsBsNGfMLRra3ODEEMKSBEl54R+RVH5oi9KHW6Gxvgwyd7U1Tf9xSE0Ptww2sedjp9tbK4Hby\nbAcCAUKL30RkKtsb0/PdC4nOucFXm8jCRxk241A2//76bD37QWJbb82QEcMILZhX0VwyW25NcNEb\nlWeGO+p/iL56q+21QGIF7Q/9hLa7DiO48GlIVt/GGOj4V8s77BQqocqs2aVnVrPUeWGg1+uXqoU9\nzJkzh50mFYc9eH9tp+AQp4VWEgxlJavz4vreVCTsklH4UXhQ233Z9Xre++uWBEMlY+5Yj5IsUHuw\nS3jhW2TALuzBLWTBrj3Awi7YtNO5rlq/HLUHq0xiOAktgQCnPrwkpfCj1JDtgmin9/qeqWXCCwsv\nXtWX6O/9LTeRhJ927RiGbw8w3KGuXX9u16GJZDc0dUJNEmAXamBRD/mychQkKh1TxTKyg/FVtMyo\nbKMbAMM6CK2c77uZFQ8cC99G+PabIbAWuaHDCaz0Lk9WTPys82ib9suy21tkN9mM0Cul90OEvnyH\njmkHkfzaISR3/QW5UeMRgapGgzYMxaES0BcWYXeo7dQkHPVKClNrGtbzC9Bjpjpuz0sqNRdpQvls\nbwMdutEQqApXzffr1PTD2vRiZXvTaKpPsbfX6cO5HvOwS01cS29v8VqhUDIt9MU8QovfqmicxMRD\nCX/8WEV9iPRqAq1B2r44jd7/u4buq64mV8bvJAeIKARWfFHRfDIbbU3oyzc9e4+j7zxAx62Tic66\nCpZ+2NSP//14YFXN4WLvsJ3mcLF3WA2VaLZ7Vl2d30yOYNT7JjfjdcamzPx2T4AkYaKk6WA1KTP1\nsYqzrrC/DWqlytfq3BpcvMd2HuEQQTIECZMlKlLEZYttW6Oy0q+XVMd+HGNuG94sr69TXbV+uRve\nMvRle5MYhnDAoY9qp1628/oW1y/Vb8Ozo/I6bHPdj+avkwavXd0o0ALEMby/HQ71NZrysLy9Th+w\n9fBCOSXJqEc8sR35caUk8tq/Kx4rtdcxdDx2dEV95EKtCJYT6n2P9g9OID16Ej1d/yB852PEbvpf\n73M59kTCLzxY0VwA4secR9tT/rzHIpeh5elLiL74F3r3u5TsxnsiO9YdFF5Or6je4XA4XLCRrjjU\nqFhzWL1PzWAIN7TnF5o/21smn+q4+fSKa4JlW2lH4SDBMnib8+9T05hYGqbFH7gWdimCa7HD3Mnb\nW0/D1ymkIrzsI2JP2ce0eiXXOpxA8nNEtrLPp/hu5xP99Oa+ua2cTfv7h8KUXlY/+RCp3To99ZP+\n9oFEnqvM+M0BokUQ6CnPe2zEA59My/0/Qqz6AFIrfb+nmsH484K6kc5Nc1hNKmNpDjfyfWhQnd8+\nVpubatoHcFPNiq43ym6bj/sV/SXPGoZ5XfUbSzV+63U7kl11GmigqLfOr4pl/DZnaJKm8chms46p\nieuZrKKYWo9rF+ZgN6Y1t9Ci1xHpeEVj9n7v98Re97fRzY7culsSWvVCQZkAYp/fQfv8I8j8dhKr\n//1PMhuNde5j5CgCyxYhspU9fkvt90PC75WfHCPfzzeOpu2FY2h5+WTEslfJpuJlGXP19BzbyY1V\nGyfNYTWWGBjQZBteqGpkdzBjaP3mzx03v/UPjXC6HleyvbXQS4qopxTDheEL9lrCFqoWg115gKwS\nnlE6RKKgXETy2d6CIkdLMEGKSMHmN0vz19L7BZ+av9XY8BbEe8iBn9TEdhRne/MTWmE3H6c6ftdn\n186OAQ3dVv+ZqeENAdzTE7v1Z7cZzUtdK9tbGiPbW0tRXbswCi+pkDVrGqpm70CEGlgUGzj10At2\n8vY6SaYFMisJfzC78nFHjiL00jsV9ZFedydC3S84xtcKmaL1o4vIhYbTe/vvyX06lPaf/IxAd2EC\nq97zLyT27ysrmgtAeo9v0/7P71bcj1xrbUIfzoOeeYSXzCAx7lQSG36PZOu4/JcSVTVhTcUKlbBi\ngwOBAJFIhFwu19D3pmF1fvsQ+Y1vAyV5Nrxzm4raN3y2t8066zfWQGR7i3XWaaCBYkf3KjVDZ3vT\nVIabfFk9Qg2sebhtMKvHmF48zOHwPHJHbMSqP/yTzDrjyho7uf0UQh/PLKutSmLXM4l+cqNrvUBm\nOe3zTqNV/p6e/9xA95VXFWyKk6OGE/q0Mpm03LBRBLoXIXKVfZFOjtuH8LKn8+eCHC0f/olhs/el\nbfEdBOKLSaVSxOPx/CN+9WnFmoi1bvWLQSPTFJoePbQyhG6GsIqvapJNqrZYoQ922d7WSNRsb437\nxVDjmVpne9MMVhrJ21vvx7Ru3l4nBFmiuX8Qk7eSGzKc+K9/R/yzEbRddxqBXu8SY8nJP6DjsaPK\nnj9ALhRDBLsJZFZ6bhOKz6Pjg++T3mh3err+QWj6fwksWkx4TmWKEwDxEy4k+kLl3uPUbifT/sYJ\n/cpFtof2N8+hNbY+PdtcRmLI9mRCw/Jf3ixU9ZFqZfbzQrNp7Q4kVY35DWUhmMn2HahHJn+EyOaP\noM1RfD1JFImx6S1MyrG9il0dFbtxnY5VXXPyfbmNUaw4ESSLQJKVgqCQREzNX+uoGSGXQ2Vul3s7\nu+tuYzvNxynbm1s7P+OpJLrs+3Nr5wvhcLgNYlc3hBFKUHwElUPlxTLn6dSf29yKUbO9ZUrUdevL\nbryG35OrKQMpJel0ukAuqVG8vZbnaiDG9LLecGAh0dw0ox3LaZM/p2W98+m59Gq6T72BXCji0gPk\nhowikFyMyCbKXwgQ3/lXRD8tLw1xeMUs2t8/lMABS4n/9pfQvbSiuQDkRg4ntKxC73EohmAFIuO8\nzyiQ+JSOl77PsFeOpa37NSIi1U8/18JJGmyw0WyGd1N8suQIkjCzvXU0ZTYpQTqf7U3HNepsb4MN\nne1N448f/vCHBbvDyzUEK2EglRwqGTMsX0IUhdCF5Ed0yB8Q3eIWeq68k56jf1dSUKf3e78n9up1\n5SyhgOwG4wmtfKbs9gIIL51BKPoW8ofjWHX9g2Q2Li/MMLnLFMLzHy97LhbxzvOIfnSbp7rhFa/S\n8cyBtL9xBrHed4hFg8RiMcLhQslJSxbM0smNx+NlZVHTVI8miPk16MXQyO0YgLjftSqM+YW+uN+w\np4xddaaeMb8W9Yz71TG/dcCK+9XGr8adJUuWMHPmzH670wfa21uLsdU0spWOGQ4upTV7hfN1+Sod\n4kjCOz9P9zUPEP/mSf3q5AA5fCihFZV5SFPrTyK8+rmK/Ri9m19IrPc6WuJX0SG+T/KCY1l9xT3k\nhq/nq5/kt44n+vqdFc4GcmO2IbTUu0EvgOinD9Dx1D7E3p1KcPUHeS+wEMJRGiyTyZBKpUgkEvm4\n4XQ6XVHc8EB6X5vNo11Vz6/IYCS6sA4l1ME9vKB03YSZ4KKD7hL99fWhYhdOUXjdqZ1zX8WHil0o\nhFO2t1AoS0gJgwiGskbCi/whlQPvhxt+27mFJPgJkbCe6lsU/82UaldqnvW6F2Whhi/UY0CnkAW3\n8coNixhqllUr25vat2YwsXDhQrq7uznuuOOYPn06UB3j04vO70B5e4vnWe6YYfE+AT5xrReRj9IR\nOBQxJcmqKx8i+Y1v56+l9voRkQ8rlwJL7vILYh42urkh20cSyr4HgJCraes9l7a20+m9+rd0X3Ar\nuWirax+5dlOvOFNZGEdmve0Irnq1rP86QmZpmXsdHU9NJvTpw0RZYpQ7SIM5ZVGzjOFEIkE6nW66\nUIk1LuyhVjq/FhnCJAkTJFf3hBfLut6sQi8i7/01NH8biA+66j+mle2tHqgxv4MSPzG/tSKEIXMm\n0aoPGjuy2Sw33HADkyZN4q233mL48OG0txtPDAabt1cdU6WSMYOBBC0578amQBLL3UFH+DByJ2zG\nqksfJD1uIqmdDiTywT98j6+SiwxBiKWIbGVPYhPrHEY4PaNfeSC3hPaek4mtdxk9f7mJ7tOvLJku\nufeEC4m9+OeK5gIQ3/tcYvP/UlEfItsDLTGGfnYIbYmHIb2k3xMOK4OaZQxboRKqdFoul7NNKZzJ\nZJrKGG5Uqutuyhhav/nOld2PIRfNX+c0xX0d9tJKlJUMYwVxMwzCSbvXawrlUu2s8gA5W63gQo1h\ne83ffF8iS5YgkCEWMPR+gfymt6Ci7Vug+duvpxIUe11Lvfain2unpWtX5tSHmyZw0HxtOSf9pCy2\ne+c6zcePzq/T2BYDqvPrhOohtZu0l1Abu/Z+Q3Q66J/q2E7TV/0lOGn+NuSN1lTAm2++yQUXXICU\nknXWWYeHH36Y9ddfv+bjlquqUM0x1bHLJRz4kHDGvzSZIEOLvIZYy410/+JKMnIE2WGbEFo+t+y5\n9O5+IbHFlRubqTHH0NHzPcfroez7dPQeQ3r87vTcfB/Bmc8Rm35lP6+dXG9dQrPfrmguuUAIEUoQ\nSC2rrJ9QOyKwjGB6IR1LTiSzfEvi61xMNvYNCA7r9x6w3ovqJkvri5qa3rv4y5vVJhgM5r9QNULY\nwxrn+a11zC9Aj7mpZgirXGpWlxGdW1elnz7JszQNJXm2eefAjFuvbG8tnTXsvBFohJhf0NneNKWY\nMGEC5557LtOnT2fHHXckFovVdLxqeXv9eNmctIKhQqNASqLykYoelgl6yYRHkBh5JsuOP4MVR99L\nrtVfXG1+OmtvQKj79QpmA7nI+gTER/0279kRTs+ivfcwgnsvoPvmB0lM7pNoS+5yEOEFVdAr3vMc\nIh9XHjPcO/43RFf8NX8eSr1Hx+LDaPvkBwR6X0Rm3Z+MWSmFI5FIPqVwNBrtFzeczWYL4obT6XT+\nmvYOl6Yp1B4s4sTIEiBGigiV5SIfCKxsb0JYBvAaTnG2N02TY2V7y2Jke9M0Ko8//jg77bQTEydO\n5Lrr7Hf9n3feeeywww7ssccevPmmEfqVTCbZZ5992HPPPdltt9247LLL8vUvu+wyxo8fT2dnJ52d\nnTz+eP+d9+eccw777bcfbW1t9PTULjym0tjecgzVWsYTh4MLacn+b0V95IiRCaeRwfmkO35D79gL\nWfqjS1hx2N/IRYZ47iexxZGElz1c0VwAere4iFjvtZ7rCyCa/CcdiUPh6KGs/t8HSW23N8kDjyf6\n2h0Vzyc7dgfCXzxRcT9yrXGEki/3Kw/Hu+j4eD9aPj8T0fs6MufdBrBCJezihlWJNeu9l8vl6i6x\n1mye36qFPcyZM4e9Nzf2aFkEM06pjt3SGzuFJOSI00I7PQxjJUsZUSLUof9jU6dwCqcUyRYrut5g\nROf4kv3ZpUW2C4XIEiBIjigJsgQKxrbFLdWxlzCEgv5s2v0/e2ceH0V9///nzM7svTkIhwFBRS7x\nooCiRTECVtBaK37rVapU22q9i613q221FtuvrUfrz1a/tZdX8baiBeoiisghKogIaLhCIAGS7Gbv\nOX5/bHYzSWazx2wuzOvxGNid+cz7897sMe95f97v1+tzP4yt6mgjW7lEoSUSxv0xWjO/+ZRk5FMi\nEfG3Zn/zKZcwQ7evzGeSNDbifWBKy+N8bqqylSRkO699iURK7a2BZOmD22RMP3oamqZxyy238NJL\nL3HIIYcwY8YMZs+ezZgxY9JjFi9eTHV1NWvWrGHNmjXMnz+fxYsX43A4eOWVV3C73aiqyqxZs5g5\ncyaTJk0C4Oqrr+aaa67J6kNXB7/ts71dXeLQmThHMYIOWVuDQNiSjZD8SxTnk+nnuriHeOlNJDxH\nkPjBYzi2N+L99w2IWueZ2MTxF+H91Jp8sAbobidSYHve5wpoOCP/Dwd/IXz9XajSINSBY5D2Ft6b\no1ROxBZYa7kNJT7wVKTYu5mlngFH8BnswX8RLb+WROlFaPaxCHnySqeC4VTgm/r8pRrkUkitQiiK\n0ua81ApIV/JZ93b0uVce6kHKs2JATZc+KPSnO2n9BPZTHR4kSGWQ+inPeivWrl3LyJEjGT58OLIs\nM2fOHBYtWtRmzKJFi7jwwgsBmDx5MoFAgLq6OgDc7mT3fSwWQ1XVNoFlroGe1+stevBbTFaFfObs\navYIm1CHS/21ZTtxeTSavK7Dfl2qJl5+Lc1HP8uBq58ieMYCtAyhgVJ6JGJsM4Ju7UY2Nvw6HLFn\nLNkQiKHYB6MPvInAVZfSdPVC1NLhBdmKzLgF5+d/sOQPQGz8DTibHs86TkDF1fAgvu3TsR/4I8S+\nsHSTlPrcpYJZSZK6lWItZTvlS19An6r5BYjgQgc8hNtQhnUlzLK+hUJDQNUFREHH1lsivlTWtyeQ\nSe2tmDjoa36nZB/SbXDTqvbWn+ntjaitrWXYsGHp50OHDqW2tjbnMZqmcdpppzFu3DiqqqqYOHFi\netzjjz/OtGnTuP766wkEMvdmtM/8Wr3otr9wdxeTQ3ewR8hsxMYuSzYi4lwSjo6sCkbo8npi5VfS\nPGk5Dde8QPMpt3e4QkWqfoFr5wOWfAFIHHI6cuxVSzY0QHP6EOT1CL6foR1+I03X30bTFf9Ec1fk\nbkdyIoghxESjNX8kL4LYgKDlnpgT9AjufXfi2z4DufEfEN9VtPKELxvFWr4oOs+vcWvL+Zu7nHBn\nnL8CScGLJLNoU042zHh3M0ssm82dXZrZiM55hY1qb4k0t69k2IrO+Vso520hx8lwPNN5Mh0/hfnM\nYcVPs7FFod3tTOY4RXJsxvmbjQu4GMhVsjiX88yQi9pboT70ozdAFEWWLVvGhg0bWLt2LZs2JTla\nr7jiCtatW8fbb7/NkCFDuOOOOzLaKFbZg1ng29XoTq5ggSAu9WHLdiKOC1AdL+Q0VpPfI1p+BcGv\nVtPww1cJT742uV9yItgTiPG9lnxRfJOQ9DUIFrMdMffV4DS8JnE/QulNqKN/TtP839A093E0KTtH\ncGT6nTi2/dmSLwDho+/C0VgYTZqoNeDZex2+HWciRleja3sL+kx3ln3tSoo1s/29PXDuMzy/RjS3\nqEl1F9/vPv/GotrrdWpvn/l7dv5UuWlXfVci/i4y3Fvwfk870A79am+9GZWVleza1ZpJ3L17N5WV\nlR3G1NTUdDqmpKSEU045haVLk01CAwcOTF9AL730Utat67jEnoLVsodMmdeuRHdzBeu6jixsRtbf\nsWRH4XgU+dNkRipXCKA5/kO0Yh6B6VH2X/UawXP+jqPGWtMdQGT0rTjDj1i2E/OdCfbXOuwXpJ1Q\ndg3qMY/QdMvjBP/nITQx8821duhRSAfes+yPPuAI5NgHlmyISg1IzbiE8xD1/6LrB7osiEzdtMmy\njMPhSAfDqVIJYzCcKpVISTPHYrG0NLNZuVFfQJ+r+QUItmSWksFv7767MEMmtbcvLYxNZH3v7exH\nB6SC32KpvfWjmJg4cSLV1dXs3LmTeDzOCy+8wKxZs9qMmT17Ns8++ywAq1evpqSkhMGDB7N///50\nOUMkEsHv96cb5fbubc0Ivvrqqxx11FEZffB6vYTDhTVw9ZRKW3fOmWxgiuPUnrJsK+j8KQlXgUps\nAqiOF4kO/C7hQ4eyf8IviAyeU7AvmlSGIO1H1K3RlSrS8eiOj0HI/PsiSJ9B+RUkJj1H0y1PEzr7\nng6/RrFRX0Pa/5blRrfYIbORo9aZIhLOE7BJq7CJG3HbzsfJXER9Bboe7JZMaqEUa7FYK/tWb8/4\nplC0tcYJEyYky/wcrfuMghfZxCgyHTdDAjsxZBwkKCFAqOVim4vghdk+s+PG/QOrxuc8tq0f5iwS\nkpAsopBRcdmiRHGmxS66HGZsD0dXtT7Oh+3BzK5xTC5sDwqtam86yUBY7WRsZ3NnOu6rMt+fLRFi\nlRmi22BW85sLS0S2F5NJgMLsPONYB0m1t0yCF5lsmc0n0n9HVFzYbDYWLFjA+eefj6ZpzJ07l7Fj\nx/Lkk08CMG/ePM444wwWL17MpEmTcLvdPPJIMlO3d+9err766nQG9LzzzuOMM84A4O6772b9+vWI\nosiIESN44IHMtaFer5ft2/Pr9M/GqtBV6M45ja/RKX2BQ3nakj2NChSpCcQmS3bE2Dc54HyDRseb\nVEycQ3noSso2PoBjf+d1xO0RHnsvzrA5tV4+CJXdAc4bcxoryGuh4lJiU6uIH/cijpXv4XzrfkQg\nNvVKfB/OtexPbOz38dV/27KdyJCbcQnfSz+XxBXY9LNR9LNI6D9C42gEIXMpR7GbzsxYJdoLcEBb\ndpVIJJIOonszm0SfLbRrxouDBkoIpoPfvgQFCRkVO3GidC3Ze59ASu2tP1F4kMBM7a0fvQUzZ85k\n5syZbfbNmzevzfP777+/w3njx4/H7/eb2nz00dzrHfOt+e0JlTbj3Cl0lxyyIIBDfwPB4spg0L6A\nhMt6qYKe+BaN3jtBUNnv+hcHnC9RMflblIXmU7b+HhxNy7Pa0ADdW4EU+NSSLxpeNEcziA15nSfY\n/TDAT2zm14md+DL299/BptQgqBFr/jiGYKMGQbdoBzeCPYAgtL1REQSQhdeR9NdR9G8T176PLhyF\nIDgyWOo6ZKJYUxQlTacGyWC4t5c/9MmaX4DmtNpb11OeFbvmF3qZ2tsmf8/OD23V3oqNsL8LjPYm\n9LaaX+hXe+tHZ/B4PDQ3Z68J7+46W+OcRlgpc8jG92v2Gh22HbjUh/KeywgNiYTsQ5e+sGRHUI4l\nZPschNZAXBcS7HM/xecD72b7lG+xd+obxH2dK03Ghl+H3SK9GUC47FdQaEAvAI7XYODFhKfNpHnE\nOMKHWcvYho//JY6G3MU6MtoZ8jNkMfPrEgSQxX/iFmcg83PQNqDrPVs2aZRYhuR3M0Wx9qUJfoFk\n5k5t3dqSFajpzYxdwZwZgYxj49hb1N5iabW3zAwOHVkb2s6Rjc1By4MZQu3U99RYER0VwVTtzSYp\n6U2Q1PSGpBg2isf2YMtjbC5282F7SO0zan3YsowtBsNDJj9zPUdq8TO1dTuMjAnGP1iKLSJf58zY\nF7L9QTtjbbCq9pay24+DEanMb6bA0BgQ9mRtbwpd2dRm9hqDsoMm6Q5LuYCwdBcJ1z8s+yhEfsw+\np3nQqgtx6j1/5fNBv2THyd+l7quvo3iPNx2rVE7HHnvZki8akHANA6lwQQsAdJ2EEGX3gB+x+6Qj\nqDv7DaLDvlmQP7rHh5T43Jo/gOYbhSSuzjpOEFQc4h9xi9ORuR+0Teh68pPSG7h2U9nh3o4+x/Pb\nCoEwydqXrs7+DqrK3LhhBa2CF9m1zbsUR1X17PyQjHO6qjzIXdVFhnsLTuppB0wg0Jr97R5Wln70\nHXTG9tBbeHtT6Mqg1yyjHZMD+Ev+xPJSgc89fhqlXxYUBMfsx6JJK6w5qlUQFYJoYudZel2Istfz\nOJ8Pvo/tJ19D3Vf/jeI5Jn08XnYakvqOdXoz1/fB+aIlGwBa7AYCjtdB0Ai6nqdm4I+pOWUidWcv\nIjbkzNz9GXUN9uZnLfsT85yNzZZfw5wgxHGIC3CL05F4BLStlv0oFL0h6M4Xxa35VdqxqRgb3jJK\nHXcub2wmIZzaF8aJj2ZKaaKB8jaumDWgZWqCy6c5zggzSWPjfjVLvZbaUujqII5NUkhluiRD85tq\neJxXr5VZs5rxcT6NZMbHXdHwZtwfJ7lKbqagm8lGrsfbjylkbN4w+zEodql9oZR5Rt9SPuViK5O8\ncXv4gAMkSx8GZZjDzAfopZ2F/SgSzIJfs4a27qjtNStzEEWxgy9dNV/719gg7yAmNrPH/il75E85\nxDmecZFlDI778Sl35ZQjiIjfI+F83fLiiS38C+qduWePNSHMHu9j1Lk9BL96IyXNh1D+0Y+JjroB\nX6gIjWUlXwf7JZbtJJRpRJw3te4QVAKupwk4F9J82iV4m2+k9P1f4djfeS2zMnwm3j3nW/YnNuQK\nXEJhr0sQwjiFn6Hrv0Gxv0RCGwCMsOzTwY4+W/ML3af2Vue3VqCfCUa1N6knL/af+ntubiO6ivIs\n5C+isd6IlT3tQAa4Sf7E9Ku99aMt3G53B4W3YmR7s9XXtodZINqVGeZs9ctxWzMbXAbuWgH22Dfi\nL3mct0vtfO5eRlMOmeCw41xUu8UMqWYnjouEVJt9bPtTxRB7vI+ydfBv2XXyLwl5DkUVD7XkTkKa\ngu5Y2ym9WS7Q46cSlj42vzEQEjS5/8ruQbeye/o3qZ/1b2Ll5itrSvkkbIm1CBYbVTRpKIK0A0Eo\npDysFboeIiE10lQ+j6jjFRLs7jbasb5Cb2ZE7+WhyAEaNkK4WxZY+yKhfqvam1OMZRn7JUBXlj70\nowcgAilanr74/exHV8Fms2XMrHZnbW93NtKl5oXMr7FRriEs7e94YpsgWOJzzzIapXtNw66Y+DUS\njhWWg0Rb+A72ORZasqGJQTTBx+rSf/DJ0F9RO/DfKOLogmyFy28GV2EKakYo0RsIOJ/rdIwubdp2\nLgAAIABJREFUxGn0PE7NkDupnXkx9bNeQymb2GZM5NhbcTZYa0oECB1yDw7RumR0TP8RYfsr6GIj\nAc/dHPB9h4j0Ogp7ui047UtlD8Wt+VXIuLWVOu7YYGZErlLHNlRCadaHQEa54c6b4LLPXVk1Jmd/\nsvnQ3g+t5S1wCDnU/ZpKHZN7f1ImHFvV8w1vqf22dsdysZHtuKcqdxuZ7BXyd+02ZKv5NTamGSWU\n82mKa99g19k5xrElLfv663770RZut5vbbrutDUF+dwWg3S1YYUSm+RK2MBvdr3duzBAELy+lJQi+\nL30dAQg5rkV1PmnNaQ0U/UgisjWmI1FzERUgaKthg/dplg94jk+G/jrvIFgTK9Ece0CweBOtVRK1\n1aMLudGS6UKUBs//o2bIXew643Lqz3wNpfR4NLkcQdyPqFkT69AQ0Z0ORGGHJTsAUdvpxO3LWm2L\n+2jy3s5+32VEpP+gUNcnM7RdhV57Oc8VQTwMod6g9tZ37jwgSXmm6yALCiIqWs9QB/Qe2CDN/tb/\nPT0IYGx60+hP7fdD13WefPJJ3nvvPcLhMIMGDWL+/PndEvT2lGBFLvMF5N00STWmx8ywx76JPfZN\nDI6P5ajofxkUX4Mn8QwJ+RPIJZnSCcTY1dTb/2PJBsCg8PVsdC5KP0+IzWzwPoXs9jLWeR+Doy4G\nHbgRSdvSqZ1g+QJw/cKyP0roXho9+avd6UKYBs8faHR7CJ9xJe7wRHx1v7LsT3Tgzci2v1m2o2gn\nEHNsAKHjRVMT99DkvRmbcije6Hzs6nHY9IFF/dz3xYa3Pl3zC61qbza0lgC4+Njr39QldpMQ0py/\nOWV/uwIb/T0zrxlSam9QvOC3v+a3ByGRVHvT6c/+9mPXrl3MmTOHm266iXA4zOzZs5k7N9kIdbBl\ne80o0zLNp9iifOoqLNiss3/GspIn8JeGqXE9QVyvBM1aXktTTiVof9uSDTQRTR9EUNrV4VAyCE5l\ngu9j98DXUcQx5mZwojlEsOV+Y2BuyE5ccKCKe7OPzQBdCHHA/TABV5gtR1xI7chFKPbx2U/MAKX0\nRCQhP5U8MzQLtxFy/r3TMaq0iybvfA54vk9UWobC/i91Jri4md8Ux6/xeQuMUseS2pH5wVwe2JyJ\nof3xMG4cNFFGIxFcHcakSGQzzZHL3Gb7jKFqW3u2jPs6+CbY02pvTjFKHHsbqeMkC0QSqtRqQ0/t\nlwzStdkYHoyPc132b/+4GGwP2ZCSOtY6sZHNdr6vrzNb+drtUd7x1MW1UEljM1uQndmhs7Ht1d7y\nkU3ux8GEeDzOqlWrqKioYMCAATzxxBNdOl9vyPYKgpA1yAjKteyXrYlRRIUmtsn1fGYPcVLoJQYI\nm7C5bwcxv6SKED2PRvk9y4uoFZHvss3xVqdjUkFwMhP8KwZFPQxu+BGS2ppwCpfeg+76f5bXdNXw\nXTQ6rNOS+WKXUeN4i332NVS73Ix03UlFpIxBu36MFM+9TCTumo5NWo7Vj6KmlRG3BdFzLAlRpWoa\nvTdgU0bji96ArByNjXJL34kvdea3+3l+WxHqYrW3IVXjusRuCj2u9ja+qvvn7AypT6VGcf4cxprf\ngxK9kefXiH61t34kMXLkyHTJw6GHHtqm3rfY6Olsb67zKWKcTc4lluc/Ovw/rHS9x265hhd8r/Ka\nI0hd6HnU5gdBc2c3kELiAhocr2UflwWSdgz18ie5TdkSBL8z4Ck2DP0luwe9gSIdkxS1cB+BIK+1\n5owGCX0scflja3YAmzKFffIaABQxzGbv31ld8X9sGv3TvDLB0UOuxS7kX4LRHmEWEHL9Ne/zVGkL\njd5rafD+kKj0LorWYMpzfbDioCjAi+DsoPbWl6AjktBtpmpvX0r0nZvHfuQEq2pv/egKLFmyhClT\npnDCCSfw4IMPmo659dZbmTx5MtOmTWP9+qSqViwWY+bMmZx22mlMnTqVBQsWpMc3NjYyZ84cTjzx\nRM4//3wCgY4NQWeccQYDBw5Mq7x1BdpTmFlppMuWtbXKHNEs11Jn/yxvv4xwqeU02WJExNZGrj3y\nHl70vcYrzn3sCT2DEvwjaN5O7QjxaQSljy0zRZRGv0GNfXXev+UJMcwnnmdYXv5PNlT+lL2DV4H9\nPUu+AKjxywnard9gOGNT2S9t7PC6FDHEZu/fWF3xhCEIPsbcCKBKhyLK2xCEsCV/NA1itiGoUuEK\nc4q0iUbvNURs1TRJ64jrTXmXQ3ypM78ffvhhp2wPRqICm6K2biYsCtlkijse19LlDmU0ZRiTG/uC\nEal9+/wbszI7mMkz5zNHomWp2EEUm6Smty6DkcHgM3/Xsz1ksmG2PxPlWaHzRf3WGB6KUhwkZNgK\nlRA2sjasoSODQzH8zMYGkevraK/2lmmsmb2D4v6810HTNG655RYWLlzIihUreP7559m8eXObMYsX\nL6a6upo1a9bwwAMPMH/+fAAcDgevvPIKy5Yt4+2332bJkiWsXZvMzP3+97+nqqqKVatWMW3aNH73\nu99l9KEzlbdiwUq2N5dz8s32tg8qVDHOZ67/5u1bexwbvpAVrndNj9VJdbzs+zcvunaxO/xPEsEn\nQBtgbij2Q/Y7n7fsjytxOrssBK2KGOYTz3MckAU+1qtoDLyBnphUuL342YSK0MDnil3CLmfmGt3W\nIPhxPh19O7VHvoFiP7bDuHDlfdjF/7XsT0y/lrD935btiNoAIuI+tvjuYrPnbpps64jrgYO6Jjjr\nlUUQBIcgCO8LgrBOEIT1giDc1R2O5YtQS/Dr62Kp465Ciu/XjkL/0jCtn8z+P8VBAmPpQz96GmvX\nrmXkyJEMHz4cWZaZM2cOixYtajNm0aJFXHjhhQBMnjyZQCBAXV0dkKQpg2QWWFXVdLC3aNEiLrro\nIgAuuugiXn89M3WXx+Ohubk4n4fulkTOJ9vb2fxBeQ97ciwNyAS75iUkqITEzm8kDkj7edX7Os+7\nPmNX+AkSwb+Ddkirn4mvELJtRbfYeO2NTWWv9Kkp80A+OCR6AtXyZt5zL+EF37/5KPETGgJvoMen\n5mVHi1cRkj60nM2WlMMI2vaiCdlXZxUxzBbv31k94M98OubWZBDs+ErSH+zg1BAFiw18QFScTcy+\n2LIdV+hWap3/AiAsb2Gz72ds9txNoy23THBfDJKzBr+6rseA03Vd/wowAZgtCMKJ7cf1ZM0vdK3a\n25CqsUW1ZwYVsefU3o6u6t75coHxemH1e+Wtsmigt+PknnYgB7hJvqn9am+9AbW1tQwbNiz9fOjQ\nodTW1uY8RtM0TjvtNMaNG0dVVRUTJyYFAOrr6xk8eDAAQ4YMob6+PqMPxSp7yJdZodjzFZpdVsU4\nm11LLZd5TQhdwrtu86yvGZqkJv7tfYPnPB+yPfwHYoGnQTkcIXIT+1xPWXMG8MW/xXan9Wx2ZWI6\nGx3JFYWEEOd991u84HuVdeo1HAj+By02Iyc7SvQ6gi7rjW4lkRvZ5nopr3MUMcwWzz9YVfEnNo6e\nz+5RbxIa9hiy+EfL/sTVU4jaP7R8k4EGCj5i7ZT8wvJmtvh+xhbPz2kUPyCqNqCqaqeBbl8qe8hp\nQVfX9VRhiqPlHPNXnypzaIGgtDvWApvSegdmcyQPtGVcyPS487FhXHiIUEoT0ZZMsHGMGQNEextm\nbA6Zz+vcXvsSB7M51PRjOwlkbMRxijGatWQmWDKUPqiGx0rqsWR4CyXDBy8b20Mu8XUx2R7yYW1I\n7VMho3JkoewShTA8WDkvL2RiaEih2EFjJoaGbPOlzsuFqcE41gsESWZ/y3P0re/8mH6ZIIoiy5Yt\nIxAI8J3vfIdNmzYxblzHxuDOLobtg19d1/O6eBbKrGAFZtnlQi/4QXkPtZazvh7CAgTF/Fc8m8Vm\n3vD+B7fmZnroYcq0cmR1GDFpa8H+uOIT2Cd9gSZY+3Esi4+hRqpBa5etVQSF1a5lfKDbOD56GSOD\nt1FmfwSbI0NQqownIm2znM0WtRIiQoKEWJiohSpE2Op5imqXk2Olu7Dxawapd2C3rSjYp4hwM2Hn\nLQWfn4I7eiV7HJnroUPyZrbId+FOjGZo+BIc8SOwaV5EUcRmsyGKfbM0LSevBUEQBUFYB+wBFuu6\nvrr9mJ7i+TWimWQxf7H5fvf4N2cfVASk6367m+/3E3/3zpcrUrGV1WtZs9+igd4O6w0h3QNj3W8/\nehKVlZXs2tXKv7p7924qKys7jKmpqel0TElJCaeccgpLly4FYNCgQenSiL179zJw4MCMPni9XsLh\nwhp+eprJAawFvqoYY5NrieV7u+ObL+FdZ+5ZXzOExTCi7uHPvpXsjl9HaeBRnPGOdaq5oCx6KV84\n37DkD8AR0XP5yJk5MFQFlQ9c7/KC93lW6d9gX3ApavTbHcYlInfRZFXtDigN/4Rq54uW7QyJV/GJ\ncwWvlSxkjfNGdul+4ur0vO1o2lBich26xYY5ANQTaZJXZR0WlrewtfTnVJf9krBrPQmaiMViRCKR\n9PfCbAWmtyKn4FfXda2l7OFQYIogCB24PJYtW8a8X8Hdf0xuv/8b+N8jzf3rfzu5JaWO4Z23kpuk\nqkiqymp/lNX+aLo5bI0/xBp/KN0Et84f4GN/U/r4ev8B1vsPpI9v9Nez2p/8IHgJscW/my3+2nQz\n3ef+XWzz70g3oO3wb2OHf1v6+C7/5+zyf55uQNvt38oe/2fphrp6/ybq/ZsMTXCf0ODfkLbX6P+I\nRv9HaXsB/zqa/K03BGH/asL+1WlZ5Kh/FVF/6wdOXbaC6LJV6CTV3vTlb6Mufyfd+KavWI6w0o9N\nUpLcv6veSm4pvO+H1f7W52v9yS2Fdf7kluoj2uhPbhLJIHOTP7mljm9ueZ7CZn9ySx2v9sP2ds+r\nW8ZLwC4/7DCcv8uf3FLH9/qTWwq1ftjnb01A1vlhv+H4AZPnBwz2gn5oMhwP+5Nb6vVF/MkthVDL\n8dT5CX9ySyHmh7jhefvjih8Ev6Evy5/c0glUf8uWz/Nlhudvt2wpLAeMF7kVLVsK79E2CH6/ZYPk\nFXZ1y5Zy+ANgneH52pYthdTxFD5q2VLNaBtanqfwccuWwvqWLYUNwM6Wx+GW5xtpbXDbBGwm+WZt\nBh4HHmft2r/0ihvrgw0TJ06kurqanTt3Eo/HeeGFF5g1a1abMbNnz+bZZ5PLxatXr6akpITBgwez\nf//+NItDJBLB7/czZsyY9DlPP/00AM888wxnnXVWRh8KaXizyqxQKIodaAfkPey1W5MOtmteIqJI\nQLImsVuhVLDHFqbBFuIV94f80fcB1ep3KQn+CU/sqznbcSpjaZB2o1pM3viU4eyTDqDkUFurCRof\nO9/nBe+/WMFp1AeXokSvajlYSVRsRCsgK952EjsJvYRIu7KAQlCWmEK1/SMUIcE61xJeK3mOVc4f\nsFNfRlQ9O2c7IX5Ds+vPlv2RY6fQJK3P6yYsLH/O1pKfU11+DxHPejRba91+PB4nEomgKL2fs13I\nN0oXBOGnQEjX9QeM+5cuXarPEGZCiWGngVVFN+xPeFofR7zJpd6gzZfeF8ZteNxavhBp2d/Z8cPY\ngZ0EWzmCUIsDqTGRNue1Po4ZShbMxsQNx43nZdqfshfJMEccR8Y5XESQUQnqHqI4icdaz4tFDTai\nSRt6s4G/MWr4BBsZpYyPlSzHsz1WchibbY5MNszOi5DM/Eq0VRUxK6nJNEe2+bIdzzQ20+OsbHt6\nhsdGI4lO9nW23+w84+NC5zOW8Ogmx3PxUwe+IPmmDiWZCc7kW3K+73//CC68UGHGjBn99Q8W0dDQ\n0ObHfsmSJdx+++1omsbcuXO58cYbefLJJwGYN28eADfffDNLly7F7XbzyCOPcPzxx7Nx40auvvrq\ndBB63nnncdNNN6Xm4PLLL6empoZDDz2Uv/zlL5SWlpr68+KLL1JXV8dll10GZM+ktqcvEwQhvZmN\nsdmsScWbZbEKDXrVFmEnURTRbHE+8D3Lboc1ztkTgj9gietdy8HvN4IX8jfP+4TbiWHYdJFp0bEc\no5QjyC8SdGZuXgSoDPyW1b7HUQRrdIZfCd7EG55XiIsF2NFhdPxYjo4dRakmUO+7FdVWZ8mf0ub5\nfOH4hIBsjY6uLH48unocG1z+DsdE3cb46FSOiB/GIO1hXLbnMtrRNCcHbH+j0fcTS/4AeAOPs8l3\nX8FlIbJWzlGB36JFkvGbKIpomobD4egV9b/l5eUZncha8ysIwkAgoet6kyAILuAM4NdF9K+oCOHG\nThMlBNPBb19CSu3NTpwozp52p+dhVHvrx0GA9mpv/egpzJw5k5kzZ7bZlwp6U7j//vs7nDd+/Hj8\nfr+pzfLycl58Mbfl4Vwb3rpbpc04ZwpmgXahqJY1lMTXmRCfzhbXPwhJ+/K24dRKCAtYDnzLlQr2\niuEOgS+AKmi85fqUZbrACbGvMjk4B1laRpPj7x3WjB3KSJps9ZYDX7cyhAaxubDAF0CALY71bJe3\ncHpoLoQfwCOuI+T6HYgFXEQ0QD+SgPxCYf4YMDR6Lkt8/zCfRlDZ4HqbT5wi42JncWT8OgapT+K2\ndVRAjPArmrNIGecCURlByLbHUj10ZeQi7Pogoi1ZI6fT2eG701uRS9lDJfCWIAgfklxHfVPX9Q63\ngGmeX9WwGbl+DftNOX/bcOEWzvmb4vstJdBhTCaOXiPM/Kj1bzE9nuk8s31mPMDJManXmhynt6w/\n2Elgy6XBSVIMG9k3M2zwG+zlcX62MfnaMNtnVHuzZXkdmeYIZnh92WwUyvObjR636FhJa/lAiu+3\nGC8kH87fTOe1n7s95VlRyZT70YeQS/Brpba3kAuwWVkFFC/YDtk0/ubeye+927jXcwAx9j2OD9xM\nuXJ4XnaOC13MO+53LPtzamQmb7rWdzpGE3Ted37OH7zvslQ8HEfoccpC14LWGj4MiFzNZterlv0Z\nE7mE1SaZ0Xzx1fDXedW1gr/4lvKa3YES+iue5rtBs2c91whf7DJq7MuyD8wCjzKcA7Z61CylHLqg\n8alzBf/2/YN3XCexjeWE1BtJfRw1DWLiKJQiKNW5IzdT68qcYc4GQZcpUVprw1Pfj96Q8c0FWa84\nuq6vByZ2gy9FQRQHKiIO4tiJtSkx6AvQEVB0G5KgIusKkeynHNzoG9+jfuSMFGGMQrLGpH9148uK\nzmp+C832Wrnwti+raH+sKFlfe4TP5OSNX5Oo8JhnBy7dxv9EvsVxYYl6x7+pzVIO4VLLCQoqzRZr\nWSuUCvaKEdOsrykEWO/YxXrHLkbFh1AVeoxSoZqQYyFN4n4U0VrzlVMdQECMEbVox6ZJ6LjYJzUC\nsE2uZZtcy9DEQKrCj1PBHsLuX6CJ2TmmbYmTqPctyDouGw4Lz8XvzT17rAs6W5yr2eJYzRHx4xkX\ne4dB2lJsegMhh/WbDDQ3MUElITYUbGJw7Os49WHZB/ZSFI2joqd5flshpLO/viIR6ldWjS6KnVwR\nb7knkbuLD/WYqu6ZpxBkUnvLB76qIjjSm9EXeH5TEGhtBugXvPgyI1Pmt6eYHNo30VmtGW6PZlnn\n7+6dHfZHBJW/u2u407eDrdpMjg7cyRHR0zOWeh0Xuph3i5D1nRqZyRuuwjKIW+17edy3gqedUaTw\nL9G1Ydg1a2VM48LfYbXrrewDs+Cr4bPxOz7qsH+3vI+nvG/xtHM3wfDDeIIPIWqDMtpxR89hr32N\n5QSMXSsnKEaIFRLUC1Dt+IhFvr/xX7ePPeL3ITEFNGsrZZ7wrdRaUfLTYUD8FETB1mGFpS+UPECx\n1xpTyZwUDEnXbJy/NkcuPL8d+XrNjkdw4CVECQEaKTXl3TXaMOfdbd2f6bxs9tR2JQ5m56XGGu+9\nk2pvMey0MDu0fPvMOH8VowRyPpy/uXDwmiEfLt18OIEznZfaFydZ+yu0259pnmL4mcleNrtZkenX\ntBhfR6s3TJm4f7PZzec8L9BIMvjNTIXVj4MbXq+X5ubmNDevpmkdeHq7o7Y3WxNdsbDFHmK7lHkt\nTxF0Xnbt4RUnnBY/humhqSBuZJPrpXS9qlcZTIMtklXNLRsGKYPYLYaI5Jr1zQAVjc+kEIscB/hW\n+MeM1CLsdP+FkLQ3LzsOrYxmQSGcQza2M4iaiKSXUitnrqPeJzXxnPdtSjQ3MyL3UalpJFz3oUjV\nbX1KnMVub8ea93xxZOhy3vVklkTOCQKIusx6x1b22DRODj1FmfAFcffdkG99tAaqPoRIu9ebD8oS\nJ+HWDmvzs99Xyh1SKFrmtzfREUVb1N7cRIqi9rbbUPPbHeh2tbf1/q6fwwqMCZhCbiqNNb8HJQon\nSu8ZuEn+9PSrvX2ZYZb57a7Atzsp03Rdp8mu8aSnY9bXdLwAfsd+fub9goX2QYwM3c6xzZcjaU6O\niVzAuy7rWd+TwzP4j7vzWt9ccFbkBBa6tlEnRfmD9zN+460lEbuScYGfURbPfcX0qNClrHL7Lftz\nUng2y525va6AGOZFz7v8xfMBNbFbcAb+D3s8KUHsjE1jn7TBsnqaTXMTE2yExCZLdgBGxqfygeNj\ndsq7ec63iJedBwiGn8Te/BBo5owqZnBFr6bO8R9LvgyJnYPYx0pK26O4md/iqgoXDA0xrfbmJUSo\nz3WVC6Zqb19apEof+hkfDhKIJAPgZnJTe+vHwYhU8Ltx40aOOuqo9P6uzL6CeW1vVwXaqbk2OJqp\nt+WZZRXgYznIx3KQEYqL7zbfgqZJ2HV7uru+EFTGh7JDaiKaA49uZxiqlLNTjBESWxM0ATHBXzxb\nceo2vhH5FsfEnDTYX6XO0UEXK41k1lclVKB6WhoauPRB7JDXZR9rQESM8brnfey6xKnRyxkVLMWj\nwqbSn1vzBxgVvpw1TuulHIMSI6ix1aMKrUHWXqme571vUq6UMS38KIP1MKr7p2i2zvmIBXUSTa67\nC/bFpRyBSz08/X0xlif1JRS35ncvmdkeYobNsN+W2nJieOh4PBOMam/5sEgYkdo3vGpkzgwPxv2Z\nxhr9MDsuCSqakHxrHEIMm01NblLrVlQcW9X6uJhsD5nGZttvts/W7riZjUwor+oahodiECoUBbkT\n0beFkZUhxRJRKKtDLucZx6aIv0Mmx432+qZ0Zj+yo66uDkVROPPMM9mwYQPQ9YIVZmUOXR347rMr\n/NWk1jcf7JAiKNi52RdgUPRCvhaYxyFKZfYTTXBCdBqLXRss+QNwZngy/3KbL51HBZXn3Nv4ufcz\nPtWrGBW8hxGRs00TGOOKlfWNzMo562uGuKCw1PUBSx1b2W7zMbz511RGzX3OBaImoVJCo7SnYJ9S\nODoyi5WutabHGqRGXvYu5mnPh9RGfo0Y/Cs2ZZTpWEf0XA7IKy3VMQ+NXoLcRtChb6K4VxZrXNJF\nRZCkkkZS6rhvFGAboWBrUXtTi1K60edhlDrue29nPzogtRoTpj+l/+XDCy+8wNSpU1m9ejVutzst\no3ywlDmk5tIFWO1solm0Vr52QqyMD+Q4O20KCzwN3OgLkYifxczAFYyJdhBczYjDYyPZKu0nIVi7\npoxIVFAthYlksaMKOm84a/iFdyNviaM5LHQPo5q/g9jSsOXUygkVKevr0Q5hm2xdhW1KbAJ/9H7A\nAu+HvCOMZ1jotwwPfacNtVsuGBm+jPUO6zRpPqWCfbZm4ln4eJvFEIu8fp7yvMf22G2IgaeR4ie0\nGSMlzqXeQsmDrFXgVUd1EJaBvpf5LVqe6sMPP2RGHW2bknoQCezEkHGQwEOYEJ7sJ2VAjX8rw6rM\n76S6DgIKthbBiwTRriSNXe9vm/3tjRBpFbzIN/gN+KGkqtge9SKsoPDsb09BAlz0C158+fDaa6/x\nve99D0iKYixevJihQ4d2a7a3q8oq2s+116HwrLvGst0zY4fyI199+nlY0HnM3YRNh29GT2R64BQC\n0kbWOt/pNKV1XOwk/ux7O/OAHDEzMonf+HKXZ9YFWOmoY6WjjjGJEr4RuotSoQ6XZmeJd5Flf06K\nzOJdp/Vs9oj4ELbagiSE5Hv4vmM379t3M16p4GuhBXiEnWx3/wktW5OZJiLqh7BPtlZbCzAxch4v\ne3IvnYiKMZZ43kHWJaZEL+fIwI+x258E8QBN0kYQCk82DIvMxa4P7BUxnlUUd5E2BuwHylqeG28K\njTe+RoICNfW/gTnBlp2VofV45rFh3DhoooQAITxtzs/MKGF01J4+ntqfjRnCuL9tWYN58GrOYJEc\nqyFCBrW3JAsEqFKrXV0y+C4Z6oSzsT3YDM+zMSPkw6KQjdUh0/5MY41qb2Y28vGtszGFjM10Xgrd\nnrzPxL6QCdleYDZ7meoHzc5Lje1M7e0g+HXthylmz57N6aefzjnnnMNzzz3HsGHDikqP1BPsEWa8\nxJpNYKlzH3GLTVOzIkNYbI+gmLitCvC8q5nnnXBK/AjmhMYjC7W8536TeDsmh/HRY1kv16BaCH4A\nRscr2SQHiRWYPd4sB/itHOCYeBnnR0cwOXQBH7leoknaX5hDGrjVQ/iiCMIPp0ZP5EFfu+Z9ATbK\n+9ko72e44uPr4Z9ToQfY5XmUuHjA1M4RkUv4xGG9EdmtlRAQ4kTE/Bn/E4LCO65VrHCKTIyeydGR\no1DsS5LXzwLW/G26G586vsP3p69mfovP82u9vKVoSGV7S7BGBj6s6shiuJM31JYg2E6CLl3rP66q\n62wXE0a1t3z+HAd11hf6XtY3BaPaW38tS09gyZIlTJkyhRNOOIEHH3zQdMytt97K5MmTmTZtGuvX\nJ2sqa2pqOPfcczn55JOZOnUqjz32WHr8ggULOProo6mqqqKqqoolS5a0sWez2Vi4cCHz5s1DFFsv\nQV3BD9odXMGZeIl3OeK87syP8qsDNJiYGMSrjiwUYAK844gw33eAh5xexofncUbwYkqU0rSdUfHj\nWOHcas0f4NTYcbzs3GHZztdiR3Cbdzd3eCI4YhcxLfBDhsZH5m3npPAs3smiUpcLRsTYhCdYAAAg\nAElEQVSH8LkUJN5JUL9TCvKo92P+4NkDkR8zMvhLvMphbQdpYFePYI/d+t96UmgOy90rLdnQBI0d\n8m4+lRpZJh5JWfMfGRz6Qd5lHJWRC3FqQy350ptQ/PacWiBVIZCB29eM89emZMr8mvH8mh9vn9mN\nI6Mi4iSGizBx7KbnZcoup8ZkyhgbYbbfeF48w/5MXMDQVu3NqUdRDTy+Kc5f1dD8lldVWSae33z4\nfwsdmy0LnGmsnMV2JrtGZBuTS8Y429i80JWcvykU2tXd1Zy/RrW3GG3V3rqB4u9LDk3TuOWWW3jp\npZc45JBDmDFjBrNnz2bMmDHpMYsXL6a6upo1a9awZs0a5s+fz+LFi5EkiXvuuYdjjz2W5uZmpk+f\nzumnn54+9+qrr+aaa67JOHcqCHU6nUSjURyO4tAmtc++QtdSphmDXuNcYVHjWVcNusVpL4scxtPO\nYF52tkgJ7vQeYKBm4/LIt5gSVtCFPbzn2IpuMQs9IXoYH0gN6bKAQjFMcVMj6jSIyevXw559OHWB\nb0XP5JSgRL28ks+cmRkiUhA1Ebd+CNuKkPU9JXoiD7fP+mZAgxjlSc8nuDWJs6NXMCZip8n+HAcc\nH3B45CI+dVoLWAHsmpuoIBC0yH0McErkVJ7wrCUiJlhr38mYxGCmhx7CJ+ygzv1Q1jIOQZcpVSaZ\nfo/6iqhFexSX51ckyV1fOAtLkVEctbdd/i+K5VDe6Ba1t4/8XWe7mEiRAOSLJn+RHelteLenHSgQ\n/WpvPYm1a9cycuRIhg8fjizLzJkzh0WL2tZfLlq0iAsvvBCAyZMnEwgEqKurY8iQIRx77LFAUqxi\nzJgx1Na2NhvlekH0eDw0Nxfnve8KCrP2dE7t58pUUlFtD7PObo3b1aGJDNR8rLQXdkHdJ6rc72nk\nJm8IQRvHuNgkpkTHWOovnRgfxxvOXYUbaMFFkbE84WorRBEVdP7uOsAN3jpWCROYErieyaGzEDvJ\nUJ4UPou3nR3V3PLFiPgQqqXmvEs5wqLCv9yfscD7CVu1sxgR+A2+xERqpE2WfToxfD7Lne9btlOq\nlFAvxoiILTGEAJvtdfw/3yqeckawhe6nMvhLZK0io40h0XNxacM7nedLW/YAtNJ1WlzpKSZC6eDX\nWulDTyGp9gZ2FPqXhmnL+tCPgwD9wW9Poba2lmHDhqWfDx06tE0Am+uYHTt2sH79eiZNmpTe9/jj\njzNt2jSuv/56AoHMnfyZJI7zgRmTA9DlTW2ZSiqabCqPu7dbnufq0CgedTVatvPDcAX3uBS+7YFV\n+rHMaZ7DWc0nIuW57H1q5CiWOerQLGaPRyV8bBVVgqJ5FK4J8IYjwHzfXp6yD+bY8LWc0nwJTs3d\nZpxNk3DoA9ghWw84TomewGuuwssUFEHjDVc1n0gR3rHLHB/6CceHzus0cO8MkuYkgZ0Gyfr7Pz0y\nnddd5s2JNVIT/+dbw589u4iFf8ohwf/FpbQrPdFFyqJfJRaNE4vFUBSlw3etL6Joa6sTJkyAD0g2\nvO0BhpGx7MHscUrmGMDmKKzJzawcIo4DHfAQxk4M1eQlZ2uEO7RqZIbj5g1tqf1t93VeOpGpFEJF\nRDOovSl0IniRj9Sx8T04viqzzfbn9WTDm0LbzK+NZPIwW7lEaVX2uXM9nmmsEd2+Yj+1CDZSn5FM\nn698GuKMb5LZecaxPtqqvX3JBV36GJqbm5k3bx733XcfXm/yRuaKK67g5ptvRhAE7r33Xu644w4e\nfvhh0/OtBr9m2d6ugllTm1lmuUaKsVuKWZprkGqnWZColqyt+Hk1EbfuYG2LnRcdKi86YHLiUC4P\nDadUb+RN77sEsrIXwJHKCJ71Wi8vOC8yhtt9OTQHCbBOjrBOjnCoInNp+AqG6RHWu16mQapnauQc\n/uuyrix7eLySrVLhDXxpaDBcHcid3moQ4NjEAM4P/xgf9XzkfpaYGM7Z1InhOfiLkPX1aG6aBI2g\n2PnnsUGM8E/vB7g0mTOjV3FkxEnE/g+CjlUMjJ2BFKtE13VUVUVtISdI3fT11UC4uDW/A4AvgH30\nSrW3EoI09Dk1qSTlmR2lX+0N2qq9aRRWBtGPXgQR8ABB+tXeuheVlZXs2tW6hL17924qKys7jElx\n8LYfoygK8+bN44ILLuCss85Kjxk4cGD68aWXXsrFF1+c0Qev11tw8JuJwsys7tcq2tvMRJdWrcs8\n0zSEG2Ol1LvqeNZTjVJA8u8H4VH8zNNg1W1ubR7Eva6ON6BrZI01MgzTSrgufDaHa1FWut5nm7zP\nxAp8PTKZ15y7LJOwfCVWwTopRjTP7PEuKcGvvHWUaCJzoxdwaghcJKj1WA8QvxqbzEPe/FThzPCN\n6Fhec+xP/43WyyHWyyGGKna+Hb6aoXqETa6FNEqdZ6olzY6Gi/2SOZNEPpgRmsmznk9yHh8RE7zk\n3oCki5wW/QbHBS9joAYupze9uqKqanrlQzWwdMXjcVRVxWaztWlk7a0obs2vg6Rwk0YyA9xLkFJ7\nK6UwIu2erPkFUFruURxZSK4LRl+p+U0hFfDmesPZX/Pby5FifbC2/N2P/DBx4kSqq6vZuXMn8Xic\nF154gVmzZrUZM3v2bJ599lkAVq9eTUlJCYMHDwbguuuuY+zYsVx11VVtztm7t/Xi/uqrr7aRLm6P\n9jW/uQSt3S1Y0R6Z5koAz8SdPBZ18c3GMv5WP5J5dSdzQ+PRVGj2DnYyYUK8hA02hcYMZQG54jBF\nol60sd2W+W9aI+rc6lb5nkdGj5/GhYFvdqgLtmsSpVo5H8vWg7Ez4kfwtKtwOwFR44/ufey1OXlT\nLuWc4CVMDU8quI55dGw4n0lNxC028KWyvivljjHGbinOb7y7uMvTiB67hCnB+QyLZRYmOSE8h3dy\naPbLBqfmJCKINBRAk6YIGktdm1lm341DS3Jw22w2ZFnG6XTicrlwOp3IcttknKqqfaYBrriZXwUY\nCARI1v0aS0fUzh/bjBS1GTl/O3LiZi5ZaB0TaekiLyHQsl8w5fPNZENEyzq3GZuDcV9+JRJGagy7\nQe1NQbbF0bClJY5tBm7fvDh/M/H89ga2h2ywQZr9TSd7uUQm5MptbEQuPmabu0dXRYwXbLNVhHxq\nNvJlg0iNbz+2vdpb788aHAyw2WwsWLCA888/H03TmDt3LmPHjuXJJ58EYN68eZxxxhksXryYSZMm\n4Xa7+cMf/gDAypUr+de//sX48eM57bTTEASBO++8k5kzZ3L33Xezfv16RFFkxIgRPPDAAxl98Hg8\nhMO5Lwd3t2CFEdnm+lR38FAkxVgisFyRWR4o5dBmLz8JlzHKEeFN7xY+dnTef3JOdAQ3GgQtCsX1\n4UFc48nt+9wswIMulYd1ODd+LOc1H0NC3M0b7lXMCZ3MMy5zGeN8cHq0Er8cMuUrzgcDNJEIEg+5\nI6DD9MRoLgqNQxLrWOpaRkzMPUl0Yvwr/M77gTWHgG9GxvGSY1+nmfGAqPInTy2yLnBudAYnBs8m\nJK1lk+O/6Z88SbOj46FeMs/A54MzwjN53pl71rcDdDgtNgq70PGClvoeiKKIoijouo7dbkfXdWy2\nvrEcW9ya353AYJKlD/X0KrW3ODL2AtXehlcd0UWe5YouVnubUFVce12NfNXejDW/ByWKUfPbk+hX\ne+spzJw5k5kzZ7bZN2/evDbP77///g7nnXTSSezbZ36BfvTRR3OeP9eyh1zrbYGilD5kYo7IhCZs\n3BNyoZlc8HZpNm5o9uFp9nJV2Mt8Z4St7hpece3ucJ93fngYLzvClgPEqTEXqySBQJ52NKG1LniC\nMpTrgnMoVQSiLosMDxpMih/Kj33W1e5uDA3jZ56WGmUB/mtX+K9dYbRSzpXhC6jUm3nHtYx6qfOy\nkaOjR/KRtB/FYtZX1KBSHcBq97acxicEnYWuep7XYWp8NLNDk5GEHXzsfqGIWd+kwu0+qfDVtGMS\nlQzVyrLeWKa+ZzabrcvKjroCxU+x+EiWP8RI0p71EoRIdoqWFFj60NNIlT7Y6aLSh76G1Pexb9ba\n96MD+ksfvozw+XxZM7/Z2BWKic6YIzrDatXOMqXz0oYQAv8bcXNuwwDeqh/L1fUn8cPGcXi1lt92\nTeRIpZzFduvfgfNjA3jUYa3z9kNJQ9Nkvhcp5fj9p3D9galMiA0oyNYFkSN53tlkmfd4uCJTK4rs\nFTsGV1skjR97o1znkSmLncV5wQsZFzs8o63jE0ezxLnNmkPA/0TG87yr86yvGXQB3nE0cYdvB487\n3BzZfANOZRRRwVqzJMDM8Exet5L1BWZEx+IoID/aFwJfKGLm98MPP2RGKckl3QpgN1BD6zUtC9uD\nkaggs+BFR4nhXAUvIrgop4lSAtQxOCfhitSYGv9WRphkfzNLJHcU48hWIpFJ7CJlQ2/5ZtlJYCOB\nTSpi9vdDv3n2N5sscrHZHrIdN+43Nr0JLVum85r9UFaV/3xm6FKGB7Nfz1zKCd4FTjEZnw2FOp3y\nMxurg3EsdJQ3NsIH1NFKeZYa2zeW0PpRGDpje8gn21sMmJVU5HIh34XM/FDuq4k6Aq/GHbwadzDG\n5mV+ZADD7WGcUpQHPI2WV0svD5fylF21nD2eFBf5JG7nY83GTTE3rpiL78dO4Gp7lF3Onbzi+iKn\n9JmkiVRq5ayw77bmEHB1eCg/8nYeHB4Qde7zxJB1uDj2Vb4eOJmA9DnvOFelRc0mR4/mfXmPZdo2\nUYNyrYwP5W2W7GyRw4Rig7nfGWV69H+YqibY4PSz055/xt2u2VFwUCcVTh85NjGEYXruWd++iK4p\nrks1+/YiqeMoDlREHMSxY/3OqruRUnsTBJD71a96RTlNP4qJlNqbSi9SyelHFyOTyEVPZ3tzbaBT\ndXgx7mBvgXyum1WJq4Il3NVUQaJ5AFfWD2VOqKTgFS27BqMUL6/L1pfErgs5+VWsVXkvgsBDCQfn\nhEp4uXEs8/afzg+aJlCShYHoitBRPOGy3gF/fNzFBgmaTLK+ZkgI8DdnnHm+BAulkZwe/jZfbz4T\nt+pkdHwU7zisi3VcEj6Op511lu24NRGws9Ie51eeINf4YgTVGcwKzuMr0Yl5fR6+Fp7Jvy1mfc+M\njsOp58cs1ddELopb85uqiS8nGVY3kLyOOTOe1o0QCOKljAA+mmmiLOczzbK+PYE4EhJq8dXe+lrN\nL7SlPMuGVNb3oMUp2Yf0eqTU3hpJZn97xY9GP7oY7TO/vSHbm08D3Sbs/DrssuzHnY4IF1R7adYE\n5pR6+EVFhLAnzMOldYRyDPYA7ggN5n6nYjk5cEnExktxBxFTQwJvqDJvRGRGRd3cFKvgMDnMm96N\nbJbbqtqVa3ZUwcGWLPW3OfkUG8KV3vyZCxDgbbvC23aFw5VS7g1eSFzXOEwtZZtUuAqfXRNx6l42\nZaCHywfXhkbwsKu1ETIq6DzuCvF/OnwtPp5zQhNA2MVy939RxMzJL6dmJ4GDvRayvqMTg3Oq9e3r\nKC7bg0rr6mcZcIBkE9xwkomdFIxkBkrHfZkEL8zKCfIRvAjhpoxAC+tDdhspFohcyhfMz8uFUSJ3\nwYsY9pZ/U2pvApKhXkQ1PFayCV5kYmootASgGKUMuYhctN8fx7yxshglF0b0CsGLXO7Ei3ljlInN\nIdtchQpelJAMfkPAoFwc7Ecfh1nwm0JXMjmk5mqf7W0/V2cNPE3YuCfsRrEYaV5qj/JGo0ygJXu8\nsMnBwiYHRzu83DDYx2BPlL8NqONTqfN+j8MUiQZkNlsUxhA1mB5xMSeR/fdmq27jh1EPvqib62NT\nuEaOssW9jf84doAIl4eO5j6PdeaKr0VLWCqrxCx+FHaJGgc0me8lZK5vPIUrbDE2O7ew3LE973Xw\nueEJ/NVVm31gFpRoNmKCne1Sx9r3pNpdlDccUcYnKrgsfCkD9SDvuf5Do0ngPjN0Bi+6rGV9Z0WP\nwq3bc7qBMq7M9DUUl+fXiFRdvPUVgaKhGQ864CbSLjDtHNv927rMp3ygIqIa1N6KhnX+4tnqThjj\nqs6SI43+Lnakp7G8px0oEjwkf5KiFDeI70dvhc/nIxQKsX9/22XxrqYwMytzyHeulaqd/yZy5+81\ng4TGN21xHtvfcaXjk5jED3b6mLelgmM+P5wFtYdzfsiXcbXr+vBg7nNb/978POzgt1FHus8kFwQR\nuDfu5BuhUpYfGM8VB07n2sYJbEdjv2hdOe30eAX/dFhv9v5pyM3/KjYCCNyjypwb97AqeBxzG8/k\nwuAE7DmWr/g0OwnsbLeo5AdwbehwHnF1Tn8HsFFOcIs3wM0egYrYHM4KfIcjY62r0i7NSUyQqbeQ\n9R2TGMQwC1nfvlQDXHye39TnPFVVsI9kdk5tNy4FteO+TJy/ks0s85s756+InQhO3EQpo4nGFiez\n2bChGvh4c2uwy8WfJDpmiW2YN/lIgoaKDRsKLluUMGKa7xc64fw1tZYB2TLCvaXhLUnX3Fr6IJKZ\nP9fIY5yNCzjba8r3nsNsjl6iftgWZhy8RmS7qObL+WuGfrW3Lxs0TaOpqYkZM2awdOlSKioqenWZ\nQwo7kJnfnB9lphkecYe4t9bVaaDZqIr8Yq8Hca+b80rd/LwiSswT4pHSegItQhhnRT28JekELf7Z\nBmngitl5VyssNNAQeEG180LYzmuyDTUh8POoj6fLa9hUYKB4RWQg/3DE0Sy+thINXHE77+ut10YV\ngWd0G88kXExURnBNvJIhUpDXPeuo7YQmbG5oAg+7rWd9B6kyDYJIrS33i8J+UWOBJ4hDhwujp/K1\nwGk0SZ8xRBnIv9wbLPlzZnR8zllf6M/8Ai01v0YY1d6sC8MUDSmO33wozw6rOqyr3MkbXUJ59pWq\n4tnqbuSi9lZe1Q2O9CRO7WkHiogUPUzh2Yt+9A28++67zJo1C7/fTyAQSK8eFvNCmro4F1MVLo7A\nP2IO9unWLp+jRYVEXGBtJLfGIg2B55scXPBFKfdsHsx3t4/k13WH8pW4g+nxMv7isH5XfW/Qxe1R\n6/X23xVjvByw84NaH5duG8iY7WP55d6xfDNcnlfzll2D4ZqX/1qkbQP4RdDL3UrmoP4DXeQKxcF3\noxUMb6zi+w0zOCEyrMO4IYqbfSLU2axn2X8YPoxH3NmzvmaICfA3V5gf+JpZLh6Jpg1nRmQinjzU\nBI0YmxjCoV+CWt8Uipv5bY9BJNXe6oFRXTpTzgjhZhD78RGk16hw5IFWtTcVUe+VKcTuhVHtrR8H\nAdqrvfXjYMTChQu58sor0XWd0tJSXnnlFUaPHl2UC297G8VWhdug2XkoYr3J7TeuMJdWews697OY\nxFU7ffhEL8+NsKPpOlfpOo95FAoknuDkuMj6mJ1ai0G9iMY5gsb5jUlu/SZN5Bf73Ij7XMzxubmj\ndAgxd5A/ldamM9eZ8OPwMH7nsl5acJgiUpeQqc4h31ePwG2qjKxKXKp8hUsjx9Bs380r7k9QRI0L\nIsfxK491sY7DFSc7xWQm1xIEODXuZZ4s4NUHcl3gLEYIYZZ7VrMt10ZDHWZFjsKVR9YX+nbmt7g8\nvxJtl4VTq5b1JAOU1N/HrATC2J+VhfM3t1KHjiUJNlQ0bMSRsKPgI0gYT1Yb2/3b09nfbOUL7cd0\nts+4P5dGulQ5hIqIhIaTKFFy+BE2kzo2vvMf+2FiVfJxoU1uZqUKuTTEWW14g6Sgik4yEBZMxjb4\nW7O/hZZcmB03Ip/EhLGqpSj3L8vpPPubTdLYiHyyGfk0tmU6r32JRHu1t34cjJgxYwbDhg3j4osv\nZvny5YwZM6ZL6gWLzRxRj42bQ5686mHNcJUjwssN9nSTW6EYYFPZHrTxww0eZg2K8/sRMbTSBL8u\nj7InT9NXhpycH3dkH5gFv5dj/KbO2eFvpCGwMOhgYdDBOLuXH1WUUemK8mxZDZ/IHekNh6gSEWQ2\nSwUwPLTDbUEvl6v5hTsJBJ7QJJ7QbJysHM4PY4dSKTZTI0cJWq1jBr4bHsFPvIWzTaQwXBGp1W3s\nFWCvIHCjHUp0D1eFqpirJ/jC8RkrHFs6Xec/OlGZE6/vwYSu4flNwQctBAVg/T0uGsItam++Prq0\nqrYEGv18vy1IfV/7s78HCfpLH7oTS5YsYcqUKZxwwgk8+OCDpmNuvfVWJk+ezLRp01i/fj0ANTU1\nnHvuuZx88slMnTqVxx57LD2+sbGROXPmcOKJJ3L++ecTCLQtMysvL2flypXcdtttncoGW0UxeYI1\nHeqDEhfYYtgtrEp40ZghJPjLgSIEmoeEue0zNzoCi+odfHttCXe8V8b3N5XyRK2br8Vy+9veGJL5\nv6iDuMWgfgga3oTAe9HOb7I3xSWurPUxd1sFI7aP4Rd7xnJhc0WbxZ4bw0NZ4LbO+T01JrFKsdFQ\n8GsTeE+3caniIBQvZXfDUO6sP5ZTI7nTpbbHcXEP6yWF5jxo7DJhfriCBe3i+oAA98vwLVlmpXIM\n5we+wZzgSdjNarl1mBkZg5QQUFU1r5vQvtTg1h5dV/MLyaCkFwpehFuypSXkVmvTm2p+oW3wKxQj\n4ktlffsqjJ9isz9Hf81vH0Nr8NuXf1z7AjRN45ZbbmHhwoWsWLGC559/ns2bN7cZs3jxYqqrq1mz\nZg0PPPAA8+fPB0CSJO655x7ee+893nzzTZ544on0ub///e+pqqpi1apVTJs2jd/97ncd5na7k0mI\nYr/H7e0Vizlic5OdWS+W8Mbbdh4LhXlaCnKMLf8ExGOeELfvdmO15O6ysiiL98o0JNpexndEbNz4\niZeLVpRR+lEZf9ru5fYmGWeGeN2rwaiogxdVa8wVAI/IUW6vc+c8PqCJ3Lffzbnby1ixfQS31h7F\nbQ0jmBn1sU7i/7N35uFNVPsb/8xksictpdCyyCLKIm4oqHj1ahX4ed3vBWRR1LqgKFfxuoGggCJ4\nwSsCIqAgoIKgIu6iAlpZlH0RBS+g7JSy0+zJZOb3R5I2bZMm6QRovX2fJ09mzpw5c5JMZt7znfe8\nX46lgRze7bLyShUn8EWjpxDka5eRp47Z+EdhNscK2/B0UTvuczTFkOJYqLvvDKaZtQ/u28gSW1Ud\nR+OcSooAH+mgj0HHaBpyteMm+hR3oZGcWVLnIv8Z5HitBAIBfD4fHo8Hr9dLIBBImgzXxIhx+t0e\nouU5RkLSh/1AIaW6X2+5OkT5/UbaCaOs528in9/KPX8j7wH0JdneTLjxx/XgrZhOORhDThFvv2Rc\nKWKlNU7kKxzJ9iYJQcx6Dz419CWm5PkrRZ2syUgZUnE7SFQ3XW4PEehjtJOKK0VV+xmvbjSqHJxP\nlOq4qkiHhVgsZ4hk2k12v0i2N5lDh4qJlhTVIr1Yu3YtLVq0oEmTJgB07dqVBQsW0KpVq5I6CxYs\noGfPngB06NCB4uJiDh48SG5uLrm5uQDYbDZatWpFYWEhrVq1YsGCBXz++ecA9OrVi1tuuYVhw4Yl\n7I8WIhwrQUYk4qsVJwISL6y24AsKLC/Us7xQTz2TwqPtPLzQwM1Cg4HJAQOJ4knXSH5+d+nY5tf2\nXzagcKvFT7ct9rh1vIrAlF1mpuwyc1lmgBfP9GLPDDC+rpfNUul3NMZhYmAaJrl1EgJsckscCKb+\nfasIfO408rnTyJl6K9NzrBTrFK4SgyzRMNkt323kA1mnOaINCj0V6OoM3Wv9CEx1mpnqNNPRYOOh\njPpkmly8l7GDPQlcLTp5s/hB78OfBr74sKsu90nJ/Wd+0cHDOoEs1UZ/97VcqwbYZtjMlYHmWCQT\niqKUkN14k0N1Ot1JdWM5lTh5Pr8R1Akf5TjVKGupgDPs+mBPQle4s2D3ye5QyvCHCYRRSEOq5rUF\n2ts4nRAoKzktj2MFp6gjpwtLTncH0oxItjfYvVu7QX4t4qOwsJDGjUtntDdq1IjCwsKU6+zevZtN\nmzbRoUMHAA4dOkROTg4Aubm5HDoU/3c0m814PNp0neXTIUeQrpv0siITi/eWHYQd9ooMXWGl+6d2\nDqwReM/n4i29g4ZxJzApPGbwMqJI+2S5KY1cDAvLHZLByhN67tlg58Ef69Dp10ze2msl36XjUp/I\nVp+BnWplF9BkoDBAF+Clw9o/Wy+bnwm7TfReW4fcX+sxaU9dHj9hTjm6KilwqdfMbM2fDYYKClOL\nTSgxvu8Vfj13H87ggf25XLz/QoYcOp9rPXVjtAIocLU/h/eNFRNapIqOPgOrBBFniqf4MQFelKCH\npMfib0ejYB0kScJgMGA2mzGbzRgMBiRJKvn/KIqCLMtlIsN+v59g2Iq2JpLhk+v2ACFSEsn2VgRU\nEwWBEyuZOLDVUF1hAD3gwyjES3H2PwYdocljtV/FnwShVMe7dx8GKtoN1aL6wOl0kp+fz0svvYTV\nGtv7trKbo81mw+VyYTKlHn2Mlw45OmqlBYIgsMNl4vGl8V0ZFFXg4z+MfPyHkeZ2macv8tCsfpBZ\nooH5culnGm92858DJgKqtgvUxaYAR1wim5yp376PBESGb7UionJLrolBzXz8oVNpiEKhhljY85Kf\nN48aCWi8+FpQuFAX5KXDIenEhL1mJuw18ddMCyPO8GLO8DEuy8UfUuLfd7jLykuyhNYbggmFNrLA\ncG/lT6AOKiKDjluRjlvobbXxpNWDy3ycGfbdeMMDotu9DfnA6NHsWRxqqw53Jhn1jQUBaKUKGMSy\ngwNBEJCissKqqkowGKw0MizLMqqqotPpagwRThv5bdeuHawEoq9fkaftWYTI7wFC97FYbg/l5RJh\nREuqYskQkpEWxEJ0tjcD/hIdbaw2zsor3+lYx07d4SF+W4ldJIKCiIKATlAw6vzISGUSXqSE9nnJ\n102320OstlN1e5ApG/nVlatbP6/yY6fSt2ikIgFJdb+UcFW6GwwjkUtEMh8kliNEvP2i69oBkSNH\nquaBWYvk0LBhQ/bu3Vuyvn//fho2bFihzr59+2LWkWWZ/Px8evTowQ033FBSp5x1SNIAACAASURB\nVH79+hw8eJCcnByKioqoV68e8RBJcZydnZ1S39NtYRYLjoDI2A1mHIHk2tzpkPjXEgmjTuXONj4+\nONNBoVXg3aABKQBL3dolPMPqeei1Nr7cIRkoCFxsC/LyBhO/HtMx8HwvzbIVphslPk9R+5uFwllB\nlWEu7RP4puS6GLqtfPRYYOkJPUtP6MnRW3msqZlz6wRYXMfJh+ZAzOfXuQrgN7BGo20bwASCvHA8\neUs6GYF3XSbedZlop7fxz4xsckwePrHvpEUwg3HmJO3HKsGtHgsLBBG/UHXy+2BQoHUSA4PKyLAs\nyyVlEQKs1yfnW326cXLdHiKIWJ4dptpkt1LQ4caMAGHP35oGATlMJtKa8KKmQqCUO9Xaw/4JEMn2\nVouTiYsvvpgdO3awZ88e/H4/8+fP529/+1uZOtdffz3vv/8+AKtXryYjI6NE0vDII4/QunVr+vXr\nV2GfOXPmADB37twyxLg8rFYrTmdqT+DKE9/yCSsi71on060oMvLR76lHpH1BgWm/mujxhZ1pi0y8\nHPDQyKdwtUXbtfqFHBfTdhnxaAwd5hoUmusVvthjZIdT4rGfbPReYKfhryIfejy8IniwJXkhnaz3\nMiiFSW7xcL5B5pBbZKsnfkzuYEBk8O9Wuq7N5NAv9Rm/O5uRx2xklevq8GI7QypJaJEsmqDgD0hs\nrmJbGwJ67j+SwZ3769PjcBsottDHZdN2j1Kgk8/O27qqn9smFf6hiOiF1ClghAwbDAZ0uhAHkSQJ\nSZJK1msC0uvzK1M2qBNZ1hEK5DgIef5G39NipDeO5/kbSXWs06UW7S2d8Fa2rhsLVjxkUFyS6jhW\nVHlXwU5a5DWp0EbZqGzFfsSbHBeMEeWNl9I4/iQ+HUp47GLAX2LfVrI9XqrjSLkUNTrbUAAd8iId\nLUUqE9601o2un+qEt0h5JMWxUq7uwQKom1d5G4mOEQup1I23XzSqPDBcQtWiv/H8dmOhqt690Yg1\nuS3efjKQwy23tE1w3FpogU6nY/To0XTr1g1FUejTpw+tW7dm5syZAOTn59OlSxcWLlxI+/btsVgs\nvP766wCsWLGCDz/8kLZt23L11VcjCALPPvssnTt3ZsCAAdx7773Mnj2bM844gxkzZsTtQyTymwzi\nyRxOxqPWHQ49jyzRPgDr2sLHhB9NLPzdwP3tvTxydjG/STpePGzGm0L8qZGk0ASVoQe1R1gntXHx\n8LKyn80bFHjzNxNv/maiXd0AY8/zkVVH4RXJwIo4bgnXCgG2uCX2ytpJz8i6Hm7/JbkIaxCBOUVG\n5hQZaW2WGdDUTOOMALPqOhGAdbKeg2nQv41Fpe9x7eeASYB9Hh33/27l5iwzL+b4UG0eJmQd5VCK\nSS4e8mQwXQda1DNPBgVaJa6WEJH/oU6nQ6fTVfhvVmecfM1vBPUpJb/NT9lRK0VptjcnNVEsGkRE\nVWuzvZUgQn4j/72a9XPWogLM5OZmUev3e3LRuXNnOnfuXKYsPz+/zPqYMWMq7NexY0cOHz4cs82s\nrCw+/vjjpI6fLPk9FTKHyHEcAYFxG80cS9InNx7OsAVpZlJ5fkuIsI77ycy4n0xc3kRm4iUu7HVU\nxjgtrK0k2hnB6w2c9N1YtYxw0ejRwMuyQokiT/zPtuGongeW6LHrVR5q6+Xphh7WmQX+rRqQSwi7\nwmO6AN0Oa5NgADyc6WV+kR5nMPXf8r8eiYf/a8MiqvRtZKRbvQDL9WAQFfwaHm53Icgaj56jGhOR\nAEzIcPLY7zZUBD47ZuSzY0aaGy38q5GVM+1+Pq1zlAJT4snrBgVayBaG66tOMOuocJ0iIlYh6vtn\nQno1v8srqZAD/EGI/FYTnhnAgB89BgJYceOK85g1EvWtfhDwo8dIAAOB5LK9xUIk6lvTEZE+lL8u\nRKK+f1qcLM1vLWpx8hGZ8BaBqqplCO2pjPZGCPaKg1bmbtNu//X6lS7yPypPWAV+2qPnpz16Mk0K\n/S/1MqSZh7U6HaOPmKLIZSn61fXw1QE9h/3aCItBVOid46frwuQIqyMgMGajGTaqXNVAZlobL4ZM\nlVE6A3frZMYfNmue5GZC4VpDgO4HtBF7tyKQIar8Z5OJwz6Rya18mDNlXjKIbEqZBCv0V6FbsfZz\noL0+wHaXjsJyfsw7fRIDdtgwCSr35Jh5OdtHoc3FxIzjxPuZB7vqMkaj9/EwWaB5mghYTYnyxkJ6\nI79BYsseADIozfZ2FMgsVyeqbnzP31iyh+SXY0ka3JgxECCTE3gpe6LHk0vEOka88srKovfzxyiD\n2D7A0ZCRMBLAiK/MhLe4nr+VtlahcxWXU5nEdionvEXKlPB69AArmTaqsj0aaff5jSDeRSrdD22q\n4v9bWZrik7FfLf6MKE9+o3Eqo72R106XiUeWaI+wDrzIzfsbjRyrJMJ6wisyaokFULnmTJlp7V0Y\nM2FUsZlN3tB/o46ocK1Rpsce7X2a0tbFsLXJW6SVQmDJAT1LDoT8jYde5OairCB7JJnF6NAyfWhK\njpvnfjejNSKWISqcY1AYsS8UZf/xsJ66BoVHWnsYliuz1AKvCWKJXLAyDBEUphebNBN7gKE2L73/\nG/+386oCk4vMTC4yc6nVylMNM8iy+Xir7hG2RMkXsxURWTHwi4aob1MFrlDTP3CsKQ4P0Tj5Pr8R\nRGd7K0rXUbUjopWtLNvb7wV742473Yj4/WrK9ramIH0dOt2Ilp5Fvo4jBaehI6cSP5zuDtSiFlWG\nzWbD7S7re1qZ0f7JIL4Rj2CHrOPl9RaOa5Q7NLIotLUHeW9Tsvpcge936MmfZ+efc6z847Cf+VnF\nPFXXzdRGDp7YrD0jXMcMP4eKRX4+qm3gfNgr0sSo8I+5dnasEHlXcjGzTjFnSqmP9C82BDjkFtji\n1j6Yn9zSxeB1ZZ9+HvWLPL/JSrdFGWxbY+btYzBDlmlWyYwzGwrnBkU+8WjXVt9r8fL5ET3uJCco\nrnLpuXe7nXs31eWirWcwdl8j7nbaEBUY7KzLixqszQCeD4o0rA6P3asBTp3mF0Lkdz8h8psOtXUa\n4MWIHM72ZsCHp6rSgdMEFbEk25tB8Jdke/ufxf+2jKkWtahxKK/5jTxKPZUyhwiWHjDz8R/ar6GT\nr3JyTwW5Q3I44hZ54XsLAir/7uLGnC3w72ZuRu4zs7kK3r4hKAw500v3Rdr1ufe29PLtNj2H3SKf\nbzPy+TYjjWwKj3b00LqBm68wMNWRONsdwPC6Hnpt0t6njjY/O4/r2BmHRKsIfLHfwBf7DTQ2KzzW\n1sPZdWU+NcM7glimr68LCs8d0z7JTUThZn2ArgdTPw+OBUVG7LUi7LVwfR0LYxt4qKNXMdiDVR4D\ndQhCezW9T00i/9F0uaucSqRX8/sdZWesRy/7AAul2d6chDyBY8ge4i1HUh3rjLFlCNFInG64dNkV\nTniRSTFOKv4RW+c1LPkwibx9o8vLuzOU7090eTLtxpJDSASR0SERxCj4EpPfiAQiyrePjnnRBylF\nVR0MTpfbg0xptrcgoXNNB2TnJW4jXdsrq5/Kfinh6nQ3GAPp9PyNDs+n/cuoRQ1DLM1vBKdC5hBB\nkc/EkJ+0W3Y9297N3I1GjlYid0gGZknl7MwgN0+yU8+q0v8aLxe0dLPcJ/HqblNSj+8jeLW1m1c3\nmfBptEizSArX5wa4bV5ZQrffKTJokRWdoPKPNn7eO9eF1wZDHZa4ThCDs9y8s9+YdFS0Mgxu4uW2\nH5Ij0fs8Ik+ttSIJKrc19fNecz8Om8xQSSQXKPJJbEuDTdqrmW5e3meqgsSkFCoCXx038kBdH/es\ntvJACw+tsmU+ywjwgSQkH+xR4ZmgSFYao741iejGwqmN/OoIaX2PEZr4Vk3mkdX0bG8Rv9/abG9h\nRMivQuVpj2tRi1qcdkQiv9u2baNly5Yl5VqivYIgxLVdiqUjPubS8/rHZl5o4yG7nsqU7QYW7Us9\nAtzMLnOWReHFTdpJ9PRbXTz1kQVVFTjkFBj+uQVBULnuHD8zLnMh2UkqGtzGKmOU4btC7Qk2pl7u\nYvCi+PrcoCowb4uReVuMNMkI8thlXlo0CPKJYuAdZ2k0OFtUaCsGGXVI+/c0tKmL6duMKRN7WRWY\ns8vInF1GzrbJDDrHR/s6ASYHtCdpaCgq2GX40am9rXvqefliv4HtLh1Pb7IhCSo9z/DxVhM/xRky\nIywKRxOQ4O4KnEf6B5ER1Gp+k0Ek5fXBdB1ZO6KzveliRKK2F+yruFM1goKIooayvUlViaStLkh7\nn04rIoRXDb9qNb+1qEW1xaFDh/jhhx/o0aMHR44cQRCEk6rtLa8jBpEFa4xM+8bEg+Nt3P2ijTbH\nFD643MG4jk7qGJL3YX3tCjePLdBO6Hqd52XtDok/Dpcltqoq8PVmI3fPsPPYdCs9fH4+alnM003d\nSHF0rGNauhm4Wvtj/M6N/Gwr0rHtWHIxsz3FOp5caKXHbDv+DQJzDC6mZTloJClMyXEycLv27ylL\nUmilV/hkrzapynanxPbjIjM3mjD9Ch+IDl6zOslK0YM3ggmZTp7Zrf3ziSjcbA/w1s7SzyerArP3\nmOj5YwYvL8tg4A4j7x6R6BKIHYnVq3B/UMT6P25tVh7pjfzGS3IRvZwRfj9MyOIg8iQ/nlwiajmS\n6jiS7AIqc36oKI2It13EgAcTFrzU4URJwotYRDh+0omK5dEyhXhuDv5y+4SWK5dIlCkXDESyvRmQ\nMeu8uBHLOD/ESnihRk9O0JHYzaG6uT1UhmjLs0j0t7K2k5FnJPp80UglOUY8nDbb5kTyBkhNqhDL\n2SGeq0OsurUX7D8rVFVl2rRpDB06FJ/PR7NmzTh06BD16tU76TKHaDnFpl1GBs0oJYcun8DEz8xM\n/AzOby4z6mY3uTkKb+8y8tnO+CRrdEcnb64ycsKr7Zy1GRRua+On+5uVP8Y/5BQZ/kUoGtypdYC3\nLneht6uM3m9hoyP0/xl5toupW4xJp2eOBxGFR1t56fpB6vpcWRGY+6uRub8aaZ4p8/r/OanjUrkm\nI8CswwJa/uNvnOXkX6vSkIRCVLiqrsxtS22AwFubTJyTLfNiezcNsxWmKkYW+JIj2J0MfjYUSxQF\ntF+7Xm3q5pX/xpdObHVK9F9vx6xTyW/qZWYjP/syZF4yqzjDh39Mhha+AAGdktZJo+X1vjUN6dX8\nfptERQMhAlxMyPKsbuXVTxVcWLHgLZPtLYKz8xqfpl4lDxkJA3LMbG8JcWneSenTaUV0trd6eae3\nLycdp0LzW4tapBcTJkzg+eefB6BZs2YsXLgQm027nVd5xJI5hCK+UHhM4pEpVgJxkits2inx8Gs2\nTHqVPp28vN/RwTGdwLB1ljJJIi6sG8AKfLFV+2S56bc4eWJeSO6QDFRVYNFvBhb9ZiDbqvDQ1V6G\nne1mOwJZgsrnu7WTw8mXu3lxiRlZoz53r0MEWeBvb9rp1s7Pexe6cFtg6H4r+1P0ML6xro/1h/Xs\n82jXtr15iYuhy8rKObYckej/rQ2zpJJ/no8PWzjYZxYY7rZwXI3XV4VHLV66/1f7JL5cSSEjCMuP\nJpZOeIICk3eYmbzDTLvMAM+f7aV+ZpA59gA3yoCiECj3xCOSlS1dmvqapgE+PWGV+uH3Q6fl6DHh\nChPG0mxvNQsyutJsb6cvbFh9EDmzI9KHWtSiFtUKd955J23btmXGjBk0btwYu107YYiFWHZpAN6A\nwIyFJn7bkzgG5A0ITPvaTM8X7fxnqolnGnuYf3Uxd7X0IhLkxUs9PPW1dpJ5TzsPy7bq2XmkanGp\nIy6RF7+y0PV1OxeoKtIRgfcvd3BZ/ap7aLevG6DYKbBqv3b96pvXuxj+pRmfLPDeGiO3v2VnxGwL\nj6se5jcrJj/HC5XYkEUgovBAfR9jNmtPQnFxnQAHTohsifOde2SByRtM3DbfzlvfmHjJ7WaeycH/\nGStmZHvB7mFKoZGAltzDYUxs6uKZX1KXTmw4oefBtXbuXpJJ/2NGWogSBoOhhOhC6D8RCATwer14\nPB58Ph+BQKDE8i8Z1DSyWx7p1fxGklxEXt6oV3R5VninQ4SegMrJvaRg6KWTg6Uvol9yyUsiWPLS\nxXiV366gw4+ERBA7jjJ1dhTsKdkvGvGOEUGs48Z7RbdVtWMoBMKBfBNedFKw5JUQqwoS14kFKcEr\n1f1ibU+mjVhlEekDwOGC5PdLdLxkkMp3kRKEOK9lCQ4UXTe6U/oYL13UKx39TNRevL5F/4C1ONlY\ntGgRl112GZdccgnjx4+PWWfQoEF06NCBq666ip9//rmk/JFHHqF169ZceeWVZeqPHj2ac889l7y8\nPPLy8li0aFGZ7XXr1mXJkiXceuutab+Rlm8vlo541X+NjP80dWvL7fslHptipcdwO75fBb7r4kDx\nqjSwaws6ZFsU/namzITvtRO6kTe7mbzAyD2v2XngFStXe2TmdXAwsp0Li5SKjlVh2IUenvteu371\nskZ+Dh0X2biv7HVq11EdT8630mOSHfd6gfdyXMxo7qCZKb686vWzXIz6xUwwDSRzWFsPw5Yl9/k2\nHZZ46Bsbd82z0XKryoeig1etTjIFhWxR4UxUFpzQHv2/xuZn0zEdBzT4TZ9pCdLQpCKKIpIkYTQa\nMZvNmEymCmQ4GAxWmQz/aWUPgiCcAbwD5BIakk1VVXWCpqPaKc32dgLKqQxOG9xYMFCMHSfuOKmO\nqzMC6DEgo6+1jwohovut2QPUWtTipEJRFAYOHMgnn3xCgwYN6NSpE9dffz2tWpWasS9cuJAdO3aw\nZs0a1qxZwxNPPMHChQsBuOOOO3jggQd46KGHKrT98MMP079//7jHjkRh04lkUiH/fkDPA6+F9J1V\nhRwUcHuhYLWBqZ+a6H+bhzZXull6UGL8ytSsyACm3eTkodna+gTQKlemnlHl09UhEnbCLTLmEzOg\ncllLmXFd3NTNVpm005jQAWLCpW5eWW7GK2slOArP/sVL96nxo/uyIvDBOiMfrDNyRp0gj+R5adnM\nzUKfgckHSp0i2lpkAj6BlUe0R6IHn+Pm7U1GPCl+Prcs8Pp6E6+vN3FBPZl/t3dzbnaQt46mw2df\n4V85Xrqv0PIkRGXUeR5yTBXdnyJPPyRJKvmvKIpCMBgsIbvBYLCEEEcGjjqdruS/VFMJbzSSiUnJ\nwOOqqm4QBMEGrBUE4VtVVX+LrtSuXTvYAUT/9tED2PKT2OoCB4C94XrR+yVIdRzx+4Wynr+J0hvH\nn6AWWvaGO5FBMYfJLilvnZcLMdoIMfiK7cVKWRx/PzlGWfKev9Hpjz0YsUKY/Jae9LFSHcvREeG/\nXE0JQ5SiTupEE95SmdiVjglvyfj8RpcJhAZY9fJiO8BVZYJduie5pWWckhe1nOiGkM4UwvHSFCc6\nXvR+tZ6/pxtr166lRYsWNGkS8p7s2rUrCxYsKEN+FyxYQM+ePQHo0KEDxcXFHDx4kJycHDp27Mie\nPXtitn0qH43G8u6FipGpI04dw2ZZOebURrwzLAr51/i4bYgdRREYPMkasiK7zM/Mv7kwZMCY1WbW\nFSa+zQ660s38dQYOFGsdDCi8cqub28fGIk4CK7fpWblNj82kcs+1Xh682MEBQWD4JgvHymluL6wT\nAD/8sFs7yRzfxc0ri0Jyh2Sw97iOgZ9YEQWVm8/3M6uDC9UGIw6Y+XczN7cv1S6RyTYotLUEGbVN\nW1T758MS87foOVxfxFIMH7QqptAoMuyAheNK6r/n0IYe3tphxK9BX927iZ92dYIJSWqEyJYnwxEi\nHAwGy5DhyD7Rg9aaSoQT/jKqqh5QVXVDeNkJbAG0zwDLDr9XI8szH0aCiBgJoC9DXWsGItneBCHi\n+fs/jlqjgFrUIiEKCwtp3Lj0kt6oUSMKCwtTrhML06ZN46qrruLRRx+luLg4bj2tN9DoFMXl24sm\nw3IQPl9hYuF67Z63MwY4eWycFUWJPpbA1yuM3DXczsPDrVxn8PPRjQ5GXePCFscy7awsmVaZCu+u\n1C53eLWbm9e+NOHwVv59Or0Cr31lpucYO1NmmRjR2M38y4vp2TyiuVUYeZGHgYu0PwE9r76MToaC\nbamTaEUV+PRnI32m23lqppXx2W4MDujXwoOYhDa4Mkxp7+KpgnQ84VV45EIfLywyM/knEz3ezmDq\npyZGSm7mNyrmljoVtcHxUEdUaKNX+LSw6hFkk6jSv4UPmz71/1SE2Or1+jIyCb1ej04XdooqR4aD\nwSA+nw9ZrlnBi5TogSAIzYF2wMry25L2+Y2gTvjoJwhpgqsFBJxhuYOd0oxD2woSX+SrC/zhCJxR\nSP4Px8qCk9OZ042I5DRa8/unRMHp7kAtalEB9913H+vXr2fJkiXk5uYyZMiQpPZLJVocz7s3npxi\n404jg9/Wrl995jY3nxQY2FMUXxt/tFjkpbctdHvKxifvG3ilvZuPbi3mhpbR12aFcde5GfCBdhLW\nvmkAUYZvN6ZG7Lfsk/jnVBu9XrJj3A5z2rko6FTMuxtTlwNUhMJLV7sZ+In2zycAB4+KXD/Szs8F\nEjPOdjO3vYOLs1InXV3P8LJqr45Cl/YIyX+ucjNuibmMY8gvRRL959u4fbqd3G0q72c7mNzYRf0E\neuspzV0M2pS6Dj0aw8/x0DZD28AggsrIcPQAM5oM1xQkPRUnLHmYBwwIR4DL4IcffmDTf6F5vdB6\nHSO0awF5LULrBZtD73mtgCAUbAGOQ14GUAQFe8Pb2wEyFKwNr4ddnApWgWqBvL+E/H5/WBoqv/T6\n0Be+tEDBo/NyeV5odLmmIEReL8szoUNmTYEbH34uzgtZ6WwqOApAu7xMdMhsKjgWXs8gEwfbCvaz\nD5E2eTmIBPk93MEm4Q+0vWAfPkycmRd6VLi34HcAmuU1Q0eQPQU78GKkcd7ZABwqCKlEGua1REeQ\novB6Vt4FABwv2AhAdt556JA5VrAJAFPeZQCcKNhAAD32vIsA8BaEBhtC3l8B8BSsIogeJa8DAMEf\nlhPEhiHvL+ikIPKSHwHQhW3N5FXLQ/v/5aqQ4CFCgC+8JvS+uiCk22gfqs/68Pbzw+sbwtsvCK//\nFt5+Xl7orNoc3t4mvH1reHur8PZt4fUm4e2/h+ufGd6+M7y9QXj77vD2M8LrReHtjfNCT8sLC0LK\nlEj9/eHtdcPrhwtC7drD60fC9euGj3csXN8c3n4ivD0jvO4Ib9eH113h7ZbweiBqfxnwhdd15bZH\n9pfD61J4PVgQGgyKUetAqaQh2fXIpKMl4ferwu/hPwwdw+/LCX2Av4TXfwq/dwi/rwhvvyy8vjr8\nfimhL2xVePslUfUB2off14Xfzw+/rycUUWoX3j8yWD43/L4x3N4FwM9EfBPXrj2L1q3b0KlTJ2px\nctCwYUP27t1bsr5//34aNmxYoc6+ffsqrVMe9erVK1m+66676N27d9y6ZrMZt9uN2Zz8jT+WhVll\nesRdh/T0HW8jqNGu67xmMmdmK7w0NVkSLbBqs55Vm/VYTCp3Xu/l/escHBcEJEOQVxeZE0ZqE0EU\nFYb/zcNtL1ddDuCXBd4pMLFlr477rvRxsSrT8wYf3xfpeX2tMWUNM8Doa928/oMJl1/7o/FJ3Z30\nnWJDVQW+/dnAtz8bqGtT6NfFy5ALPPwqi4z6zYw3gdRAQuGuJn66fqJdOtHEHiRThO9+jx3V9soC\nU1eamLrSRKv6Ms9d4aFJoyAfeA3MOVqqYwb4q83P1uM6dnuqPkO6qVnmpoYBRPHkZXKLlj0EAoES\nLXBNg5DMKFsQBAn4AligqmrMqcCLFy9WO33YOZS+OIJEyweA3wlZn+VFbc+IWo6yfVTD5YGoQaTH\nVnrSOXSlJ3O0162b0AXVU6as4nYISR9asBOAX2lLEF2Z7fHa8EVpdiN1orf7o7bHKk/UVvlyf1if\nXLEtFRtuRFSOqZnISPh9pfv5vKFlv7f0sYrqjLqIR1+EoyPykWU5Rlm85XjbE7WRzDFi1YlVpgKe\n8LKekAa4fBvxjhcrSUui7fHqJEr+Un45YeBejbMcaSQQoyyZ8njbo5fVGGXJHC8SGVDjbK94vL59\nG9KzZzGdOnWqmcKyaoRjx47FvNgHg0EuvfRSPvnkE3Jzc+ncuTNTp06ldevWJXUWLlzItGnTeP/9\n91m9ejWDBw8umfAGsHv3bnr37s3y5ctLyoqKisjNzQVg0qRJrF+/nqlTp8bsW35+PiNHjiQ7O6SH\nizxijYfyxDfWpLZIJEoURU64JZ6ZaWP+j9omJImiwmdDnPQYYsetkbDm3+jltqv8+IBFu/RMWmqk\nqlqt6Xc4mPyFidVxSFiyEEWFTx53cttzdnwBAVFUuf4yPz07+5Hs8PJaM+uLkiNnbbJlHmvnpd9c\n7d7N/f/qwVcsMO27eNIQlY4tZe7v5KNOtsqkPUa+Oxg7Av7WJQ4mrDCz8ZB2G55Pbi7m3vdtHHUn\n/7vpdSo9L/Rz43l+3GaBYYfM7PULfH6Wk24/2TVpfT+6zMG1uYm1vumA3+9HlmX0ej16vT5uOvHT\niaysrLhfRLK//nRgczziW2VELM+OELovaveq1gwFXUm2NzuOCgkvqj9Ks70Z8COnOYlfjUP5bG+1\nqEUtykCn0zF69Gi6deuGoij06dOH1q1bM3PmTCBETLt06cLChQtp3749FouFiRMnluzft29fli9f\nztGjRzn//PMZNGgQd9xxB8OHD2fTpk2IokjTpk0ZO3Zs3D5YrVacTmcJ+Y2HWJPaEmWsCgZh5w49\nf2/v45ddOrbuq/o18e1/uXjuDYtm4msxKfz9L35u7WdHVeHGPD/v3upCZ4OXfzCzfm/yfbz5PB+7\nCnWaiS/AG/e7eHGmGV8g4gcr8OVPRr78yUh2hsKDt3p59jo3W1w6Rq0w45bjJ3t4+Ro3vadrj65m\nWRT+2kym1/jKSLTAim16VkQm8+V5eeg8Bwd0MHyLlSPhyXyX1fVzpFhMncfCjwAAIABJREFUC/G9\n91wvX28xpER8AQJBgVnrjMxaZ6RpnSADrvTSvkmALQ4dfiXWzOzkcEsDH5fUVWrsBLRTjWSszq4A\n7gA2CYKwnhCNGKyq6tfR9TZs2ECnIGVdHRJFuHSEbM8cQCHQIFwer41webRRgU6Ol+o4UXrjiu4M\nkXIPZix4yaQYB3Z+L9hH67wGlbYRjVjuEvHcHJJtq3w/K0uLHHk8ZcQXjhYn0ICtWQwdw/oSKeoC\nGstpIRl5VSqpkBMdQ4vbQwRHCkLyBqWSNhIdI9nt5eskqhsPkYFgUjKqAso+OqkKIhfMZG6gqThG\nxHJ2qFkTI/4X0LlzZzp37lymLD8/v8z6mDFjYu4bL5o7efLkpI9vs9lwuVyV1klV5hDBxl9M3NzT\nTk49lYfu93JuDzc/F+oYPd+MN4WsYn2v87DuV4n1W7UTp7eHOPnXSAtyWFP72WIjny02kl1H4cHe\nXob0crPVqWPUt2aclfQxw6Rwz6V+ur+sPbra+QI/RQd1rPot9jXgSLHIqHctgMplbWXG3eQmu77C\nW/818tX2shH1/4TlDk6fdiI2taeLAdMtJEsKnV6B174289rXcE5jmWHXeTijQZCPDuvp1cTPbZ9k\nJG4kASySwvVN/dz2rjZyv/u4jv8UmHm5i8K3aw3MvsyNalMZtdPMZkfy55lRVHmipRu7/tT5o1e3\nKG+qSPjtqqq6nJMZk82mIvk9zXBjIZtj2HBQE01ig4ioKkiCgqDWhjvLZHuD2twJtahFNYPVao1L\nfqsS7Y1gzz4j9//TRjAoUFgkMHRkiLxd2VFmYh83dXJUpi8x8NXqyuUQZ+bKXNVG5s7ntZPMp+9w\n89ViAztiZJY7clxk1ORQHy85X+Y/Pd3kNFSY9bOB+RsrPvKffoeLx96yoGhM9mAyKPyzs5fuzyVD\n5gRWbtazcrMei1Glz/95eb+Tg+MiPP+TlWyzglmFrzdrd9S4r6OX736W2He0ahRkyz6JR6dLGCSV\n9x914D8sMCXPyYg1Zn4/UfVBzJudXQxekDwhrwyTbnHx8EwrRcUin64zkpuh0L+Tl/Paeljj1/Gf\nP0z4E+iYh7Zx08rsRxC0O4akipoaaU7bM/F27drBb4nrVUA9YCch/W/VI/5pRcjoTMKAjAV3SdS3\n5kAgEO6/ARl3ouqRqO+fFTl5oWBlzRvHJIm8092BWtRCEyKyh/IoT3yTjfYCHD8hMWK0lf0HyhMn\ngWUr9CxbocdiVunT08vchx04gRHzzOw6WPa2KIoKEx5wc/tzdrTeoNo2l2nZQGHMhEST5QRWb9Kz\nepMek1Gl100+5nRz4NXDCwvN7Dgi8WQnN1+u0rP7sPbY1Ix+Lp6ebEEOpvb53D6BNz838+bn0KKR\nzOP/cNOxbZCPN+sRRQWlCj63EdQxKVzXMkCPcdoHHGfnBik8JPLwazYaZyv0v9VDm0s8rDimY+x6\nE3IK/ezU1M/vB3VsO6ydPvU438uPWyWKovydi4pFhn4cGgDltZGZcqUbW5bKuH0mfjxaMSrfwiJz\nY46HGspBTxvSKwiNpCKOIJ58IXoyTyTbmxc4SmgyXPSEoagBeUnCi6i2yia8SJTkIrYsIlZdD2YM\nOMikmOMl4uT4bURLEiKJJ8rLKSo7dqK2ykMX4xjRzr6l2d4CZVIcRxJeBKPKyiS8kKJOiVgJL+LJ\nEKqa/CId0gK5krJIuRIuix5gJZJypKOfsepGo8oKgHhXOq1/6XQkwYiX/CJR27H2qwYTAWpx0mG1\nWnG7S4fpEbJbXuaQ7KzyQAA+/tzCF99UHtF1ewTenGnmzZnQtEmQh/t6adXazcqdEq98EiJF0wc4\neWGaGYdbG7uQJIUxD7np+Uhqj8q9PoGZH5mY+ZGJMxoE6X+nl/NvcpGZqdLpI+2P8O+7xsvKTRJb\nY0SiU8Ef+yXMehjyqpkMq8qMG1wY7SqvLDezugqJMqb1Tk3uUBn+3dPN7aNC3/u+IyKDp4cSknS+\nKMDUzm6smSrjfjXx4/7K+ymiMOBCL93e0a5llkSF3ucH6PZaPHIvUPCbnoLf9NhNKn3zvDzWyste\nUeCF7RaOyyKg8uoFbnL0AU61sX0sT+2ahLSR3w0bNlAlMyKB0mxvRZR1hTiN8GAiEwc2nPxWUESb\nvNzT3aWU4EcqyfYmoKJWdgH5aQlcflX87TUdBwsgO6+UaFaTJwzpQwG10d9a1GSU1/xGk15IXuYQ\nwap1Jp59MTU/3917dAwaGiJF11wV4I07XTRtpvDHQZHVW7RPJpv5jIvnxlpweap+8dl7QMczL5v5\nYoqTF0eamdzNTUY9lTeWGlj0c+pOFg3rKHRuG6B3GuQcf73Aj/OEwA9rQnKHz38wkpWh8GAPL0/3\n8LDTLTJykYXj3sQkrd8VHhZvrLrcIRov9XLx5pdGnOUmKaqqwMJ1BhauM5BpVbj/eh+PXe1lnyLw\nwmoLx2L08/Vr3YxcVNbTt6p44x8uhn9sTkqy4vAKjP3aDF/DBU1kRl7rpkF9hV2IXJjhB7XmktDT\nhephBZBNKfltlaDuKUJ0tjdDWlPCnhpEsr1JQhCD4MenpiPneA1GzbMhrEUt/mdgt9tjZoxLReYQ\nwbbfDdzzUMgPtipQVYHvfjCwd5/IkMc8bFwpMXegg+IgjHjXUmlii3jo93cPq9ZLrN+s/ZY7fZSL\nEf8xs3KNnm8WG7BZVe7q6aXv/Q6OKwIjPjWz90hyfZzS18l9o2xojQYYJIWnenjp9ljZiOixYpF/\nTwsNQtq1DjDyNjcNGyl89F8Ds9eU9bmNoL5N4eozZXpX6u6QHFrmymSbVL5YWfn974RL5JV5ZpgH\n5zeXeeEmD40bBpm/x8Cs30L9vKheAK9XYOUe7QOhSxoHOHpcZGMVou0/75Ho/7aNejaFrx4/gUEN\n8ZNgMEggEChJ8nKyyXBt5DeMdu3ahXzrk/EtjdZkBwlJH0TgOOAstz1WG1HnsS5aAhFHOpBIWhAb\noWxvmTi4PE/icII2Ejk4JOPmkErd0n7EdpGQhCAyOiSCmERvieVZtASiBOmO+qbT7SFWu/HaiNdu\nTl7oXUfofBPDy4nkErGOnYrDQ2X1te5XBnmpVE4joi968W4IiT5ILDcISNLmohZ/ElitVnbv3s2s\nWbPo06cPkHq0F+BAkcSjT1s5UaxttCtJCmNfdNOrpx2nU2DSJGjePMg/+3tp2SbIiq0SYz80Ice1\n+ipFyyYyl7eWuftp7WSu941etm2TWLmm9P/mdAlMmm5m0nRo0VxmwL1ezm4ZZNlOifEL4utZ/32H\nk7c+M3L4hPbIwPSBLgaPsxCoJCPchv/q6f+iHoNepXsXP7P/7iJoUvn39xY2R3kHv9nTSb83tBNy\ngLF93Nz+UmoShU07JR6ZKKGXVLr/1c/sv7hQLAq5dpVbZ6bj0bTC0Gs93DZRm3RiZDc3zbNlgkGh\nhIgGAqWBOlEU0el06HS6lAeQVUFNc3+oHpFfHaHo76Hwq17l1U8VIuQ3EweHqX+6u5My5DCZMODn\nT/isP3VEyK9CrZS0FrWoJnA6nUyfPp2vv/4ag8HAFVdcQYsWLVK+WTucIq9PtbBuo/bI3Ow3XQwa\naMHpLO3Dzp06Bj4VkkVce22AKQ+4yKwH07418M2K2JFFUVR49Z9ueg/QPlmuYX2Fv18boNf98Un0\nHzslnhoqIQgqXfICTO3pxlpXZXKBke9/LQ2UdGzpx6QKfLZc+xPB2zt52bhZ4pftydEJf0Dgva+M\nvPeVkQb1FPr19HLBtW5+OabDr8D8nwwUpYGQR+QOVdVqB2SBOd8bmfO9kUn9nbj2wuybHPx8XMe/\nl5rxJjHwiYXRf3MzcaEJb6Dq58PlZwW45hwZSZIQBKFMxDcYDJZJ+x0hxJFMbOkiw7WR3zA2bNhA\nJx9lI7zRy9H/sVjR4fqEiG8R0DJqe6xJc9Hzs8osV+75Gy/aG28ymhcTKrCl4CCmvGYo4Uhq7P0S\nRWWTnxwXjNMfXQzGFn8inQ5QURDQCSqSGiyT8EInldaVVy1H+Eso+qtGlcf0/K3qhLd0101lwtuR\nAsjNCxHeyDhAJXHEWOskt+j6qU5si/XPjBsMLeDkRH/jTVyLhWQ+YPmZhuVR8+RFtdCGjRs30rdv\nX7Zv345er+f555+nefPmKd9QFQW+WWzizZnarZ6ee9rFgi/1/PJL7PNUVQUWLzaweLEBq1Xlzju9\nzHnagUuFkbPM7Cgs3e+dZ0M6X4dLK0FQeOMFJ/f0T07OoaoC335v4NvvDdhtKvm9vfS738ExRWDM\nlyYG3+ql+7PaJ21lZyjcenmAnk9WLap94LDI8NdDzgbdu/h5sJuP4qwgLi/MX13137JNI5kso8rn\ncQYlqaBtUxkC0G+UDVC54kKZ1/7uJqu+yvRfDHz1W/LHOCtbJksP3/xSdRs4SVQZ0dVFpsmPLAsl\nmQwFQcBgCLWrqirBYJBgMIiiKGXWA4FAyeTRCCGuiemJtaJ6RH6hNNpbDbO9CbjIqKHZ3oKIiARr\ns71Bbba3WtSimmHBggVs376ds846i1atWnH33XdXqZ11G40MGGhNXDEBrr7ST7YdRiRJol0ugSlT\nzEyZAk2aBHnoYS+t27rZuEeH1w8/rkqPznfiUDfjJps4cjR1kuJwCrw21cxrU0OyiLfGuXC6BR7t\n6mHc/OSkG/Hw1lNOHhyeDomCyt03+ej+gA2fT6DXrT7eu9tBQA8jvzSztTCV71Dh5d5ueo/UTu5B\nYXS+m94DI20JLN+oZ/lGPRaTyh03+JhzowOXTmDEUhO7jlXez1dvcHPnFG3ylyE3u2md4yUYLCsz\nUFW1JAIcIbeSJJVYBSqKUkKAo8kwhIhz+chwZahpEodYSK/md6WGBkxABlBMKAJcTax1XVjpkOfl\nWI0kvxBEhz5Mft3Env0cifr+aZGbV7osUip9qJlPa2Ig73R3oBa1qBKefPJJ7HY7N998M0OHDi0p\nV1U16ejvHzv03PWgvSRbWlWRXVdhQF8vPXpUjTTt2aNj8DNWQOX++73cdlsApzfIoSMCH34de3JX\nMuj6fz4OF4l8t0R70oib/i/A+3MNvPGGiU7XBnjzPhf2bJi2yMA3q1KLkr5wn4vZnxspOqI9avjK\nE25en2Eq0WrP/MDEzA9MNMpVeOhuL+fc4uGXQyJjvjDjTpCV79U73Yyfb6rg7lAVvHyfm9fnmnDG\ncOhwewWmzjcxdb6Jpg2CPNzTS6trPKw8pOOV5RW11s/kuZm93MgJT9W/r7NzZLq196OXBBSlLAGN\nyBygVC8fIbSRsmgyHIkKR8iwLJc+vUuFDP/Pyx6Aij6/yXj+Rnv31iVEfvdTGgmOUVeIc4z4qY4r\nT29cWapjb3j2nZ3isKwg9gSzROmUU5kcF414Pr6R8ng+wBFEsr3phSCS6icohULqUpRepIznb6Wt\nVehc5cup+vWerAlv0eV6QudidLa3ZKQVyW4vX6cqdVNGrItPuqP8VZUkxJJO1MobqiMWLVrEkCFD\nUBSFPn36MGDAgAp1Bg0axKJFi7BYLEycOJELLrgAgEceeYRvv/2W+vXrs2zZspL6x48f595772Xv\n3r00adKEGTNmkJFR6k0rSRL9+/fH5XLhcrkQBCGlqNKBAyJr16hMHXeCtT8beGWiGW8SVloVoTBz\nkpP77rFpJtEWi8ottwS49dYQie7Z08d7o1wEdTDmLTObUkiP3LC+Qq/r/fS8V/tkuVZny7RrE+Te\ne62AwKLFBhYtNmCzqdzZx8fcxx24EHhxjqmMdCMWLm4VINuk8uG32mUFHS/wIwYFvi6oSO73F4k8\nNyYki7i8vcyrPd3Ua6Awd62BD1dWHFC0bxGAgMCi9doHCm2bylhE+PrHxG3tPqBj0PiwHvzSAG/e\n4CYjW2XKBgOLthtplKHQJkvhpXmp2e+Vhcr4O9zkZgQIBkMkN0JSo6O7UGoVGInsRqQN0RIHnU6H\nXq8vow+OlklEk+HIftFkuqYjbZ9iw4YN2huJEN4iqk02rgB6firwI6FgSZwrrRoilO0NiGvZpixf\neio7dOpRVFC6LPInivhGUHC6O1CLGg5FURg4cCDz5s3jxx9/5KOPPmLr1q1l6ixcuJAdO3awZs0a\nxo4dyxNPPFGy7Y477mDevHkV2h03bhx5eXmsWrWKq666ildffTXm8c1mMx6PJ6U+FxcLjBsn8M9/\nQreuKsu+8zJh1HE+evsYt/3DQyrappmvuxj9kpmDB7XfEmfNcvLYYxa8XgGvV+Dtt03c3tvOk49Y\n+ftlfua94uDlp51kZSbqn8LUEU4eesJaZdu2CERR4ZVhbh59NER8o+F0CkyeYqJXDzvDnzDT9xIf\n8wc7GHaXC5OhYh8lSeH5uz088bJ2mYkkKQy+18ugUYkz3v20Vs+DT9u4o68dy354724X7/R10KaR\nXPIZh//dw6C3tBDMCEJyh4HjUvuMqiqweKWBe4fZyH/KRqtihbk3OvioZzFjv9amRx/Q2cv5jX1l\nCK0kSSWkVJIk9Ho9kiRViNYqioIsy/j9fnw+H36/H1mWkWW55CmLTqfDZDJhNpsxGo0lbUfv7/P5\n8Hg8+HylE7rKpx6vKaheItDobG/FVJuEF27MQBA7To5UFyuKFOAvyfaWljBjzUfE5qzWAKMWtQBg\n7dq1tGjRgiZNmgDQtWtXFixYQKtWpcbrCxYsoGfPngB06NCB4uJiDh48SE5ODh07dmTPnj0V2l2w\nYAGff/45AL169eKWW25h2LBhFeqJopjSDTQQgE8/FZkxI/QHVlX44QeBH34Ak0mlRw83s6d4UAUd\nL79mZWOcyWsAT/zTzdrVEsuWaXeJePllJ7NmGfnjj4rHKyoSGfFCiJhdeGGA5+/3cEazIN+sMDD1\nfUOFVMBTR7gYM95cJZ1vebw90cWwYeYy7hWxsGePjsGDQ9KNK66QmZDvpl5DhbnLDHxQEIq0vjPI\nxTOvWvD6tV88Z77gYvBLFnwptOX1Cbz9oYm3PzTRMEfhwTu9nH+Th+z6QYa9a8GnwUUhglcfdDNu\ndmy5Q7JwegQmfWDGYnCzepXE7Wf6GNbFw8r9Ol5dZMKfgta6YabCnVd4kMKPvSMWZuUR7eIQHRGO\nRHfLr0fvo9PpUBSlRDIRIb+x9MLRSWg8Hg+iKKLX62uUBCK9mt8fiC97iCeBiCxHBhJZhCK/hYA1\nThtxZQ/RqY4r9/RNJdXx2XkNgb1kUJyUPCGWzCLRsaOdHOI5PCTyDY7nGBGJ/OrjMD7xir9GNZIg\n1XGqbgelnYu9fCrcHhrnlS2P9vjVkZxcItntydaJVTcaNcLnNxony/P3z/GIrbqjsLCQxo0bl6w3\natSIdevWJaxTWFhITk5O3HYPHTpUsj03N5dDhw7FrZvKjfOnn3Q89VTs+l4vvPOOwDvvQP36Qfr2\nPcGQx0UKD0q8+B8rhw6XnlN//Yufs5ooPPywdllB164+/H6B+fMTSwE2btTz6CN6dDqVm27yM2OY\nG7NdZfIHRr5fYSC/m5fft0ss+Uk7IX8o38OalTrWrUulLYHly/UsX67HZFLpfpuP2QNc1GsQZMPW\n5G3NKsPdt3pYv1HHL/+teluFB0WGv2Lhli4+unSU6XmunwHXeflknYF3FldNZ33x2QEEfyiCqxUN\n6ym0OztIn3DyD0FQufYvAab8w429rsq0VQa++SXR+aIy8U4njTJCJCk6IpsI8chweSJcngxHZA7R\nZDjaSSIQCJSRRaSi0a8uqF6RXwjpfouAg8DZp7kvYbgxl2R7M+LFh3Y7nVMJFZGgKqITFIy12d7K\nXg9r3tOaWtSixqKyG2Sykd/Nm3Xcc49AMtUPHYJRo0IWL+ec42fwgADNmgn8uNrAnI+MPN6v6hPc\notGsmcxtt/m5/fbUSHQwKPDpp0Y+/dRIRoZCfr6Pf712gtwchV4PaO9Xq7NlLr0wyD33VF2i4PUK\nzHrXxPJlEiNe8FC8W2TeSAe7jwiMnG7hyPHUCWbDegrXXSpze3/tgw6bRSG/m5/ut9tQFAG9XuUf\nt/iZ1c+FaIVXPjOzdltyVEcUFYb39tDjqXQ4RcDkQU7uj0puoqoCi5cbWLzcgNWs0qerjzm3O3CL\nAi9+Y2LHoYr9vO+vPi5qEpIEpUJ8YyFChiNtxCPD5Z0govXC0YRaFEUMBsP/tuxhw4YNdEpHQ5mE\nyMkJQvKHaiB92FxwhEZ5kYQXxRysYeQXQtFfHX6Mgq8C+VWWLy0b/f2z4UABNMgrXRcoTXhR8/6z\nMVBA9Yj+1qKmomHDhuzdu7dkff/+/TRs2LBCnX379lVapzzq169fIo0oKiqiXj1tsrFdu3Tk54PT\nmfq+W7YI/OsxEEWVLl28zH7DzYkTIjfe6OOTT6p+TZckhUmT3PTuXfWUygDFxSJTphj5v//zkn+3\nygN3FdO6jcAvWw2Mec2M05Ua6ZEkhbHD3fTqpT3BBihMGO/m9tvtOByhts4/X2ZYXw9Nzgzy3Xo9\nr79vrCDdiNfWm885uXtAerK4vT3Wxb+eNqMoobYCAYEPPjLywUdGsusq3H+Pj0E3eCj0CIx438Kh\nShJovPmIixFvmtMi6RiY7+bDL4wcjiNbcXkE3pht4o3ZJpo0CvJQHy9tbvKw8bDI6AWhJBr17QoP\n5Lkx61UkKf2yglhkOEKEI5HgWGS4fIKLZcuWcdFFF2GzaR/MnCqkN/IbJLGrQ7zl6LK6wGFCEeDo\na2Ww3Hu55ehUx7ESXiRyZ4hXR0cQN2YycVCHExwhu0IbsVwg4sspKh47lpND+fJYcoj4EomovgmG\nkmxvRsGHTiejk6Lq6oKI4eQWwajymAkvkklyUR3cHhIhOttbKtKKZPoTr06iuon2i8Zpzf4buQBX\nVd4Qqy2I/YXWrEdpNRUXX3wxO3bsYM+ePeTm5jJ//nymTp1aps7111/PtGnT6Nq1K6tXryYjI6OM\n5CHWxJfrr7+eOXPmMGDAAObOncsNN9wQtw+CIKAoStwbfFGRyJNPwq5d2s4JRYH8fIXHH3fw229B\nevZ0MXu2EVU18PLLdjZuTO22+N57TgYNslCsMaUywKxZDp5+WmHLFoFnngFQ6djRy3+e9ZHTQODz\nhSZmvGckmcf570x0MvgZS0KdbzKYPt3FCy+YS4gvwKZNEo8+KqHTqfztb37eetqNrY7K1E8NfPtT\n/KeL4552M3GGiaNViBiXxxMPuPniSz27dsf+zY4cFRn9ihmAc9rIDLnPQ9MWQZZu0/PaF8YyHsc3\ndPBRWKhj9a/apSZNGgQ5p4nC6HHJTb7bs1/H4DEhrfWVHWQmdHeTnatgyVBomuUvyeR2shHR/kYQ\njwwDLF26lOHDh9O4cWMOHjzIO++8879Jftu1awffpamxHELkN7487JTi3Lx6uAmiAlZc6AgSrA5Z\nOFKAglgm21s0qRavvPK09euUIDrqG0Hk54u2PKuxyDvdHahFDYdOp2P06NF069atxOqsdevWzJw5\nE4D8/Hy6dOnCwoULad++fYnVWQR9+/Zl+fLlHD16lPPPP59BgwZxxx13MGDAAO69915mz57NGWec\nwYwZM+L2wWKx4PV6MZvNFUh0cbHAhAkCS5Zo/6OOGqXw5Zce1q0LjSBnzPAxY4aPnByB++938+yz\negoLjYwcaaeoqHKC9tJLLubPN7Jpk/Zb6YgRTj77LMjmzWU/44oVAitWgF6vcuutHt6Z4MVgEpk4\n3cKyFbGJ2qBH3Hy/2MDPaejXPfd42fyrjtWrYx8rGBT48ksjX35pxG4PZby7Z7gDjwovzTCzLYqY\ndu7ox+sU+CaGrVmqaHmmzLlnKdw7JjmCueU3iceekhBFlc7XBph6lxtbtsr07w38sElP3+t8dH8y\nPXKH1592cddjVSGCAsvW6Fm2Rs+Dt3sY2M95yohvzN5EkeHo6K/H4+GBBx7gxIkTbNmyBQhxwBtv\nvJF33333tPQ1VVQ/zS9U62xvFrzYa2TCCwEZHQbkShNe/M8gOttbLWpRCzp37kznzp3LlOXn55dZ\nHzNmTMx9y0eJI8jKyuLjjz9O6vhWqxW3243ZbC5T7vPBvHki06ZpJwC9eysEgz5mzfJV2HbwoMqo\nUSE7yzZtdDz9tIszzzSwapWJsWMt+MslV+je3YuiwNy52udQ3HCDD5PJz6xZ8esEAjBvHsybp5KZ\nGSQ/38E/8wUcHh0vjrWwa0/odn7pxQGaNlD49wjt1/gzz5S59poAd96ZHJFzOAQmTTIzaRI0bqzQ\nr5+Xtue52XpAZOJcE/1v89I9DVpmUBj7nJvb70q9LUUR+HaRgW8XGbBZVe7o7WXBEAeHTgicdUaQ\nrbu00aKRD7uY8b6R4xqeBORkK9zX04vdJpz2iWTRbg8Q0vlarVa6deuGyWQiKyuLpUuXsnLlSurX\nr39a+5oK0qv59RJyaIggjjyhzFNRb/g9+vphJWR75iDk+tCg3H5xJBRSGQlELNlDMlKHiokpthQc\n5Ly8bDyYseAlkxM4sCdMXJFoe3R5qgk4/DHK4iW8iLShhB+VGfGhi/qylGXLTk70NxmJRDrdHuK1\nsbegNPobXR7J9hZtgFFVacUpd3iIRgGl0d9ECS/iJZiI9QUkQlU7HMvVQUt7tfgzwGq14nA4yM7O\nLilTVViyRMczz2gnABdeqHDddTL5+Yn92n/7LcgTT7gQBBdXXy0xcaKZ7Gw98+ZZmDPHSKtWCn//\ne/KksDI0aqRwzz1uwi5ySeHECRg/HsaPV2naVKZfvxO0aiOyfZfEuS2DdOumfbKMKCq8NsFN795V\n0wzv2yfy3HOhBBUXXywz+1UHDodA39u9vDk7WX1wbEwd7eKlMWYcGiUdTpeAToT35xj49FMjDz7o\n5dz7PWwvEnhppoXjztT6eN5ZMllWlY+/0TIgUpn0opMWTU9/GtLoTHAQekIUCATo378/l112Gf36\n9QPgiSeewOPx4HK5Tmd3U0L1jPwCZBMivweoNqmO3VjI5hg2nPxevffzAAAgAElEQVQ/e+cd2FS9\nvvFPVtOkg5ZCS6FlSkFkCSrzQqQVBe5PuYiCgoJsuHJxIHivuFGpCoigIHsVUBRBuaK0YBUuqExF\nZUopXbRQoDs7vz+StKftSZM06dI8/zTnnO9KmvGe9/u8z9MQU4Z2tze5xIwUE+b6kFKvS9iDX/Bp\n/vrgQx0jICCg0o+nwQAtWlh47z1YsQLOnKnehzQsDF57zcSoUQVu9bNYIDnZSHJyAUolPPhgEVu3\n+tO6tZQXXwz2ivnEqlV5jBljwey6J0c5XL4M//mPdRtrzx4dly+b2Lb1Ot98o2bV6uoHmRs3FPHS\nS+V5vtWDhJEjdSxbKmHnTgnDhulY95YWdZCUVdv82fu9e4Hig0O1pKXKOOSA8uEOoqNN9LnDaLuJ\nkfDSS9Zg/fbbjcyfVEzzlma+OerHqp2VdZgrw8yCJ4sZNcOzzPb0sVru6l73Lph2lzc7BUkul1NQ\nUMDEiRMZO3YsI0aMKNdepVJV2rWpz/Au5/dLyjK5UD6b6+ixvci2YmY4FLiENfPbAWtgohRct8Gx\n1XFlzV9XsqtiRWrdNCGACTNSdChQYiCQAvSCJyI+hrgVslgG13HxnLOiOue6wxU1f/0wopToKbFY\n36h+mj7Y/wHlrI7FNH/lgi9CZ5lddwu7PC14c3Q9SiN+XkGZ2YWr89V2kZtLyVCNK41scPaD4e0v\nXUcFbTU1nw8NFRWDX4vFgkxmpkMHEx06wJAhci5dknLoEHz0kYQrV1wbVyqFDRtMTJhQgFbrvL0j\n6HSwZYuOUaMUTJ+ew6BBeUyapKawUMUbbwSSkuL+z+mWLQW88IKZmzc9v/NetszMkiUlfP21Cbkc\nhg0rYe0aPwICFKxapWZvoutB5tNPl3DokNxNbWBx/O1vOlQqA59+ak227NolYdcubPzgEp54rxid\nUcaCFWrOONEPDgs1M3qYgYfHeqOwysyHi4p4bGxF1QkJJ04oePKfCuRyC0OH6ln7bDHqRhZWfKFk\n/0/ifOUV/ylmwQcqijwwxoiKNDH5ER3qOhaUEgt8s7OzmTRpEs8//zwDBw6s2wV6AfU38xtIvXR7\nKyQQJTcIoojrDdjtTSnRlQa/f2n43N588KFeIDAwsFzwK3SRkkqlhIRY6N7dRPfuMHKklIsXJXzz\nDWzaJKGgioTuxx+bmDevgJwcz3frVq8OYMmSG5w8qefkST2QR3S0nKlTg7n1Vn8uXFDz1luB3HRB\nyWD+/EJ27zZy8qTnXzyPPWYmK8vA119bExZGI+zaZWTXLiNBQTBmTAlbEhQYjQrefjuQX39z/NN/\ne3cDt3Y0MWWK5wFmcLCZZ58tZuTIyq+HlR8ssfGDLUyZUshtT8GlK3LeWKbmhshruPadQiZP90xS\nzo733y1m6fv+Vf6vjEYJX3yh5Isvyor5Js8rQAu8tUlVyg+O66Un96q1WK26kEgsfPh6IZFNtRiN\nkkqaurUFu4mFHQqFgvPnzzNz5kwWLlxI165da3U9NYX6p/NrhwSr5NkVrKoPdRj8/pp8nc6axgAU\nEiCgPjQ82N3elBI99ojPdOB/yP7Wr07XVaPISoZIjfg1ocNbw2Oy2JCMT/HBh4aOgIAAMjMzSU9P\nJyoqCijTIa0YAISHmwkPh169YOJEKX/8IeGTT6xZRcHvNsuWmdiypZiTJz3XBnz+eX+OHy9m//7y\n6eO0NCPz5l0HoEcPP+bPb0Tz5koOHAhg6VJVOTktO0aM0CKV6ti82fPApmNHuOceM48/XrmID6Cg\nAFas0LNihZ7ISAmTJ5fw8isKMjP8ePOtwHKKFmq1mVdfLfGK8QfAxo35PPmkBKOx6ueZkSHh5Zet\n1I2uXY28Mj2P6FYSDhxTsHSd9TVc9GIhK1crybnquURa3CA9JYUS9u51XXWiYjGfnR986Sq0b2Vi\nxFTPgpQ500ro2rHEoeOao8+CN2E2m0ud2+wWx0eOHOHll19m9erVtGrVqsbmrm14N/NrxLUiN2c6\nv/Z+oViD32ygjeC8I6vkcrSHssd2zV+5zDnVQaxITYqptE2JwO1NRXEp9UFsDHcslB0VxznTIHZE\nkZA54PPKJBZMWN3eVDItevyQysylBXAygbZvOc1f0dEcQIyGUJcFb47OGykvl2nX/q2qn6M1CFFd\nTeCq5q2IOtX5FYMzegM4pziIjeGzN/4rwGKxkJqayoYNG+jUqRM7duzAz8/PqZuVRAJRUWaioqBf\nPwnPPivl7FlYtw7uvNPCxYs6Pv9cX+UYrmDYMAVNm5pZsCC/ynbHj+s5fvwqUincc4+KlSuDadRI\nybZtAWzfbtXnbd/eyIMPFjN2rOdBjFoN77xjYvRo50V8AFlZFl57TQfouPVWKXPnlNC6tZyjR5Us\nWqwmYXMh//qXGq3W87W9+24h69dDero7n2EJv/wiYda/rGYksbEGPnpVT2QL0Gql/PdrzxUsAgPN\nPDlZy8iR1Q/wMzKkpfzgL74oIOMPKduX5JN8xI8PNitFb3iqQqdbjIwdriNALXfouGaHPRC2//UW\nxALfr7/+mhUrVpCQkOCxQU19g3c5v64p2rgOu9tbPnXq9tZFEyo4klCEmmAKCSafazQcaQ877G5v\nfujR44d8QN+6XlLNwlHWF6zxlhSr2UWDzfxq6noBPvhQbRQUFPDcc8/xySefANCqVSsMBgNKpXuF\nUHK5hbZtTbRtCxqNhJwc+PFHKZ07y/j11+rfLcbESBkzRs7YsTku9zGb4ZtvSvjmmxL8/SWMHBnA\n5s2BKBR+RETI+Pvfccme2Rm2bDEza1Yx1SmyP33azDPPlCCRwIABxXzzdTFaLQwcqODSJSme3HgO\nG6ZFrzeyc2f1xzCbJSQmSjhyxMzatUZ27dKyebUeqUzO4mWBHDlWPYrBho+KmDVL7TQb7QpmzNCy\nZ4+M5cv9kEot3HuvkVUvFxIUAhu/8OOLROfkXYXcwtLXiogMt6o7OHNcs/8VSo95SpGo6OAml8vZ\nvHkz33zzDVu3bm1Q5hWuov5yfsGaibO7vV0DIup2OXbYg99GFDTI4Nfu9uaHnfrwF4c9+K1mtbUP\nPvhQfUyfPp2vvvoKpVLJ0KFDWbp0qccZLZXKQqtWEBUlYfBgNampcOSIieXLtaSnu/5BDwmBhQvV\njB59pdpqDFqthc2bC9m8uZAvvwzn668LWL06kKIiPxYsUHD+fPXGXbbMzMqVJVy86Nl3uMUCERGQ\nnFzCG2/kcf/9eWzcGIC/v5KVKwNJSnLvJiQy0sz48SWMGuWdXZsNG0zMmKEjI8PChg0mwsJ0TJig\nZ/a/ZOQVKHjjnQBSXdTmnTe3mJ2f+7ncviq0amWkd28Djz9uDXDNZgl79ijYs0eBWm1h9GgDCfH5\nmGWwaK2aE7+Lzxn/fDGdY8S3A4UmE/biM7PZXBoQC4/t7SvSJJxBGPjaA+mFCxdy+fJlNmzYgELh\nedFjfYR3Ob9GHNMbnNEhHPULwxr45mBVfXDUv8J5Mc1fmcx1qoPw8e/JuXTVhJSe06EsdXtToMeM\nTHQMZ9q+5dchrgzhqJ/YOddtkS2YLFa3Nz+LnuLvjznP/trpEHLBB8EdKkO5sZw8dkQtqK7aQ04y\nNNc47mffjbdgveGyf194w9LYHUqGu/bMdpiSqfnsr/BL1JuKEY40f+sdr8OHGsJ//vMfsrOzmTx5\nMqdPn/baVq49OAgKstC5M3TuLGX48EAuXbLw7bdG1q7Vcv2648BRKoXNmwOZOjWHoiLPkwRr14ax\nePEV9u8vBLJp0ULB1KlN6dRJTVqaH2++Keeqi66mU6aYSUvT89VXnn9O2rWT8sADMsaOvYHFAp9+\nWsKnn5YQFCThsccCmDBBhdHozzvvBLngZGdm1ap8xo2TYjZ7/n9cvNjIqlV6MjLKXv/cXHjnHQNg\noHVrHVOnaOnQUc7ZC368vSiAm3niQXeP7gaah5uZ/4o3DJ7MfPBBEWPGqBCrlC4ulrB2rR9r10LT\npmYmTtTy78kmruZJeesjNelZ1u+6Qf30DBukR+aC6qj9cyGTyZDJZOVoERVpEq7whcU0fC0WC3Pm\nzKFx48ZeuQmtz6jfmV+wur2dBa5Tr9zetPijQksQheTVFykKlyHBgMJGffBJTfnc3nzwwYqkpCRe\neOGFUovjWbNmVWrz/PPPk5SUhFqt5oMPPqBLly5V9o2Pj2fjxo2l7k/z5s0r5yTXqVMn9u7dy6+/\n/sqRI0e88jyEAYAdUqmUpk2lRERIufNOGWPGKLh40cx//2tg2zYdxRVos1u3BvDKK9fJyPA8wJw3\nrxE//VRgC3ytyMgw8NJLmQB07uzPCy80oWVLNceOKVi4UOZQlq1nTzN33mli8mTPucx+frBkiR+P\nPHK1Eg2joMDChx8W8uGHhTRrJmXSpCBefFFJTo4/b74ZTGZm5SBz3bpC3nwTcnM9D5r+7/9MlJQY\n2b3b8et/6ZKF//zHGgj37Klj/rwSmreQ891Bfz5Y6V/KvfX3N/PqCyU85AHPV4jly4t4910/8vKc\nP8+rV6UsWGDNnrdvb2LWlGLatbfwe4qMQf30hIVWb0tBGMwKg+Gq+MLCYNhkMpXeIMpkMvR6PTNm\nzKBfv35MmTKlWmtqSPAu53e7t0YTQEmZ29tV6sTwwp71FaIYVQMOfq28X3/0KDD8+Tm/9qxvVRBz\ne2sw0NT1Anz4E8BsNjN37lx27txJs2bNiI2NZciQIcTExJS2SUxMJCUlhaNHj3L06FGeeeYZEhMT\nnfadMWMG//znPx3OLZFIRE0uqgOxwFe4fWw0GjGbzUREQLNmEvr3VzFjhooLF0xs3arjv//Vs2iR\nmu3bCzh6VFxBwR0MH66iUSMz8+dfc9jm11+1PPVUOhIJ/O1vAbz3Xhjh4Sq+/lrO6tWyUspFWBjM\nm2dh1KgSj9cFsGWLP88+e52Cgqrv/K9cMTN/fh4AMTFynn66gHbtlPz6q4q33w6gsFDKk08W8/PP\nZg4d8pzuEBFh5vHHTYwa5XqAf+yYmWPH9EilegYP1vLRewoahcj4eIeKh4brmf1sgFcK+YYN03Lt\nGiQnux8+nT8v47nnrLuvX31VQkxb73HthJQHoFwwbP88VAyG9Xo9R48eJSoqirlz5zJu3DiGDx/u\ntTXVZ3g386vDuapDxcdiCg7C7xslVtWHAiATaybYgZGGM8MLmdIVk4vKlASx61rbxEEUIMOATNSA\nQpxaYRKhKrimDFF5PGeWxhXntn+VGJCXur0p5PpStze5gC8ianghF7xlnBleeIMW4Q1qgTOVCDni\nbm/VnUOsTY2aXIjB0Ze8Nz7ynu4WOFKG8O1C1CWOHTtG27ZtiY6OBmDEiBHs2bOnXPC7Z88eRtl8\neO+44w7y8/PJyckhNTW1yr4WF6q7AgMDKa6YfnUDwmyX2DWhdilYs132LFjr1tC6tZSBA+VcvqzG\nYjHz2WcmJBLPCtM6dVIwcqSKxx675OJzgO+/L+L774tQKCQMHRrM2rWhBAYq2bJFwYQJMGFCMXrP\nk74sXOjHli0FnD3r3pfMuXNGnnvuBgC9evnx9ttBtG6tICBARmysN7ZmzaxZY2L8eG21eNZmM3z9\ntZmvv9bh7w/r1xtRyM28+qqRZcuCOXiw+hzW0FAzEyfqGDnSM4386dMNdO5cs3buYsGwkOZgNpt5\n4IEH+PnnnwFroemRI0cIDg5m0KBBNbq2+gCv6QidPHnSW0NVht3qPZs62Zr+OflmpXNGFOhQIMOM\nGu/chdcuJKWav3x3oG6XUtPITHbeRkoDzPjakVzXC/DhT4CsrCxatGhRety8eXOysrJcauOs7+rV\nqxkwYAD/+te/yM8Xlwuzm1zYt3JdCZjtEG73Qtn2rqwKMqVYsKxQSGjXTsott8jZvDmc779vzgcf\nNKF7d9f1YO0IDZXy1lshTJlyuVoBtMFgYdeuPMaPv8Tjj59n+vRiCgryWbJERt++nv10jxkjJz/f\nwI4dnv12/fijnuefz8Vg0PP22xmsXJnHZ58V8/DDJqpbQbx6tZkFC3Rcc5wodxmdOkm4edPIP/5x\ng2nTrtKzZxZbt2azbt1NOnZ0P/hct66QJ59UesRnbt/exNSpetTeoB67CeGOSElJCXFxcfTo0QOl\nUklqairLly/n/fffr5G5k5KS6NWrF3feeSdLliypkTncgfd1foVZW12Fa1U9FrYVqoOYABXWGhst\ncMN2LDZWxYyxDXbNX9eK3MTbiMHu9hZIETcpk0Ozj+FoDiHcKY5zdt7R8xArppNLTJhsDg9+Uj0G\nmV3ntxYKjbxd8ObsuszJ2EZBOyNlWd+q2ro6t9h1IdzJgrvTr97AWaFcg3kiPlQTEydOZM6cOUgk\nEt544w1eeOEFli5dWqmdSqWipMT9YKwizUGswEe41WtHxSp5e6W7/VilknDrrQpuvVXBkCEqLl0y\ncuyYnuXL87h4ser3rVQKmzY1YeLESxQXe761/fLLEaxdm8XWrTmEhsoZP74Z//pXCCUlfsTHmzhz\nxvU5OneWMniwhHHj8jxeF8CmTWH885/ppKcb+e9/C/D3l/Dgg8Fs2tQIhcKP5cv9+O471zLCU6aY\nOHPGwMGDnr9m/v7wyityHnrIakBy86aFJUuKWLKkiBYtpEyaVEDnzkoyM5UsWBBEVlbVNxTx8YVs\n2CAnM7P62W2FwsKHH2qJiqpdaSExDd9z587x/fffs3btWiIiIjhy5Ajfffcd7du3r5H5nVGqahve\n5fzWFOxub9lYVR+a19xUYugmwvmFhu/2Zpc8a6TpzrWGSXZ1DS00rrWzB78NTvNXU9cL8OFPgMjI\nSNLT00uPMzMziYyMrNQmIyOjUhu9Xu+wr1Ac//HHH+eRRx4RnV8ikbid7a2Yua241Ws0GkuvCzPB\njgqDHGmnBgdL6drVj65d/bj/fhUpKSYOHdKyalU+WVmVA+tPPmnKCy9kkJ3t+c3d+PGhFBXp2LrV\nqjN844aRxYvTgXRatPBj0qTmdO4cRHa2gjffNJCZ6Xis4GB4800Fo0Z5Ia0KfPRRCB98cI309LLn\nqdVaSEjIIyEhj+BgKY8/Hsq0aYEYDEreeUfBqVPiQWbnzmZ69zYyYYJ36E8JCQqefjoPnQhtOyPD\nzKuvFgKFdOwo49lnC2nb1o9ffvHn3XetHGYh7r5bh1xu4fPPPZP9WrhQR7dutatkIxb47tmzh5Ur\nV7JlyxbCwqxb6/3796d///41sgZXKFW1jfqv9mCHMPitJygWuL35oSt1e2sosCAtdXvzsxjQ4/7W\n3p8Kwu+7BhX8+uCD5+jRowcpKSmkpaURERHBjh07WLVqVbk2Q4YMYfXq1YwYMaKUHxgeHk5YWJjD\nvtnZ2UREWEXav/zyS2699VaP11ox2ysMeqVSabkffAC5XF7OLc4VIwFHclFhYTLCwmTccYcfo0YF\ncPGikX37StiwoYAbN8ysWBHGhg3X+Plnz+lwvXur6NdPxeTJZ0WvZ2ToefXVSwDExKh46qnmtGsX\nwLlzMuLjjdyswNhLSPBn2rRcSko8/4KbPl3NhQsl7N3rOPmTn29m2bJcli3LpVkzORMmhPLiiwFc\nv+7HW28pSE0tU2N46y0jo0Z5XmAIMH++nO3bi/njD+eB5pkzJmbPtlJx+vRREB+vJjLSj2+/VbF8\nuQq1Gv71Ly0PPeQZz3f4cANDhxpwYlroVVS8oZPJZGzcuJF9+/axdetWAgICamUdYrSo48eP18rc\njlB7Or+O6BD2x8K4UWyMAKzBSR5QSBk1wg3NX7lg68sVzV87TiVfp7umkUhbs6jbm3gRW9WUBHeK\n44TnXbI0Fi3ik9nGkaJN/gm/gf0qBb9iVscWwTmnmr/uFrw50+sVayt87IgukZpclv11VPBmh46y\nzK+zttWlQFS3raN+lmSQaKyPazWp4IqlsRDOnqCY5q/P3ri2IJPJiI+P58EHHyyVK+vQoQPr168H\nYPz48dxzzz0kJibSs2dP1Go1y5Ytq7IvwCuvvMKpU6eQSqW0bNmSRYsWebROZzQHMbeqqvRKKxoJ\nuGIva58zIkJGRISMPn2UPPFEENnZRgoKDOzfX+DRcwRo3lzOnDnhjBr1m0vtz50rYc6cPwDo2TOI\n115rRnS0mh9+kLFkiYGVK/2Jj8/zinTbHXcouP12GVOmZLvc58oVI2++eRW4Sps2CqZNC6N9exUp\nKUo6dICnnqosN1cdDBokQaUysW2bA624KnD4sIHDh/OQyeDee5V89JGKmBgZn36qwmis/u5os2Zm\nXnhBR0hI7WRV7O/hijsZ77zzDhkZGaxfvx65vOHkPmsCDefZC93ergCt63Q1pWjobm8mn9tbeQjd\n3v6kLBAffHCEuLi4chq8YA16hXj77bdd7guwfPlyl+evKkitLs3BHaF+sQp5V7PCzZtLadFCidns\nx/fft+fCBR3bt9/kiy/y0Ovd+27194dVq6IZO/Z3DAb3v5ePHSvg2LECJBIYODCEPXtaYTLpue02\nGYcOUW23OrAW8s2bF8TDD1+u9hgpKQb+/e8rAGzc2JybN828844fx4/LWbTIVO0gOCwMnnxSxsMP\n36j22gBMJvjqKx0ajYIPP7wBSNi0KQilUsnKlWqSklzfJZVKLaxZo6VNm9rh+Toyr5g9ezZNmzbl\n/fffr3XzClcoVbWNhsH5tSMca/CbRa0Gv/asrxiKUZe6vUkxlUqGNRSYkeA/8C5kEjNyiwkvKOjU\nP7jK+YWygNdS4bg+w5719cGHPwHMZnOlH2dHNAd71tYZzaG6EMsKV8wMV8wKSyQSWrZU0KqVHwMG\nBDB7djjnzmnZsuUGiYkFiNTeVcLHH7fhqafOc+OGZ5xhiwUaN5bz44/XefHFcwwd2pQ1ayIJCvLn\nk0/0fPKJ+9nRTZtCmTgx3e2AXgyPPhrMxYtFvPJKGhIJ9O8fxKJFEYSHq/j2WynLl5sxuvESrF+v\nYOLEm271cYTBgxWAga1brVn8rVvzCQqSMnZsME88EYjZrGTx4gCOH686jHrjDS1du2oxGsvvUtQE\nLBZLuRtAuVyOTqdj+vTpDBgwgEmTJtXIvM7gCqWqtuHdzK8JxzQEZ49d6WcXVLiKdXta5ritmOav\n3eYYKtIeqn7sSDNXqPmrQkcIeeUML1xRkShVX3BDGUIIR5bGjqgTlWGVPJOhxx8tOnkZ/0RM89et\n7xRnqg4VHztTSfCmtq/wvPCcAut7seJNujNqhRDO2rhCl3DW1i3UpOavHdUtUnFEnTCKXPfhzw61\nWo1Wq0WlUpX+gHub5lBdVOWoJcwKQ3l1iZYtJbRsqWLgQDXp6WbOnNGyfn0uBw8WiUqgrV8fzZIl\nlzl/3nPOcOfOav7xj1Aef/xnLBbYtSuHXbtyUKmkjBjRjI0bw1EqlaxZo2PvXud8282bQ3n99Wyv\nFPLFxPgxdKiasWPPAdZA/cCBAg4cKLDRDkL56KMmhISo+PxzKZs3V33XsHq1gnffLSQnx/MMa1iY\nhKlT/Xn44Yxy5wsKzCxffpPly2/StKmMJ55oxNy5ARQUKImPD+T8+fI3XPfdZ+CBB3TIZGbMZhzy\nyL3xfhULfPPy8pg4cSITJkzg/vvv93iO6qIqWlRdwbucX28N5ghCt7drQERNT2jFyeR8umuCHV4v\nRo0KHUEUNEi3t4LkY/jf3QXFn9VkID0ZojSut5dRxvttCLGXkPPrgw8NGHaXN5XKWlwk1O4F79Mc\nPIFwLfY12ANhMdUKhcLCLbfIiYkJ5p57grh0Sc+vv2pZvfoax49bA9033mjGd99dZ//+ytry7iI0\nVM4bb7Rm9OjjlYLskhIzCQmZJCRkEhQk59FHm5OQEAb4sXSplh9+qLwH+NprQSQl5fPjj54H5Wo1\nLFwYzujRZ0SvW2kHN/jqqxsolRKGDw9j48YwVColGzbA7t3ln9C0aTLOnNHx3Xfe2bvcsCGYCRMy\nq8zSX71q4u23rwPXiY6WM2lSCJ06qcjMVLFggRqzGV57TUfTphIsFrlTHrkwIHYXYoFvVlYWkydP\nZt68eTWm4uAOHNGi6goNh/NrRxjW4DebWgt+naEYtUDyrOHxZk3ISt3eGiJ1w+uQUZbIbCgBsA8+\n/AkQGBhIYWFhqTya0LQCygLcmqI5VBfCjLBEIim3NiHsWWqFQkJMjJyOHYO5774gUlMNZGfruX5d\nx7p1Vzxej1VnuAMTJ/5MSUnVmdCCAiMffXSZjz66TFiYgvHjo5g1KxSdTsG77xbz669GRo70R6Ew\nsX6950E5QEJCFLNm/UFRkfMsrU5n4eOPr/Hxx9cIDJQyalRTEhJCkUr9+OADCQUFFu64w8KkSZ5b\nYwOsWBHE4sXXyMlxvTAwLc3Iyy9b5eM6dvRj9uxQ+vQJoG1bq3uSM9vhijsGFaX2qoKYlNnZs2eZ\nNWsW7733Hrfddptbz/+vAu9yfrVYVRnscIcC4UCpodxjHWBPwGZjDVDcoFbYbY4BZErnZhZ2mkFP\njbp0EDFahBkpOhQoMRBEgajkmWNTDdfNKoRqDhVVG1wZV7gOIRVCrbkLIyUoMKGU6CmxVCHpIjTB\ncGZ17O7OWE2pPQizvq4oONjd3ixYA2FpFW2dra26tshibYUQ9mswWV/7e8SRVqbP8OKvjoCAAM6e\nPUt4eDhqmwVWxS3i2qI5VAeO1iYMdipyh/39oWNHGZ06BZCfryIxsStHjxbw0UdZXLrkPicX4OOP\nb2XevLNkZ7uXCc3NNbBwYQqQQvPmSiZMiGbBglCaNlXy6KMZTvu7guXLm7FqVRYXL7ova1ZYaGbN\nmmzWrMkmNFTOlCkRDBkSQmYm3H67nBMnPPsOGTfOn9TUEvbtq352+8wZPWazmbZtxd+TruwYVCW1\nJ3yviwW+P/zwA6+//jpr164t1dX1oTIaXuY3ECv9QQvkA+L+E7UOodtbLk2cd6hnMCK3Bb+6qoPf\nvwqEhhc+tS0ffKhxWCwW8vPzmTp1KiNHjuTdd9+t5LwmrPyoU1cAACAASURBVGKvbZpDVahYYV9x\nbfbCuYpc4Yrb4AEBcNttfnTp0pThw8O4dEnHDz/ks2pVFpmZrgWyy5a1IyEhnZMnxW2kXUVmpo5l\nyy5x111BjB9/lCeeaE2HDk3JzIQFC26QleV+oDl9eigXLxbx1VeeqTGA1eyjb99AHn/8BHq9hfHj\no3j++VAKChTEx5dw/rx73N+YGBlxcXIee8wzM4HhwwMZPjwQudz5+1K4YyB8b1RVVCnMIle80frq\nq69YvXo1CQkJpeYVPoijYXF+wZo8CgfSsBpetKz5KU8kF3C7JqjKNgUN2O1Nl/wjEs2dACgldsmz\nuv9B8Rrc5fxCw3J783F+fWjgyM/P56mnnmLnzp2ANRiw0gMUojQHe7BQH1CRb+lsba7KqTVqBN26\nKenePZyHH25CSoqe77+/ydq1V7h2Tbw+47nnorhwoYCdO13X33UEqRQ2b+7KlCk/kpmpZd68XwDo\n2DGIZ55pR9u2oZw/D/Hxudy44TzQ7NPHn+7dFUydmurx2gBWrGjLhx+mcPmyNTu+YIFV47hlSxWT\nJkXTqVMjrlyRsWCBlvT0qtfn5weLFgUyenR6le2cITpazosvhhEaWr33pitFlRWD4UOHDpGXl0d6\nejo//fQTW7ZsqTXzioYM76s9CHdphLv/zugQ7ihDhFEW/DqiSIg8lgn9GRwaXogZQpgdGFeUDVgi\ncHtTUYwepaiZheM5nCtDiKk5CM85o0gIz5dbmwQskjK3N5VMix4/ZAKKg93wwm52AS4YXtQXtQcZ\n7lMxKrq9OaNWOKNAuKPwUFV7sX5i2enaddCsAOGNkxjFwUdv8KEMFouFf/zjH5w4cQI/Pz8mTZrE\nvHnzAGsQaDAYynF/6xPNwRvcY1dMNkJDJYSGKunRI4KxY5uSkqJn374bbNyYzc2b1vlHjAgjIkLG\n7NmXvPLcEhK68uqrp8jMLE+9OHOmgOeeOwnA7beH8vLLbYiODuKXX0wsXHiDwsLKgWZEhJznngtj\n1CjxAjd3MW1aOH/8kc8331S2ab58uYSXXrIqSMTEqJk5syXt2gVx6ZKM+HgtV69WXl9CQiOeffYK\nhYXVz3T4+UlYuzaSVq08s0AWouKNkt24wv552LdvH4899lhp+9tvv5333nuP0aNH065dO6+tw46Z\nM2eyd+9emjZtysGDB70+fm2iYen82hGG9cc+HygBaniXvocm0IVWElG3t4YApaYXQKnkmR/6P5fV\ncbTG/T4Sygwv6nvmV6qp4wX44EP1IZFImDVrFu+++y733nsvgYGBSKVSCgoKeP7554mLi+OBBx4A\nyrKk3pSIqg4qOmh5Kyh3JSvcpImUJk38ueuu5owfH05Kip6jR/Pp3FnF2LEnPXtiNixc2IGdO9M4\ncuR6le1OnLjBiRNWCkOfPk2Ij29NZGQgP/xg5P33c9FqraUha9ZEMm7c2WoZdlREz55qevZUMXny\nKadtz50rZu5ca8DdtWsQ//53NK1aBfLbb1IWLSrm5k14660APvvsJmfPeqZ2tGxZBN261dzvpvC9\nANbMcIsWLRgxYgSnT5/mwoULnDhxghMnTtCrV68aCX7HjBnDlClTmD59utfHrm14N/NrxHH2VXjz\nKJYFdlQcJ5ZJtmDV/M0FMigzvHCSMRbWajnW/K2cdXVUSFaxiK0Ef5vbWz43aOySdq/YHEJUV4PY\nHc1f+xgWW8ZOiZ4SDMjktbCt6MwW2RsFb+5kZYX9xNze3NUSdmc9jtq7088pnGn+OvoBcNfK2A5f\nlrehISkpiRdeeKFUj3PWrFmV2jz//PMkJSWhVqv54IMP6NKlS5V9b968yYQJE0hPTyc6Opp169YR\nHFwmH3n//fczdOhQdu/ezdq1a/n888/Jzs4mOzubAwcOMHjw4FL5M29KRFUHFWkONck9dmay0ayZ\njGbNVPTpoyIz08Ann9zO7t05bN9+heLi6m3/zJjRkqtXi/j4Y/cc3A4fvsbhw9eQSmHgwHCWLGlN\n06ZqmjTxZ9asP8jN9fy7IDRUzosvRvHww8fc7vvLLwU888zvANx5ZyPmz4+mfftA5HIpr7/umR31\ntGkh3HOPGqm09swrtFot7777LnfffTerV6+msLCQw4cP8+2339K3b98aWUfv3r1JS0urkbFrG073\nZyQSyRqJRJItkUh+qardyZPeueN0Gfaasqyan+pYsms83hJUNre3YqR1u+/sFrTJPwFWtzeTRYJU\nYkFWyeWhASMtuXr9hG5v9Tn7a06u6xX48CeB2Wxm7ty5fPrppxw6dIjPPvuMc+fOlWuTmJhISkoK\nR48eZdGiRTzzzDNO+7733ntoNBp++uknBgwYwOLFiyvNLZfLGT58OI8++ijnz58nOzubqKgounXr\nxtNPP8327dvJzc0tRyuwZ18NBgMGg6G06ExMZ9dbr4+QhiGXy2uNhmEP8mUyGQqFAoVCUY5m0by5\ngn79gnjzzXYkJ9/Ftm3dGT06En9/12kYcXFhdOrkz4IFp6u9TrMZvv02h6lTfyIzM589e/7gn/9s\nxGeftWXy5KZ4oki3cWM7pk79xWN3uSNH8njnnQvcuFHMq6+eZOFCNTt2NOHpp0PwczN527Onkhkz\nQggKqpnKaLHA9+bNm4wZM4ZRo0YxceJEwCoTeM899/Dmm2+WKqX44BiupHDWAUuBjTW8FvfQBDiL\n1e3NBPVBmtaMrNTtLYhCinCFLlGfIMGAwkZ9MOC5lHkDh4QyyTMffPgL4NixY7Rt27ZUImnEiBHs\n2bOHmJiY0jZ79uxh1KhRANxxxx3k5+eTk5NDamqqw7579uzhyy+/BGD06NHcf//9vPzyy6JrOHLk\nCCUlJYwePZp33nmHgIAA0tLSSExMZO7cuVy/fp0+ffoQGxtLjx49SqXExIwDvGknW98k1oQUifKS\nVxAVpSAqSkG/fsE8/XRr/vijmO3br/Df/+Y4DBzbt1czaVJzxow57JX1zZjRnrS0fOLjrfQEhULK\n0KFRrF7dmkaNVHz+eR6bN1fm7DrC5s238Prr59yWbxODXA4ffNCJRx/9kfx8I99/fw2ZTMKgQU35\n8MOWNG6sJilJz8qVeVVaJYeESFm6tBnNm9eMcJbFYsFgKNuNUygUZGRkMGXKFF566aUay/D+FeD0\nP2axWA5KJJJWztp1794dgw4UjqgHjigQygp/Kz72FxnDiDXYDQQKgUygaYV+YlbHgnOONH/FqAV3\nadSlk5cvHqvctgR/VOgIJp+rAt6vo4I2eyGcK/QF8X6uFNVVbYscoOlZ+vwMyPFHX8ntzW51bBJw\nR4zONH+rW+RWfqGu93N0vY2m6jZVURksWJkAYgIY3qBACFFtzV+Nk47uwJViDW86ATqjU/h05moT\nWVlZtGjRovS4efPmHD9+3GmbrKysKvvm5OQQHh4OQEREBFevXnW4hjfeeIMBAwZw//33lwaX0dHR\nTJgwgQkTJqDT6Th06BC7d+/mtddeo0WLFsTFxaHRaAgLCyunmOANO1lnMmZ1DTGtV7CuWyo1Ex2t\nIDq6Ef37N2LOnDZcuFDCxx9n8fXXVzEarYFwSIicRYs68MgjhzCZPL/bv/vupnTuHMCMGWWBtMFg\nZteuy+zadRmlUsoDD7Riw4aWBAT48/HHN9m+PdfheK+9Fk1SUg4//ZTn8doAtm7tzpw5v5CfX/al\nazJZSEzMITExB7lcwn33NWPlyihCQlR8+aWWDRsKELhsI5XChg2RxMR4r8BNCLH/6+nTp3n66adZ\nsmQJnTp1qpF5/yrw6u1KkbmWZXcbYw1+s6G+1JeVoALyCKSIhigZZkDuc3sToqLbmw8++OAxqgoc\n/f39SwvcxKBUKrn77ru5++67AUhJSSEpKYlnnnmGgoIC+vXrR2xsLN26dQPwKCssJmNWm/ziquCs\n6K6ikYJMZqZ1ayWtWvkxcGAj0tPbcu5cMVu3ZjJzZkumTPmRwkLPeblt2gQwffotPProtw7b6HRm\nPvkkhU8+SUGlkjFiRGs2bozC31/J5s03+OKLMh3ghx9ujFxuZP16z2TI7Hj33Q588kkav//umOdr\nNFrYvTuL3buz8POT8ve/N2Pt2iiCgvzZsUNLQkIB8fFNuesuf4djeAKxwPfw4cO88cYbrFu3jqio\nqBqZ1xXYP08NHV7V+Q0xQk9vDegKwoDLWCXPavB/cTS5iDs0runmGVGUur0FUkRhA6A+lCT/hEpz\nl+1IggE5fhidu701FFxOhpaa6vUVur3VV5iTfYoPPngFkZGRpKeXBRmZmZlERkZWapORkVGpjV6v\nd9g3PDy8NPubnZ1dal/sDbRp04bJkyczefJkiouLS/nGL774Iq1btyYuLo6BAwcSEhLiVla4vlko\nC1ExG11VUC5mpCCXW2jbVkqbNko0mkZkZuqYP78rmzZd4rvvcsplON1BYKCc99+/nUcfTS7NKjtD\nSYmJhIQ/SEj4g8BAOQ891IbNm6NQKPxISipkwIBAHn/cOzVFjz4aSWGhnu3bXQ+k9XozO3ZksmNH\nJv7+UoYPb8G337YjOlqNQuH9myAhvca+y7B7927Wr19PQkICjRs39vqcrmLy5Mn873//4/r163Tp\n0oXnn3+eMWPG1Nl6PIHXgt/vvvuOXSUwyLabFSKF7hawq4Ql23Y0NI0Ak+DYft1WWKppDhgFx11s\n1y8CAaCJsfU/DVhAowR0kHwYCAeNTXEt+Udbf9uOfvJPYFGDxkaROWi7KR34N6vm74Fk66e9e6z1\nTXc42YAWC700/siwcCLZ6pZzm8ZKLTieXIgWLd01jQD4Pdn6xLtoQilGzankTG5wiXDNrQD8kWz9\nsMVomiHHxIVk649Hc017ANKTrQLdrTStkGEiLTkFgDCN1Zc7I/kCRhRE2tpfS/4NgFBNVwCuJp9G\ni5IwTWcA8pNP2K53AfzIS7Z+efjbglyt7dhKebAGwAByTX9MyChK/gGLRY5MY7UusRw6AIDsLg0A\n5oMHQa9A0neA9fqPydYXtJf1OkeSrZyNnrbjE7brt2us77qTtuOOtuu/2Np3tl3/3Xa9re36Gdv1\nGNtxiu16e1v7P2zX7RSHdNv11rbjy7bjcMF1E9BCY6UbZNmuN7Vdv2IbL1xjzf5eSbYGwiG267m2\n/o1txwW2/qG28fJsxwEVrgfZrhfZjpW268W28VS2Y/t1me1Yb7uusB0bbdfltvUhOAYw2Y6xHSN2\nbBG53t/29zusCx1gOz5g+/s329//YV2QnXNm397sY/v7g+3vHba/P9ra34X1H/aT7XwP298jtus9\ngWPAFwAcO9aGDh3aEBtbKxY6f3n06NGDlJQU0tLSiIiIYMeOHaxatapcmyFDhrB69WpGjBjBkSNH\nCA4OJjw8nLCwMId9hwwZwtatW5k1axbbtm1j6NChNbJ+tVpNXFwccXFxAFy4cIHExESefPJJtFot\n/fv3Jy4ujttus36vOnLQkkgk5YLjuub3CiFWAOVOUF5RTk0ut9CunZw2bVQMGtSEy5e1nD1bwKZN\nlzhw4CruJPm2bu3NP/95mIKC6lGjCguNrFt3nnXrzhMdrWbt2v5cuVLC1q1dWLkyg/37q5Zeqwqd\nOwdy771hjBt3pNpjaLVmfvstj5AQGcHBVq65t94XFTP59sB33bp1fP/99yQkJNR5IVvF74KGDIkr\n6WuJRNIa+NJisXRx1Gbfvn2WH+PimBNZRvlEeIPSyMnjYDfaCs9dwip31o6y39GK49kCbIvgnEGQ\nyC0JLOPsFMjKnNyKUdv+lmU/S1BXul6xDUiIIhMtfpylg0tj6AR8XUdzCLV37efFzlU1nv28XkCQ\nrjiHBDNBFGOxwDUaAxL0Oms/nbZsXL22bAxLoeBDqbW9AYTcbuFjR1J22irOuTKGO3MI2zjrZwLs\nNvRmB20dzSdm4uJoPrE27pi/CB/rcAEWkcfCwYQ/YGLnHbV11M/+2OLgurCf9Qdg8uQQRo1KJzY2\ntn5EHg0YN27ccCmMSUpK4j//+U+pXNlTTz3F+vXrARg/fjwAc+bMYd++fajVapYtW1ZKMRDra5ub\nCRMmkJGRQVRUFOvWraNRo0Zi09cYCgsLOXDgAElJSZw6dYr27dsTGxvLgAEDCA4Oxmw2U1hYyPLl\ny5k1axZ+trJ/exACVdM1agMVs9EKhcKraxJKqZWUmEhLK+H06QI2bLjE4cPXqgyEt2zpzfvv/8oP\nPzjmc7sKqRS++CKOKVP2kZlZTKNGfowZ04G+fZsjlSpYvjydAwdct0gODpazeXNXRo/+odoScACN\nGinYvbsv7dqV0R084ZPb4SiT/9Zbb5Gbm8s777xTyuX2wXWEhoY6/Gc4DX4lEskWrOmhMKzs2pct\nFsu6iu327dtnORgXx9jGUPq+qI3gtxg4Yet/r+B8HQa/JahoyyVkmDlNDHqUDSr4BatcmwwzeZYg\nq+3FXzn4tUCp9IUv+MUX/DZMuBr8/hVgsVg4e/YsiYmJJCcnYzabufXWW9m7dy8XL15k2rRpvPTS\nS5X6eVtBwp311oSphqvzFhebSE0t5vTpfNavT+HHH8tnYBcvvp3DhzP55JNLXpl327aBLFx4nCNH\ncipda9xYydixHejVKxKQ88EHGRw6VHUg/OWXPZk27SgZGdoq21UFqRQ+/7wvffqElnPgq9zOPe1p\nscDXYrHw7LPPEhUVxZw5c+r8pquhoqrg1xW1h0ddmcSu83uuBNrZRxX+ADv7sXZkjiHWVngumDK3\nt0LK1CHExhCKE7hheHEiuZA7NSrbOVcML8yUoCKQIkLII5cwh4YXYkoMzpQhXOnn6LyYLbIu+TBq\nzZ22ttYMhwkpMswo0WFCWm5uUYhZHXtb4cGZuoKj6xnJ0ErjuI0rqg06rIGvjLIaRlcMOKpreOGO\nyYUpuYweYYewTrFWJKedWRoL4U21CB98cB8SiYSOHTvSsWNHZs6cyZYtW3j22WfR6XS0adMGrVbL\n3r17+dvf/kZAQECVXOGaLoCrS7UJu8lGUJCM225T0KlTMPfd14zU1GJ++y2fdetSGDCgCenp+V4L\nfBcuvJMdOy6IBr4A16/reP/9X4BfCAvz5/HHO/Lkkx0xm+UsXZrGjz+WV4TYsKEr8fGnPQp8ARYv\n7kavXqGl/3MQd+Cz/zWZTOUoJmI3TI7MK6ZOnUpcXBxPPPGER2v2wTG8nkc/p4P7Aq1ag7UCGWVu\nb1coc3urYxTZgt8gCsglrK6X4zZMyAAjfhgopmYqWhsUhFbHvptwH3z40yAnJ4e5c+ei0+kYOXIk\nCxcu5PLlyyQmJrJu3TqkUikDBw4kNjaWW265BSjPFRZyNL2dFfaU3+tN2J9XUJAfnTv7cdttjbjv\nvgiuXdNz5MhVevQI4/hxx3JlrmD69I5cu1bEJ59ccKl9bq6WxYutibcmTfwZN64js2bdiskkY8mS\nNIYNa8KBAzkcPOjZuqZMacP//V8kcnn5196ZA5/w2N5eGDyLmVdMnDiRyZMn8/e//92jNftQNbwW\n/Hbv3p1jwE0zXDVBeG3SU5pgDX6zqJHg1571dQcNye3NnvUVwu72JpNYkFkauNubPevrCYS/ZfUt\nAK6Y9fXBBx9cRnh4OO+99x65ublMnjwZiUTCbbfdxm233cZTTz3FzZs3SU5OZvny5Zw7d44uXboQ\nGxtL3759UavVNZYVru9qE2azGZVKQnS0kpYtoxk6tIUtI3yDNWvOceKEe8VpgwY1o0uXYGbM+K5a\na7p2TcvChdZAODxcxaJF/WjSxJ+cHD+OH7/B8eM3qzVu375hzJx5C8HBVe9oCW967NQF++tkf19U\nvGECKCoqQi6Xk52dzdSpU3n55Zfp06eP6Bw+eA9eDVGjgXPA2RJoqhKYS4BzCoQr5hhifEYlZeLC\nV23XZIgaaUgczFHe8KIyJcERTcGZ4UUxKgIooRF5aAWcX7ExhLQIk0M6ReV+jtbjaDyxscRNNcq7\nvclsPBG5gC/i1PBCLvjSd4XKYH/sitSkN6kFrhhUKLC+F80utHU2h9j1qtqItRWi2tKcYj/K3vhK\n8NEafGhYePDBBx1eCwkJYfjw4QwfPhyz2cypU6dITExkxYoV+Pv7M3DgQOLi4mjdujXgnaxwfXOT\nE8JRcVZwsIQuXZR06RLK0KFRpKYW8euvN1i71nkg3L59EFOnxvDoo3u9ssbwcBVgZsiQ7YSHqxk3\nrjNz5nRHr5eyePEfnDjhmllG8+b+LF7cjchI93c/K6pqVORtg3XXYdCgQeTn56NSqXjkkUdQqVSY\nzeZ6c6PzZ4XXXt2TJ0+WJl3P1fZvnxJrUZsJcN0t0WX8lFw9rpBd49dqeFF/UZR8VPS8wRYIVXR7\na3BITfbOOHYebX0rGyqVNfPBBx9qElKplG7dujF79my++OILli9fTnh4OIsXL+b+++/npZde4rvv\nvkOv15cLXuxZXIPBgMFgwGQyiRZL2WkOwqC5vgW+RqOxNPCVy+Wi/OPgYD+6dAnlkUfa8tlng/j2\n2yEsXdqb7t0ra9SGhPixaNGdTJy43yvucqGhfrzxRi+mTPkGiwWys4t5++2fGD16F3Pm7GXwYBXb\ntnVnw4bbuf12x4oj/v5SNmy4k3btXNP4d4aKNz4SiYSjR4/SqlUrzGYzBQUFrFy5kkGDBrFs2TKv\nzFkRGRkZPPDAA/Tp04d+/frx0Ucf1cg8DQFezfw2wxofpBshVwtNhO8ZR1lgnch1R4/tbcUsj0Ox\nFrxlYdWlcCVjbINMmAUWyZ5KsQiywOLZVTEUEEAEVwmkyNZP4nAMV4rVqlvkJnZe5iBdKOxnkiiw\nYHV7U8j0mJGVZoBrFN4ueHM0tjsFb0bKu73JnLR1Zd6q2jhrK4RMpK/nRk21BGeFcvXjR98HH8QQ\nFhbGQw89xEMPPYTZbOb48eMkJSWxdOlSAgMDGTRoEIMGDaJly5blOKBiWWGgXFBsN6WoL6guDcMa\nCFuD4WHDoklNLeTXX63UiF9+uc7mzX9jypT9FBZ6nmSRSmHTpjgmTfqa4uLKX4JXrhQRH281AWjW\nLIBx4zozd24bdDoJ7713sVxGeO3aO+je3XtyfGLmFdaMeTBHjx7ll19+Yf/+/ezfv58BAwY4Ga16\nkMvlzJ8/ny5dulBYWMigQYO4++67iYmJqZH56jO8yvlVANEyuGSCi0YrFbfWEAqkYaU+eDkz10tT\nvYIvA36lbm8BFFFUT93eAjR3OLgiwYgMBSb8MKBtqFbH3uD8Qnm3t/qU/bUbW/jggw91BqlUyh13\n3MEdd1i/T3Nycti/fz8LFiwgLS2Nnj17EhsbS69evVAoFKVBrtls5uLFi7Rq1ao0M1if+L0gbrdb\nnWx0cLCCLl1CSwPh3FwtaWkFRESoycws9nid27YN5qWXDnLlivPdVkeBsF4vpajIwsCBTb2ScXek\n1rFmzRoOHTpUal7RunVr7r///hq1Do6IiCAiIgKAwMBAYmJiyMrK8gW/3kA7W/D7h8nq5VRrCMSa\nzdVilT0Lqrp5baGQQJTcIJiCehv8VgUjclvwq0frU30oC34beA2gDz74ULMIDw9n9OjRjB49GqPR\nyLFjx0hMTGTRokWEhIQQGxvLoEGDOHDgAHPmzOHFF19kwoQJgFUFwJlMVm3AkeuYN9YSHKwgOFhB\nmzZB7NgxhEuXCvntt1zWrPmdEyfc5y8uWdKfbdt+5/jxbLf7CgPhp5++g3/+83aUSs9vPhzxo998\n801u3LjBmjVrKmX3a+v/fPnyZU6dOkXPnj1rZb76Bq8FvydPnqQtZWILKSYwaUEmponqTJTf0WM7\nVcHRWE2BdKxWHBGC8yaRtg40f+UCMrpd8/dIchG9NdbJHVEdHBWxFaMizBb8ZhFZaQzxojpH2r6V\n6RKOiuNMDsaTiWRvtck/ldocV2xrsW07+2GgYrpTJtD2NcnLxrXYz8sF29jeKHhzRzdYeD09uczm\nWIyq4Ap9wX7eLnlWleavNygQ7rQ1JlfO/jr6ZNe68Ijwi9zZ143wCUoq/PXhz4akpCReeOGFUje4\nWbNm1fWSagxyuZxevXrRq1cvALKysti7dy8jR47k4sWLAPz222+YTCbkcrlTmazaCJAcBW41MXdQ\nkB9dujSmS5fGDBvWitRUayC8erVrgfBTT3Xl8uWb7Nhx3qN19OnTnCee6ExIiNJ5YycQk6kzmUw8\n/fTTtGrVioULF9YZl7uwsJDx48fz1ltvERjY8JJy3oDXM7/BEmgigWsWuGSAdk68EbyKJliDX8/d\nFb0GLf6YkOKPDj905ZzVGgIsSDBhlTzzsxga3Pq9Dl8s5oMPHsNsNjN37lx27txJs2bNiI2NZciQ\nIX+Z7dfw8HB27tzJxYsXUSgUzJw5E6PRyEMPPUSTJk2IjY0lNjaW8PBwUa5wTWeF61Jf2Koj3JjO\nnRszdGhrUlML+O23XNatO83Ro5V/3IcNa0WbNoHMmrXPo3lbtAhkyZJYmjf3PBgUe/1KSkqYOnUq\n9957L+PGjfN4jurCaDQyfvx4Hn74YYYOHVpn66hreJXza0dbKVwzWQ0vajX4DaPM7U0L3tqlt2d9\nqwcJxagJopBg8rlGU+8syouwZ30dwYQMGUb8yvnCNSDYs77egISy7G99gY/z60MDw7Fjx2jbti3R\n0dEAjBgxgj179vxlgl+ZTEa/fv04c+YM69evL80IA6Snp5OUlMS///1vcnNz6d27N7GxsfTo0QOp\nVCqaFXbXUrcqWCwWDIay4rO65B8HBSlKA+Fhw+yB8HXWrz/NTz/l0KlTKI8+eguPPfZfj+YJDFSw\nadMw2rb1vMCt4uunUCi4fv06EyZMYPr06XUecM6cOZMOHTowbdq0Ol1HXcOrmd8SwGCElhb4CWvw\ne6+/1e1N4sy+2BW1BzH6gvCxhTK3twygleM5HGv+VqY9ONb5rdrquEzv158gCmlEPjcoL/XiTEXC\nsYWy68oPYjq+znSAhbC7vSnR26gO9qIMB5q/VY5W+X56lgAAIABJREFUaXGVH7tri1xbag/Cc3rK\nm124Moar1yu2qU5bt1FTmr9CNHDJPB+8hqysLFq0aFF63Lx5c44fP16HK6p9PPPMM4wfP54mTcqX\nhkdFRTF+/HjGjx+PXq/n8OHD7Nmzh9dff53IyEji4uK4++67adKkSbUsdauCtwrbagKBgQpuvTWE\n9u0DGTy4BenpxQQGKnjuuW89KhKTSiVs3DiMrl09T0yJvX5paWlMnTqVV199ld69e3s8hyf44Ycf\n2L59O506dWLgwIFIJBLmzZtHXFxcna6rLuBVzm+k7XE4oKKO3d6yKQt+PcQPyXp6a6qfwq7vbm+F\nyccJ1PRweF3o9ibHiFFUkqoe41Kyd7O/Qtp0fXB7E+P8+uCDD/UaUqm0UuBbEX5+fgwcOJCBAwcC\nkJqaSmJiIrNnzyYvL4++ffsSFxdHt27dkEgk1c4K12Rhm7cglAoLCJBz222NkUgkbNgwlEuX8jl9\nOpeNG3/l0KFM3ImFly2LpW/fSOcNnUAs8P3tt9+YPXs277//Ph07dvR4Dk/Ru3dvrl2rATOEBoga\nCUulEmglgTMWq+FFrQe/Z7GaXZigPqhzmZFRhJpAigmisAGqPpS5vflLdRSaG1jw623UR+qDDz40\nIERGRpKenl56nJmZSWSk5wHInx2tWrVi0qRJTJo0Ca1Wy6FDh9i5cycvv/wy0dHRxMXFodFoCA0N\ndTkr7EiKq74Evs4Cc7VaQadOYXTqFMaQIW24fLmAM2eus2nTrxw4kIHZ7DgSnjPnLgYPbglYX4Pq\n0kbENHwPHjxIfHw869atK7fL4UP9gFc5v0agxJbYbA6cAc7pobcfKIQmaULzC2dUBrHHjigUdmWI\nAKAIa/Y3HLeoFeWtjq0X+mv8ECuTd2Z1LLxeRACBFBNMPldFeL+ObYxdN6sQKjk4Pl95bcKsryM6\nhNlmBqiU6CkUXZHwydj6yQVvL0dWx+5s2VdX7eEWjXjb6qg92M/JKAt+5S6O4ep1R2tzBH9N5XMN\nxuRCCDFliPqjdeqD99CjRw9SUlJIS0sjIiKCHTt2sGrVqrpeVoOCv79/qYkGwB9//EFSUhIzZ86k\npKSE/v37ExcXR+fOnQEcKkgIKQP1zVjDXcUJtVpBx46N6dixMffe25rU1HzOnbtOQsLvJCenlXOQ\ne+ihDowb1wm1Wu4RbUQs8N21axebN29my5YthISEeOOl8MHLqLGcbAtsbm8mKDJDrf77G2MNfnOw\nBr/1AEK3t/qxV+4ejMiwWEAhMSLFhLk+pNTrEna3t/pmeOGDDw0AMpmM+Ph4HnzwwVKpsw4dOtT1\nsho02rVrR7t27Zg6dSpFRUX873//Y9u2bfz888+0a9eO2NhYNBoNwcHBmM1mzp07x8cff8y8efPK\nBXhms7nOdIWF8FRxQqWSlwbCgwe35vLlAs6fv8HWrafJz9cxb14fIiICS28GzGazWxJzjgLzVatW\n8eOPP5KQkIBKpfLiK+KDN+FVzu89gmM/oJXc6vT2hxFqVUa5MV51ezucbKCPxrOtfqHbWyBFFNYj\n6oMzzq8VZW5vSomeEksD+lCnJEMbjXfHrE9ub4ZkUGjqeBE++OAe4uLi/pKFNrWBgIAABg8ezODB\ng7FYLJw/f57ExESmTZuGwWAgKiqK3bt3U1BQQJs2bRg7dixAaQYTvKsg4S68LbXm7y8nJiaUmJhQ\n4uJakp9voGlT62+YRCIpzXgLA9+q7KglEklpGygLfOfPn09hYSGrV6+uVxl0HyrDq5lfA+XrudtI\n4SJW6kNP4e69kAJhVxETo0KAOD3BGX1BSZnb203K3N4c0SUEj2WC8eyGF1JkTs0oxI0ryl8vRo2S\nPEK4SQmqCm38KvWvOIYjIw07hEJkjs7b+wmpEFJMoufLmW1I/Erd3vylWvT4IRMoPIgZXljkwhfT\nDcOL+qL24AxCtzdX6RKurMfRdSHcMcdwhDqrvRT+kDq6qbQvrmHtkPhQvzFz5kz27t1L06ZNOXjw\nYF0vp1YgkUiIiYkhJiaGGTNm8P777/Paa69hsVjo1asXP//8M02aNGHAgAEEBgY65AoLaQA1GQwL\nC8fAKhXmzfmUSjlNm4p/QQopD0ClrLB9fXbo9Xr27dvHLbfcwocffsgtt9zCSy+9VOdZcx+cw2uE\nOqHOrx3tbHFUigmMtZkdk0AprdYLhhd9Nd65RyiyRfjB5HtlPG8hSHO7S+2MtsBYzO2tXsPbWV87\n7J8eM3X7cviyvj744BLGjBnDp59+WtfLqDOcOXOG+fPnY7FYmD17Nrt372b69OmkpqYyadIkRo0a\nxYoVKzh//ny5jK89+2k0GjEYDBiNxnIBobdQUTHB24Gvu7BnhRUKBQqFolw212Kx8NhjjzFx4kQG\nDhxIYmIimZmZ7NmzB51OV8Wo1YdOpyMuLo6BAwfSr18/4uPja2SevwK8rvNbzphXb/WdyAVSSwSG\nF2JZV2cFccLHwknEsshgpT6kY+X9ulHwJi+XBbZlcGWuZ3uFjyte16Owub3pUVGMHmUlTeCKcEfb\n1x0NYkdZYkeav/YxjBYZcokJf4sWk7zGKOPCxTl/7Cxj6s2srPCcI9na6maXq2t7LITHhW6Ofmic\nPXF3bIyFaJCVeT40UPTu3Zu0tLS6Xkad4dZbbyU+Pp5GjRrx4IMPAtCpUyc6derErFmzyMvLIzk5\nmZUrV3L27Fk6depEXFwc/fv3R61Wl8sKV+TEepoVFiscq28ZVCEtRCKRMHz4cMxmM7/88gvXr19n\n3bp1bNq0iQsXLqBUet8NValU8sUXX6BWqzGZTNx3333ExcXRs2etEkv/FPAq57eXyPnWEsi11IHb\nWyjWzFwBHru9/S/ZSD+vZH8llKAikCKCKCS3nlgF5yefINjF7K8eOXJMKBqSYcHFZGir8f649UXy\nTJ8Mfpo6XoQPPvjQEDBhwgSH1xo1asQDDzzAAw88gMVi4dSpUyQlJbF69WrkcjkajYbY2FjatWtX\niRNrh7A4zJXg1V1Fh7qAmIZvamoq27Zt4/XXX6dnz578/PPP7Nu3j9zcXIKDg2tsLWq1GrBmge2U\nFB/cR42n7lpL4Jgt+L0v0Or2ViuQUeb2dgVoXUvzOkFRafBbQC5hdb0ct2FAAejww0hDVK3wOuzB\nr++l8MEHH/5EkEgkdO3ala5du/LMM89w48YN9u/fz9KlS7lw4QLdunVj0KBB9OvXD39//2plhSsW\nttU3qTUQD3xPnTrFnDlzWLZsWakld48ePejRw1nhuHfWc/fdd5OSksKkSZNqZc4/I7yv8ys4ZzRZ\naQ/+WN3eskqgqQwUzrR7HVEZlCLnhBndioVyjSmzOm5WoZ9LVsfWD/AATdmF/2/v7IOkKO88/nlm\nZneAXXZBEJBXxQAeBBFPkGTZYlhWg17FK0yV0VgSX4pKQGMSK+rVpahoYpUVTe7qqk5NTr3TE5Ei\npCwlpTnZTYYXKTGFriBKeBHFiIC7EZZ935l57o/unuldurdndme6Z3d/n6quaXqel9/M7LK/efr3\nfL/ZlRm4t+0imnZ7K6GTLnOjm9smN7eNcE7lC+79zr9uH2ts7HKcdj85lUN0UuLo9uZkdZyw15Bk\no/mby8a1noH23W9mzHk+p5KEXEokIhhJr3XNKQHORUvYqZ8dt7b2Vd9c+vUbL+WTQXRXQBCErBg7\ndizf+ta30vJ0DQ0N1NXV8eSTTzJy5Mi05vAll1zSQy3BbVUYyKuiQyFwKsXYuXMnjz32GM899xyT\nJ0/2PaZQKMT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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "fig = plt.figure()\n", + "plt.subplot(121)\n", + "\n", + "exp_x = stats.expon.pdf(x, scale=3)\n", + "exp_y = stats.expon.pdf(x, scale=10)\n", + "M = np.dot(exp_y[:, None], exp_x[None, :])\n", + "CS = plt.contour(X, Y, M)\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "#plt.xlabel(\"prior on $p_1$\")\n", + "#plt.ylabel(\"prior on $p_2$\")\n", + "plt.title(\"$Exp(3), Exp(10)$ prior landscape\")\n", + "\n", + "ax = fig.add_subplot(122, projection='3d')\n", + "ax.plot_surface(X, Y, M, cmap=jet)\n", + "ax.view_init(azim=390)\n", + "plt.title(\"$Exp(3), Exp(10)$ prior landscape; \\nalternate view\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These are simple examples in 2D space, where our brains can understand surfaces well. In practice, spaces and surfaces generated by our priors can be much higher dimensional. \n", + "\n", + "If these surfaces describe our *prior distributions* on the unknowns, what happens to our space after we incorporate our observed data $X$? The data $X$ does not change the space, but it changes the surface of the space by *pulling and stretching the fabric of the prior surface* to reflect where the true parameters likely live. More data means more pulling and stretching, and our original shape becomes mangled or insignificant compared to the newly formed shape. Less data, and our original shape is more present. Regardless, the resulting surface describes the *posterior distribution*. \n", + "\n", + "Again I must stress that it is, unfortunately, impossible to visualize this in large dimensions. For two dimensions, the data essentially *pushes up* the original surface to make *tall mountains*. The tendency of the observed data to *push up* the posterior probability in certain areas is checked by the prior probability distribution, so that lower prior probability means more resistance. Thus in the double-exponential prior case above, a mountain (or multiple mountains) that might erupt near the (0,0) corner would be much higher than mountains that erupt closer to (5,5), since there is more resistance (low prior probability) near (5,5). The peak reflects the posterior probability of where the true parameters are likely to be found. Importantly, if the prior has assigned a probability of 0, then no posterior probability will be assigned there. \n", + "\n", + "Suppose the priors mentioned above represent different parameters $\\lambda$ of two Poisson distributions. We observe a few data points and visualize the new landscape: " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "observed (2-dimensional,sample size = 1): [[3 4]]\n" + ] + } + ], + "source": [ + "# create the observed data\n", + "\n", + "# sample size of data we observe, trying varying this (keep it less than 100 ;)\n", + "N = 1\n", + "\n", + "# the true parameters, but of course we do not see these values...\n", + "lambda_1_true = 1\n", + "lambda_2_true = 3\n", + "\n", + "#...we see the data generated, dependent on the above two values.\n", + "data = np.concatenate([\n", + " stats.poisson.rvs(lambda_1_true, size=(N, 1)),\n", + " stats.poisson.rvs(lambda_2_true, size=(N, 1))\n", + "], axis=1)\n", + "print(\"observed (2-dimensional,sample size = %d):\" % N, data)\n", + "\n", + "# plotting details.\n", + "x = y = np.linspace(.01, 5, 100)\n", + "likelihood_x = np.array([stats.poisson.pmf(data[:, 0], _x)\n", + " for _x in x]).prod(axis=1)\n", + "likelihood_y = np.array([stats.poisson.pmf(data[:, 1], _y)\n", + " for _y in y]).prod(axis=1)\n", + "L = np.dot(likelihood_x[:, None], likelihood_y[None, :])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(0, 5)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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f0A0Ht/PnGrinrCA+Zv5LI3ubLvVHA/dk2TULuUxeyY5JJ3KoPA6b3GIWCuAi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/Vac668bwK/EeFa3of9B+6nPVO+ll5a5Lo2OMeNWAP0R8AhqrPmR+vyvdXVewE7y/mrwI97+7e5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 12)\n", + "# matplotlib heavy lifting below, beware!\n", + "plt.subplot(221)\n", + "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", + "uni_y = stats.uniform.pdf(x, loc=0, scale=5)\n", + "M = np.dot(uni_y[:, None], uni_x[None, :])\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "plt.title(\"Landscape formed by Uniform priors on $p_1, p_2$.\")\n", + "\n", + "plt.subplot(223)\n", + "plt.contour(x, y, M * L)\n", + "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "plt.title(\"Landscape warped by %d data observation;\\n Uniform priors on $p_1, p_2$.\" % N)\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "\n", + "plt.subplot(222)\n", + "exp_x = stats.expon.pdf(x, loc=0, scale=3)\n", + "exp_y = stats.expon.pdf(x, loc=0, scale=10)\n", + "M = np.dot(exp_y[:, None], exp_x[None, :])\n", + "\n", + "plt.contour(x, y, M)\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "plt.title(\"Landscape formed by Exponential priors on $p_1, p_2$.\")\n", + "\n", + "plt.subplot(224)\n", + "# This is the likelihood times prior, that results in the posterior.\n", + "plt.contour(x, y, M * L)\n", + "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.title(\"Landscape warped by %d data observation;\\n Exponential priors on \\\n", + "$p_1, p_2$.\" % N)\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot on the left is the deformed landscape with the $\\text{Uniform}(0,5)$ priors, and the plot on the right is the deformed landscape with the exponential priors. Notice that the posterior landscapes look different from one another, though the data observed is identical in both cases. The reason is as follows. Notice the exponential-prior landscape, bottom right figure, puts very little *posterior* weight on values in the upper right corner of the figure: this is because *the prior does not put much weight there*. On the other hand, the uniform-prior landscape is happy to put posterior weight in the upper-right corner, as the prior puts more weight there. \n", + "\n", + "Notice also the highest-point, corresponding to the darkest red, is biased towards (0,0) in the exponential case, which is the result from the exponential prior putting more prior weight in the (0,0) corner.\n", + "\n", + "The black dot represents the true parameters. Even with 1 sample point, the mountains attempts to contain the true parameter. Of course, inference with a sample size of 1 is incredibly naive, and choosing such a small sample size was only illustrative. \n", + "\n", + "It's a great exercise to try changing the sample size to other values (try 2,5,10,100?...) and observing how our \"mountain\" posterior changes. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exploring the landscape using the MCMC\n", + "\n", + "We should explore the deformed posterior space generated by our prior surface and observed data to find the posterior mountain. However, we cannot naively search the space: any computer scientist will tell you that traversing $N$-dimensional space is exponentially difficult in $N$: the size of the space quickly blows-up as we increase $N$ (see [the curse of dimensionality](http://en.wikipedia.org/wiki/Curse_of_dimensionality)). What hope do we have to find these hidden mountains? The idea behind MCMC is to perform an intelligent search of the space. To say \"search\" implies we are looking for a particular point, which is perhaps not an accurate as we are really looking for a broad mountain. \n", + "\n", + "Recall that MCMC returns *samples* from the posterior distribution, not the distribution itself. Stretching our mountainous analogy to its limit, MCMC performs a task similar to repeatedly asking \"How likely is this pebble I found to be from the mountain I am searching for?\", and completes its task by returning thousands of accepted pebbles in hopes of reconstructing the original mountain. In MCMC and PyMC lingo, the returned sequence of \"pebbles\" are the samples, cumulatively called the *traces*. \n", + "\n", + "When I say MCMC intelligently searches, I really am saying MCMC will *hopefully* converge towards the areas of high posterior probability. MCMC does this by exploring nearby positions and moving into areas with higher probability. Again, perhaps \"converge\" is not an accurate term to describe MCMC's progression. Converging usually implies moving towards a point in space, but MCMC moves towards a *broader area* in the space and randomly walks in that area, picking up samples from that area.\n", + "\n", + "#### Why Thousands of Samples?\n", + "\n", + "At first, returning thousands of samples to the user might sound like being an inefficient way to describe the posterior distributions. I would argue that this is extremely efficient. Consider the alternative possibilities:\n", + "\n", + "1. Returning a mathematical formula for the \"mountain ranges\" would involve describing a N-dimensional surface with arbitrary peaks and valleys.\n", + "2. Returning the \"peak\" of the landscape, while mathematically possible and a sensible thing to do as the highest point corresponds to most probable estimate of the unknowns, ignores the shape of the landscape, which we have previously argued is very important in determining posterior confidence in unknowns. \n", + "\n", + "Besides computational reasons, likely the strongest reason for returning samples is that we can easily use *The Law of Large Numbers* to solve otherwise intractable problems. I postpone this discussion for the next chapter. With the thousands of samples, we can reconstruct the posterior surface by organizing them in a histogram. \n", + "\n", + "\n", + "### Algorithms to perform MCMC\n", + "\n", + "There is a large family of algorithms that perform MCMC. Most of these algorithms can be expressed at a high level as follows: (Mathematical details can be found in the appendix.)\n", + "\n", + "1. Start at current position.\n", + "2. Propose moving to a new position (investigate a pebble near you).\n", + "3. Accept/Reject the new position based on the position's adherence to the data and prior distributions (ask if the pebble likely came from the mountain).\n", + "4. 1. If you accept: Move to the new position. Return to Step 1.\n", + " 2. Else: Do not move to new position. Return to Step 1. \n", + "5. After a large number of iterations, return all accepted positions.\n", + "\n", + "This way we move in the general direction towards the regions where the posterior distributions exist, and collect samples sparingly on the journey. Once we reach the posterior distribution, we can easily collect samples as they likely all belong to the posterior distribution. \n", + "\n", + "If the current position of the MCMC algorithm is in an area of extremely low probability, which is often the case when the algorithm begins (typically at a random location in the space), the algorithm will move in positions *that are likely not from the posterior* but better than everything else nearby. Thus the first moves of the algorithm are not reflective of the posterior.\n", + "\n", + "In the above algorithm's pseudocode, notice that only the current position matters (new positions are investigated only near the current position). We can describe this property as *memorylessness*, i.e. the algorithm does not care *how* it arrived at its current position, only that it is there. \n", + "\n", + "### Other approximation solutions to the posterior\n", + "Besides MCMC, there are other procedures available for determining the posterior distributions. A Laplace approximation is an approximation of the posterior using simple functions. A more advanced method is [Variational Bayes](http://en.wikipedia.org/wiki/Variational_Bayesian_methods). All three methods, Laplace Approximations, Variational Bayes, and classical MCMC have their pros and cons. We will only focus on MCMC in this book. That being said, my friend Imri Sofar likes to classify MCMC algorithms as either \"they suck\", or \"they really suck\". He classifies the particular flavour of MCMC used by PyMC as just *sucks* ;)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Unsupervised Clustering using a Mixture Model\n", + "\n", + "\n", + "Suppose we are given the following dataset:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 115.85679142 152.26153716 178.87449059 162.93500815 107.02820697\n", + " 105.19141146 118.38288501 125.3769803 102.88054011 206.71326136] ...\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "data = np.loadtxt(\"data/mixture_data.csv\", delimiter=\",\")\n", + "\n", + "plt.hist(data, bins=20, color=\"k\", histtype=\"stepfilled\", alpha=0.8)\n", + "plt.title(\"Histogram of the dataset\")\n", + "plt.ylim([0, None])\n", + "print(data[:10], \"...\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What does the data suggest? It appears the data has a bimodal form, that is, it appears to have two peaks, one near 120 and the other near 200. Perhaps there are *two clusters* within this dataset. \n", + "\n", + "This dataset is a good example of the data-generation modeling technique from last chapter. We can propose *how* the data might have been created. I suggest the following data generation algorithm: \n", + "\n", + "1. For each data point, choose cluster 1 with probability $p$, else choose cluster 2. \n", + "2. Draw a random variate from a Normal distribution with parameters $\\mu_i$ and $\\sigma_i$ where $i$ was chosen in step 1.\n", + "3. Repeat.\n", + "\n", + "This algorithm would create a similar effect as the observed dataset, so we choose this as our model. Of course, we do not know $p$ or the parameters of the Normal distributions. Hence we must infer, or *learn*, these unknowns.\n", + "\n", + "Denote the Normal distributions $\\text{Nor}_0$ and $\\text{Nor}_1$ (having variables' index start at 0 is just Pythonic). Both currently have unknown mean and standard deviation, denoted $\\mu_i$ and $\\sigma_i, \\; i =0,1$ respectively. A specific data point can be from either $\\text{Nor}_0$ or $\\text{Nor}_1$, and we assume that the data point is assigned to $\\text{Nor}_0$ with probability $p$.\n", + "\n", + "\n", + "An appropriate way to assign data points to clusters is to use a PyMC `Categorical` stochastic variable. Its parameter is a $k$-length array of probabilities that must sum to one and its `value` attribute is a integer between 0 and $k-1$ randomly chosen according to the crafted array of probabilities. (In our case $k=2$) *A priori*, we do not know what the probability of assignment to cluster 1 is, so we create a uniform variable over 0,1 to model this. Call this `p`. Thus the probability array we enter into the `Categorical` variable is `[p, 1-p]`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "prior assignment, with p = 0.32:\n", + "[0 1 1 0 1 1 1 1 0 1] ...\n" + ] + } + ], + "source": [ + "import pymc as pm\n", + "\n", + "p = pm.Uniform(\"p\", 0, 1)\n", + "\n", + "assignment = pm.Categorical(\"assignment\", [p, 1 - p], size=data.shape[0])\n", + "print(\"prior assignment, with p = %.2f:\" % p.value)\n", + "print(assignment.value[:10], \"...\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above dataset, I would guess that the standard deviations of the two Normals are different. To maintain ignorance of what the standard deviations might be, we will initially model them as uniform on 0 to 100. Really we are talking about $\\tau$, the *precision* of the Normal distribution, but it is easier to think in terms of standard deviation. Our PyMC code will need to transform our standard deviation into precision by the relation:\n", + "\n", + "$$ \\tau = \\frac{1}{\\sigma^2} $$\n", + "\n", + "In PyMC, we can do this in one step by writing:\n", + "\n", + " taus = 1.0/pm.Uniform( \"stds\", 0, 100, size= 2)**2 \n", + "\n", + "Notice that we specified `size=2`: we are modeling both $\\tau$s as a single PyMC variable. Note that this does not induce a necessary relationship between the two $\\tau$s, it is simply for succinctness.\n", + "\n", + "We also need to specify priors on the centers of the clusters. The centers are really the $\\mu$ parameters in this Normal distributions. Their priors can be modeled by a Normal distribution. Looking at the data, I have an idea where the two centers might be — I would guess somewhere around 120 and 190 respectively, though I am not very confident in these eyeballed estimates. Hence I will set $\\mu_0 = 120, \\mu_1 = 190$ and $\\sigma_{0,1} = 10$ (recall we enter the $\\tau$ parameter, so enter $1/\\sigma^2 = 0.01$ in the PyMC variable.)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Random assignments: [0 1 1 0] ...\n", + "Assigned center: [ 107.08313959 186.02196393 186.02196393 107.08313959] ...\n", + "Assigned precision: [ 0.02216706 0.0013977 0.0013977 0.02216706] ...\n" + ] + } + ], + "source": [ + "stds = pm.Uniform(\"stds\", 0, 100, size=2)\n", + "taus = 1.0 / stds ** 2\n", + "centers = pm.Normal(\"centers\", [120, 190], [0.01, 0.01], size=2)\n", + "\n", + "\"\"\"\n", + "The below deterministic functions map an assignment, in this case 0 or 1,\n", + "to a set of parameters, located in the (1,2) arrays `taus` and `centers`.\n", + "\"\"\"\n", + "\n", + "@pm.deterministic\n", + "def center_i(assignment=assignment, centers=centers):\n", + " return centers[assignment]\n", + "\n", + "@pm.deterministic\n", + "def tau_i(assignment=assignment, taus=taus):\n", + " return taus[assignment]\n", + "\n", + "print(\"Random assignments: \", assignment.value[:4], \"...\")\n", + "print(\"Assigned center: \", center_i.value[:4], \"...\")\n", + "print(\"Assigned precision: \", tau_i.value[:4], \"...\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# and to combine it with the observations:\n", + "observations = pm.Normal(\"obs\", center_i, tau_i, value=data, observed=True)\n", + "\n", + "# below we create a model class\n", + "model = pm.Model([p, assignment, observations, taus, centers])\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "PyMC has an MCMC class, `MCMC` in the main namespace of PyMC, that implements the MCMC exploring algorithm. We initialize it by passing in a `Model` instance:\n", + "\n", + " mcmc = pm.MCMC( model )\n", + "\n", + "The method for asking the `MCMC` to explore the space is `sample( iterations )`, where `iterations` is the number of steps you wish the algorithm to perform. We try 50000 steps below:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 50000 of 50000 complete in 23.6 sec" + ] + } + ], + "source": [ + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(50000)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below I plot the paths, or \"traces\", the unknown parameters (centers, precisions, and $p$) have taken thus far. The traces can be retrieved using the `trace` method in the `MCMC` object created, which accepts the assigned PyMC variable `name`. For example, `mcmc.trace(\"centers\")` will retrieve a `Trace` object that can be indexed (using `[:]` or `.gettrace()` to retrieve all traces, or fancy-indexing like `[1000:]`)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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KmToykexSA326RaL38OT06TP06tVTzl8CrUYQGRnJtGnTeO211wB51uJwvmtF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\ncD0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JCQxlkqqKql7TNP3xak98cazyTwcfdlWuuKvCZA4AmM05L2CMaf6609i2VWDFGMAA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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 9)\n", + "plt.subplot(311)\n", + "lw = 1\n", + "center_trace = mcmc.trace(\"centers\")[:]\n", + "\n", + "# for pretty colors later in the book.\n", + "colors = [\"#348ABD\", \"#A60628\"] \\\n", + "if center_trace[-1, 0] > center_trace[-1, 1] \\\n", + " else [\"#A60628\", \"#348ABD\"]\n", + "\n", + "plt.plot(center_trace[:, 0], label=\"trace of center 0\", c=colors[0], lw=lw)\n", + "plt.plot(center_trace[:, 1], label=\"trace of center 1\", c=colors[1], lw=lw)\n", + "plt.title(\"Traces of unknown parameters\")\n", + "leg = plt.legend(loc=\"upper right\")\n", + "leg.get_frame().set_alpha(0.7)\n", + "\n", + "plt.subplot(312)\n", + "std_trace = mcmc.trace(\"stds\")[:]\n", + "plt.plot(std_trace[:, 0], label=\"trace of standard deviation of cluster 0\",\n", + " c=colors[0], lw=lw)\n", + "plt.plot(std_trace[:, 1], label=\"trace of standard deviation of cluster 1\",\n", + " c=colors[1], lw=lw)\n", + "plt.legend(loc=\"upper left\")\n", + "\n", + "plt.subplot(313)\n", + "p_trace = mcmc.trace(\"p\")[:]\n", + "plt.plot(p_trace, label=\"$p$: frequency of assignment to cluster 0\",\n", + " color=\"#467821\", lw=lw)\n", + "plt.xlabel(\"Steps\")\n", + "plt.ylim(0, 1)\n", + "plt.legend();\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the following characteristics:\n", + "\n", + "1. The traces converges, not to a single point, but to a *distribution* of possible points. This is *convergence* in an MCMC algorithm.\n", + "2. Inference using the first few thousand points is a bad idea, as they are unrelated to the final distribution we are interested in. Thus is it a good idea to discard those samples before using the samples for inference. We call this period before converge the *burn-in period*.\n", + "3. The traces appear as a random \"walk\" around the space, that is, the paths exhibit correlation with previous positions. This is both good and bad. We will always have correlation between current positions and the previous positions, but too much of it means we are not exploring the space well. This will be detailed in the Diagnostics section later in this chapter.\n", + "\n", + "\n", + "To achieve further convergence, we will perform more MCMC steps. Starting the MCMC again after it has already been called does not mean starting the entire algorithm over. In the pseudo-code algorithm of MCMC above, the only position that matters is the current position (new positions are investigated near the current position), implicitly stored in PyMC variables' `value` attribute. Thus it is fine to halt an MCMC algorithm and inspect its progress, with the intention of starting it up again later. The `value` attributes are not overwritten. \n", + "\n", + "We will sample the MCMC one hundred thousand more times and visualize the progress below:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 100000 of 100000 complete in 66.4 sec" + ] + } + ], + "source": [ + "mcmc.sample(100000)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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v0CWlNGvg82I0u9WKaO6hZmyNDcbvvDltcY2FaRfJ2HvE4bnFWTkUJJW/WnEl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5dJa+u33Tna+QHaQMrJ5ByKnwoa8ODX5iXcxCKUjvCvO80TgG8ZM8Cl80ghpsW29XlcqjW+D42e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\n9bnUSiQjCaOj+Uj1m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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "center_trace = mcmc.trace(\"centers\", chain=1)[:]\n", + "prev_center_trace = mcmc.trace(\"centers\", chain=0)[:]\n", + "\n", + "x = np.arange(50000)\n", + "plt.plot(x, prev_center_trace[:, 0], label=\"previous trace of center 0\",\n", + " lw=lw, alpha=0.4, c=colors[1])\n", + "plt.plot(x, prev_center_trace[:, 1], label=\"previous trace of center 1\",\n", + " lw=lw, alpha=0.4, c=colors[0])\n", + "\n", + "x = np.arange(50000, 150000)\n", + "plt.plot(x, center_trace[:, 0], label=\"new trace of center 0\", lw=lw, c=\"#348ABD\")\n", + "plt.plot(x, center_trace[:, 1], label=\"new trace of center 1\", lw=lw, c=\"#A60628\")\n", + "\n", + "plt.title(\"Traces of unknown center parameters\")\n", + "leg = plt.legend(loc=\"upper right\")\n", + "leg.get_frame().set_alpha(0.8)\n", + "plt.xlabel(\"Steps\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `trace` method in the `MCMC` instance has a keyword argument `chain`, that indexes which call to `sample` you would like to be returned. (Often we need to call `sample` multiple times, and the ability to retrieve past samples is a useful procedure). The default for `chain` is -1, which will return the samples from the lastest call to `sample`.\n", + "\n", + "#### Cluster Investigation\n", + "\n", + "We have not forgotten our main challenge: identify the clusters. We have determined posterior distributions for our unknowns. We plot the posterior distributions of the center and standard deviation variables below:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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RyY34F/J/AX8WkRP9h4m7cNaucnHKqfPuxy0s/h7wYJ6PJdH8SHKts4CuIvJZfz+2znMN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\nPtiabv8vU5g6oX97DrzZkzc94FNTNf5gMO5zcCuwQNJMYANJRgrMbKW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(11.0, 4)\n", + "std_trace = mcmc.trace(\"stds\")[:]\n", + "\n", + "_i = [1, 2, 3, 4]\n", + "for i in range(2):\n", + " plt.subplot(2, 2, _i[2 * i])\n", + " plt.title(\"Posterior of center of cluster %d\" % i)\n", + " plt.hist(center_trace[:, i], color=colors[i], bins=30,\n", + " histtype=\"stepfilled\")\n", + "\n", + " plt.subplot(2, 2, _i[2 * i + 1])\n", + " plt.title(\"Posterior of standard deviation of cluster %d\" % i)\n", + " plt.hist(std_trace[:, i], color=colors[i], bins=30,\n", + " histtype=\"stepfilled\")\n", + " # plt.autoscale(tight=True)\n", + "\n", + "plt.tight_layout()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The MCMC algorithm has proposed that the most likely centers of the two clusters are near 120 and 200 respectively. Similar inference can be applied to the standard deviation. \n", + "\n", + "We are also given the posterior distributions for the labels of the data point, which is present in `mcmc.trace(\"assignment\")`. Below is a visualization of this. The y-axis represents a subsample of the posterior labels for each data point. The x-axis are the sorted values of the data points. A red square is an assignment to cluster 1, and a blue square is an assignment to cluster 0. " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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tQi8RddWiKRRoWpqjaXkOhCBUW38mJb6k1ZC0Owk0lkjYHZQ0sqIWnr3zyDIs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A7FkWZKF+nzjFaPt6kVb1MbtTub1O2sozusM8/o9Hgb2/A2tRKsqSdYU4t7bxttJn3uID5mc7LS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\nMJKw2Mhpdecupi6LMpdFncsiCeXPV0FV3YbhpcERlgZv3493j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KUqVzA7Pgnj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dW8/ORsNX/TJ4t9fxbq+TtNg5aGnjwNvKVs8AB95W/NMP0KeTJG1O5sfuceD14Qpu49zfRXno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\nhAV3KtPZeY8cneZhyRm9S+21Zkp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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib as mpl\n", + "figsize(12.5, 4.5)\n", + "plt.cmap = mpl.colors.ListedColormap(colors)\n", + "plt.imshow(mcmc.trace(\"assignment\")[::400, np.argsort(data)],\n", + " cmap=plt.cmap, aspect=.4, alpha=.9)\n", + "plt.xticks(np.arange(0, data.shape[0], 40),\n", + " [\"%.2f\" % s for s in np.sort(data)[::40]])\n", + "plt.ylabel(\"posterior sample\")\n", + "plt.xlabel(\"value of $i$th data point\")\n", + "plt.title(\"Posterior labels of data points\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above plot, it appears that the most uncertainty is between 150 and 170. The above plot slightly misrepresents things, as the x-axis is not a true scale (it displays the value of the $i$th sorted data point.) A more clear diagram is below, where we have estimated the *frequency* of each data point belonging to the labels 0 and 1. " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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rGkVfL6C+qBRT3wBA4i/GEkj0kAFU2VKNtj77NiknHk1oXLTPwB6gdls+dQVF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\nnt3X3F8fvU95lp1V5Rn8ZkcDT+xtprUnRI7TQobdTH13gL/70xH2Nvb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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cmap = mpl.colors.LinearSegmentedColormap.from_list(\"BMH\", colors)\n", + "assign_trace = mcmc.trace(\"assignment\")[:]\n", + "plt.scatter(data, 1 - assign_trace.mean(axis=0), cmap=cmap,\n", + " c=assign_trace.mean(axis=0), s=50)\n", + "plt.ylim(-0.05, 1.05)\n", + "plt.xlim(35, 300)\n", + "plt.title(\"Probability of data point belonging to cluster 0\")\n", + "plt.ylabel(\"probability\")\n", + "plt.xlabel(\"value of data point\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even though we modeled the clusters using Normal distributions, we didn't get just a single Normal distribution that *best* fits the data (whatever our definition of best is), but a distribution of values for the Normal's parameters. How can we choose just a single pair of values for the mean and variance and determine a *sorta-best-fit* gaussian? \n", + "\n", + "One quick and dirty way (which has nice theoretical properties we will see in Chapter 5), is to use the *mean* of the posterior distributions. Below we overlay the Normal density functions, using the mean of the posterior distributions as the chosen parameters, with our observed data:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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NOjk5cf/+/XznvHnbmzRpQmJiIgDXr19n4sSJeHt74+7uTnBwsEU91nkBNm3a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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "norm = stats.norm\n", + "x = np.linspace(20, 300, 500)\n", + "posterior_center_means = center_trace.mean(axis=0)\n", + "posterior_std_means = std_trace.mean(axis=0)\n", + "posterior_p_mean = mcmc.trace(\"p\")[:].mean()\n", + "\n", + "plt.hist(data, bins=20, histtype=\"step\", normed=True, color=\"k\",\n", + " lw=2, label=\"histogram of data\")\n", + "y = posterior_p_mean * norm.pdf(x, loc=posterior_center_means[0],\n", + " scale=posterior_std_means[0])\n", + "plt.plot(x, y, label=\"Cluster 0 (using posterior-mean parameters)\", lw=3)\n", + "plt.fill_between(x, y, color=colors[1], alpha=0.3)\n", + "\n", + "y = (1 - posterior_p_mean) * norm.pdf(x, loc=posterior_center_means[1],\n", + " scale=posterior_std_means[1])\n", + "plt.plot(x, y, label=\"Cluster 1 (using posterior-mean parameters)\", lw=3)\n", + "plt.fill_between(x, y, color=colors[0], alpha=0.3)\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(\"Visualizing Clusters using posterior-mean parameters\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Important: Don't mix posterior samples\n", + "\n", + "In the above example, a possible (though less likely) scenario is that cluster 0 has a very large standard deviation, and cluster 1 has a small standard deviation. This would still satisfy the evidence, albeit less so than our original inference. Alternatively, it would be incredibly unlikely for *both* distributions to have a small standard deviation, as the data does not support this hypothesis at all. Thus the two standard deviations are *dependent* on each other: if one is small, the other must be large. In fact, *all* the unknowns are related in a similar manner. For example, if a standard deviation is large, the mean has a wider possible space of realizations. Conversely, a small standard deviation restricts the mean to a small area. \n", + "\n", + "During MCMC, we are returned vectors representing samples from the unknown posteriors. Elements of different vectors cannot be used together, as this would break the above logic: perhaps a sample has returned that cluster 1 has a small standard deviation, hence all the other variables in that sample would incorporate that and be adjusted accordingly. It is easy to avoid this problem though, just make sure you are indexing traces correctly. \n", + "\n", + "Another small example to illustrate the point. Suppose two variables, $x$ and $y$, are related by $x+y=10$. We model $x$ as a Normal random variable with mean 4 and explore 500 samples. " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " [-----------------100%-----------------] 500 of 500 complete in 0.0 sec" + ] + }, + { + "data": { + "image/png": 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z6vOpc19D5V67FeTeXtj05KvY+OhL+Owbf1V+Afmg/qW3sOwn9wAAjvjTL7HH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oNMneTk47JBrCUGsaX7xmKbYMNoNgDRinHC+Od2kfcF80nQ3+uo9Rzkt98+vPJQ1n5nd4dMox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\nM6ZlnNRLatIwGh2jvPqDtjDg4oZ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import pymc as pm\n", + "\n", + "x = pm.Normal(\"x\", 4, 10)\n", + "y = pm.Lambda(\"y\", lambda x=x: 10 - x, trace=True)\n", + "\n", + "ex_mcmc = pm.MCMC(pm.Model([x, y]))\n", + "ex_mcmc.sample(500)\n", + "\n", + "plt.plot(ex_mcmc.trace(\"x\")[:])\n", + "plt.plot(ex_mcmc.trace(\"y\")[:])\n", + "plt.title(\"Displaying (extreme) case of dependence between unknowns\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, the two variables are not unrelated, and it would be wrong to add the $i$th sample of $x$ to the $j$th sample of $y$, unless $i = j$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Returning to Clustering: Prediction\n", + "The above clustering can be generalized to $k$ clusters. Choosing $k=2$ allowed us to visualize the MCMC better, and examine some very interesting plots. \n", + "\n", + "What about prediction? Suppose we observe a new data point, say $x = 175$, and we wish to label it to a cluster. It is foolish to simply assign it to the *closer* cluster center, as this ignores the standard deviation of the clusters, and we have seen from the plots above that this consideration is very important. More formally: we are interested in the *probability* (as we cannot be certain about labels) of assigning $x=175$ to cluster 1. Denote the assignment of $x$ as $L_x$, which is equal to 0 or 1, and we are interested in $P(L_x = 1 \\;|\\; x = 175 )$. \n", + "\n", + "A naive method to compute this is to re-run the above MCMC with the additional data point appended. The disadvantage with this method is that it will be slow to infer for each novel data point. Alternatively, we can try a *less precise*, but much quicker method. \n", + "\n", + "We will use Bayes Theorem for this. If you recall, Bayes Theorem looks like:\n", + "\n", + "$$ P( A | X ) = \\frac{ P( X | A )P(A) }{P(X) }$$\n", + "\n", + "In our case, $A$ represents $L_x = 1$ and $X$ is the evidence we have: we observe that $x = 175$. For a particular sample set of parameters for our posterior distribution, $( \\mu_0, \\sigma_0, \\mu_1, \\sigma_1, p)$, we are interested in asking \"Is the probability that $x$ is in cluster 1 *greater* than the probability it is in cluster 0?\", where the probability is dependent on the chosen parameters.\n", + "\n", + "\\begin{align}\n", + "& P(L_x = 1| x = 175 ) \\gt P(L_x = 0| x = 175 ) \\\\\\\\[5pt]\n", + "& \\frac{ P( x=175 | L_x = 1 )P( L_x = 1 ) }{P(x = 175) } \\gt \\frac{ P( x=175 | L_x = 0 )P( L_x = 0 )}{P(x = 175) }\n", + "\\end{align}\n", + "\n", + "As the denominators are equal, they can be ignored (and good riddance, because computing the quantity $P(x = 175)$ can be difficult). \n", + "\n", + "$$ P( x=175 | L_x = 1 )P( L_x = 1 ) \\gt P( x=175 | L_x = 0 )P( L_x = 0 ) $$\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Probability of belonging to cluster 1: 0.00968\n" + ] + } + ], + "source": [ + "norm_pdf = stats.norm.pdf\n", + "p_trace = mcmc.trace(\"p\")[:]\n", + "x = 175\n", + "\n", + "v = p_trace * norm_pdf(x, loc=center_trace[:, 0], scale=std_trace[:, 0]) > \\\n", + " (1 - p_trace) * norm_pdf(x, loc=center_trace[:, 1], scale=std_trace[:, 1])\n", + "\n", + "print(\"Probability of belonging to cluster 1:\", v.mean())\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Giving us a probability instead of a label is a very useful thing. Instead of the naive \n", + "\n", + " L = 1 if prob > 0.5 else 0\n", + "\n", + "we can optimize our guesses using a *loss function*, which the entire fifth chapter is devoted to. \n", + "\n", + "\n", + "### Using `MAP` to improve convergence\n", + "\n", + "If you ran the above example yourself, you may have noticed that our results were not consistent: perhaps your cluster division was more scattered, or perhaps less scattered. The problem is that our traces are a function of the *starting values* of the MCMC algorithm. \n", + "\n", + "It can be mathematically shown that letting the MCMC run long enough, by performing many steps, the algorithm *should forget its initial position*. In fact, this is what it means to say the MCMC converged (in practice though we can never achieve total convergence). Hence if we observe different posterior analysis, it is likely because our MCMC has not fully converged yet, and we should not use samples from it yet (we should use a larger burn-in period ).\n", + "\n", + "In fact, poor starting values can prevent any convergence, or significantly slow it down. Ideally, we would like to have the chain start at the *peak* of our landscape, as this is exactly where the posterior distributions exist. Hence, if we started at the \"peak\", we could avoid a lengthy burn-in period and incorrect inference. Generally, we call this \"peak\" the *maximum a posterior* or, more simply, the *MAP*.\n", + "\n", + "Of course, we do not know where the MAP is. PyMC provides an object that will approximate, if not find, the MAP location. In the PyMC main namespace is the `MAP` object that accepts a PyMC `Model` instance. Calling `.fit()` from the `MAP` instance sets the variables in the model to their MAP values.\n", + "\n", + " map_ = pm.MAP( model )\n", + " map_.fit()\n", + "\n", + "The `MAP.fit()` methods has the flexibility of allowing the user to choose which optimization algorithm to use (after all, this is a optimization problem: we are looking for the values that maximize our landscape), as not all optimization algorithms are created equal. The default optimization algorithm in the call to `fit` is scipy's `fmin` algorithm (which attempts to minimize the *negative of the landscape*). An alternative algorithm that is available is Powell's Method, a favourite of PyMC blogger [Abraham Flaxman](http://healthyalgorithms.com/) [1], by calling `fit(method='fmin_powell')`. From my experience, I use the default, but if my convergence is slow or not guaranteed, I experiment with Powell's method. \n", + "\n", + "The MAP can also be used as a solution to the inference problem, as mathematically it is the *most likely* value for the unknowns. But as mentioned earlier in this chapter, this location ignores the uncertainty and doesn't return a distribution.\n", + "\n", + "Most often it is a good idea, and rarely a bad idea, to prepend your call to `mcmc` with a call to `MAP(model).fit()`. The intermediate call to `fit` is hardly computationally intensive, and will save you time later due to a shorter burn-in period. \n", + "\n", + "#### Speaking of the burn-in period\n", + "\n", + "It is still a good idea to provide a burn-in period, even if we are using `MAP` prior to calling `MCMC.sample`, just to be safe. We can have PyMC automatically discard the first $n$ samples by specifying the `burn` parameter in the call to `sample`. As one does not know when the chain has fully converged, I like to assign the first *half* of my samples to be discarded, sometimes up to 90% of my samples for longer runs. To continue the clustering example from above, my new code would look something like:\n", + "\n", + " model = pm.Model( [p, assignment, taus, centers ] )\n", + "\n", + " map_ = pm.MAP( model )\n", + " map_.fit() #stores the fitted variables' values in foo.value\n", + "\n", + " mcmc = pm.MCMC( model )\n", + " mcmc.sample( 100000, 50000 )\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Diagnosing Convergence\n", + "\n", + "### Autocorrelation\n", + "\n", + "Autocorrelation is a measure of how related a series of numbers is with itself. A measurement of 1.0 is perfect positive autocorrelation, 0 no autocorrelation, and -1 is perfect negative correlation. If you are familiar with standard *correlation*, then autocorrelation is just how correlated a series, $x_\\tau$, at time $t$ is with the series at time $t-k$:\n", + "\n", + "$$R(k) = Corr( x_t, x_{t-k} ) $$\n", + "\n", + "For example, consider the two series:\n", + "\n", + "$$x_t \\sim \\text{Normal}(0,1), \\;\\; x_0 = 0$$\n", + "$$y_t \\sim \\text{Normal}(y_{t-1}, 1 ), \\;\\; y_0 = 0$$\n", + "\n", + "which have example paths like:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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CpZCBc463znZg67F2iCsiJoQr8flFSbgiPw4hPk6x+XddE9690AkA2FIUhkdXp0qer+rS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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "import pymc as pm\n", + "x_t = pm.rnormal(0, 1, 200)\n", + "x_t[0] = 0\n", + "y_t = np.zeros(200)\n", + "for i in range(1, 200):\n", + " y_t[i] = pm.rnormal(y_t[i - 1], 1)\n", + "\n", + "plt.plot(y_t, label=\"$y_t$\", lw=3)\n", + "plt.plot(x_t, label=\"$x_t$\", lw=3)\n", + "plt.xlabel(\"time, $t$\")\n", + "plt.legend();\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One way to think of autocorrelation is \"If I know the position of the series at time $s$, can it help me know where I am at time $t$?\" In the series $x_t$, the answer is No. By construction, $x_t$ are random variables. If I told you that $x_2 = 0.5$, could you give me a better guess about $x_3$? No.\n", + "\n", + "On the other hand, $y_t$ is autocorrelated. By construction, if I knew that $y_2 = 10$, I can be very confident that $y_3$ will not be very far from 10. Similarly, I can even make a (less confident guess) about $y_4$: it will probably not be near 0 or 20, but a value of 5 is not too unlikely. I can make a similar argument about $y_5$, but again, I am less confident. Taking this to its logical conclusion, we must concede that as $k$, the lag between time points, increases the autocorrelation decreases. We can visualize this:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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nmT0T/gPeAP5WyAHNbFDq/9jU/13MbFghaeU4xgQzm2dm883sgiz7HGRmL5nZ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\n14hgcX2davm9VDOowlVlEGFmE4ArgTr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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def autocorr(x):\n", + " # from http://tinyurl.com/afz57c4\n", + " result = np.correlate(x, x, mode='full')\n", + " result = result / np.max(result)\n", + " return result[result.size // 2:]\n", + "\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", + "\n", + "x = np.arange(1, 200)\n", + "plt.bar(x, autocorr(y_t)[1:], width=1, label=\"$y_t$\",\n", + " edgecolor=colors[0], color=colors[0])\n", + "plt.bar(x, autocorr(x_t)[1:], width=1, label=\"$x_t$\",\n", + " color=colors[1], edgecolor=colors[1])\n", + "\n", + "plt.legend(title=\"Autocorrelation\")\n", + "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", + "plt.xlabel(\"k (lag)\")\n", + "plt.title(\"Autocorrelation plot of $y_t$ and $x_t$ for differing $k$ lags.\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that as $k$ increases, the autocorrelation of $y_t$ decreases from a very high point. Compare with the autocorrelation of $x_t$ which looks like noise (which it really is), hence we can conclude no autocorrelation exists in this series. \n", + "\n", + "\n", + "#### How does this relate to MCMC convergence?\n", + "\n", + "By the nature of the MCMC algorithm, we will always be returned samples that exhibit autocorrelation (this is because of the step `from your current position, move to a position near you`).\n", + "\n", + "A chain that is [Isn't meandering exploring?] exploring the space well will exhibit very high autocorrelation. Visually, if the trace seems to meander like a river, and not settle down, the chain will have high autocorrelation.\n", + "\n", + "This does not imply that a converged MCMC has low autocorrelation. Hence low autocorrelation is not necessary for convergence, but it is sufficient. PyMC has a built-in autocorrelation plotting function in the `Matplot` module. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thinning\n", + "\n", + "Another issue can arise if there is high-autocorrelation between posterior samples. Many post-processing algorithms require samples to be *independent* of each other. This can be solved, or at least reduced, by only returning to the user every $n$th sample, thus removing some autocorrelation. Below we perform an autocorrelation plot for $y_t$ with differing levels of thinning:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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eutuh9S+ZPIHVWa5/bfOS6o5ytuoPfT25qr+seUlO6s92PBdMGs+MwHjOXrqG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\nXr16cfLJJzN//vxayznssMMA6NGjB92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gwQIAVqxYweLFi6ufmxyDqo561V2WVq1aAbBy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\nbNkykpKSKjx/VcnoqFGjmDNnDsePH+fgwYMsXLiw0rY33XQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "max_x = 200 // 3 + 1\n", + "x = np.arange(1, max_x)\n", + "\n", + "plt.bar(x, autocorr(y_t)[1:max_x], edgecolor=colors[0],\n", + " label=\"no thinning\", color=colors[0], width=1)\n", + "plt.bar(x, autocorr(y_t[::2])[1:max_x], edgecolor=colors[1],\n", + " label=\"keeping every 2nd sample\", color=colors[1], width=1)\n", + "plt.bar(x, autocorr(y_t[::3])[1:max_x], width=1, edgecolor=colors[2],\n", + " label=\"keeping every 3rd sample\", color=colors[2])\n", + "\n", + "plt.autoscale(tight=True)\n", + "plt.legend(title=\"Autocorrelation plot for $y_t$\", loc=\"lower left\")\n", + "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", + "plt.xlabel(\"k (lag)\")\n", + "plt.title(\"Autocorrelation of $y_t$ (no thinning vs. thinning) \\\n", + "at differing $k$ lags.\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With more thinning, the autocorrelation drops quicker. There is a tradeoff though: higher thinning requires more MCMC iterations to achieve the same number of returned samples. For example, 10 000 samples unthinned is 100 000 with a thinning of 10 (though the latter has less autocorrelation). \n", + "\n", + "What is a good amount of thinning? The returned samples will always exhibit some autocorrelation, regardless of how much thinning is done. So long as the autocorrelation tends to zero, you are probably ok. Typically thinning of more than 10 is not necessary.\n", + "\n", + "PyMC exposes a `thinning` parameter in the call to `sample`, for example: `sample( 10000, burn = 5000, thinning = 5)`. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### `pymc.Matplot.plot()`\n", + "\n", + "It seems silly to have to manually create histograms, autocorrelation plots and trace plots each time we perform MCMC. The authors of PyMC have included a visualization tool for just this purpose. \n", + "\n", + "As the title suggests, the `pymc.Matplot` module contains a poorly named function `plot`, which I prefer to import as `mcplot` so there is no conflict with other namespaces. `plot`, or `mcplot` as I suggest, accepts an `MCMC` object and will return posterior distributions, traces and auto-correlations for each variable (up to 10 variables). \n", + "\n", + "Below we use the tool to plot the centers of the clusters, after sampling 25 000 more times and `thinning = 10`." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 25000 of 25000 complete in 11.7 secPlotting centers_0\n", + "Plotting centers_1\n" + ] + }, + { + "data": { + "image/png": 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p+0UkA7A+jW60pPgaATyMMWI/Qil1xnWNGo0ju0/kUOg54sEj4WHQslZVqkXr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CWlH40M65zC4I7NKoW2cfHY2O4UlpTT1CPcSjT3pSZEsh9Ox0OoL98JwPLlyx2vU1U/EZFs4Bng\nFBFZpqp/crwhL4wOlrOkds+gsLQ8bO0ZHSzTXjhxTAcLyOE4jEYfjTSIj+Ov53X3eSxOpNLgymCI\nRUTkX8BGYJKq7rZf9AwGgyFqcFIHKxUrRA5UDpzqJjc3N8Tmog/XFvT6QH3pSyT64QoTdHp61dnC\n2lBfvpM65GFVfcQeXLVU1WfD0ajxwXKWQzn12yfK+GA5T73zwfLGjw5WwGj03bp1Y/Lkye70gAED\nYjZ8zuDBg1m6dGmkzXCE+tKXSPTj2vZAe4Bcli517gUilr+TrKysSsuCiYmJ1ZQOmTuAu+3PdwO/\nq6aswQ/Gv8YQCHOPhI5jOljAMoKIRm8wGAy1RUTeUNWb7c+vqOqkcLRrdLCcY++RYm6ZtjqsPlg1\nxehgGWqjgxXsLsIEYDoVOli/B57Aijk4W1UX2eWOu2j0BoMhInwgIh8B5cBrkTbGYDAYvHFMB8su\nFzAavcFgMNQWVZ2JJQlzN7A6XO0aHyxnMT5YzmN8sKKH8Ea9NRgMBgcQkTew5GNKsVQyHoisRbGJ\n8a8xBMLcI6ET6i7CGiMifxOReSISlt0+TiAi6SKSa4f++drOu0dE5ovI2y4laRG5WkS+F5HPRSRq\nJNFFpJ2ILBGRAhGJs/PuDsZ+ERkhIj+IyGwRaR/Jftj2+OrLIfu7+VZEUu28qO6LHWbqe/u38Iyd\nF9Q9FU39sO3x1ZdwfScrVfUeVb1fVcM2uDI6WM6S2r1+61IZHazYb682hGWAJSIDgURVPRNoJCIn\nh6Ndh5hph/45T0RaAWep6nAgGxhv+6e5BFbftj9HCy6B2AUAtv1nV2P/O4ArhuRDwDlYu7OiYXag\nUl9ssj1CMx2Kkb5sBkbYv4XWInIm1d9T0doPqNqXvlhaeOH4Ti4WkRdF5EkRebLWPTEYDAaHCdcM\n1hDgG/vzLOD0MLXrBCNFZK6I3AkMBubY+a5+9MAWWAVmE0V9U9ViVfWUBA9k/yzgdBFpAhSoaoG9\ngaFPGM32iUdfPHdznGR/N4/Z6ajvi6rusYV7wVre6k3sfifefSkDeofpO7keeBJ40f7nFxHpY8+g\nzRWR1+28kGaijQ+WsxgfLOcxPljRQ7h8sFKxYhaCpZfVO0zt1padWH8gioDPgSRgj30sD6tfKQQQ\nWI0ivMVgfdnvyvPcpBC2peQg8NQV6W7PkkwVkQuxZrlioi8i0h9oiaUX59qnHpPfiasvqrpaRML1\nnYwH+qrqL0XkIeDRasquUdWhtq2vi8ip2LOGInIv1qzhZwQI9VUfMf41hkCYeyR0wvWQzsMSHwU/\nIqTRiKqWqOox++37S6xBonc/AgqsRhG+vgdf9ud7lANrZiLqUFXXtf4M6EuM9EVEmgMvADdT2b6Y\n+068+hLO76QbsM3+3Ky6gp66fVhBorsR4ky08cFyFuOD5Tz1/Z4xPlhV+REYZX8+h8p+NFGL1zLB\nUKx4i64QQa5+rAf62I7X0do317LaIoKwX1ULgMYikmi/7a8Kt8HVIICISFOXszvWd7MBWEeU98Ve\njnoHuFtV9xLD34l3X8L8nSjQxPb7CugkLyIXiRUcujXWzH2gmdxonok2GAwxQFgGWKq6DCgSkXlA\nqaouDke7DjBcRBaLSCaw3fYXmS8i84EBwKeqWooV2Ho+ll/Iy5EztzIikiAi32AJxM4AOgPzgrT/\nr1h+c48BjxNhvPryNdbsyCIRmQN0BKbFSF+uwPKFe1JEvsUKnB6T3wlV+9Kf8H0nz2ANtq8D7g9U\nWFW/UNV+wA6sGbOQZqKND5azGB8s5zE+WNFDjULlGAwGQzQgIjd4JFVV36qmbEOXM76I/BlYA1yp\nqheJyD3AJuBTggj1NW7cOE1MTKRTp04ApKSk0K9fP/eyhevh71R66tSpdVp/JNvbe6SYc3/z6P+3\nd/ZRUhXX3n42EMJ1kEEkimJEAiJ+wADvqKhgRDSKSQgrGlCyvG8g1xiF6E28SmKMxuDKhSB+8AZf\nxTF+EBKjEAQlJhGUCEQNCY7OFZRvByGgiMwYQQVm3z/Oaejp6enu6a5zus+Z/azF4lR1de3a3TVn\naqp+Z2/ad/vCwaO0xIIkqPL2ZXM57NjeObdPTZUTtL2Wlscf8z7HlXdo9PnW1NRwzTXXZP38XZXj\nZq+mpoa6Ou/ZsNraWiorK7nhhhvySpVjCyzDMCKHiFzkX5YBI1T1qgxtRwI/wDtWXKeq3/HF7V8F\n3ga+par7ReSbwLX4qb7SZaOwXITusFyEhWO5CIMn8FyEhmEYpYSq/ilxLSInZWm7EO8p4OS6X+CF\neUiumwPMcThMwzBaMaEusK655hq97LLLwjQZGHPnzsV8KS3i4gfEy5fq6uq8t9ibQ0SexNuRagBe\nd9l3JqqrqwlzB2v58uWBPjWV0NYkHsUP2l4qu9dX0+GE/qHZq99QHeqTfWHbA/ffYeocCdpeNsK2\nVwhZF1h+YL6vADtUNe1PgojMAEYAH+Ftt6dV9m3YsCHUm1OQVFVVmS8lRlz8gHj58uijjzrvU1W/\n4bzTVojFODKyYXMkf3J5ivBh4KLmXhSREUAvVT0RLw3G/c217datW4sHWKokRK5xIC6+xMUPiJcv\nQSAiL4nIC37Ow5dE5Ikw7FocLLdYHCz3xH3ORGX3CnJYYKnqcuCDDE2+Bjzmt30FKBeRo90MzzAM\nIy2LVXWYqp4PLFHV0cUekGEYRjIu4mB151BEZfDizHRP17CsrMyBudKgvDw+cQjj4ktc/IB4+VJR\nURFEt71FZKiIDMWLJRYKFgfLLRYHyz0WB6t0CFXk3rt37zDNBUq/fv2KPQRnxMWXuPgB8fIloGO1\n64AxeEJ3E4nkielrjGzYHMkfFwusrcDnk8rH+XVNWL9+Pddee21oQfqCLA8ZMqSkxmNlDtaVynha\n6/xKXNfW1gJQWVnJ8OHDccyX8IKB3igiE4CZrg2kwzRYbunce0CocbBMg2X2wiSnQKMicgKQSDWR\n+tolwARV/bKIDAbuUdXB6fqxIH2G0fooJFBfc4jIL4F3VfVnIjJNVW902X9z2D3MHRZotHAs0Gjw\nFHL/yqrBEpHfAH8F+ohIrYiME5GrReQ7AKr6B2CTiKzHyzN2bXN9ha1fCJIonQNnIy6+xMUPiJcv\nAbEfQETKgdAeTzYNlltMg+Ue02CVDlmPCFV1bA5tJroZjmEYRk48gpf+5n5SIrIbuWP6GiMbNkfy\nJ1SRe9j6hSCJ0jlwNuLiS1z8gHj54hoREeBcVf33sG2bBsstpsFyT9znTJTujZaL0DCMSKGqKiKn\ni8gVQJ1f94ciD8swDKMRLuJg5YxpsEqTuPgSFz8gXr64RkRGAouBrsDn/H+hYBost5gGyz2mwSod\nctrBEpGLgXvwFmQPqerUlNc7Ab8GjgfaAtNV9RG3QzUMwwDgYlW9VkTuU9VmH6oxsmP6GiMbNkfy\nJ5enCNsAv8TLR3gqcIWI9E1pNgF4Q1UHAMOA6SLSZPFmGqzSJC6+xMUPiJcvAdDDDw/TQ0Qu8a9D\nwTRYbrFchO6J+5yJ0r0xlyPCM4B1qvq2qu4DHsfLP5iMAof714cD76vqfnfDNAzDOMgTeMeCif9D\nOyI0DMPIlVyOCFNzDb6Dt+hK5pfAQhHZBnTES2HRhOrqauISpC85YnjUiYsvcfED4uWLa1T10WLZ\nDvseFvQ8SGhrEsdAmez9s/4Tqrd96Mz2x/sb2Ll2FR2/EN4uT/2G6lB3lcK2B+7nTOocCdpeNqJ0\nb3T1FOFFwKuqer6I9AKeE5H+qvovR/1npb6+nueff55Ro0Y56/Pll1/mBz/4Abt372b16tXO+jUM\nwygFWqKv+Xh/A3cv35K9YQtoyJ5IxMjAX9/ezaZdexvVvbGlnj1r38+rv75HlXF85w6N6kyDlT+5\nLLC24onXE6TLNTgO+G8AVd0gIpuAvsDfkxsFmYuwrq6Oqqoqunbt6iy3Wn19PXfccQc///nPm7we\nVK44VWXo0KHO+mtN5URdqYzHchEGmoswZ0TkDOBu4ACwUlVvEJEbgZHAZuBbqnpARMbi6UnfB8am\n+wPRNFhuibsmKmh7c17dkab2GJ59sTav/qaM6NVkgZWNuM/RQsiai1BE2gJvAcOBfwJ/A65Q1TVJ\nbWbi5QW7XUSOxltYVajqruS+suXx+vjjj/ne977H9u3badeuHfPnz6e6uprbbruNAwcOMGLECCZM\nmMDUqVPZvHkzu3btYu/evTz55JNMmTKFOXPmcPLJJzNt2jS2bNnCXXfdRUNDA1dddRVf//rXmTBh\nAmVlZWzYsIGbb76ZH//4x3To0IFevXoxffr0Zsd1wQUXsHjx4ib1S5cuZfr06ezdu5eRI0dy3XXX\npfVh2bJlTJ48GRHh29/+NqNHj240lltuuYWf/OQndOvWjX79+nH99ddn/E4MI0oEkYuwJYjIUcBu\nVf1URGYDDwI3qepXROQmYAOwAHgeOA+4FC+R9J2pfbXmXISbdu3l6t+/WexhhEqp5yJ0zZQRvRjU\nvVOxh1FSBJqLUFUPABOBPwNvAI+r6prkfITAHcDZIvI68BzezWtXal/ZYsg89thjDBw4kKeffpr5\n8+cDcPvttzN79myeeeYZVqxYwc6dOwHo1asXv/vd76isrGTp0qWMHz+ec845hwULFtCnTx/uvPNO\nFixYwKJFi3jwwQdJLCQrKiqYN28ea9asYcyYMTz11FMZF1fNsXz5cgYPHszTTz/Nc889x8KFC/nk\nk0/S+jB58mSeeOIJFi1axKxZs/jkk08ajaVr165s376dBx54oCiLqyjFFclEXPyAePlSbFT1XVX9\n1C/uB04Bl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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from pymc.Matplot import plot as mcplot\n", + "\n", + "mcmc.sample(25000, 0, 10)\n", + "mcplot(mcmc.trace(\"centers\", 2), common_scale=False);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are really two figures here, one for each unknown in the `centers` variable. In each figure, the subfigure in the top left corner is the trace of the variable. This is useful for inspecting that possible \"meandering\" property that is a result of non-convergence." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The largest plot on the right-hand side is the histograms of the samples, plus a few extra features. The thickest vertical line represents the posterior mean, which is a good summary of posterior distribution. The interval between the two dashed vertical lines in each the posterior distributions represent the *95% credible interval*, not to be confused with a *95% confidence interval*. I won't get into the latter, but the former can be interpreted as \"there is a 95% chance the parameter of interest lies in this interval\". (Changing default parameters in the call to `mcplot` provides alternatives to 95%.) When communicating your results to others, it is incredibly important to state this interval. One of our purposes for studying Bayesian methods is to have a clear understanding of our uncertainty in unknowns. Combined with the posterior mean, the 95% credible interval provides a reliable interval to communicate the likely location of the unknown (provided by the mean) *and* the uncertainty (represented by the width of the interval)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plots titled `center_0_acorr` and `center_1_acorr` are the generated autocorrelation plots. They look different than the ones I have displayed above, but the only difference is that 0-lag is centered in the middle of the figure, whereas I have 0 centered to the left. \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Useful tips for MCMC\n", + "\n", + "Bayesian inference would be the *de facto* method if it weren't for MCMC's computational difficulties. In fact, MCMC is what turns most users off practical Bayesian inference. Below I present some good heuristics to help convergence and speed up the MCMC engine:\n", + "\n", + "### Intelligent starting values\n", + "\n", + "It would be great to start the MCMC algorithm off near the posterior distribution, so that it will take little time to start sampling correctly. We can aid the algorithm by telling where we *think* the posterior distribution will be by specifying the `value` parameter in the `Stochastic` variable creation. In many cases we can produce a reasonable guess for the parameter. For example, if we have data from a Normal distribution, and we wish to estimate the $\\mu$ parameter, then a good starting value would be the *mean* of the data. \n", + "\n", + " mu = pm.Uniform( \"mu\", 0, 100, value = data.mean() )\n", + "\n", + "For most parameters in models, there is a frequentist estimate of it. These estimates are a good starting value for our MCMC algorithms. Of course, this is not always possible for some variables, but including as many appropriate initial values is always a good idea. Even if your guesses are wrong, the MCMC will still converge to the proper distribution, so there is little to lose.\n", + "\n", + "This is what using `MAP` tries to do, by giving good initial values to the MCMC. So why bother specifying user-defined values? Well, even giving `MAP` good values will help it find the maximum a-posterior. \n", + "\n", + "Also important, *bad initial values* are a source of major bugs in PyMC and can hurt convergence.\n", + "\n", + "#### Priors\n", + "\n", + "If the priors are poorly chosen, the MCMC algorithm may not converge, or at least have difficulty converging. Consider what may happen if the prior chosen does not even contain the true parameter: the prior assigns 0 probability to the unknown, hence the posterior will assign 0 probability as well. This can cause pathological results.\n", + "\n", + "For this reason, it is best to carefully choose the priors. Often, lack of convergence or evidence of samples crowding to boundaries implies something is wrong with the chosen priors (see *Folk Theorem of Statistical Computing* below). \n", + "\n", + "#### Covariance matrices and eliminating parameters\n", + "\n", + "### The Folk Theorem of Statistical Computing\n", + "\n", + "> *If you are having computational problems, probably your model is wrong.*\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion\n", + "\n", + "PyMC provides a very strong backend to performing Bayesian inference, mostly because it has abstracted the inner mechanics of MCMC from the user. Despite this, some care must be applied to ensure your inference is not being biased by the iterative nature of MCMC. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "1. Flaxman, Abraham. \"Powell's Methods for Maximization in PyMC.\" Healthy Algorithms. N.p., 9 02 2012. Web. 28 Feb 2013. ." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [conda env:bayes]", + "language": "python", + "name": "conda-env-bayes-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter3_MCMC/Ch3_IntroMCMC_PyMC3.ipynb b/Chapter3_MCMC/Ch3_IntroMCMC_PyMC3.ipynb new file mode 100644 index 00000000..4dfc5213 --- /dev/null +++ b/Chapter3_MCMC/Ch3_IntroMCMC_PyMC3.ipynb @@ -0,0 +1,1325 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3\n", + "\n", + "\n", + "`Original content created by Cam Davidson-Pilon`\n", + "\n", + "`Ported to Python 3 and PyMC3 by Max Margenot (@clean_utensils) and Thomas Wiecki (@twiecki) at Quantopian (@quantopian)`\n", + "____\n", + "\n", + "\n", + "## Opening the black box of MCMC" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The previous two chapters hid the inner-mechanics of PyMC3, and more generally Markov Chain Monte Carlo (MCMC), from the reader. The reason for including this chapter is three-fold. The first is that any book on Bayesian inference must discuss MCMC. I cannot fight this. Blame the statisticians. Secondly, knowing the process of MCMC gives you insight into whether your algorithm has converged. (Converged to what? We will get to that) Thirdly, we'll understand *why* we are returned thousands of samples from the posterior as a solution, which at first thought can be odd. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Bayesian landscape\n", + "\n", + "When we setup a Bayesian inference problem with $N$ unknowns, we are implicitly creating an $N$ dimensional space for the prior distributions to exist in. Associated with the space is an additional dimension, which we can describe as the *surface*, or *curve*, that sits on top of the space, that reflects the *prior probability* of a particular point. The surface on the space is defined by our prior distributions. For example, if we have two unknowns $p_1$ and $p_2$, and priors for both are $\\text{Uniform}(0,5)$, the space created is a square of length 5 and the surface is a flat plane that sits on top of the square (representing that every point is equally likely). " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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1lixZwoUXXsiTTz7JU089FVEsjhkzhnfffZeuXbsGzpXfS2232/n6669p06YN\n999/P+3bt+fWW29l7dq11K1bN9BHUdUGYo0n/Lo89dRTrF+/ntatWwcqLTRt2pQ5c+aQm5tL//79\n6dy5Mw899BD5+flxKeQ/fvx46taty7XXXku/fv2oVatWoKycnyFDhpCVlUXXrl1p2rQpq1ativlc\nRaJSpUpceumlbNq0KeKEDOHnZdq0aVx11VWMHj2ajh07MnDgQObNmxfylKJGjRo0btyYjIwMzjvv\nPEAf0FexYkUaN25MjRo1SnqKYkbE4xd2cVmwYIG8eGivct+vQnGmc1V3Fw9ev4xevXqp6XYMxtGj\nR8v/P+vTgGgzixkZKWVSz5hV0lnbwnE6nTRu3JjJkydz3XXXxTFChRGoVKlS1JtceV5jxYjeRqPF\nbLR4wZgxKxQKQ6JpWqB2qX8wkNfrjYvNIxlZsmQJbdu2VcJVUQBVbUChUCgUpy3JnKGMFb9o1TQN\nIQRmsxkhBG63G03TsNvtBY4z0YI2Huf98ssv5/LLL49DNIrTDVXnNVaM6G00WsxGixeMGbNCcQYx\na9asRIdQYjRNQ9M0pJRFitFInuSSDnArLXXr1i0wZa1CEU9U5lWhUCgUiiQiXLSWNIsZbYBbuIBN\ndJZWoSguyvMaK0b0NhotZqPFC8aMWaFQJCV+e4DX6w3U+iwL24MQIuRlMpkKrDsd7BaK0xeVeVUo\nFAqFIoFEyrSWt3iMJUvrj09KWWQdVYWiLFGe11gxorfRaDEbLV4wZswKhSIpiJdoLcvH/uHx5OXl\nAQWnJVXWA0V5ojKvCoVCoVCUI1LKEOFaUtGayEf7yTRATHHmoTyvsWJEb6PRYjZavGDMmBUKRULw\n12X1+1rh9Cjl5SeSbzaSn1ahKC0q86pQKBQKRRniz7IGD8I6k0RctKmFVdUDRUlRntdYMaK30Wgx\nGy1eMGbMCoWiXPDbA9xuN0AgC6nQidV64Bf9kbZRnJmozKtCoVAoFHEk2NOqKB6RxGl+fj4ADocj\natZWcWahPK+xYkRvo9FiNlq8YMyYFQpFmRDsaS1L4XqmCrdwL63y0565qMyrQqFQKBSloDwyrf5H\n6lJKXC5XwIoAhFQtONNQVQ/OTJTnNVaM6G00WsxGixeMGbNCoYgL5WUP8O8nfJ0fj8eDx+MBCGQk\nwzOTZxJqWtzTH5V5VSgUCoWiGJSnaPW/grFYLJjNZtxuN5qmhQizSHEFP2b3v/zrzyRUlvb0QXle\nY8WI3kZothQYAAAgAElEQVSjxWy0eMGYMSsUihLhF63l4WkNnsQgHJPJhNlsDohQi8VCSkoKDocD\nm82G1WrFbDaHDG7yer243W7y8/NxOp04nU7y8vJwuVyB4zkTRVu02rTB9owzMXud7KjMq0KhUCgU\nRRBpKtdYCfarFrZdtEyrX6T6BXMkkRksvML79McdXm82lixtogdDJVJQa5oWUt5MWQ+SB+V5jRUj\nehuNFrPR4gVjxqxQKGImkmiNt5ArSrRGe7wdC0IIzGZzxP2Fi1r/eq/XG5gBLDiW4ONOxACxZMh+\nKutBcqAyrwqFQqFQhOGfXMAv0spigoFgn2owZe1JLWmWNhin05l0Wdp44r82sRyLGiBW/ijPa6wY\n0dtotJiNFi8YM2aFQhEVv6fV6/WWqdiINOgrWCQnQgD6s7QWiwWbzYbD4Qjx0losofmucC9tXl6e\n8tIGEclLq2rTxgeVeVUoFArFGU80e0C8hVekslelFTJlKQ7DBzH5S3KlpKQY2kubSAqzHvh/EAAF\n7B6KUyjPa6wY0dtotJiNFi8YM2aFQhGgPDytfsJ9raUVcIkUfoV5acMFbVFe2mSsS1ve2eLgY/ZP\nQGG1WpX1IAoq86pQKBSKM47yEq2RBmKdrlnH4GMKFralqXiQ6HNU3vsP99pGytIGtwvf7kxBeV5j\nxYjeRqPFbLR4wZgxKxRnMMGeVr9oKivRGkmYJYsoK08K89La7fZC69K6XK5AP8Fe2rL2JCc7kfy0\nkWrWnq6ozKtCoVAoTnvKO9NaWC1WReFZ2vAMrfLSxsaZVPWgzMSrEMIErAb2SSn7BL+nPK/lhNFi\nNlq8YMyYFYozCH8WL1Gi1T/Q6XQQDOVBeBkvTdPIy8sDwG63l8hLW5JSZ8UplRVPymK/p2Nt2rLM\nvD4A/AJkluE+FAqFQqEoQHjx/USI1mj+REXx8VsP4pWlTXRZskQT6Zi9Xi8ulwuz2YzNZgOS994t\nE8+rEKIOcAXwVqT3lee1nDBazEaLF4wZs0JxGqNpGi6XK+CNhLL3tAZ/wZtMphD/pqLs8AvQknpp\nI9WlTbSXNlEZ33ASvf+iKKvM63+BR4AKZdS/QqFQKBQBIo1kD59Bqrj4H68Gi5lYpnItL1RmtyDx\n8tL68Xq9Z0yWNlmEcyzEXbwKIa4E/pRSrhdCdAcKnIXt27fDH4PA2kBfYaoIjtan/IP+bFayLftJ\nlnjUcuKX07onVzyRlv96GfLXg7UBW3/0sr5xRXr16oVCcToQbVR/WewHCk6TeiYPEDISkabELawu\nrR9/Jt9Pab20RZFIAWkk8Sri/YtNCPE0cDPgAVKADGCmlPIWf5sFCxbIi4eqL0+Fory5qruLB69f\nRq9evZL/fydFCEePHlXptSAKE63+wTulFRaRZsPyUxzRGtxPSWdNCu7DarVitVrxeDwBj6Ldbi9R\nv8WNwel0ApCamlrm+4NTA7aEEKSkpJTLPqWU5Ofno2layMCxaMTTS+t2u3G73QErRHnit074769E\nDzSsVKlS1BMYd8+rlPIxKWU9KWVDYACwMFi4gvK8lhtGi9lo8YIxY1YoDIzft+jxeMot2xpMMhXQ\nV5QNwcLTYrEEvLQpKSmG9dLGgpEyr6rOq0KhUCiSnvKyB/j3Fe+pXONJsougeJLoklV+gn20ZVnx\nwEgCMpGUqXiVUi4BloSvV3VeywmjxWy0eMGYMSsUBiLRotVPaQd/xZMzSbwmmqJEZCQvLRQcQBhr\nXVr/fZ6Ia2wk4awyrwqFQqFIOhItWpNtJH+woEi0F1FRNKWtS+u3Gqi6tJFJyE9J5XktJ4wWs9Hi\nBWPGrFAkMf4vd7+ntSxFWqRarUbwtGqahtPpxO12B5aN4Kk804lUlzY1NTXESxv+I6UwL63b7Y7r\ndVeZV4VCoVAoikn449WSZpmC67NG2j6WWbGSiWiZVv86/+h4CBXfwZm6ZDyuZKY8hVxwltb/Q8Q/\nKEzNHhaZhIhX5XktJ4wWs9HiBWPGrFAkGZqm4Xa7A2KzrESkUUVrpHjtdjsejyeQfQ0W7IV5KsNF\nrSK58F/r4GsV/n5JvLSxPFFQmVeFQqFQKIog/MsXym4q19LOihUti1tWxFJj1h+/yWTC4XAUe+R7\ncYSNIjkorZfW30f4dY9EMttQEiJedc+rwSYpyFlsvCyb0WI2WrxgzJgVigQTyR5QFgR/qQcTq2hN\n1CxH0WbxKmrwWmGzSAWf8+B/C3v8nAyC1kjZwHhQkuMtacWDaHg8noRMd1wcVOZVoVAoFOVCvDyt\nxd2nn2T2f5ZVbdl4l3IK3j4Zz2O8OB1Ec6xZ2vD7zm9FsdlsSXv8yvMaK0bMrhktZqPFC8aMWaEo\nZ8pTtEayB5yJorUoSvv42el0FsjOJjpLezpQ1o/qo/2Y8Xq9gUF/ZrM56X+cqMyrQqFQKMqE8hat\nkR6rJ6ugSsZZvGKxHXg8nsB7RrAdGJVEnTP/YEAg4ucpWVB1XmPFiPU8jRaz0eIFY8asUJQxfpHj\n9XoDX4Cx+kuLm3kqbDKDZMy2RqotC5RK6JVlti64NqnVag2sD65NajabQ66fvzZpfn4+TqczpDZp\nedTvLS2Jii2ZzkkyxRIJlXlVKBQKRVzwC5fytAdEylwCSSuQSjp4LBKJFObRbAfhg8GCM+/Rqh0k\nc/muRGbByxOjeXyV5zVWjOhtNFrMRosXjBmzQhFnwrOJiRKtyTala2Ek2iJQFvgFbTCFDRCKxXZg\nhGupKH9U5lWhUCgUJSLRohWS19MKyelrLW/iVe3A6/XicrmSOktbWhKZ/TRa5lV5XmPFiN5Go8Vs\ntHjBmDErFKXE7XYHPI3+ATxlPRArkkc02GuZTESLGZLTh5sI/Flaq9WK3W4nJSUlxEdrsVgKCF6P\nx4PL5SIvL69MfbRGE3LxwGjHnBDxqlAoFArj0rdv3zIfiXy6iNZIWUdFZIIFrc1mw+FwYLHoD4j9\ng8aCz6V/YGCwoHU6neTn5+N2uwP+a8Xph/K8xooRvY1Gi9lo8YIxY1YoSkmwIIi3OCjtrFjxRghR\n5ExgRrQ0GAX/+TOZTNhsNuDUPRer7SB8+ttktR0o20DsKM+rQqFQKIqNX9SVBUaaFQviW0Eg1v0m\ncw3OssZ/XqNVO4g0FW5hs4adzj7a0xXleY0VI3objRaz0eIFY8asUJQSm80WmI0nHkSbFSuZi9xH\nGi1f3lk9I1VXKA/CfbQOh4OUlBQcDgc2my1m24HL5Qq0Kc9zqzKvsaMyrwqFQqEoFpmZmRw/fpys\nrKxS9VMes2LFe5pLVUHAWBQ1a1i4Tzn42kopcTqdBcp3qeudeJTnNVaM6G00WsxGixeMGbNCUUpK\nK16jeUT9lFYUlIWoCBY7wftRIsZ4FFW+yz87XPD60912oDKvCoVCoTit8YvX4hLLrFjJRqTBaUq0\nlh/lKar8tgO/WDWZTNjt9og1aYECthGgwMCw4jxFMJqATCTK8xorRvQ2Gi1mo8ULxoxZoSgl4eK1\nKF9gYSWkkt3TGk4iY1Ye1/IlOENrsVgC5bvCfbTBpdv8mVt/HWSjlO8ymnBWmVeFQqFQFIvMzExO\nnDhRZLuS+kPj7VMtDtEqCAAFpj5VnJnEa9awcNuB/54r73s/kphORoEdjPK8xooRvY1Gi9lo8YIx\nY1YoSkmFChUKtQ2UpO5pMmR8CitBlQzx+ZFS4na71eQHSYbfdhBevqs4tgPQp8INFsjlee8l031e\nGCrzqlAoFIpikZmZyc6dOwusN2qx/sIyxIUNLCvpvkpyLsLjCM/kOZ3OiAOIFMUnno/Qi6p2EJ6h\nBV3UBpfrCq92EO9razTLACjPa+wY0dtotJiNFi8YM2aFopSEZ14Lm8o1mUVUeXpxS9NXpIywxWIh\nz2UN8cF6vd5CvZbh10eRGKL5aP0C15+9Lera5uXl4XK58Hg8Z9y1VZlXhUKhUBSLogZsJWoq11gp\njhe3LLKvsRItk/3XMSsrf3Iw6UMHF7Tw0PE8N7WqSqpV1qhUwUulDG9gYNDpXuLpdCJ45jCLRZdn\nkerRBmdqo1U7KM61Dc+8GkEEK89rrBjR22i0mI0WLxgzZoWilGRmZpKbm8sTTzzB2LFjA196yVRC\nKlh0Bn8pG8HWEE1cn8w1sWmHnVET0/hlp/71velXC+/Ocvi3pE51jQvbeOhyvodaVTWqZXmpnKlR\nKdODlLqILazEU7IJWiM+0i4pkY7V76MNb1eYmA2/tmVtO0gEKvOqUCgUiphZu3YtTz75JMuXLweg\nV69edOvWLam/EKNVEEi2mKOJVk0zsWW3jf++l8JXS+yF9CDY96eZT+aY+WTOqXY1qmh0aOmha1s3\nnVu70TTITNPIquiBYgjaM4VkF8zxqHaQiMFg8SQh4lX3vPZKxK5LTs5i42XZjBaz0eIFY8asUJSQ\nt99+m0ceeQQAm83G8OHDadu2bdyydJGypaUlUqY1mTLEfqI9At79h43pc+1M/DAFr7dk8R44bGLP\nfhON62r8b6aDt2baqZQpadvCQ6+ObhrU0qiapZGVqVGlogeTyRs1i+fH4/EYXgAlG6UVzdGqHQQL\n2eC/w+0kmqaRl5cX8OMmM8kdnUKhUCiShksvvZT//Oc/DBo0iBUrVvDggw8mrT8uUlxGEq0Hj1jI\ncVpYusbCsrVWvF4JFD/uSpkaU0blsPeAiZseTSfHqfdx5Jjgu5U2vltpC7TNSJOcf7abnh08NKnn\npVqWRlYFPUNrNYcW1y/P0fCKkhNL+a7giROScZa7SCjPa6wYMbtmtJiNFi8YM2aFooTUrVuXTZs2\nkZaWxlVXXZXocCJipExrJIvAiVwL67fYePS/qez700yLRh66t/VwZ998MtIlNgts221i9nIby9ea\niV40SOP54bnUqAqP/jeVvQeKnmDhRI5gyWobS1afErSpDknLpm5eHOHk8N8mHDYvVSp6qVpZYrd6\ninwsrQRt8hFuO/BXLPDPFpasP0iDUZlXhUKhMBDz589n1KhRaJrGzTffzAMPPFCgzciRI5k/fz6p\nqalMmTKFli1bBt7TNI2ePXtSq1Ytpk2bBsCYMWOYM2cOdrudBg0aMHnyZDIzMyPuPy0trWwOrJRE\nG4wFJJVfM3j0uB8hBG6Pia277TzzVgoLV50Sjxu2Wtmw1RpYtpglzc7y0vUCNzdflU9GmobDBjv3\n6oJ2yWoLN1zqYkBvFxM/SGHRj1ZKw5Vd87n5KhdjpqSycJXel80qadHIQ8/2Hs5rqmdoq1bSyKrg\nIcVufEGbKM9ror22/ixtoqprFAfleY0VI3objRaz0eIFY8asMCyapvHoo4/yxRdfUKNGDXr16kXv\n3r1p2rRpoM28efPYtWsXq1evZvXq1Tz00EPMmzcv8P5rr71Gs2bNQqZ37dGjB2PGjMFkMjF27Fhe\nfvllnnjiiZjjSuQXXWGiFZJn0E1wfKHC1cTO322896WDNz5zIGXh8Xq8gp+3W/h5+6mvb5NJ0rS+\nxs1X5zP2PicHjwg0Cdf0zMdhl8z73oLHUzwB36iuhxcfzmXJaivXPZiBpp2Ky+UWrN9iZf2WU8LY\nbJY0rafRo72bC87xUD0gaL2kp3pCfJbhgjZc1CZblvx0J9GiuSSozKtCoVAYhDVr1tCwYUPq1q0L\nQN++ffn2229DxOu3337LjTfeCEDbtm05fvw4Bw8epFq1avz+++/MmzePESNGMHXq1MA23bt3D/zd\ntm1bvvrqqyJjSUlJITc3l5SUlDgdXfEoqoJAMhVtj5YN3n/Yyncr7Ix9NZXcvJILh/QUyai7czl4\nxMSV92VyIlcghKRRXY0L27h5+V+5VMyUpNglfxwy8d0KK3NXWHG5Cgpam01jyqhc8l0waHQ6x07E\nJnq9XsHmXWY27zplT7BYNN75Ty5ej508F9SsolGtskbFTC+VM0/Voi2sXql/fbJcy7LidD++eBN3\n8SqEsANLAZuv/8+klGOD2yjPazlhtJiNFi8YM2aFYdm/fz+1a9cOLNeqVYu1a9cW2Wb//v1Uq1aN\nUaNGMW7cuJAJBsL58MMP6du3b5Gx+CcqSIR4jSR2wn2tiZxcwE+0rPDxHCu/7rGBhBSHpHs7N/N/\nsEQUk4Wj8dRQJw3raDwxJYUde099pUsp2L7HzPY9Zt6dFVhLg9oanVt5eHGEk0qZGmkOycEjJuZ9\nb6V+TQ+dW2uMey2Fn7aVTh4MuDyPAb1dPP+/FFZsCLYuSOrW0LiwtYcuF+i1aKtWLroWrX+WsPLI\n0CY6E3mm2RVKQtzFq5QyXwjRQ0qZK4QwA9lCiG+llKvivS+FQqFQxMZ3331HtWrVaNmyJcuXL48o\n6iZMmIDFYuH6668vsj//FLHVq1ePW4xFCc5YRGtZEmsJr2iiNc9lYstuB09OSWXVJitCSBrU0rjw\nfHdATKY6JPsPm5ibHT07CnBtj3xuuy6fV6c7eHyyLWKbggh2/25m9+9mps3214GV9OnhYthN+fy6\nx0RuHowZ7OToMcGCVRa+WWLjeE7sovqs2h5e+lcui1bpdoOCNgjB3gNmPp5j5uM5p2KoWUXS4Ty9\nFm3d6hrVszQqZ3qpXMEFnMqyG2VyBUXZUia2ASllru9Pu28fIZ9g5XktJ4wWs9HiBWPGrDAsNWvW\nZN++fYHlP/74g5o1axZo8/vvvxdo8+WXX/Ltt98yb9488vLyOHnyJIMHD+bVV18FYNq0acybN49Z\ns2YRCxkZGYVmcONJcaZzjTfF6T9anCDY9puNt2ak8P7Xdvwlr6QU7PrdzK7fzXwQcGro2dGLWrtD\nsqP7D5uYu8LKjr0mnhrqZNlaK32HZ5S49ivoZbReHZ3Dzn0mrh6agTPf35ekVlVdTI4Z7KRKZY20\nFDh5UrBotYUvF9k4ejxU0FosGpMfy0VKuG10On/HaDfwnSX2HxZ8sdDGFwttgMaT9zlpXM/EJ3PS\nubC1iwa1JdWzNLIqamRlFl6L1igDw4JJZPZTZV59CCFMwBqgETBFSvljWexHoVAoziTOP/98du3a\nxd69e6levTozZ87kzTffDGnTu3dv3nrrLfr27cuPP/5IZmYm1apV4/HHH+fxxx8HIDs7mylTpgSE\n6/z583nllVf45ptvsNsLm8HpFH7bgJ94TiwQ3GeiRGtxiebb3HfQxtdLbDzzVir5rlhiPpUd/eCb\nQO80P8vLq4/nsO9PEzlOwUWt3TStrzF3hYU5y6zkFctyoPH0A07q1tB45KVIZbQEfxwSfL7AxucL\nTmV1q1XWaH+um5F3OKmepQtaZz4cPyloUFtjzJQU1vxSuuoGF7Z28egdebw5w86TU/V78avFp2LI\nTNdo09xDrw4eGtf3Uq2yXou2SkUPFvMpD61RKx0oYqOsMq8a0EYIkQl8IYRoIaX8xf++8ryWE0aL\n2WjxgjFjVhgWs9nMc889R79+/QKlspo1a8b//d//ATBo0CAuueQS5s2bxwUXXEBqaiqTJ08ust+R\nI0ficrkCXte2bdvy4osvFrpNZmZmSMWCeBNpwFUyCo5oVoYjx62s3GBj5H/TOPx3aUp1aTx2Vx7n\nNfUy+Kk0tuzyf22f8o4+OzyXrIoy4F/9boWVOdlWcvMK7tdvN5j8kYN5K2O1G+gcPGLi66V2vl6q\ni8rmZ+kVCX7ebuHYScHQgfmkpebhcsOK9XqGdt+fRdeXBX262teeyGHnPjP9R2REFfrHT5qi1KL1\ncHFHD80aeKlRxUONLEmFDC82S/FLdyUiE5lMmVcjDB4TZR2kEOJxIEdK+ZJ/3eDBg+Vr05xgbaCv\nMFUER+tTQiBnsf6vWlbLarn0y3+9DPnrwdqAJg283DOwIiNGjEguBaAokqNHjybVN8r06dM5ceIE\n//jHP4D4CMtoFQJK0newqAyeXagk+AVPcBzRssLOfDO/7LTjzBcIYOtuE18usvHDxsImFIhM7wvz\nuffGfN75ws4XC2PJiEtqV5dc2MZN51YeKlfQs6OH/xas/dnM5V1cZK+z8d/3HaWyG9hsGq+OzuVk\nrmD0K6mcyAntq0KGxvln63Vg61TXSEuReLzww0YLXyyw8tv+0LzZyDtyadXMy2MTU9j1e+lyapd2\nymfoP/KZ+IGDv/4W9Oqg16KtWkmvdFC5godUhzfqTFLB4tVqtWI2m8sl0+/1esnPz8dkMuFwOMp0\nX8FIKXE6nYBeQcRfqSMZqFSpUtSTHnfxKoSoArillMeEECnAXOBZKeVsf5sJEybIh98aEdf9ljlG\n9DYaLWajxQuGi/mq7i4evH4ZvXr1UuLVYCSbeJ07dy6//PILgwcPBkovXqM9doeSZaPKSrz6+w4X\nrZo0sXW3jVempfgetYvAhAI92rk5t4mXzHQNm1WwZaeJrxZHF7T1a+qDnn782cKL76TgKYXQtFg0\n3v1PDs48wfEcQZVKuqA9ckwwb6WF2ctsnMyNXVTfN8BJz/Zuxr6aysZfYxeaGamS1s099Gjvpn4t\njYxUid2uUauqxsffOpjwbumqVlRM13h9TA4/7zDz9JuRz5nFLGnawEv3dh4uaOGhemWNqpVDa9FG\no6wHhnk8HlwuV0LFa2pqKpA8U8QWJl7LwjZQE3jX53s1AZ8EC1eFQqFQGJ9wz2tJiSRagaT1tUay\nMvy238aMeXZeei9UNEWaUMBiljRv6KVneze3X5dPRrqGzSL4ZaeJ2Ust3H5dPl6vibueTOfIsdLN\nDHbvjXlc0tHNf95wsG5zaLmq2tUkHc/zMG6Ik6xKGukpcPS4YL5P0IZXGGjZ1MN/hjqZOd/K9Q9l\n4B90FisncgXL1lpZttZKqkMXmjt/t/D8/2x0b+fm7bEnSUuVmEywYYuZL5fY2Bhjua6Rd+RyXjMv\nD08ofBpcj1fwyw4Lv+w41a+/Hm7XC9x0OM9D87O8OGwamWkeKleQgR8u5VXpQJXJio2yKJW1ETi/\nsDbK81pOGC1mo8ULxoxZoYgDFSpUKJXnNdpj97L4Mo3XYLLgWE0mE4eOWli6xs5jk1JjLubv8Qo2\n/WphU1DW0mqRvPBQDiPvzOfQEROVKviyiL+a+HKxnbWb/bmg2GjT3M2T9+Xx+QIr/YanU1BoCn4/\nKJgx38aM+X7vqF6uqmMrD08MdlK1si5oj52EWlU1duwxc9Oj6eQ4S3ceH/ink86tPIx+JYVff9PP\nQfa6U8LaYZOc29RD7wvdDLspj/RUDYtJ8POOgueiTXMP44bm8t6Xdp59O7VE8fjr4e47IOjR3s2K\n9RaenJpK9SyNzq09dDlfr0VbrbKXShU0Kmd60LTyFbSKgqgZthQKhUJRbPyZ1+DarCWtgRpcQSB4\nQE1piJdYDc+0CiE46TTz0zY7I/+byq97Svc12vUCFw8PyuODb+w8+LxuNwBd0LZo5KFnezf33uAl\nPVXDahFs2m7iiwV2NmwrKGgrpmtMeTyHfQdMDPxXejFn7dLLVQVXGBhxq5MO53n4v1kO2p7jYero\nk6Q6JCdyBAtXWfl6sY2/T8Ymqls19TBuqJPp39m48eFIglonzyVYvcnK6k2nBK3NKjmnkYfu7fRz\nUSlDo3oVDbtN8O+XU1m4qnS2kEHX5HF1dzejJqUEBsTt2W9mz34zH38buRZtvRq6oK1cQZJVwQNE\nL90VLmYjWWwSlQE14mAtSJB4VXVeywmjxWy0eMGYMSsUcSAzM5Njx47F3D5a4f5krSAQKVaP18TW\n3xwcPmrCZpUMvyWPOdlWvssubqkqfarUSf/OYeOvZq5/KAOXO/QcuD2CDVutbNhaUMRd3MnNkIFe\nMtMlZpPkp20mqlWSVK4oGT0ptdSDntqd62b0PU6mfWNnwghdaJ4ScXrJrA7neRh1z6kM7YlcwaJV\nFr5aHFoD1mHTeO3xXP46LkqcuXW5Beu2WFm3xcqtffK4pqebYc+m4fEKerRzc2PvfDLTJDarZPse\nE7OX2Vi21oKmFX5N6lT38spjOcxbES1DHUx4LVqdrIoa7c7x0LODix7tPeQ4BZUzNbIqejCJ2GvR\nGkU0Jgsq86pQKBSKYpOenk5OTk6R7fxfypGyUUYRrQC7/nDw0WwHUz9xoGmC4FJVzz3k1Ef2OyT7\nDpr4dpmNed9b8HgKiieLRWPiyFxsFhgyPo2DR2IXvcEizs81PfK594Z8fthoweHw8syDTswm2LDV\nzBcLbWzaHvvXfGaaxqtP5LBnv4kbR2SQF6Vc1cEj+oCz4PqrVStpdGjpYeSdTmr4asCmpmhUqagx\n/Lk0stcXryxXOHVrenllZA7zvteFpn/mrmD7hdksaVpPo1s7NzdenkvFDInDLtn9u4k5y20s/NF/\nTTSeedBJ9SzJnWPS+asUpcz++tvEob8FzRtqjH4llbnZNjLT9WoLvTp4aFzPS9XKGlUq6IK2sFq0\noA8OdLvd5VaL1qie1zIvlRWJBQsWyIuHGizzqlCcBqhqA8Yl2aoNAFx11VXMmDEjYBnwj8b3U5IK\nApHKUpWU4vQVLdYDf1mZ/72NJ6emcTK3qHgkZ9XW6NrWTbtzPFTI0Guv7v7DxNdLbTRv4Obijl6e\neSuFH38uXTH/OtW9TBqZw6qNFl58N3SgmN2m1z3t0c5N0/peMtLAbIK1m83MWmjjl50FBe3ou3Np\n0cjLqEmlL1fV/CwPzw138tUSK38cMtHtAjc1quiCNjcPlqy28uUiG4eOxiIaNV56JJeMNPjXS6kF\nZvYqCpNJ0qiORpcL3FzQwkOjel7SHPD3CcGrnziY/4Ml6hS8RWGxaLw2Ope/TwpGT0qNKvYB0lL0\na9Krgz4orHqWlyoV9UoHNqsnaua1rCdX8Fc5MJvN2O32QqdnLm/Ku9qAQqFQKM5gohXuT8bBK9Fi\nPZZjYe0vdv7131T2FTKCPZRT072+O8vfl6T/pfmMusvJzn1mnC4YeaeTHXvz+WqxnWVri1f/1WLR\nmPhoLlYr3D02PeIECPkRfKP+gVB9ergYcauTtFQwCdh/GFo09DLl4xT+80bJBj35sdk0pozKxZkn\nuDXczUoAACAASURBVHlkOid8Yn/20oKP2Ufc6qRmVUmqQ+LMh2VrrHyxMFTQXtopnyED83npPUfI\npATFQdMEv+4xs/eAoFtbN+u3WBg7NZWaVTUubONmwsO5VMrU49h/2My8lbHNWNanRz63X5fPuFdT\nWLu56B8iOU7B9xusfL/hVFu7TbeBXH6Rm2t6uPjrb6haWVKlopcUuzdQ9zjS5Arhorakny2jZl6V\n5zVWjOhtNFrMRosXjBmzQlFGxHM617KYbja8/0ix5rtNbNll56nXUsleX7rsaNVKGpNHneTX3yxc\neV9mIDNnMkma1dfo1s7FTVfmk5kusdtg667CJzS4/TonV3Z182wJMrfhA6EqZWq8MeYkJ3PMLPjB\nzFXdXAzonY8QgrW/mPl8gY1tv8UuEQZdk0efHm7GvZbC+i3Rt/vrbxNzsm3MyT4lRitX0Gh3roeH\nbnFSo6qkYrpGViWNvDwTtz+RFvMsXdG4+eo8+vZyM3pSSiDrvHOfmZ37zLz/lb+VpF5Njc6t9BnL\nKleQ+gQPRwXzv7fw7XK9Hm5mmsZbY3NYt8VC3wczfBaSkpHvEjQ/y8sFLbzcPDKdX/dYArVoe7T3\ncP7ZHqpn+SdX8JKe4gkI2mhPCooraJV4VSgUCsUZRXBpq3iJ1uA+y4JoohUE2/fa+fMvE0LAtT3z\nMZkodmYUwGTSmPBwLhUzYfhz6fxxKHR7TRNs3mVm865Thfn99V97tHNze998MtN81QV+NbFxu4lb\nrnbx1RI7/YYXv8ZqKBrjhzmpW0My/IW0AlnlFLukVTMP11/qomEdJxmpEolgzc9mZi6wsWNvqGxo\nVNfDhEdymZttC/GiFocjx0zMzbYxN9um12xtKrl3XDp1qmkMvjGP2tV0y0G+G5attfLlQhv7Dxd9\nTWpW0Zgy+iQLV1ljiE2cqjAw51SFgVpVJZ1a6fVw253jxisFB4+Y2HNAkJkq+ftkya5FpUyNN5/M\nYfk6C9c/dCq2SLVog60PHc7zULOKPrlC5UwvFTO85V6LNhlQnleF4gxCeV6NSzJ6Xm+66SY6depE\n7969qVOnTmB9aXx5/sxSJA9tcQmfGcvffzAmk4k/DtmYvczGf17XfYsmk6RpfY1ubV20OdvrG8kO\nW3aZ+HyhnTU/R6+7eus1eVzb08WL76SUOnNbuYLG+0+fZN9BXVBnpmmYBPy0zcwXC+3FGowFcNmF\n+dw3IJ9XP3aEZD6LItWhC9qe7d00rOMlPVUiJWSmw7GTgnufSou5zm00WjX18NT9uXzwtZ3pcyNP\nhVsxQ6PtOR66t/NQu7pGeorE5YHsdRa+WGAP+pGgC/Ta1SSPTEiN0VsbHf9gsa+W2Hh7pp0aVSTt\nzvXQ9QI31SrrwvpkrmDpagtfLSnay3v/QCcXne9hxITiWFLCkdSvpXFJRxd39nNx4C8TVSt5qZSp\n16KVMvJUyxAqaD0ePZtrs9mwWCyG8bwq8apQnEEo8Wpckkm8Sin58ssvGTlyJH/++Sf9+/dn4sSJ\ncRlMEk/x6u8rEiaTiaPHLfyw0ca/Xip61L/VIjm7oZdeHdyc3fBUmap1my3MXGDDboWxQ3P5ZomV\nt2Y6SpSBDIqcx+9x0qKRxuhXUkKynf7BWD3be2haXxeSQkjW/mJh5nxbxLqz1bM0Jj+mP+p+/n+O\nUk03CzDg8jwGXOHi/S/ttGjkpUFtLxmpEk0KfvjJwsz5Vn7bH5uwtvlKaR09Lnj8ldRi1qaFChn6\nyP6e7T3Uqa5Rs4qXipmSzTstPD4lpRTiEEBj/P26N/fhCamFznhWpaJGu5Yeul3gpnoVSXqqJC8f\nlq/VB6ftP2yiZhWNVx8/GRDBpcug61aNK7u5efjFFH77w0LwRBPd2rqpU12jepZGZd/kCv5atJHw\nf97MZnOpP3fxIunE64QJE+TDb40o9/2WCiN6G40Ws9HiBcPFrMSrcUkW8XrixAn69evH6tWrATjr\nrLMYPXo0vXv3xmwunTcRyibzGowQgrx8M5t22HliSkrYtKnFw26TXNTGxVP357H7dxNWi8SrCVZt\n1D2jJRm136uDiwduzuOtGXa+XBw5AxmOPzPaq6ObhrU1MtIkXg1++MlMk3oeHA4T/345lT//Kn0G\ncuKjOSxeZeWVjwoK9PRUSevmHnq1d1Ovli6svV7BDxt1gb93f+j94a/ZOmZKCht/LZ2L0WbTeOPx\nXP48Kpjwfym0aOShR3sP9WpopKVIPBq6sI4QRyTaNHczdqiT16fb+WZpbNchnEqZ/kyxm+7tPDjz\n4NhJE4tWWZi1OLY4IlExXeOtcTks/tHC5I8cFCWCq1TU4+jV0U29mrqHNstXukvgCWlrsViwWJLD\nUaqqDSgUCoUiLmRkZJCRkUG1atU499xzue++++jcuXOiwwoh2sxYUgq2/mZnykcpfPrdqdmsSobG\n2PtyqVUNBjySxh5fpjEtRdLmbA+3XuOiXk3dM+pyC5autfLFAltUAVmzisakx3JYv8VMv+EZuD2x\nx5abJ1i5wcrKoJHsA6/I459XuVi/xUzNFMkr/87B7YUV6yx8HvKIvWhMJo3//iuXFDvcOSY9agby\nZK5g+Vory9eeiiMjVT8ft1+XT70auqA1CahdTWPuili8qEUzsHce/S9z88TklICV4uARG4t/PGWN\nyEiTnH+2mzuuy6deDY30VImmoQvroEyxyaTx6ugccpx6rVtnfsljO3rcxO7fTbS8SePl9x18+p09\nNI6auvVBk7Bqo5lZiwp6isO5+/o8Lu7o5oHnUvk9xoFsh8MGyQkhGX+/k2t6msiqoPtkrVar7/iT\nI+taFMo2oFCcQajMq3FJlswrwL59+6hYsSJvv/02jRo14uKLLwbiU5u1NJnXwiYZ2HfQwfGTJvYe\nMDE328rXS/XR4yVhwOV5DOjtYtKHDhauKto7WiFDLw/Vo72b2tV04ZTjhAU/2PhmiZUx9zlJdcBj\nE1OLNWlBJOpU9zLp3zlkr7Py8gcOvEEWgcx0PQPXo72HutX1jGSeC5auLlimys91F+czqE8+z7+T\nQva60nl4/TVb09Pgkzk2ul7goW4N3XLg8ghWrrfwxUJbzNUFqmdpTB2dw9I1FiZ9WHyrRkaqpFVz\nD706uKlfS6Nudd0O8uMmCxPedZSy3q3GCyNyqZAOD09I5Xgh0+imp+qZ8x7t3JxVRxe0CFi32cyX\ni/S6vJUyNd4ed5L5K61M/aTobGs0GtbxMGWUk/NbeLHbBE6nEyklDocjMNOX8rxGQYlXhSIxKPFq\nXILF6/z58xk1ahSapnHzzTfzwAMPFGg/cuRI5s+fT2pqKlOmTKFly5aB9zRNo2fPntSqVYtp06YB\nMGvWLJ577jm2bdvGggULaNWqVZExvfPOOzgcDq677jogPuI1uARQcWwIkUoHAfz1t5XsDXb+/XIa\nR4+bqFFFo3NrN13O91Clkj4r1h+HTXyzJPqsWH5aNPTw9AO5zP/eGjTTVsmoWkljzOBcGtbVOHJM\n4LBJjhwT/8/eecc3Va9//H1Odtq0pUBp2SB7KFsQF0vlonAFEURR9Or1J8plKhXkorgvuBAEN3qv\nE0HEAdKyZIiyBWRbVimjrNLs5JzfH6dp0zRp06Yret6vFy9pmiZP0mCefL6f5/OQ9rOO73/SY3OU\nPuHg9cmKOpr6ujnsrVE14iS6tfNwYzc3dWvLmE0yVpvAlj0ifbq72bBdz6sfR/ZYQclsfWyEk1c+\nMrF2S9EmOC5WonNrD72v9lCvjheLGVweWL9Vy5JVhiLpAs88aqVxXWUgK9KGP9asxF/tPqjhzc+M\ntGvmpVc3N43rSVjMMsiwZY+ysSyYpziQjq3czHjMzpzPjPxYisE4f8xGmXbNledjwHUu7E5wOAU2\n79by3Vo92/eFHhoMhiDITLzPwb0DXTRILoihi9bmVc15DZco8zYC0VdztNUL0VmzSlQjSRKTJ09m\nyZIlJCcn06dPH/r370+LFi3yr5OWlkZGRgZbtmxhy5YtTJgwgbS0tPzvz58/n5YtW3L58uX8y9q0\nacN///tfJkyYEHYt8fHxZGdnl88DKyOhoq+sDg2/HdDz5Osx7D9S8FZ3KltkcbqBxekFcUiN60lc\n39nN65Nt1LDIGI0yh4+JLF1jYP02DbFmeOupXM5e0DByioXL1sgauTZNPbwwzsby9TrGvBiTpxjK\n1EuSuaaDmxfG2qmZIGE2ypw8q6ybXfFz6Mb6rv4OhvV38fL7pkLWgXC4kCPy40Y9P270NVkS856y\n0aWtxMGjWq5s4eHLWblcvCyQ/rO21Ip1QqzE29Ot7D6kYfA4S8hhsZxckdWb9az2O+qPt0h0aeNh\n9F0O6id5iTUrsVEN6niZ96WJ6XONpXqswXhoiIObrnHzxKsFm8U2bBcLqcwxJkUZHdbfRZN6DmLz\nGtqtvysNrS8PVxQl5k6x4XQL3Bmh5cDmEMg4oaHbP+x8tNTAe4sMGPTQ9goPvbu7GT3ciyVGRquB\nPYdFvlurZ/Pu4LFujeoqamuXtl6MBiUWzkdgzmt1aVxLQvW8qqioqEQRW7dupWnTpjRo0ACAwYMH\ns2zZskLN67Jlyxg2bBgAXbp0IScnhzNnzpCUlERmZiZpaWlMnDiRt956K/9nmjdvDpTuzSs+Pp4/\n/vijPB5WqQnVtHolkf0ZemYtMLNsfTiql8CRTA1HMjV8vFS5RKNRorJ6X+1k1iQb5y8JyBIcPAqN\nUryljqjyYTYqx9wXckRGplryN1D56sg8I7BwhYGFK4o21q89oQTnm/Qyf2SKfLtGT+YZgZkT7aza\npOP2sZaIvaP9ezr5v+FO3viviVW/Fm6Ck2tJ9LjKwzOj7dSsIWExKwH+P27QsXyDLqhSPOUhG+2a\neZn0ipnjZZj6v3RZZOUvelb+okevV7yoF3I0zP/CyI3d3Cx47nKe9UFg3VYd36wO7SkOpG5tJQN2\n+Xo9QyfGUtwxvNUusHGHjo1+0We+Ibk7bnJxRQMH9ep4SYiV2XVQwxufGCNqXAHGjrTTra2H/5sR\nm68sO12wba+u0EYvnVamzRUebuji4cHBTix5sW4Hjon88JOezm3c3H+7m0YpRZd+REujGowqaV47\ndOhQFXcbGdGorkVbzdFWL0RnzSpRTVZWFvXq1cv/um7dumzbtq3E62RlZZGUlMTUqVOZMWMGOTk5\nEddisVjK5XZKQ3FbvDJO6vlimYE3PzMV8nqWFq9XoGUjDzf18PDMPCPL1hkw6GXaNfMw4HoX40c6\niDVLyLIySf9VesmT46n/sNGxtYdpb5pLsbmqaGMtijKtG3uZO83KqWwRp0vghq4ekmvbWLIqtPpW\nHLVrKE319n1ahoRQR09li3y9Us/XK30fCGTq1VGU4hfHKg2t2SCTdU7DroMCf7vWzX+/NfLCu5Gt\nnAUYdrODYf3dPP2Wid8OKM9d2qaCDyY14pQNXWPvsVO3tuLltTuFoCtnQbEcNEqReWh68PW64eAb\nktu6V8M7/7axbY+Wlz4w0aqJl9v7uGnawEGcWfGu7tin4ZtV+vztXsXhi9NaskrP3anFN9UAbo/A\nzv06du4vaGi1GpneV7uZP81KYoKM2SiWeDvRtrhAVV5VVFRU/iKsWLGCpKQk2rdvz/r16yNWXuLi\n4iq1eQ21EvPMeR1Ol8jMD00sWaWLyJ95RQMPMyfa2LBNx+Dxlvwm2OkS2Pq7jq2/Fz5O7tTawz9u\nd9KorpfYvKbppy06vl6l59xFkRu7uphwr4OPlhp46X0TkWZ73jfIwW3Xu5nwH3O+AufbztXnajcP\nDXHmZdAqywy+XqkvRimWeGGsEuY/5sUYToWxtaoAgczTAgt/NLAwb6mAQS/xvxettG8mcOSklkG9\nlZWzJ06L/LBOz8pfivcUB1K7hsT8f1tZt01TbCrBhRyRFRv1rNgYZOXsfXZSaikNrSDINEiWeOvz\n8rEcDOzl5IHbXUx7syDq69ddIr/uKniNGPNyeQf2cjP+XgdxMTKiCDv3a/hmjZ5dBwp+NxPvtdGh\ntZcHI2iqQebhoU4evMNJvTogCKFvJ1pXw4LqeQ2faPQ2RlvN0VYvRGfNKlFNSkoKJ06cyP/65MmT\npKSkFLlOZmZmkessXbqUZcuWkZaWhsPhIDc3l0ceeYR58+aVqRZf8+pb6epLCShvgjWtgiBw2aZl\n+149k183IyBwQ1c3b06xkWCRMehg/xGRxSuL34jlw6hX1EerXeCBabFcDGNjlNUusG6bjnV+0VCJ\n8RLd2nt49jErV7WUcDjhaJaIKMiYjXKpQ/h9tGri4aXxyhKEwQErYj1egd0Htew+WHiZQbvmHm69\nwc24kQ5l8AjYvFvDonQ9jetJjB/pYN4XxjDtFcUzapCDgb2KZrYKgkyTespq0zcmK78bo0EmI1Pk\n+5/0rN2iRZKKPtf/fsRKs4YSjz5f2qZawX/lrCgqSxpcbg0ffK3j+s5uPnr+cv5w2potOr5ZpedC\nTnj3E2tWVrv+dkDL4HGxxX5YcrgENu/WsXl34Ya2XQsP/a91M/ZuB7XyclfP5wg8NTumzI1rci2J\n+dOsdGvvxWwq7G0Nh2iyEajKq4qKikoU0alTJzIyMjh+/Dh16tRh8eLFvPvuu4Wu079/f9577z0G\nDx7M5s2biYuLIykpiWnTpjFt2jQANmzYwNy5c4M2ruG+iSUkJBQa+ipvQlkE3B6RfRkGnn/XxNot\nBY1XRqaGBUuUv2s0BRuxHr5DiUASBJkte7R8taLwAoHUf9jo0MrLjHmmsI52i+P8JbiphwuTQeCO\n8RaysgXq1pbp2dHNC2NtJCbIxBhlMs8ozVvaz8GbNx++pjrHGswnGxqnS2DrHh1b9xRWim/o4uKT\nl60cyVQsByNvc9Kkvpev04tO9IeDb3XqihCZrbIs8McJDX+c0PDRN8ploijTrIHEDV3cDL3ZRkKs\njEEvc+iYyO5DGobe7OLDr43MmFe25QD+9O3uYszdDl5418QvvynPxQ/rCl4ztRKUDxup/7CTnKfQ\n5toEVv2q49s1RRvaUYMc3Hajm8dfMfHHibK9VhwugS27dWzZrSP1QRs6LTz6bCzJtb3cdI2bMSMU\nhVargd2HRL5ZZSghXUDmn0Od/N+dTprUC/8DpKq8lhLV81pJRFvN0VYvRGfNKlGNRqPh5ZdfZsiQ\nIflRWS1btmTBggUAjBo1in79+pGWlkbnzp0xm83MmTOnxNv9/vvvmTx5MufPn+euu+6iXbt2LFy4\nsNifMZlM2O328nhY+fi/kfqrrcrlAn+c0LPgGxPvLTYUO6DkDaJG+oZsRt7monFdO/WTvcTFwu6D\nWh59PibseKlQ+PJfX/nIVEiNPXm26CBW0/pK8/bmkzbiLTImg8yBoyLfrDawaafiW330Lju9urp5\nZp454g1UABPvs9GyscSdk2Lz16b6MmgfG6HYB2JMMjYHrN5ckhqpLC6INcP902LDVi0BJEngwFEN\nB45qYJFymUEv8enLuSTEwckzGu682cXdA1zs/UNk6ZrSe3nNRiX+av8RTUgfLygB/j+s0xdqaGvX\nkLj6SjdPPminTk2lobXaoWl9ie9/0jNkfMle1JJokOJlzpNWPl9u4KX3FF9w5hmx0IcNvU5W0gW6\nFU4X2H1QScLYtlckKRHmTbPS/SovMWVQW6MVNedVReUvhJrzGr1UpyUF/tx6660sWrSoXFa6+t6P\ngvlaT55V4pxmzDNHPMndIMXLa0/Y2LpHw/uLjXRqowTEJ9dSFghkXxBYtkHP8nU6HK6SH0+LRh7+\nMyGy/FeNRqZlYy+9u7m56Ro3lhhlE9WKjTq+XhnesE8oenZwMflBB+8vMvDN6pLVzFoJEldfqaw1\nTa4pYTbBhRyBHzdo+f4nPdd2dPPYCCevfmxizeZIFxfAkL4ORg5UBrJ27Ct4nP5e3nbNvMTGyOg0\nsOughiUr9ew8EFyNvP92BwOuc/PkGyYOhj0cF5qx99jp3t7DwjQ9Pa70kJTX0F7KFUnfpOX7tXpy\nrOG/7v/9f1aa1JeZ8B9zqZp+UBraNld46NXVw4gBLvQ6aBgkSSAcPB4PLpcLjUaDwWCoVhmvoOa8\nlg/R6G2MtpqjrV6IzppVVMqR8nqzC+VrzbVp2b5Px9iXLGU61vZHr5d480krsiTw8DMFSuvy9XqW\nry88RX9dRzczJyrxVD6P5rdrFI+mr2HyHenn2gXunRpb7BalkvB6BY5kinRr72b/EQ1Pv2XG40UZ\n9untYsJ9DixmCUmGn3fo+Cqt5BWvcTES86dbyTghMnSCBacrvAYn+6Jiafj+p4LnpG5tmZt7Oln5\n/mVOnBbweGDoTS5iTDJpm7S4wmjyA/ENZG3cEdw7GszLq9cpqQ99r3Ez5m5lO5cowra9GtZt0zDx\nXidpm3TcMSFydbR+HS9zp1pZlK7nrsnK7RXkAyse0+5Xupn+iF1ZeGGSuXhZDJmH2yjFw+wn7fzv\nWz0z5pfNEuFyCxw/paHHVQ6Sa8lYYv46aqs/qudVRUVFRaXKCLXS1eEU2XvEyCffG+jQ0stLE6zE\nmmTOnBP5dm3xof3BGHePnWs7uXn2bTM79xf31qdM0X++3MDny5UGQxCU3NdeXV3c1d9FnEWiTqJE\nvEXmubdNLFkV+eT6pFE2urT1Mm2OuZBa6PNG+rCYZTq3dfN/dzpokKIkHNgcsHaznq/9jvmfuN9G\nx9ZeprxhinDNKYDAvQPtXNnCy50TY/MyW2Ua1VUyaF+dZCMhTsZklDmaqfx+Qg1i+ZjykI02V3h5\n7PmYUn0ocbmFIlmnRr3M3Kdy6djay/kckRu6eLihcy6bd2v4epWew8dL//iffsRKo7oy90+L5fyl\n4PWdyhZZssrAklUFdpCUWjLdr3Lz9Gg7tWtIxJhlLlwS0etlBBnunRrDpTCGAUNxz61Oxt7joFnD\nyIcjo9nzqtoGVFT+Qqi2geilutoGBg0axGeffZZvFwh3pWuoYSxZFjh4TM/bC018+oOBwqqSTMMU\npWHqcZWHhDgZo15mX4YmZKrA9Z1dTLzPwefLDXz2g55IVaoeHVykPuDgs2UGDhwR6dfDTYvGEhaz\nhFcS2LBdy+L0klVRH13buXnqn3Y++d7Alz+Wrb6aCRI9rnRzQxcP7Zp7MJvA5YJ5Xxj5IUzrQyg6\ntvLwzKM2/vutv2c3OIKQN4jV1U2nNh4SYpXA/INHRZas0vPLLg3tW0g8P8bGx0sNfJUW+UBWm6Ye\nXhpv56Olehb53Z5vK1bf7m4a11XsIF4Jft6pZXG6nhOng79OWzVRLCAfLjHw9crI62ve0MMbqTbS\nftbRMEWiZoJErEnm7EVFoQ13FXCNOIm3nrLRs6Pi0y4PXC4XHo8HnU6HTqdTbQMqKioqKn8NYmNj\nuXz5MvHx8WFdP5TSKooix0/r+XaNkofqcgd73xI4lqXhf99p+N93yiW+VIF+3d3831AvcTFKMPyu\n/SKd27rZsU/PnZPCPzIPRc0EiblTczlwRFvo9vwVQItZpktbN48Mc9Ag2Zs/uZ7+izL85H+MHBej\nHJkfyRQZNsmCI4L6zl0UWfWrjmH9Xfx2QMvTb5lJTJC5tqOblyfaqRUvYTLKHD+lWB9W/Vq8KgqK\nxeLtfyvbxYY/bgkr4kv54KHh4LGCQSyNRqZVEy/9eriY/aSV7AsiLrdAm6Ze2rfwFMo5LR0Sc6ba\nkWWZEZNjyQ1IYQi2FctilunUxs2DQ5w0SlEaWpcb1m/TsmSVnicesGPUw92Tw091KI7nx1qpnSAz\n7PHAlcJ5Cx6ucvP8v5RVwDEmmbMXBNJ+1rNsXeGNZXfe7GTS/Q6al4Pa+mehSpTXV155RZ703sRK\nv9+IiEZvY7TVHG31QtTVrCqv0Ut1VV5Hjx7N+PHj89fVFqe8hloycP6Slg079KS+HvnEv1ar7JfX\naeH4aZGGKYovMtcqkBakiSwZiZkTbSQlykyZbSYzhGIXito1JHp2dHNdZ49yjGySMOjAEgsP/tvM\nwWORDzyNvdvONR09PPVm6AElQVASDm7s6qZzGw814mT0OkW1DtzMFSqztazc3tfJfQOdPDvfxNbf\ndfm+1T5Xe2jZRPn9IMCW3RoWryz5mL93NxfjRjp4+QMTG7ZH9vzFWyTuG+hgUC8PJ84ImA0ydies\n3aJnSd6iidLSqomy6OLthQa+WxuueitTv47ENR08XNPBQ2KeQqvTQvvmEglx5f+/bKfTidfrRa/X\no9VqVeVVRUVFReWvQVxcHJcuXcpvXoMRahjL5tCw65CBqW+Y2XM48rejh4faubmnm5feM/Hr7sJN\nja+JnPFowXDNiVOKPzOUEjmkr4ORt7mY/YmRVb+WLcj/7IUCX+T1nV1MGuXgf98ZMBhkxo10khDn\nwKiXOZChYXEp17u2b+HhucdsfLVCz7BJxQ8oybLA4eMaDh/X8P5i5TKfKurbzJVcy0tiPORaYezL\nMew/EtnvpGaCEpq/eY+WweMs+QNZwXyrZqNMx1Ye7vqbi6b1HMSaZdxe2Lhdy9crFRuGUS/x7jNW\nMk5oGDLegtsTWUMnihIzJ9i4bBMYMLpA/fZt53rifiUqK9YMl20CKzdp+W6NnoshB/OUDzqxZhjx\nRGnVW4ETpzV8+aOGL380cHsfJ5NG2WhS1wGAwyEiigV/fCuR/6qonlcVlb8QqvIavVRX5fWFF16g\nR48e9OjRAyisvIbytXolkQNH9WRf1KARlXD6r1cV5JuWFp9v9OuVehZ8E+iTDUWBEtm1nYf4WEXl\n2nNIZNMuDQ8PdfHTFh1vfFK26Ct/aiZIvPVULr8f1vLie0UtEb4msu/Vbto28xIXKyEKsOV3LQt/\n1BcZuNLrJd6eZuVCjsi/55qLHJmXHiWzNcYM0+eYaZDipW93N80aSMTGyHg8sHFH6by8qf+wcWUL\nL4+/YibzTOnUah+WGMWG0bubh+s6u5EkyLEKLF1VeDitLCjqrZNn3zYW2n4ViqREJT7shi5u6gD+\n5AAAIABJREFUaidKxBjhYo7Aip+1/LBOT+O6Ei+OszH3MyPLN5R9Y5klRmb2k1au7+Qk1uxFkqSQ\naqh/M1uWhtbhcCBJEgaDAY1GoyqvKioqKip/DXwrYn343vyCNa2CIHAkS89XKwy89l8TXq+AKMq0\nbCTRt4eLB/7uVDZhIbPpNx0LV4QerAGfD9XKoWMahj9uKWX+a8Hmpw++Vi6JNUn87+VcGteXOXdR\npPuVSmO7YbuWr9IMnD5X2mZJ4rkxdhqmyEyYGRPScuD1Cuw5pGXPoYK3ZJOh8EKFWLOMyyOQa4OU\n2hJTXo8pF7X65p5ORg938upHxvxtZVnZIr/u8vOK5jWRo4c7qFdHOea32gVW/qJj6arCSqRvgOp/\n3+l56X1zRLVdtipRWY/d5WBxup43PzWSGC8rG7EetJNSS8JshEuXBdJCxFMFotdLvP+MlSOZGgaP\niw25vCCQM+cVv/C3awoa05RaEtd0cJP+bg5Z2SJeL/y9jwuzUS7ToNyt1zuZ+rCTVk0kBEGLr0Xz\nnVz4//G/zJ9IG9poQc15DZco8zYC0VdztNUL0Vmziko5Eh8fX6R5DTaMdfa8jjVb9UydbS6UhypJ\nAnszNOzNMOVfZjbKdG7j4aE7nDTMi4O6bBVYvkHHd2v1OFwwKy+DdeLMGDLPROaTBRgzws4NXdz8\ne46Z3/yGiCwxMl3buvnX3Xbq11HsBhdylFq+X6sP2aDc3NPJ6GFO3vrcyI8bS6/E2Z0Cm37TsSlv\npWmLRh5eedzGzv06Ll6WeOIBOzEmmfM5IsvX6UrdLNWIUwbGdh0sfgMVKE3k6l/1rP41cAuVh6n/\nZycpUfFnxsdKgMidk2I4f6lsaqs/Tz5ko01TL6Ofi83/4HDuosCydXqW+W3ESq4l0bODhxmPKrWY\njHDqnMjy9Vp+3KjLz6Ad0tfBPbe5eWq2qVwa/6REiVF/d/LUmzGkb9Lh861e29HDyxPs1IiXiDHK\nZGWLLFunD5mHG2uWee2JXHp1c1OrhobAkwNBENBoNEVONSJtaKM5KktVXlVUVFRUykxcXByZmZl4\nvd78o0cfoihy2aphx349qa+bw87btDkE1m3TFVqxmpyncn035zIuj4AgyOw6qKFJfS+ZZ6AsdgMo\nsBx8+aOBOyZYCGwcLlsFVv2qL+R5TaklcW0nNy+NV/yzprwlBt+sMnDomMjsKTa2/674MsNV9kKh\n1Uq8NdWKwyUwYnKQqfUkmWs7KakCiXFKs5RxUmTp6sILFfyZ8qCNNs28TJxlzl8TW1rOXhD5bq2e\n79bque0GJ/8Y4uTF980kJco8PdpBYrzyvBzLUta7lpT76o8SV6Woty++W7J6eypbZFG6nkXpBUsV\nfJFqsybaSanpJbm28rp8dr6JvRmRftiRmP2kHZAZNsk/iUHxrX6+XJOfEQwyjetJXNuxIA/XbFSe\nlx9+0qPRykx9yE7Tenb0+vA/5JRHQ+u/0c6/mY0GVM+rispfCNXzGr1UV8/r0qVL+fLLL/F6vXz4\n4YeA8sbq9orsyzDw8vsmVv5Sdg+gj6taeHjmMRvL1ul45ytlKUCLRhJ9urvo0NJLXKyMKMhs3q3l\nq7SiPtFAlNxMZfvUs29HtnJWWWLg5a2nrJy/JCIjIwDb9yq1HCjjitL7BtkZ1MvNjPnmQmtTS6ql\neUOJG7u56dTKQ7xF8fL+dlBk90ENowa5yi1jtUacxNv/zmXb71pmfqTYQAJradZA8RV3aqPUYtDB\n3j8Uj3PRXF6JN1Jt6DQw+bWYcomr+sftDm6+1s3kV01oNIJSS2sPCRYZg17mwFGRb9cY2LgjPL91\np9ZunnnUzisflX01riDItGvm5cPnrNRMkDHpnUiSlD/1X56EamiDodfrI1rvXN6onlcVFRUVlXLF\n4XAwb948Zs2ahd1uR6vV8scff3DFFVcoimuOFpsDBvVWVohu2KErU+xQQqzE3GlWMk+L3D3ZgtVe\n8H62/4iG/UcK7AYmg0yn1h7uHVjgE7XaBdI2+UdkSTw/1k6DOhJPvGrO2xYVGQN7ubh/kJMZ882s\n3aI0NAa9zJUtPNxxk4um9e3Exci43AJrt+hYvLL4CKYrGniYNcnGjxt1DBlvQZbDb+JkWeDAUQ0H\njhY8rliTxGf/yaVRisyZ8yJDb3IypJ+LTb9pWfhj+ENY/kwaZaNzGy8TZsWEVG+D5b5q83J5+3Z3\n88ideetdNZB1Blo39TJjfkwhxb2s1K4h8fb0XNJ/1nHnxIIkhkPHCmrVaGRaNlbSFkYNUvzWGhH2\nHBb5Ot3AzgP+zbXEvKdsOFwCQydElsvbu5uHZx61c0UDJbfVoQQKVMjxfSiF1uv14nK58q8jy9GV\nIavmvIZLNHobo63maKsXoq5mVXmNXqqb8pqamso777wDQIsWLXj33Xdp3rx5vqfOH1kWOHtB5OwF\nDaeyRfZlaFm2XsfO/doQywgAJF4aZ6Nuksy0OSaOniyb1uKLyLqhs4erWnnQaWXOXxJ59WNjyGP1\ncGmQ4uX1J6xs3KHj9f8ZiyiPgSRYFJ9on6vdJNeSMBtlsi8IfL9Oz48bdXg88OaTNgRgymwzFyNY\nI+pj1CAHt93oYvpcM7v9BsJ8a2b7XO2hQbKXWLOyUCFtk45vV+vJsQa/7zZNPbw4zsbny/R8tizc\nZIfQ6PUSH87I5fhpDbk2gab1Ff+s2wvrt2pZvLL0g3KTRtno0MrLxJkxpf5Z/wzaFo2VpRdmo0Td\nJIlXPzbzyfdlV6xNBplZk2zc3NNNzYSCZjVw6r8ykGUZu90OgNlsrnZJA6AqryoqKioq5cxjjz3G\n1q1beeyxx1i8eDEtWrTIfwMMbF4FQSYp0UtSope2V0Cfq+HBwSJnLmg4c07k5FmRTb9pWblJT0am\nyNB+Tu6+1cWbnxojthycvSCyfa+Gewc6+WGdnjf+Z6RxXYneV7sY8TcXcbESWg1s3avEUoXjyxVF\n5XjboIN/PhMbtqJ88bLIjxv0/LihwJtZv45yrP7D3MtIEsjAtr0aWjb28ssuKGtz3SjFw+upNlZs\n1HHHhKLq7WWbwJrNetZsLjyEdU0HN9MfsefFQclknVO8mem/aHjtcTuSDPekls8Gqrv6O7jjJhdP\nvWlm7x+Fn/e4WImubT3862479ZIKslbTN2lDNteNUjzMftLGwhUG7kktW9KBfwatKErMn2bj+Gkt\nL76vp/fVbj6YkUusWcbjVVbNLkoLT7m+rpObF8baadtMQhQDP9xV/uBU4H2qntcwUD2vKipVg6q8\nRi/BlNf09HSmTp2KJEncc889jB07tsjPpaamkp6ejtlsZu7cubRv3z7/e5Ik0bt3b+rWrcunn34K\nwMWLF3nggQc4ceIEDRo04MMPPyQuLi5kXU6nk+HDh/P555/nN65l9c1dytVwMUfEYBBY9YuW5Rv0\nbPpNy6UyKpBarcScKVZkWWDqbDPnLwW/HaNepkMrD/16uGlSz4slRsbuFEjfpGPJysKN0t1/c3DH\nzS5e/sDEpp2RH283SPHyxhNW1mzR8eanRkRR8fL26+GiXTPFyysIsHmXhoUr9BzNKqm5Lshsnfyq\nOaIsVJBpVFdi0n02WjSSuXgZtFo4cETZhFWahQr+1EyQePvfVtZv1/LG/4xh2yKSEiV6XOXm+s4e\npbk2KRFWP6zT0v1KFym1BCbMLB/FumcHF5MfdPDCO6b8xAd/LDEyndu46dPdQ4O8FAplM5eu0GYu\ng17mPxNs/O06N7VqBG9Q7XZlza3RaKw0z6kkSTgcDgRBwGQyRZ3yWu7NqyAI9YGPgTqABLwry/Js\n/+uozauKStWgNq/RS2DzKkkSXbt2ZcmSJSQnJ9OnTx/ee+89WrRokX+dtLQ03nvvPb744gu2bNnC\nk08+SVpaWv7333rrLXbu3Mnly5fzm9enn36axMRE/vWvf/HGG29w8eJFpk+fXmxtAwYMYPHixRE3\nrz7yh0xkgfOX9Jy9IHIqW2TXQS3LN+jYfVBb4hT/w0Pt3HSNm+feMbF9b+mbzJoJSqPUq6uH2jUl\nalgkaibI7Dmk5ZHnzHg8kU+svzbZRowJUl8L3VhDgZe33zVuGqV4iTWDzQFpP+tY6qdC+jJbX1lg\n4qetkTfWCbESbz9t5bf9Gl76QBnI8veJtm/uG5SDLb9rWJRWsnL9+P3Kkf6kmTFkZUf6HMr06+Em\n9R92Dh7VEBcrYzTIZJxQEg7WbQs/4cCHKCqNdfZFkelzzcXYWoqSGC/Rrb2HG7u6SaklUTtRJj5W\npnVTuYja6o/NZgPAZDJVmvrq9XpxOp2IoojRaIy65rUibAMeYIIsyzsEQYgFtgqCsEKW5X2+K6g5\nr5VEtNUcbfVCdNas8qdg69atNG3aNH8t6+DBg1m2bFmh5nXZsmUMGzYMgC5dupCTk8OZM2dISkoi\nMzOTtLQ0Jk6cyFtvvVXoZ7799lsAhg8fzsCBA0tsXisKUZCpU9NDnZrQrhn07Q7/N1Tk7EUNp7NF\nMs+KrNuqY81mHSdOi4BAp9Yepj9i4+uVeoaMLxp9FS7nLop8t9bA8g065k61cjlXQ+rrRrpf6ebN\nJ20kWGS0Gti+T8NXK0qXKDCot5MH/u5k5odG1m8v2RZhdwps2KFjw46ChrRmgsQ1HTxMf8ROgxQv\nKbVkRFHmhXdNrN8euW9y4n02urT1MmlW4aE2r1fg98Nafj8csFDBb7WrJUbG6YGfNuv4eqXy4eOK\nBh5efdzGF8sNzPwwsuUFCop1QyPCoH/F5W8ZE8W8tIWubu76m61gc9phkSUrDWzfF5hwUECvbi7G\nj3QwY76JLXtK3/yfvySyfL2eVb/oeHGsjR5XeaidGF2DUNFCuTevsiyfAk7l/T1XEIS9QD1gX7E/\nqKKioqISNllZWdSrVy//67p167Jt27YSr5OVlUVSUhJTp05lxowZhRYMAJw9e5akpCQA6tSpw9mz\nZ0uspTLfnE1GiQZ1vNRPkukkywy8QeBCjoZzF7XYnAINU2DSLN/Uf2R1PXC7g1uvd/Gsn3q755CW\n9xcr3zfoZdq38HBHPxdXNLRjMcs43QKrf9EFXV+aUkvizSlWfvlNw+DxlhIHvIrj3EVl41P75h6S\nawmMmByDRgO9urqZM8WWFwUFuw+KLE43sPNAeG/3LRopSQdfLDdw1xMmwnkO7U6BTTt1hWwUvuG0\niaNs3NjFg90hcOyUiNMtY9RLpd4+5c/V7V089bCDWQtM+ekOPiRJyEuhKGi4dVqZNld46Hu1m0fv\nUhIOBAE279bwVZqe46dF3plu49RZgSHjLbg9Zf+9dG3rZuYkO1e28Hlbi7+tqlI7o3lBAVTwwJYg\nCI2BDsAv/pd36NChIu+2YohGdS3aao62eiE6a1b5y7NixQqSkpJo374969evL/YNNJw3t4p8A/Yf\nAPMdbQbeX2K8RM0Ed/7X70x3c/aChjPnFbvBjn2Kf3b/EU1YDaNvov67tToGF6PeOl0CW3br2LK7\noIGqESfR4yoPTz5op04tZXI+K1sgPkbG4xUY/VwMZ85H7mvs2ErJG/14qYEX/IL8P8zU8OES5e9a\njUy75h76XuNmzN0OLGYJGYGNO7R8taLwoJEoSszOSzq4OzVwGULpuXhZJMcKba+QmPJGDKt+1VK3\ntkzPjm5enmCnZoKyxODoSZFv14a3xECrlZg/TcnSvWOCBWeYcVVuj8DO/Tp27i/4PZmNMh1beXj+\nX3ZqJsg4nGDQCzxwu5Mlq/SlTinQamReGGtjYC8PdWqWTW2tioGtaKXCmtc8y8BXwFhZlnMr6n5U\nVFRU/oqkpKRw4sSJ/K9PnjxJSkpKketkZmYWuc7SpUtZtmwZaWlpOBwOcnNzeeSRR5g3bx61a9fO\ntxacPn2aWrVqlViLXq/H5XKh0+nK5U2xaNRWwSYgf4LFcoHSSKTU8pBSC9o3k+h7tczo4RrOXdRx\n+pzIidMa1mzWsW6rrpDv0qiXmDfNyqVcscwT9RdyRH5Yp+eHvPWlt/R08tgIJ6t+0XJFQ4nXJlvR\na2H3IZGFPxr4/Y/SvQ3r9RJvT1M8mcMf99/uVBSPV2DHPh079hU0bbFmZd3t6OEO6tXxYjHJiCLU\nTfIy9c0YVm6KfKGEXi/xzr+tnDxbuMk8eVZg4QoDC1cocVO+JQa9urm582ZFLdZpFbV40UoDu/zU\n4pt6OHn0Licz5pnYWgYPcyAuj8xDd9g5eFTLvVNMeLwC8RaJbu08jL3HTr0kmVizzMXLAmkbtXz3\nky8nuCgdWimWiKtaSmg0Jaut1YloVV4rJG1AEAQt8B2wTJblNwK/P3DgQPnbtYmga6xcICaAsUOB\nimVdo/y3On3t2AE1x1WfesL52ndZdannz1avf63VpZ5gX597HZw7QNeY5o29PHxXAhMnTozO/2P9\nhQkc2PJ6vXTr1o0lS5ZQp04d+vbty7vvvkvLli3zr+M/sLV582amTJlSaGALYMOGDcydO7fQwFaN\nGjUYO3Zs2ANb9913Hy+88AI1a9YEKJesSq/XCwSP8AnVtAbDN/wVrK7sixqy87JnL+YKtGkqMe5l\nM1t/L5+Q/LlTc9mxX8t/PjAVGjDTaWXaN/dw0zUemjdSjrFdHmVSfXF66AUG9+fZGAIzW8tKXIzE\nO09b2XNYw++HNFzX2ZO/7ta31nX1r6XLwh16k4MRA1z8e46ZXQdLX6NeJ9P2Cg/9eig5qwkWL7UT\nZbxegVFPxXIsK/LX1t+udfLwnU6mzTHzWwl2ijo1lfiw6zopz02MSeZUtoYfftKx8lctTz3sYEhf\nN8m1yqa2Bk79VxYulwuPx4NOp8v/0Fnd1NhKTRsAEAThYyBbluUJwb6vLimoJKKt5mirF6KuZjVt\nIHoJFZU1ZcqU/KiscePGsWDBAgBGjRoFwBNPPMHKlSsxm83MmTOHq666qtBtBDavFy5c4IEHHiAz\nM5P69evz4YcfEh8fX2xtY8aMYfTo0TRp0gQo3+bVH0EQ8v+ES3HNayAuj0D2eS2nzwucytaweY+W\ntI16Dh4TS7HlSuK5MXYaJEukvhb+RH28RaJ7ew+98xYYxJplzpxTjtT3ZwjMetzOjxt0zP/SSHko\ne/+6207PDh4mv27iSMAqXX9FtFMbT/7Q0459Il+lGdiXUbThqxEn8c50K7/s0vLqx0YkKfIah93s\nYFh/FzPmm4iLgX493NRP9hJrUjanpW8qnLZQEnq9xPvPWDl0VMNz7xZdZxseSnzYQ0OcDO7ronYN\nGZ2u7DYQtXkNTWVHZfUEfgJ2oeQty8AUWZaX+66jRmWpqFQNavMavVS3DVv+TJ06lYEDB+Y3xpE0\nr8F8rWVpWv1vL9zmNRiXrZr8qK7jpzSs/EXH+u3BV9326upi3L0O5n1hZPn6SI/fZRrV9fLudBsX\nLgvIMmg1sOdQ6QawAmneUBnIWpSu5+Ol4W/I0utkrmzp4aYeHq5ooGThuj3w01YdiXEermwuM+lV\nM5mnI//gkhAr8c4zVn7ZqeXV/wbPga2Vl7ZwfRc3SYk+RVTk+5/0rPhZWyTKbGAvJeFhyhvmUls1\n/NFoZJ76p43BfezUrqH4rEVRLPSnNK/VqmpenU4nXq8XvV6PVquNuua1ItIGNgCVs99MRUVFRaXK\niY+PL5JaUBb8G00f5ZEbGwmWGC+xZg+NUiSubg939BPIvqgl+6KGU9ka9mVoWfWrlsfucrAvQ8vQ\nCZZSZYOG4uaeLkYPd/LcOwWZrVqNTNtmHm7yDWDFyHg88NM2HYvTlEiq0CgDWTotjJwSS05u6Z5T\nl7vocFqHlm5mTbKxL0ODywOzUxUv7rL1On5Yp8NVhkSB/xtmp3dXDxNnFo7oCiT7omJrWLqmYFtZ\no7oSN3R288ZkGwlxMka9zKFjAq2bSvzym5bB4y0RKcKtmigbvNo3dyEKEpIkFGQSB/FjB/4JRrRP\n/VcVVbIeVs15rSSireZoqxeis2YVlXLGYrEUal6DrYgtjlApAlC1b+rB61JW3abUhnbNPPTqauPB\n25XsWUuMxLxpXn7eqWPlJh0ZmUr2bGmoESfx9nQrO/drGDLOUsgr6/EWnZq3xMhc3d7NxPvspNRW\n7AbZFwW+W6tn2XodHo9I3+4uxoxQoqXWbYvczwsSMyfaiLfAkAkWvw1oMvXqyFzfyc0rk2wkxsuY\n9DKHjysDWJt2ht7IVaemxPxpuSzfoOPOSbGU3hohcPSkho9PavhYiSnmzpsV/+3qzXpaN/Hyycu5\naARl/e6iND0Hj4XXAomizJMP2rjzJicptb156qo2X2H1Na9erze/iQ1saH0fwgIV2qoi2pvmKmle\nVVRUVFT+PMTHx5ObW/pQmeIsAv7fq4o32GAqsI/AxkSr9dIgWaBhiowgeBnUy8WFHJGzFwSyzooc\nzdKwYoOOn0tYdTvlIRvtmnmZMNPMiWJUR38uWwXSN+lJ31SgQNavI3F9Zw9vTbXStpmEJMts2KbD\nahdQFl+WXcnu2s7NtIftzPnUyIqfA60RApmnBT5bZuCzZUqigCjKtGwk0ae7i/sHOYmzSGgEga2/\nKxmrh49rSX3QRpumXv75TGwJ6nF4mI0SHzxrZcc+LYPHFVZbjXqZDq09DLvFRZP6Sjavyy3w09aC\nhQr+NG/o4Y0nrbS7wo5Woyjd+Y82ryEVBAGNRoNGo8l/vfpeI74/sizj9XoLebkD7QVV9VqPRqqk\neVVzXiuJaKs52uqF6KxZRaWciYuLIyMjI+zrhxN9VZXh7cEa6pJq8nq9hfyONeIkasRBi0ZewM3d\nf3Nw5rzImTz/7O6DGpatV1bdtm/uCZrZWjYETpzWkBjvIsECI5+M4WiWhtZNvdzUw83o4Uq6gQxs\n2K7kvYYzVKbVKvFX2RdFhk4MP2NVkgT2ZmjYm1Hg5zTqZTq29jB+pIN2zbxYHQLnLgoMuMHFknQ9\nF0tpafBn+C0Oht7sZvKrJg4FWVXrcBVdqOAblvOp1zEmmQs5IucvCdzS003dJA+yrMn/QON7Hfga\nUgBPXlfrr7BqNJp8P2mohtb/34Ldbi/y82X1epeEqryqqKioqPylKY3nNZiiWdVHqBDauuBrInyN\nSqgG1r+RgcJDZkozAim1JVJqS1zVAm6+Bh6508GZCwJ6ncD2vVrMRpkGyV6Onyq93cBHk3oeXp9s\nY8kqfaHj990Htez2i66ymGW6tHXz2Ag79ZIkLDEyFy6J/LBO8av6b8Aa1NvJ/X93Mn2umZ37I28b\nHC6Zgb1c6PUw8F8WcnJFEuOV5Q5T/2knubaE2Shz6pzI92uDD2AFEmuWeH+Glc27tdwxIbYU6RBw\n6bLIjxv1/LhRUZKb1PPw/gwrf7vOg0EPUNBA+l4LQKFmNrCh9X8tBKqz/g2t2+0udF3/n3e7Ix8I\nC0Xg67i6DWuVhOp5DZdo9DZGW83RVi9EZ80qKuVMXFxcic1reacIlIVQx7KhGmpfo+DvZQSlgfF9\nz18583+M/o/VP7PW/6jZbILGJuU6dWt7GXC9k3MXC+wGGZkalm/QsXmXLoyFCRKvPWHDZIB7p8YW\na08AuGwTWL1Zz+rNBXaDekky13Zy85+JdmrGS5hNErUSZPb+oWXwuNgSN2CFQ/sWHp4fY2Pel0aW\nrSuwHZy/pCQFfP9TwABWF/8BLNj7h5K2sG2viM/+cM9tDv7ey82kV4rGfpUGQZAZP9LBvbc5qZ9c\nNKqt4HpC/n99g1ihXge+y6Do68CnxgL5Ta3v+v7qbDgDYWX9d1TVHxrLiqq8qqioqKhERHHNa1U3\nrcXdR3G1iaKILMv5x8FAoaPcwNv3j+Hyv93AY+bARtm/8RAEgZoJEjUToFUTL71wc+9tDs6c13Dm\nvMCpbJFte7Us36BjX4Ym38vZu5uLcSMdvPqxiTWbyzqQJZB5RuCL5Qa+WG7gsbvsXNfJw+TXjHRp\n62H+NBvxsYrd4OedWhal6TlRqlgsiTlTbXi8lLgZzFfP0ZMaPl6q4eOlyiVajUyrPPvDI8O81IyX\nqJ0okWsTeOiZ2LB9wsFokOzlraesdGztxliGlLOSXgehPtj48G9sRVFEqy06EBZuQ+v/4SoY0aay\nBkP1vIZLNKpr0VZztNUL0Vmziko5k5CQQE5OTqFBK9/fo80i4FPS/C0CviPfcCO7/BtzXzMT2MyG\n8v0G2g00GmV1a90k5bq9u3l4ZJiGcxe1nD6nQa8Dg17gvqkxxUZLhUuDFC9vplr5ZrWeYY8rtoON\nOwoa4hiTTOc2Hh4e6qRBspdYs8ylXIHl63V8/5Mem6Poc9Szg4vUBx28/IGJ9RGkHXi8Qr794YG/\nO+h/vZuHno4lKVHm4TuUemJMMrk2gRU/6/h2TeiVrgXIjBnh4P6/O2mYElptLQvBPqBJklToA5E/\ngYs5gg2E+S73nQb4N7G+vwfz34ZKOKjqf4tlRVVeVVRUVFQiwmKxcPny5fyvAxVHqHyLQCgisQhE\ngn9D6qsjUKH1vxwo4qH1XR5rkoiP9dKsoU/RhRXv5HD2vEDWWQ0HjynDYNt+12J3hr8Z7KVxNmon\nwv3TYrmQE7zps9qVyXxf9ixAci2Jazu6eXGsnZo1FL/q4eMiS1fruP92B6fPaRkyvnzyb2vESbz3\ntJXVm7UMnaA01/syKFRPUqJEz45uZjxqp1aiRIxR5vhpkaWr9azZrM23P9RLUtTWTm3cmAwRl1Ys\nvt+x/+9Uq9XmK/yhlPpIB8LCSTiIRipkPWxJqOthK4loqzna6oWoq1ndsBW9VOcNWwADBgzgq6++\nCqrslKVpjXQzlj/BVs361+ZrIAKHbAItAhVNqCYmGIF2g8A6XW44fU6xG2Rli/y6S0v6z8FX3XZq\n7ebpR+289ZmR5Rsi3QymxGM9OkxRRjNPi1hiZEQBft2l4YsVBo5nle33+dAddvpe7WbCrJhSbfIS\nBJmm9SV65627TbDIxMXKJNeUaFS3fNXWYPjsJ77fZ0mvreIGwoIRzPsaqqENhiAI6PVYZko2AAAg\nAElEQVT6Kv9gGUilbthSUVFRUflrIcsyiYmJ3HLLLXz66afUrFkTqD4WgWD4v9n7NxaltQiUJ/5N\nqE8FDlV/KLuB7zHpdQINkr00SFa+f+v1LibeZ1dW3Z71rbrVcOsNHi5cFhg20VIKlTY0ZqPEe89Y\n2XNYw22PWfDmLVkwG5V4rH/c7qRRimI3CPd4v2aCxLvTc0nbpGPY4xZKm8QgywKHj2s4fFxDnTUS\n86bl0r65G7MxkkcaHoE2gXCU/LIMhAUuRAil0ILyYS7QulDV/05LS5UorytXrpT7PhZlaQMqKn8C\nVOU1eqmuyuu+ffuYMmUKa9asAWD8+PE8/vjjEaul5aG8VpVFIBJ8CnDhJQjaQopaMLtBMEpSZyUJ\nsi+InDkvkpUtsv+IYjfYsU8bdo6rP/cMcHB7Xzepr5nC2l7lO96/obOHWokSJoPMkZMiS1YaWLdN\n2cb12F12enb0MOE/MWHl0YZG5h+DnTwyzE7juqGfs/Ii8PcoCEL+77E876OkQTAf/o2wrwEWRRGD\nwYDdbsdorIROvpSoyquKioqKSrmzZ88ebrzxRrxeL1qtlqeffpp77723ylWc4t7IfQ1gSSkCVUGg\nShcq3SCwzrIOgwkCJNWUSKop0a459OsBDw62c+a8htPnBbLOaNi4U1viqtsacRLvPm1l/bbSZaye\nOS/y9UoDX6805NUn07yhRJ/ubh6+007DZCXd4IefdJhNZd8MVruGxJypuXRpY8dkkHC7C6vUvuem\nvCiL2loWinstBPNS+9ti7HY7r7zyCrm5uWzYsIEFCxbQtm3bcq2vIlFzXsMlyryNQPTVHG31QnTW\nrKJSTrRp04brrruOJk2acPDgQUaMGFHoeLKyKUl9gqL+1+qitkZiXShpGKyk7Fl/hdZoEGiY4qVh\nCsht3PztOi+T7hM5d1HLqXMix7K0rNio4+edWi5eFhkzws41HTyMfclM5plI1XaBA0c19L/ehSAI\n3DEhlpxcgY6tPdw9wEXjeg4sZhm7E1Zs1LF0tZ4ca/HP0X0DHTx6l52Gya4iQ3GBR+2BSnXp6694\ntbUkQiUc+FtQ3G43ffr04ciRI/nXue666+jbty9ffvllpdUaCaryqqKioqJSJgRB4Msvv0Sr1fLA\nAw9w6dKlKjt+LM4iAIT0j/pPY5d0zF5RNfs31OXRTJekyIWaaPf/ed/3AOJiJGrEybRoLCIIHkbk\nrbq9bBUwGmDhCj1JiRKnz4l4vGWvO6WW4kddskrP3ZMLtoP9vFPHz37rXGslSFzTwc300XaSEpV0\ng2OnlDSBtVuUNIHEeIm3nrLS4yo3MSYZX7sTSqUO9jyU5vUQ2CBWhw9FUPC4/IfFLly4QJs2bbjt\nttsARVDcvn079erVq8pSS4Wa8xou0aiuRVvN0VYvRGfNKn860tPTmTp1KpIkcc899zB27Ngi10lN\nTSU9PR2z2czcuXNp3749TqeTAQMG4Ha78Xg8DBw4kMmTJwOKJWDChAnYbDYaNmzI22+/TWxsbJHb\n9W0F8q2IrVOnTrk/Pt/kdKjvBaqtvkbDt8oz8Cg+0PtX0jF7ea3k9Cew2alolS4we7a4AaBgTb7/\n9zUaIW/VrfK9iffZ81bdipzKFjl5VmT9Vi2rN+vCXnX7+P02rmzh5cHpsWRfLF5Nzb4osnSNgaVr\nCuwGVzSQ6NXVzbBbbLRp6sVslGhcr6i3NZhKHep5KMl24SNUBFZVExiTpdVq+e6775g3bx7/+c9/\nuOqqq/K/J0kSVqu1KsosE6ryqqKiohLFSJLE5MmTWbJkCcnJyfTp04f+/fvTokWL/OukpaWRkZHB\nli1b2LJlCxMmTCAtLQ2DwcDSpUsxm814vV5uueUW+vbtS+fOnRk7dizPPfcc3bt359NPP2X27NlM\nmTIlZB1xcXGFsl4jpaQmLpRFoDQpAuFmrha3EassEWDFDWRVFv6NbKi6/Ak20e7/XCirbr00zoue\nGtynYNXtqWyRP05o+HGjjl9/K7zqtn4dL3OmWlm0wsDMD81leiyyLHDomIbsCwI3dnXTINmLJSY8\n60rg86DcXukyeH1UF+90MPuCy+XiiSeeQBRFFi1aVOSDqCiKWCyWqii3TKie13CJRm9jtNUcbfVC\ndNas8qdi69atNG3alAYNGgAwePBgli1bVqh5XbZsGcOGDQOgS5cu5OTkcObMGZKSkjCblYbB6XTi\n9Xrz33gPHTpE9+7dAbjhhht48803i21eLRZLyBWx5U0oi4CvoSrtwEx5DEGFo86GM5BVFQTz3Poa\n6nCP2YOpkv6rbm/s6lt1K3L6vKLQWm0CjetJ3DslljPnI1Mq7+jnZNIoO80aRp7bWpLtIlRusK/B\nr2z7SWANga/93bt3k5qayujRoxk0aFCl1VKRqMqrioqKShSTlZVVyKtWt25dtm3bVuJ1srKySEpK\nQpIkevXqRUZGBg8++CCdOnUCoHXr1ixbtoz+/fuzZMkSTp48WWwdcXFxhZrX4o76y0o4FgG3253/\nvUiaw5KGoEqjzgLVJkvWn2Ce20AVONxj9lDDYP6NvVYrUDdJom5SwXN12Srw3dwcTmWLZJ4RWf2r\njnVbdWHHYsXFSsyZYuXajm7iYituUNA/qszfM+z/2iqN3aAi/m34/y599zV//nxWr17N+++/T/36\n9cv1PqsS1fMaLtGorkVbzdFWL0RnzSoqfoiiyNq1a8nJyWHkyJHs27ePVq1aMXv2bFJTU5k1axa3\n3HILen3xm5fi4+PL1TbgTzgWgWBH8eXZHEaizgbWXB3U1kDPbbh1lXTMHjgMVlJjb4kBS4yXpvWV\npmtIXwdnzwtkX1SyZw8f17J8vZ6tv2uxOQrXNqiXk9QH7TQvB7U1HAI9pBqNpli7QWka+0heD4HK\nuSiKZGdnM27cOK6++moWLlwYce5ydUNVXlVUVFSimJSUFE6cOJH/9cmTJ0lJSSlynczMzGKvExcX\nx7XXXsvKlStp1aoVzZs3Z9GiRQAcPnyYFStWFFtHfHw8WVlZkT6coARrWstqEShPilNnQ613reqj\n5VCe20ga/cBhMN/9lMZ24ft5r9dLjTioEQetmmjoc7Wb+//uKLTqdvNuLZ3beLmhs4t4S8XHsgXz\nkAYbrittykNgYx/YzIbzmgg2lJWens6rr77K888/T9euXcv8uKszVXJmoXheowzrmqquoPREW83R\nVi9EZ80qfyo6depERkYGx48fx+VysXjxYm655ZZC1+nfvz9ffPEFAJs3byYuLo6kpCTOnTuXf9Rv\nt9tZs2ZNvlc2OzsbUJqNV155hfvvv7/YOuLi4rh06VK5Pa5gjZ/vzd2nEHo8nkJKlk6nq1JV0/9o\n2b9+f4XYh0/59Hg8uN3u/MSHUE1veSBJEm63O79hEkURnU5XIfYF3+9Kq9Wi0+nQ6XRotdoidgn/\n427/Jsz/+dLroEGyl85tPNx6vYtnRtsYeKOzUhrXwOfMt2o13NeY/2tWp9Oh1+vzn4vA14SvSQ58\nTfgaZ//XhU9t9X/9S5LE1KlTWbJkCQsXLvzTNq6gKq8qKioqUY1Go+Hll19myJAh+VFZLVu2ZMGC\nBQCMGjWKfv36kZaWRufOnTGbzcyZMweA06dPM3r06Hw18Pbbb6dfv34ALFq0iPfffx9BELj11lsZ\nMWJEsXWUl22gOlgEyko4A1ml8c6WRYkLRjDlsLI9t6FUyVAJB/7pBoEKdWUo1eGqrWWhLD5i/5/1\n/xlQ/h9w8OBBJk6cyH333cfw4cMjrrG6I1TUJ7ziWLlypdz3sShLG1BR+RNw640uxt2xjj59+lSt\n4U6l1Fy4cKFq1laFyfHjx3n22WeZPXs2QJmO7oOlCPjwz2b1v6w6+EeDTeuXpjkMdcQeSFkGf6rS\nVlEcoRpqn4IYqnnzUZ6e0UCqw3MW6kOOP3v37iU1NRW328358+d5/PHHGTBgAAkJCZVWZ0VSo0aN\nkE+4qryqqKioqESMb0mB/7F5uG/2oVIE/L8ubntWVRFsWr8sjU6kE/3B1NnqoLaGoqTmsDSZq+Wd\nwRs4sV9Vz1lg/YEfkHJzcxkxYgSnT5/Ov86YMWP46KOPSvSn/xlQc17DJRrzPKOt5mirF6KzZhWV\nCiA2Npbc3NxS/UxJFgEIvdY11LFyRUURBbv/itqQVdqJ/mDrXQOPlauz2lpccxhJykNpXhfBJvar\ng6oPRZt9rVbL7t27qVevHi+99BJer5etW7eybds2evToUYWVVh6q8qqioqKiEjGiKJZq0CjYUWhg\nikDgAI/v+5EokpFSEdP64RA40R9KnfXV6E+wJr+yKc+j+OJSHkr7uvDVVh3XuwZr9mVZ5tlnn+XY\nsWN8+eWXJCYmAspykoomnDXUlUWV/HbUnNdKItpqjrZ6ITprVlGpQnxNa7DBpOJSBPyns30T34FT\n7OFMbkcyzV+Z0/ol4Wu+fFmjxdVQ3BR7cb7S8sCnaPoaV59CXZ6qpv/rpyyvC//XWnVpXIOlHBw9\nepQhQ4bQtGlTPvjgg/zGtbLqmTx5Ml999RUbN25k0aJFHDhwoNLuPxBVeVVRUVFRqXDKkiIQjjoX\nriIZiUcy0oGsiqS4ZQPl4Z2NtLaqzuD13W/gcxFsAMr3e67IYbCSCOW7/fzzz/n000957bXXaNmy\nZaXV4yOcNdSViep5DZdo9DZGW83RVi9EZ80qKhWE70g/mEexJItASRFTpakBgvtFw/VI+jdY5TGQ\nVRGEY1+IxDsbiY+4Og6L+WoXRTHo44SC10OwDzoVZUPxJ5jv1mq1MmnSJFJSUli8eDFGo7Hc7zcc\nwllDXZmoyquKioqKSrkQGxuLzWYjJiYmqMoHhY+7K0vRLMkjWVzT4n8bVd2A+SjralcovVINpVNn\nq0PMVCjCqS3UB53ybO7DqU2r1fLrr78yffp0Jk+eTN++fct8239GqqR5VT2vlUS01Rxt9UJ01qyi\nUkFYLBYuXbpETEwMEDreqqwWgfKiuAn2UOkG/kfKFa3AhaIihsXKS531fb86qa0+ginBoZIhgn3Q\ngfCb+9LaDYLVBjBz5kx27drFJ598QlJSUoTPQOSEs4a6Mqn6V5WKioqKyp+CuLg49u/fz7lz5wpd\n7lMGfUpfsKGnqo4l8m/A/C8LzJOtquGnqljtWtJKU39/ZmADVp3U1kjXu5ZmSNCnoLrdblwuV8j1\nrqFqy8rKYtiwYSQmJlabxhXCW0Ndmaie13CJRm9jtNUcbfVCdNasolIB5ObmkpmZyahRoxg6dCiz\nZs0q9MYPVNuhp3DtC4HHyZUx/FRd/KPBFElfakRgU+ar2fd8RLo8oCxU5PMWaL3w3V+4vmr/Gv1r\nW7JkCe+99x6zZs2iXbt2EddZnoRaQ11VqJ5XFRUVFZUyI8syS5cuZerUqZw8eTL/jViSpHylriot\nAsURONkNxdfm34j7fr4sw0/hHidX12ExKPoY/RXq0g7GlffjCTb4VNHKfml81f58/vnnpKenc+LE\nCVJSUliwYAHJyckVVmck9O3bt9p4b1XPa7hEo7oWbTVHW70QnTWrqJQzH330ESdPnqR+/fqMHDmS\nMWPGIMsy33//PXXq1KFTp05A4WP4qm7AymNDViTDT8WpkcGU4PLa3hUp4SiaZRmMKw91NljDX1W5\nrcEeg78aDfDf//6XyZMn53/922+/0bZtWz788EMGDhxYabVGI6ryqqKioqJSZgRB4OWXX2bDhg2c\nOXOGhQsXcujQIQ4fPsy2bdto06YNy5cvR6vVFjpOrmj1LRQVMfTkozTDT6GOkwVBqJYqNRSdiC9J\n0SxuMK681dmqUFvDJVjDL4oiubm53Hrrrdx4440cOHCArVu3smvXLlq1alVhtYwZM4YVK1ZQu3Zt\n1q9fX2H3U9GUe/MqCML7wK3AaVmWrwx2HdXzWklEW83RVi9EZ80qf0rCWd2YmppKeno6ZrOZuXPn\n0r59e5xOJwMGDMgfPBo4cGC+GrR7924mTJiA0+lEp9Mxc+ZMOnbsWOR2mzdvTvPmzQHljXnWrFm4\n3W5iYmJo1KgR48aNo2vXrnTt2pVWrVrlr5INpb6VR/RQMMozTzZcSlJnA4+TAwfG/C+rqkasPP2j\npTleD0edrU5qazACFX6NRsOZM2cYN24cPXv2ZMGCBYVqdTqd6PX6Cqvn7rvv5p///CePPPJIhd1H\nZVARyuuHwJvAxxVw2yoqKioqAfhWNy5ZsoTk5GT69OlD//79C22/SUtLIyMjgy1btrBlyxYmTJhA\nWloaBoOBpUuXYjab8Xq93HLLLfTt25fOnTszffp0UlNT6d27N2lpaUyfPp2lS5cWW4tv0nr48OFM\nnz6dpKQkjh07xqZNm/jkk0/Yu3cvZrOZzp0707VrVzp27FgkWqu8B5/CHciqDIIN+gQqwT5CeWcr\nU62u6IY/EnU22G1VJ3tFsKZ6+fLlzJ79/+3de1SU1/3v8fceUSIxKMZ7tKhYb4goAqHBRFE8x8So\nNXXZpNWUnGoTbUxs1dp4qW0q0Wq99FRjrKZN8jOalqhRm6MH9RdcMScMCcZIEi8lEvCGViQihqgw\n+/wxzHTEAQZh5nke+L7Wcgk4w/NhVPy6n+/+7v/NSy+9RGxs7G3PCw4O9muuhIQETp8+7ddrBEKD\nF69a60NKqfCaHiM9rwFitcxWywvWzCwaHV+ObtyzZw8//OEPAYiNjaWkpISLFy/SoUMHQkJCAOeq\nj+uWPjgLlZKSEgBKSkp8mus4a9YskpKSSEhIcH8sPDyc8PBw9/WvXLnCxx9/TGZmJuvXr6esrIzI\nyEj36qzrOvUt3sy+6am6wwbg9nYDz495roBWXclsqK/LyCkHvq7OVpc50JMNvOWo2sJw48YNFixY\nwPXr19m2bRv33HNPwHM1JtLzKoQQFufL0Y3eHnP+/Hk6dOiAw+EgKSmJvLw8pk6d6t5glZqaysSJ\nE1m0aBFaa/bu3VtrlpYtW95SuHrTunVrRo4cyciRzvax8vJycnJysNvtvPjii+7NX56tBq5b7r5u\n9GmIDVn+4kvfrS+rkf4a02VEe0VNPL+O2lZhq+ud9Wc7StXrVz0p69ixY8ydO5epU6cyceJEv127\nKTGkeP3Tn/4E5/4Lmnd3fsDWBu4a9J9VrGsZzp/N9P63R+DeWebJ48v7ro+ZJU9jy+uZ1Sx5vL1f\ntAauH4Hm3TnxUQVHerVxFw1CgLM4OXjwICUlJUyZMoXjx4/Tt29f/vrXv7J06VLGjBnDzp07mTlz\nJjt27Gjw6wcFBTF48GAGDx7MM888g9aa06dPk5mZydatW/niiy9o2bKlu9UgJiam2lO8Kioq3JvD\nPD+/mXog76QwrGk1si5julwf88YsM2WrU9Pxrt6mO/izwK+qutdu06ZN7N27lw0bNhAeXuNNaVEH\nqurMsQb5pM62gd3VbdhauXKlnrNpdoNf16+suDHHapmtlhcsl/nR4TeYNfF9Ro4cafzyk6iT4uLi\nar9Zf/TRR/zhD3/g7bffBmDNmjUopW7ZtPXLX/6SoUOH8thjjwFw//33s3v37ttO8FmxYgUhISH8\n/Oc/p3v37nz11VfuXwsPDyc/P78hvyyfXblyhezsbDIzM8nOzqasrIz+/fvf0mqwZ88efv/737N5\n82YiIiLcz/Ucz9UYNj1V9/nh9jFd3ngr3sy22urpTl+76gr8quq7OuttU9bly5eZNWsW0dHRzJkz\nh6Ag89zoLigo4IknnuCDDz4wOkqNwsLCqv1N8Nd/p1TlD6+k5zVArJbZannBmplFo+PL0Y0PP/ww\nf//73wFnsRsaGkqHDh0oKipy97WWlZWRkZHh7pXt3Lmz+x+4gwcP0qtXrwB+Vbdq3bo1I0aMYP78\n+Wzbto1du3YxefJkvv76a+bPn09kZCRTp04lPz+fTZs23bL6WJcjO/2huiNKG3JF01V8+XqMqecR\nt67XxCUoKMg0LRau3zvPY3F9fe1cxajrmFvXj6p9z5690a4jf2/evFnrnxHP19H1mKCgIA4ePMjk\nyZN57rnn+PWvf22qwnXatGmMHj2aL7/8kqioKN58802jI90Rf4zK2gIMB+5VShUAi7XWf2vo6wgh\nhHCq7ujG1157DYCUlBRGjRrFvn37GDJkCCEhIaxduxaACxcuMGPGDPdRnxMmTGDUqFGAcwX3hRde\noKKiguDgYFavXm3Ul3iboKAgBg0aRLdu3UhNTaW0tJRWrVoxZcoUbty4waRJkwgODiYmJob4+Hhi\nYmJo1aoV4L0vsqFvI4Pxt+F9HdNVVXl5uSFHunryxwisuszhra39wvXrnpuyKioqWLx4MYWFhaSl\npdGmTZs7zuovGzduNDpCg/BL20BtpG0gQKyW2Wp5wXKZpW3AumpqG2jq5s6dy6VLl3jppZdumYhQ\nUlJCdnY2drud7OxsSktL6devn7vV4L777vNalFUtVOpauJl9yoG3DWNVN0RVFcgxXUYeOFCX9gtw\nTujIz8+nvLychQsX8uMf/5gf/ehHpvh9trqa2gbMs5YthBBC3IGlS5d6vTUbGhpKUlISSUlJgHPD\nzueff47dbmfZsmWcOXOGTp06ER8fT2xsLJGRkbdMNXA9B3w/vtTbTFmz3IKH2jeM1ffQgPoww4ED\nNa3Ouu5OuJw7d47x48dz9uxZAHr16kV2dja9e/cmLi4uYJmbIkOKV+l5DRCrZbZaXrBmZiEaGV97\nCps1a8bAgQMZOHAg06ZNA+DMmTPY7Xa2bdvG7373O3ergWuqgWseZ23Hl7oeY5XV1upaGOpzaEB9\n2i/MXPR7W5W22Wzk5uYSGRnJXXfdRX5+Prm5ueTm5pKQkCDFq5/JyqsQQogmq2vXrnTt2pUf/OAH\nAFy9etXdavDqq69y9epV+vbt616d7dq16y2jmRwOB7m5uXTv3t1dRJt9xFRdb8P7emjAnY7pqmkE\nltGqWw3+8MMPWbFiBQsWLGD48OF88803HD16lKysLBITE/2W5+zZs8yYMYOLFy9is9l48sknefrp\np/12PbMypHg9cuQIYLE5kxbrbQSsl9lqecGamYUQ1brnnnsYPnw4w4cPB5xtA1988QV2u53ly5dz\n+vRpOnbsSHx8PAMHDiQjI4O1a9fywgsv8MwzzwD/WUU0w6Ynf2wY83V1trYZq8Att+LNtNoK3ntv\nHQ4Hy5Yt48SJE2zdupV27doBEBISQkJCQq0HdNRXUFAQS5YsISoqitLSUkaMGEFSUtItp+k1BbLy\nKoQQQlSjWbNmREVFERUVxdSpUwHn6teWLVtISUmhuLgYgJycHN5//32io6MJDQ0Fam81CORJT/7e\n9HSnhyh4Pt+zz9Ro3laDT58+zfPPP8/48eNZsGCBIUV2x44d6dixIwCtWrWid+/enD9/XorXQJCe\n1wCxWmar5QVrZhZC1Evnzp3ZsWMHxcXFREREsHTpUpo3b47dbmfjxo3uVgPXVANvrQbgn6NLjR7P\n5VLdmK6qUw5cXKucruf6Y3SZL7y9fkFBQaSlpfH666+zatUq+vXrF7A8NSkoKCAnJ4chQ4YYHSXg\nZOVVCCFEne3fv58FCxa458p6nubV2NlsNlatWkV6ejpz586lZcuWAAwbNgxwFmjHjh0jMzOTFStW\nUFBQQIcOHdx9swMGDHAfYduQR5ea+ZQs1yleVTc9ebYP1DZj1d8r1t7aBMrKyvjVr35FWFgY27dv\nd/9eG620tJSUlBSWLl3qnl/clMicV19ZsbfRapmtlhcsl1nmvFqXmea8OhwO4uLieOedd+jUqRMj\nR45k06ZNT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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import scipy.stats as stats\n", + "from IPython.core.pylabtools import figsize\n", + "import numpy as np\n", + "figsize(12.5, 4)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "jet = plt.cm.jet\n", + "fig = plt.figure()\n", + "x = y = np.linspace(0, 5, 100)\n", + "X, Y = np.meshgrid(x, y)\n", + "\n", + "plt.subplot(121)\n", + "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", + "uni_y = stats.uniform.pdf(y, loc=0, scale=5)\n", + "M = np.dot(uni_x[:, None], uni_y[None, :])\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", + "\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "plt.title(\"Landscape formed by Uniform priors.\")\n", + "\n", + "ax = fig.add_subplot(122, projection='3d')\n", + "ax.plot_surface(X, Y, M, cmap=plt.cm.jet, vmax=1, vmin=-.15)\n", + "ax.view_init(azim=390)\n", + "plt.title(\"Uniform prior landscape; alternate view\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, if the two priors are $\\text{Exp}(3)$ and $\\text{Exp}(10)$, then the space is all positive numbers on the 2-D plane, and the surface induced by the priors looks like a water fall that starts at the point (0,0) and flows over the positive numbers. \n", + "\n", + "The plots below visualize this. The more dark red the color, the more prior probability is assigned to that location. Conversely, areas with darker blue represent that our priors assign very low probability to that location. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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5e+21F59++inr169n27ZtAIwePZpIJMJ5553H/Pnz+eGHH1iwYAF33XUXn376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\nUJfu3Wuybdt5li//O+J4lSopyMpqzo03akotpozGb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zzC3z1CQUEOXKixoXGH9C60LkEe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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "fig = plt.figure()\n", + "plt.subplot(121)\n", + "\n", + "exp_x = stats.expon.pdf(x, scale=3)\n", + "exp_y = stats.expon.pdf(x, scale=10)\n", + "M = np.dot(exp_x[:, None], exp_y[None, :])\n", + "CS = plt.contour(X, Y, M)\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "#plt.xlabel(\"prior on $p_1$\")\n", + "#plt.ylabel(\"prior on $p_2$\")\n", + "plt.title(\"$Exp(3), Exp(10)$ prior landscape\")\n", + "\n", + "ax = fig.add_subplot(122, projection='3d')\n", + "ax.plot_surface(X, Y, M, cmap=jet)\n", + "ax.view_init(azim=390)\n", + "plt.title(\"$Exp(3), Exp(10)$ prior landscape; \\nalternate view\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These are simple examples in 2D space, where our brains can understand surfaces well. In practice, spaces and surfaces generated by our priors can be much higher dimensional. \n", + "\n", + "If these surfaces describe our *prior distributions* on the unknowns, what happens to our space after we incorporate our observed data $X$? The data $X$ does not change the space, but it changes the surface of the space by *pulling and stretching the fabric of the prior surface* to reflect where the true parameters likely live. More data means more pulling and stretching, and our original shape becomes mangled or insignificant compared to the newly formed shape. Less data, and our original shape is more present. Regardless, the resulting surface describes the *posterior distribution*. \n", + "\n", + "Again I must stress that it is, unfortunately, impossible to visualize this in large dimensions. For two dimensions, the data essentially *pushes up* the original surface to make *tall mountains*. The tendency of the observed data to *push up* the posterior probability in certain areas is checked by the prior probability distribution, so that less prior probability means more resistance. Thus in the double-exponential prior case above, a mountain (or multiple mountains) that might erupt near the (0,0) corner would be much higher than mountains that erupt closer to (5,5), since there is more resistance (low prior probability) near (5,5). The peak reflects the posterior probability of where the true parameters are likely to be found. Importantly, if the prior has assigned a probability of 0, then no posterior probability will be assigned there. \n", + "\n", + "Suppose the priors mentioned above represent different parameters $\\lambda$ of two Poisson distributions. We observe a few data points and visualize the new landscape: " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "observed (2-dimensional,sample size = 1): [[0 2]]\n" + ] + } + ], + "source": [ + "# create the observed data\n", + "\n", + "# sample size of data we observe, trying varying this (keep it less than 100 ;)\n", + "N = 1\n", + "\n", + "# the true parameters, but of course we do not see these values...\n", + "lambda_1_true = 1\n", + "lambda_2_true = 3\n", + "\n", + "#...we see the data generated, dependent on the above two values.\n", + "data = np.concatenate([\n", + " stats.poisson.rvs(lambda_1_true, size=(N, 1)),\n", + " stats.poisson.rvs(lambda_2_true, size=(N, 1))\n", + "], axis=1)\n", + "print(\"observed (2-dimensional,sample size = %d):\" % N, data)\n", + "\n", + "# plotting details.\n", + "x = y = np.linspace(.01, 5, 100)\n", + "likelihood_x = np.array([stats.poisson.pmf(data[:, 0], _x)\n", + " for _x in x]).prod(axis=1)\n", + "likelihood_y = np.array([stats.poisson.pmf(data[:, 1], _y)\n", + " for _y in y]).prod(axis=1)\n", + "L = np.dot(likelihood_x[:, None], likelihood_y[None, :])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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EEMWT6yOjgT7QsUj4qu9eFgn57AYu+ixSsbKyAq0Uc37RmUzKyJSy5ffkLEVT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NRZU4ksaywLMrb3jGuGROuFX3NHW8D/TBkQa/d7wumRmkoZgCXtHMK0iRJQwr6ZyYKPBw/w79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\nmSRHhiT7zJE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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 12)\n", + "# matplotlib heavy lifting below, beware!\n", + "plt.subplot(221)\n", + "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", + "uni_y = stats.uniform.pdf(x, loc=0, scale=5)\n", + "M = np.dot(uni_x[:, None], uni_y[None, :])\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "plt.title(\"Landscape formed by Uniform priors on $p_1, p_2$.\")\n", + "\n", + "plt.subplot(223)\n", + "plt.contour(x, y, M * L)\n", + "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "plt.title(\"Landscape warped by %d data observation;\\n Uniform priors on $p_1, p_2$.\" % N)\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "\n", + "plt.subplot(222)\n", + "exp_x = stats.expon.pdf(x, loc=0, scale=3)\n", + "exp_y = stats.expon.pdf(x, loc=0, scale=10)\n", + "M = np.dot(exp_x[:, None], exp_y[None, :])\n", + "\n", + "plt.contour(x, y, M)\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "plt.title(\"Landscape formed by Exponential priors on $p_1, p_2$.\")\n", + "\n", + "plt.subplot(224)\n", + "# This is the likelihood times prior, that results in the posterior.\n", + "plt.contour(x, y, M * L)\n", + "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.title(\"Landscape warped by %d data observation;\\n Exponential priors on \\\n", + "$p_1, p_2$.\" % N)\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot on the left is the deformed landscape with the $\\text{Uniform}(0,5)$ priors, and the plot on the right is the deformed landscape with the exponential priors. Notice that the posterior landscapes look different from one another, though the data observed is identical in both cases. The reason is as follows. Notice the exponential-prior landscape, bottom right figure, puts very little *posterior* weight on values in the upper right corner of the figure: this is because *the prior does not put much weight there*. On the other hand, the uniform-prior landscape is happy to put posterior weight in the upper-right corner, as the prior puts more weight there. \n", + "\n", + "Notice also the highest-point, corresponding the the darkest red, is biased towards (0,0) in the exponential case, which is the result from the exponential prior putting more prior weight in the (0,0) corner.\n", + "\n", + "The black dot represents the true parameters. Even with 1 sample point, the mountains attempts to contain the true parameter. Of course, inference with a sample size of 1 is incredibly naive, and choosing such a small sample size was only illustrative. \n", + "\n", + "It's a great exercise to try changing the sample size to other values (try 2,5,10,100?...) and observing how our \"mountain\" posterior changes. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exploring the landscape using the MCMC\n", + "\n", + "We should explore the deformed posterior space generated by our prior surface and observed data to find the posterior mountain. However, we cannot naively search the space: any computer scientist will tell you that traversing $N$-dimensional space is exponentially difficult in $N$: the size of the space quickly blows-up as we increase $N$ (see [the curse of dimensionality](http://en.wikipedia.org/wiki/Curse_of_dimensionality)). What hope do we have to find these hidden mountains? The idea behind MCMC is to perform an intelligent search of the space. To say \"search\" implies we are looking for a particular point, which is perhaps not an accurate as we are really looking for a broad mountain. \n", + "\n", + "Recall that MCMC returns *samples* from the posterior distribution, not the distribution itself. Stretching our mountainous analogy to its limit, MCMC performs a task similar to repeatedly asking \"How likely is this pebble I found to be from the mountain I am searching for?\", and completes its task by returning thousands of accepted pebbles in hopes of reconstructing the original mountain. In MCMC and PyMC3 lingo, the returned sequence of \"pebbles\" are the samples, cumulatively called the *traces*. \n", + "\n", + "When I say MCMC intelligently searches, I really am saying MCMC will *hopefully* converge towards the areas of high posterior probability. MCMC does this by exploring nearby positions and moving into areas with higher probability. Again, perhaps \"converge\" is not an accurate term to describe MCMC's progression. Converging usually implies moving towards a point in space, but MCMC moves towards a *broader area* in the space and randomly walks in that area, picking up samples from that area.\n", + "\n", + "#### Why Thousands of Samples?\n", + "\n", + "At first, returning thousands of samples to the user might sound like being an inefficient way to describe the posterior distributions. I would argue that this is extremely efficient. Consider the alternative possibilities:\n", + "\n", + "1. Returning a mathematical formula for the \"mountain ranges\" would involve describing a N-dimensional surface with arbitrary peaks and valleys.\n", + "2. Returning the \"peak\" of the landscape, while mathematically possible and a sensible thing to do as the highest point corresponds to most probable estimate of the unknowns, ignores the shape of the landscape, which we have previously argued is very important in determining posterior confidence in unknowns. \n", + "\n", + "Besides computational reasons, likely the strongest reason for returning samples is that we can easily use *The Law of Large Numbers* to solve otherwise intractable problems. I postpone this discussion for the next chapter. With the thousands of samples, we can reconstruct the posterior surface by organizing them in a histogram. \n", + "\n", + "\n", + "### Algorithms to perform MCMC\n", + "\n", + "There is a large family of algorithms that perform MCMC. Most of these algorithms can be expressed at a high level as follows: (Mathematical details can be found in the appendix.)\n", + "\n", + "1. Start at current position.\n", + "2. Propose moving to a new position (investigate a pebble near you).\n", + "3. Accept/Reject the new position based on the position's adherence to the data and prior distributions (ask if the pebble likely came from the mountain).\n", + "4. 1. If you accept: Move to the new position. Return to Step 1.\n", + " 2. Else: Do not move to new position. Return to Step 1. \n", + "5. After a large number of iterations, return all accepted positions.\n", + "\n", + "This way we move in the general direction towards the regions where the posterior distributions exist, and collect samples sparingly on the journey. Once we reach the posterior distribution, we can easily collect samples as they likely all belong to the posterior distribution. \n", + "\n", + "If the current position of the MCMC algorithm is in an area of extremely low probability, which is often the case when the algorithm begins (typically at a random location in the space), the algorithm will move in positions *that are likely not from the posterior* but better than everything else nearby. Thus the first moves of the algorithm are not reflective of the posterior.\n", + "\n", + "In the above algorithm's pseudocode, notice that only the current position matters (new positions are investigated only near the current position). We can describe this property as *memorylessness*, i.e. the algorithm does not care *how* it arrived at its current position, only that it is there. \n", + "\n", + "### Other approximation solutions to the posterior\n", + "Besides MCMC, there are other procedures available for determining the posterior distributions. A Laplace approximation is an approximation of the posterior using simple functions. A more advanced method is [Variational Bayes](http://en.wikipedia.org/wiki/Variational_Bayesian_methods). All three methods, Laplace Approximations, Variational Bayes, and classical MCMC have their pros and cons. We will only focus on MCMC in this book. That being said, my friend Imri Sofar likes to classify MCMC algorithms as either \"they suck\", or \"they really suck\". He classifies the particular flavour of MCMC used by PyMC3 as just *sucks* ;)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Unsupervised Clustering using a Mixture Model\n", + "\n", + "\n", + "Suppose we are given the following dataset:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 115.85679142 152.26153716 178.87449059 162.93500815 107.02820697\n", + " 105.19141146 118.38288501 125.3769803 102.88054011 206.71326136] ...\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "data = np.loadtxt(\"data/mixture_data.csv\", delimiter=\",\")\n", + "\n", + "plt.hist(data, bins=20, color=\"k\", histtype=\"stepfilled\", alpha=0.8)\n", + "plt.title(\"Histogram of the dataset\")\n", + "plt.ylim([0, None]);\n", + "print(data[:10], \"...\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What does the data suggest? It appears the data has a bimodal form, that is, it appears to have two peaks, one near 120 and the other near 200. Perhaps there are *two clusters* within this dataset. \n", + "\n", + "This dataset is a good example of the data-generation modeling technique from last chapter. We can propose *how* the data might have been created. I suggest the following data generation algorithm: \n", + "\n", + "1. For each data point, choose cluster 1 with probability $p$, else choose cluster 2. \n", + "2. Draw a random variate from a Normal distribution with parameters $\\mu_i$ and $\\sigma_i$ where $i$ was chosen in step 1.\n", + "3. Repeat.\n", + "\n", + "This algorithm would create a similar effect as the observed dataset, so we choose this as our model. Of course, we do not know $p$ or the parameters of the Normal distributions. Hence we must infer, or *learn*, these unknowns.\n", + "\n", + "Denote the Normal distributions $\\text{N}_0$ and $\\text{N}_1$ (having variables' index start at 0 is just Pythonic). Both currently have unknown mean and standard deviation, denoted $\\mu_i$ and $\\sigma_i, \\; i =0,1$ respectively. A specific data point can be from either $\\text{N}_0$ or $\\text{N}_1$, and we assume that the data point is assigned to $\\text{N}_0$ with probability $p$.\n", + "\n", + "\n", + "An appropriate way to assign data points to clusters is to use a PyMC3 `Categorical` stochastic variable. Its parameter is a $k$-length array of probabilities that must sum to one and its `value` attribute is a integer between 0 and $k-1$ randomly chosen according to the crafted array of probabilities (In our case $k=2$). *A priori*, we do not know what the probability of assignment to cluster 1 is, so we form a uniform variable on $(0, 1)$. We call call this $p_1$, so the probability of belonging to cluster 2 is therefore $p_2 = 1 - p_1$.\n", + "\n", + "Unfortunately, we can't we just give `[p1, p2]` to our `Categorical` variable. PyMC3 uses Theano under the hood to construct the models so we need to use `theano.tensor.stack()` to combine $p_1$ and $p_2$ into a vector that it can understand. We pass this vector into the `Categorical` variable as well as the `testval` parameter to give our variable an idea of where to start from." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to p and added transformed p_interval_ to model.\n", + "prior assignment, with p = 0.50:\n", + "[0 0 0 0 1 1 1 0 0 1]\n" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "import theano.tensor as T\n", + "\n", + "with pm.Model() as model:\n", + " p1 = pm.Uniform('p', 0, 1)\n", + " p2 = 1 - p1\n", + " p = T.stack([p1, p2])\n", + " assignment = pm.Categorical(\"assignment\", p, \n", + " shape=data.shape[0],\n", + " testval=np.random.randint(0, 2, data.shape[0]))\n", + " \n", + "print(\"prior assignment, with p = %.2f:\" % p1.tag.test_value)\n", + "print(assignment.tag.test_value[:10])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above dataset, I would guess that the standard deviations of the two Normals are different. To maintain ignorance of what the standard deviations might be, we will initially model them as uniform on 0 to 100. We will include both standard deviations in our model using a single line of PyMC3 code:\n", + "\n", + " sds = pm.Uniform(\"sds\", 0, 100, shape=2)\n", + "\n", + "Notice that we specified `shape=2`: we are modeling both $\\sigma$s as a single PyMC3 variable. Note that this does not induce a necessary relationship between the two $\\sigma$s, it is simply for succinctness.\n", + "\n", + "We also need to specify priors on the centers of the clusters. The centers are really the $\\mu$ parameters in these Normal distributions. Their priors can be modeled by a Normal distribution. Looking at the data, I have an idea where the two centers might be — I would guess somewhere around 120 and 190 respectively, though I am not very confident in these eyeballed estimates. Hence I will set $\\mu_0 = 120, \\mu_1 = 190$ and $\\sigma_0 = \\sigma_1 = 10$." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to sds and added transformed sds_interval_ to model.\n", + "Random assignments: [0 0 0 0] ...\n", + "Assigned center: [ 120. 120. 120. 120.] ...\n", + "Assigned standard deviation: [ 50. 50. 50. 50.]\n" + ] + } + ], + "source": [ + "with model:\n", + " sds = pm.Uniform(\"sds\", 0, 100, shape=2)\n", + " centers = pm.Normal(\"centers\", \n", + " mu=np.array([120, 190]), \n", + " sd=np.array([10, 10]), \n", + " shape=2)\n", + " \n", + " center_i = pm.Deterministic('center_i', centers[assignment])\n", + " sd_i = pm.Deterministic('sd_i', sds[assignment])\n", + " \n", + " # and to combine it with the observations:\n", + " observations = pm.Normal(\"obs\", mu=center_i, sd=sd_i, observed=data)\n", + " \n", + "print(\"Random assignments: \", assignment.tag.test_value[:4], \"...\")\n", + "print(\"Assigned center: \", center_i.tag.test_value[:4], \"...\")\n", + "print(\"Assigned standard deviation: \", sd_i.tag.test_value[:4])\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice how we continue to build the model within the context of `Model()`. This automatically adds the variables that we create to our model. As long as we work within this context we will be working with the same variables that we have already defined.\n", + "\n", + "Similarly, any sampling that we do within the context of `Model()` will be done only on the model whose context in which we are working. We will tell our model to explore the space that we have so far defined by defining the sampling methods, in this case `Metropolis()` for our continuous variables and `ElemwiseCategorical()` for our categorical variable. We will use these sampling methods together to explore the space by using `sample( iterations, step )`, where `iterations` is the number of steps you wish the algorithm to perform and `step` is the way in which you want to handle those steps. We use our combination of `Metropolis()` and `ElemwiseCategorical()` for the `step` and sample 25000 `iterations` below.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 25000 of 25000 in 130.7 sec. | SPS: 191.3 | ETA: 0.0" + ] + } + ], + "source": [ + "with model:\n", + " step1 = pm.Metropolis(vars=[p, sds, centers])\n", + " step2 = pm.ElemwiseCategorical(vars=[assignment])\n", + " trace = pm.sample(25000, step=[step1, step2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have stored the paths of all our variables, or \"traces\", in the `trace` variable. These paths are the routes the unknown parameters (centers, precisions, and $p$) have taken thus far. The individual path of each variable is indexed by the PyMC3 variable `name` that we gave that variable when defining it within our model. For example, `trace[\"sds\"]` will return a `numpy array` object that we can then index and slice as we would any other `numpy array` object. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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duJUZH+3lvpXZlNfa3LYpdy4Oj/1w1EWD+sqGY9TZHG79dz/YfoJ6u4N7vz7E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A/2YLRURGkyahBa3HgFhmyaj8aqal5mierQCp3/7z+KfQN+9+ZyZ5eNes99F0lfeINhml01HIAy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\nXWRtcALV72xO2+/mWD1+cs4iDk8sOtbkw9ep98h9Ll3zwobt7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NpCE62AUXMvohxiY42f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\nOpR5pvz4mRGT9axCmUTsJsUDoc/SWi3UPNJrpOOLNk/G9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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 9)\n", + "plt.subplot(311)\n", + "lw = 1\n", + "center_trace = trace[\"centers\"]\n", + "\n", + "# for pretty colors later in the book.\n", + "colors = [\"#348ABD\", \"#A60628\"] if center_trace[-1, 0] > center_trace[-1, 1] \\\n", + " else [\"#A60628\", \"#348ABD\"]\n", + "\n", + "plt.plot(center_trace[:, 0], label=\"trace of center 0\", c=colors[0], lw=lw)\n", + "plt.plot(center_trace[:, 1], label=\"trace of center 1\", c=colors[1], lw=lw)\n", + "plt.title(\"Traces of unknown parameters\")\n", + "leg = plt.legend(loc=\"upper right\")\n", + "leg.get_frame().set_alpha(0.7)\n", + "\n", + "plt.subplot(312)\n", + "std_trace = trace[\"sds\"]\n", + "plt.plot(std_trace[:, 0], label=\"trace of standard deviation of cluster 0\",\n", + " c=colors[0], lw=lw)\n", + "plt.plot(std_trace[:, 1], label=\"trace of standard deviation of cluster 1\",\n", + " c=colors[1], lw=lw)\n", + "plt.legend(loc=\"upper left\")\n", + "\n", + "plt.subplot(313)\n", + "p_trace = trace[\"p\"]\n", + "plt.plot(p_trace, label=\"$p$: frequency of assignment to cluster 0\",\n", + " color=colors[0], lw=lw)\n", + "plt.xlabel(\"Steps\")\n", + "plt.ylim(0, 1)\n", + "plt.legend();\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the following characteristics:\n", + "\n", + "1. The traces converges, not to a single point, but to a *distribution* of possible points. This is *convergence* in an MCMC algorithm.\n", + "2. Inference using the first few thousand points is a bad idea, as they are unrelated to the final distribution we are interested in. Thus is it a good idea to discard those samples before using the samples for inference. We call this period before converge the *burn-in period*.\n", + "3. The traces appear as a random \"walk\" around the space, that is, the paths exhibit correlation with previous positions. This is both good and bad. We will always have correlation between current positions and the previous positions, but too much of it means we are not exploring the space well. This will be detailed in the Diagnostics section later in this chapter.\n", + "\n", + "\n", + "To achieve further convergence, we will perform more MCMC steps. In the pseudo-code algorithm of MCMC above, the only position that matters is the current position (new positions are investigated near the current position), implicitly stored as part of the `trace` object. To continue where we left off, we pass the `trace` that we have already stored into the `sample()` function with the same step value. The values that we have already calculated will not be overwritten. This ensures that our sampling continues where it left off in the same way that it left off. \n", + "\n", + "We will sample the MCMC fifty thousand more times and visualize the progress below:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 50000 of 50000 in 215.4 sec. | SPS: 232.2 | ETA: 0.0" + ] + } + ], + "source": [ + "with model:\n", + " trace = pm.sample(50000, step=[step1, step2], trace=trace)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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n+OwPsRVb8JYjz7zlUstnKywyPK/lxNxPiPz0R6/TKxWlaDtGdVuQ6OzF41Lm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\n/p/ZPmTratBeFy/I9GJFKlsyd/VwSxpX2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MMwTA3AFneGYRiGYRiGqQFYcWcYhmEYhmGY\nGoAVd4ZhGIZhGIapAVhxZxiGYRiGYZgagBV3hmEYhmEYhqkBWHFnGIZhGIZhmBrg/wNjwpxpUzh+\nXQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "center_trace = trace[\"centers\"][25000:]\n", + "prev_center_trace = trace[\"centers\"][:25000]\n", + "\n", + "x = np.arange(25000)\n", + "plt.plot(x, prev_center_trace[:, 0], label=\"previous trace of center 0\",\n", + " lw=lw, alpha=0.4, c=colors[1])\n", + "plt.plot(x, prev_center_trace[:, 1], label=\"previous trace of center 1\",\n", + " lw=lw, alpha=0.4, c=colors[0])\n", + "\n", + "x = np.arange(25000, 75000)\n", + "plt.plot(x, center_trace[:, 0], label=\"new trace of center 0\", lw=lw, c=\"#348ABD\")\n", + "plt.plot(x, center_trace[:, 1], label=\"new trace of center 1\", lw=lw, c=\"#A60628\")\n", + "\n", + "plt.title(\"Traces of unknown center parameters\")\n", + "leg = plt.legend(loc=\"upper right\")\n", + "leg.get_frame().set_alpha(0.8)\n", + "plt.xlabel(\"Steps\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "#### Cluster Investigation\n", + "\n", + "We have not forgotten our main challenge: identify the clusters. We have determined posterior distributions for our unknowns. We plot the posterior distributions of the center and standard deviation variables below:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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p6RbCbhatwNnW3gI5B7gW2Aa4I5czcJxa8cJ3rikp3SG//35DNg4cp0FwX+A4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\ndV375zcmLSEnVu3dqq5S6a0NyfYyqTllw4mmFnYea8z7OnTKsyM7Tgz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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(11.0, 4)\n", + "std_trace = trace[\"sds\"][25000:]\n", + "prev_std_trace = trace[\"sds\"][:25000]\n", + "\n", + "_i = [1, 2, 3, 4]\n", + "for i in range(2):\n", + " plt.subplot(2, 2, _i[2 * i])\n", + " plt.title(\"Posterior of center of cluster %d\" % i)\n", + " plt.hist(center_trace[:, i], color=colors[i], bins=30,\n", + " histtype=\"stepfilled\")\n", + "\n", + " plt.subplot(2, 2, _i[2 * i + 1])\n", + " plt.title(\"Posterior of standard deviation of cluster %d\" % i)\n", + " plt.hist(std_trace[:, i], color=colors[i], bins=30,\n", + " histtype=\"stepfilled\")\n", + " # plt.autoscale(tight=True)\n", + "\n", + "plt.tight_layout()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The MCMC algorithm has proposed that the most likely centers of the two clusters are near 120 and 200 respectively. Similar inference can be applied to the standard deviation. \n", + "\n", + "We are also given the posterior distributions for the labels of the data point, which is present in `trace[\"assignment\"]`. Below is a visualization of this. The y-axis represents a subsample of the posterior labels for each data point. The x-axis are the sorted values of the data points. A red square is an assignment to cluster 1, and a blue square is an assignment to cluster 0. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Vwpg5lm92EnW5ROD2fWZv3pE1szMp6rc3aFpfQVsssN3iJ9ziI2O2sr65gLP/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QwQ72eITT8SlCIxPIWy1M2RQVrZ6ky0NNo8V3uI33eJ/T8WlOx6eQtVqYMynkrQY5q4PEoId8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\n9Vu8eaakktvWytr9u1l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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib as mpl\n", + "figsize(12.5, 4.5)\n", + "plt.cmap = mpl.colors.ListedColormap(colors)\n", + "plt.imshow(trace[\"assignment\"][::400, np.argsort(data)],\n", + " cmap=plt.cmap, aspect=.4, alpha=.9)\n", + "plt.xticks(np.arange(0, data.shape[0], 40),\n", + " [\"%.2f\" % s for s in np.sort(data)[::40]])\n", + "plt.ylabel(\"posterior sample\")\n", + "plt.xlabel(\"value of $i$th data point\")\n", + "plt.title(\"Posterior labels of data points\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above plot, it appears that the most uncertainty is between 150 and 170. The above plot slightly misrepresents things, as the x-axis is not a true scale (it displays the value of the $i$th sorted data point.) A more clear diagram is below, where we have estimated the *frequency* of each data point belonging to the labels 0 and 1. " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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EQf1IHjmEmKTEQHsutbtLiMtMp6GujujYWBrrGzDnSB4zjMRAx7S+soryVRup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\nW5XNe6+p4F+eqeNg2vuxMD/EvbfWjvmezndVuaEx519VkUV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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cmap = mpl.colors.LinearSegmentedColormap.from_list(\"BMH\", colors)\n", + "assign_trace = trace[\"assignment\"]\n", + "plt.scatter(data, 1 - assign_trace.mean(axis=0), cmap=cmap,\n", + " c=assign_trace.mean(axis=0), s=50)\n", + "plt.ylim(-0.05, 1.05)\n", + "plt.xlim(35, 300)\n", + "plt.title(\"Probability of data point belonging to cluster 0\")\n", + "plt.ylabel(\"probability\")\n", + "plt.xlabel(\"value of data point\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even though we modeled the clusters using Normal distributions, we didn't get just a single Normal distribution that *best* fits the data (whatever our definition of best is), but a distribution of values for the Normal's parameters. How can we choose just a single pair of values for the mean and variance and determine a *sorta-best-fit* gaussian? \n", + "\n", + "One quick and dirty way (which has nice theoretical properties we will see in Chapter 5), is to use the *mean* of the posterior distributions. Below we overlay the Normal density functions, using the mean of the posterior distributions as the chosen parameters, with our observed data:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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6OTmRmpqa55o373vDhg1JTEwE4Pr160ycOBEfHx88PDwICQmxaMe6LMDGjRvp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\nip54OdBOv+hslBrQiuuDasuuHXqH0O0birKX3sB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26T/vvY9hf3uRGOV/SHL8L24lbvJY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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "norm = stats.norm\n", + "x = np.linspace(20, 300, 500)\n", + "posterior_center_means = center_trace.mean(axis=0)\n", + "posterior_std_means = std_trace.mean(axis=0)\n", + "posterior_p_mean = trace[\"p\"].mean()\n", + "\n", + "plt.hist(data, bins=20, histtype=\"step\", normed=True, color=\"k\",\n", + " lw=2, label=\"histogram of data\")\n", + "y = posterior_p_mean * norm.pdf(x, loc=posterior_center_means[0],\n", + " scale=posterior_std_means[0])\n", + "plt.plot(x, y, label=\"Cluster 0 (using posterior-mean parameters)\", lw=3)\n", + "plt.fill_between(x, y, color=colors[1], alpha=0.3)\n", + "\n", + "y = (1 - posterior_p_mean) * norm.pdf(x, loc=posterior_center_means[1],\n", + " scale=posterior_std_means[1])\n", + "plt.plot(x, y, label=\"Cluster 1 (using posterior-mean parameters)\", lw=3)\n", + "plt.fill_between(x, y, color=colors[0], alpha=0.3)\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(\"Visualizing Clusters using posterior-mean parameters\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Important: Don't mix posterior samples\n", + "\n", + "In the above example, a possible (though less likely) scenario is that cluster 0 has a very large standard deviation, and cluster 1 has a small standard deviation. This would still satisfy the evidence, albeit less so than our original inference. Alternatively, it would be incredibly unlikely for *both* distributions to have a small standard deviation, as the data does not support this hypothesis at all. Thus the two standard deviations are *dependent* on each other: if one is small, the other must be large. In fact, *all* the unknowns are related in a similar manner. For example, if a standard deviation is large, the mean has a wider possible space of realizations. Conversely, a small standard deviation restricts the mean to a small area. \n", + "\n", + "During MCMC, we are returned vectors representing samples from the unknown posteriors. Elements of different vectors cannot be used together, as this would break the above logic: perhaps a sample has returned that cluster 1 has a small standard deviation, hence all the other variables in that sample would incorporate that and be adjusted accordingly. It is easy to avoid this problem though, just make sure you are indexing traces correctly. \n", + "\n", + "Another small example to illustrate the point. Suppose two variables, $x$ and $y$, are related by $x+y=10$. We model $x$ as a Normal random variable with mean 4 and explore 500 samples. " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 10000 of 10000 in 0.9 sec. | SPS: 11550.9 | ETA: 0.0" + ] + }, + { + "data": { + "image/png": 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rNmPL4+MdRQBw2yK+fewUzKnVCwvbDsSOse9j04ixruS7550vkbpgJTYMH+NK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\nxZaP0xsr/LPQ0Wbi0xbl8WeKtNjte+BF2DBiuD+RKFJEhNs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AwBZM59YKtKhh37+L7Cff\npGfo9RJo3sOQlEQqRUKAHm94e4GiQaMyZo5Y+CGO/O97dFeSKKTAFhqM8PROiOqTiXoi4FNLKnQa\n1KgxE/csQeOpUkuFBgB6fzFj3JdzUHl64cDZOE2jkV5qSkB4KBIICVoRbURje7pijSSIHtgb1bsP\nOHaLwOYRD0+Xz+aqd1FrBdqFRzwiMx1d5XRlPQFikJHyH9NvblvFWxlEOGbtl6jNLdS8ULAathDn\nqtVM45m1KL3jpY669vrXfYjq1x1haR1UuaMkguNjREmdzEJjcbnpZeoCQ1MmOgOlY8/qr5j8JLJP\nJhpPFiO0o3xaYjVYpQ1OXED1EC2cyKTJY1xBgiRa6xo0VUuKDhdMRIcLJroMcbWdq7BOKbplTi0D\nVcIxWPUYNfjIOt9U0ORiSUT17iar0qGEQR++gOTzx4HjOJGHkkXGUwmczYbzctdg5y1Pomzdn26/\nhyTFyyu42GxUkQDB628Upux4SDpZ0nmjUbFttzHtdQpUBao0Smzq8djLXJgoVGzwBifEoqmsEvGj\nlXdmpBj2/Tuo2LwTSU4pbNm8ErJ1kjSWB1SPWOE1jjgLrI5UZUWnqy7AsW8WI/n8cxAUE4Xxf/4E\nvrVVxGeyGoFRET5lhPd6/n4ULVrLlMVQCr08Tm8iokeGiJLjSbglbwJQtWOfF2qiD6yeh1HLPoG9\nqRmBknTwahxx0nPKmkreCgz9cg6KV6xHpyvlk3tIIWf8NlcbNygAuCgnckG6LCoOSqAlJzMLtEWV\nWqbX9ji2GMHw+e+hubxabLSaOG9yNltbEGvHJPR+8UG01ta5U0Z0LIgCI8LaHDma6sSBphHQ9a6r\ncPj1/2kqS+gvZ33zFnL+7zN0vv4ipF7mTofUCqntMvSrOeBbW93zMkiDn+mFyf7U85l7UL45Cz2e\nuIN+AKOxOfzH92Bvaja8wBIg4ndLd63WfYOqPQfbtL8Z+05wXLQo+VLmQzeibP02ZDAqftGSH/kK\n2oVH3FOQ46PFDR+AiXuWuCYdWkapvxu63nU1upIUAxMHf9YFmCdfJG++tEaCkSwHy7NiHGgDQkPk\nAwcVyrAFBWLEov/C3tikLVGPyUieMsa1bcoC2TTuEOvsD/zwed11Grn0EzSXVyK8Cz2wMPZs5eRX\nchj61RxU7dhnvmIFATJDqQA3w993nFpeAS3Phan+K0mGatlAT40XNZTN2GYDaBoWBnakkyaNcpOs\nMwSJx57jOKoHt89LD2H/swy5CWQQ2bMLJh1cIbsTyDpvac3Gqwax8o24bsGJcUyxdGoISU7AORvU\nc1/I4kz0iFvBEfdEwgQSscPkt80VEx34gbD0VPWDnDDNY6WXhsA6aVjMPWYFjfLU8WJKkKMXwKKy\nY5Sy1demfo24swcauoYiLHr20nTrJPiWtmCv1Iu17zoJCIqOVMz+p3eBmTx5DCVbsrlIv/lSlP62\nBWnXzURYWgcc/+5XUfZkGv5O3nArETdyEKp3HUT0oF5Mx9tb6MGJUvR46k5U7zlkaHc3NCUR9UdP\nmpI7w6r+wpoyPSihTXs/8+GbZXZ89GfzDoqJQks1XcHFUmiQFpRmTPYUOB9axfuwq83zXkjL+aVn\nMBInjkCfVx5B7BAT6DM+Qkki4elFIQkb4RGfdGglyv7YbrkRpIZ+cx5H/n+/QyahYiQHb7adEQQn\nxKK5ugaBZEyAh8YI0iNuJXx5zAvPSMXYdW0JSWhKMb5cf08jqn8PnN57WNGhxIrh8/8Ne30j00Ib\naMuoqIbMB280Ui0AQJ+X/4Hsp95E7+fvN1yWZdCoJgY4krfRYISiO/SL17H30dc93lZa5AvjRjqc\nuGbRYuTgNlb4EDXFtJpkZWWZVVQbPJC5TAT/oK4bHMch45ZLETNEXfF5w4YNpl1TE5wvXqAe+oI3\nqSnENm5QdCQ6zJjgddmuztdfhHEbv0P8SIadMINtl22vRVRfczSztWBC1iJMzlntsUyuJFg9jHog\notb50GSkBZ1vuAgA3BR42MYW31vom4FBH76Ans/chYxbLzdcli0wkNkIBxxZiAFg8MezDV9bDclT\nxmDCXwvQ4cJzDZdl1lwkBXOsCktXNNBdo/p2x6il/7N2x5ACsbKR8hgT2aMLRq+eiwl/LbC6WiL4\nkoPItz3iKg/QjzMTSZNGI7xLJySeayJnD8Dk3DXgW1tEHmZWeNPz5g1D0EwYGfDGbZ2PloWLETdM\nH5fZCGj9JLp/TwSEhyF6UG/D5SvpYfPN1nnEz9kwry0teTt1PvR9/TFkPnQTQlP1K+ycaYjs0UV7\n6nqT0HHWJKTMGO8ejKgCJdqUVnSYMQGHX/kv4seeZVqZetHt/utxOjsHade2D6le00HOWQxjDGte\nET0QMr8mSnjpcgmDvAGf5oh7fJLwoRXSmQw1Xl5AWAjO2fyDuvGr8XE5MrZpiNL3FY64LwdrMkCr\nhBaJ8IxUXPDAnSbWxhgCwkIcwVEGgs0m7FyIxuIyhGfIx1WEd+0EAAiKj5E9Ri/ILWBf8gppAcdx\nVCPczxH3HrQa4YBjQdVcUYX0W4znCInITMe5+5cjKIbduLeqvwTFRmPYPP1BmCK0Q2NdnH7eu2PM\n8PnvobWuHoGR4h2eCC8tWmlgenM4jisAUAXADqCZ53mP6LjVthiT1tKK46ebmVNp+2EtfI376U3V\nFD0TnE+hnRp7ctCzo0IitGMSQjsmKR7T5c6rwdt5pEwbZ+haaqhqtMN4yJsffuhDYEQYzvrmLdPK\nCzYhgNOjaIdGNgtECjFepr9xNpubEQ4YH8fNBGsL2QFM4Hl+iJwRbgVHvKCy0fQylVDVYB0v0482\nmMXLK6/34PPyojHZ/j3ixgZiq3icvozg+Bj0euZuxJqcAESKJkZ1h/aCv2Nf8UM/vN1fmAIx26Gx\nHhgRhh5P3oFe/7zXpwxeEqGpKd6uggusLcTBxMBOVtQ0e9YjzvuYF9YPZVQ2WKssUZtT6PrbzxHX\nj8rGFvjOkOeHCH/HIa8dGjZ+nJkIVMmICtD19NsD5FLVextj132DprJK1V1JT4LVEOcBrOI4rhXA\nxzzPu6WvsoIjHuppfUm/Ie4RtBceZ8qM8dj/tGPb1JsqJTGDeyMkJRHRA6wLaLESFQ3GFtTtpb+0\nR/BnWEA8S19parH/LdcffrjD22NL8tSxSL3sfMWEOslTx6LjpVOQcI51ybP+TpDLMuxNsBriY3ie\nP8lxXBIcBvl+nudFezrz58/HJ598gvT0dABATEwMBgwY4OrowhYQ6+dsey1O1xS5ytd6vp7r1ZYc\n9dj1/J+Nfz6wfy+EfIFWlM/zPFbNugaxZcVoLS5CzIZyr9xvYGQEtj18C+KjQiHoAfhC+6t9zrbX\noq8tAi0c5xP18X8Wj3cAkOl0Pni7Pp78XBqTgJKqU2gMCcP5gNfr4//89/4c//Lj2L9jG/I3bKD+\nzgUEIOfCcSgOCbB0vvN/Fn/es2cPqqqqAACFhYUYNmwYJk2aBCvAaRWL5zjuOQCneZ7/P/L7t956\ni7/llltMqdTyDqMBAK3BIZhR+JspZbJcr/qSWbjigycsv97fHRuIAccIti3eiPLbHwMAnF+0yXB5\nUvyRX4mX1uQDAP7vgh7o38E8qS0tyC+vx50/HwAArLxtiFfqoAfCexXx3zk45yL9CYjM6i9+tEF4\nNt2WzkXPoe1zp4UGlr5y47trMWjpQmwbPxXfPT3dQzXzwxfh7bHleFUDbv5xP0IDbVh00yDqMceq\nGnDLj/sREmjDYplj/LAeO3bswKRJkyzZTFPdl+Q4LpzjuEjn3xEApgDYa0VlpLC1NHviMi7Y/dSU\ndgVPKpl4k1VaUe/Z98AsbB9zLo526QHbAOOa235YgzONmsKCmvhELL/8JpQnd1Q/2A8/LMT+4joA\nQIOCQtwB5zGNHlaRM4rqhhbUNLZ4uxpu+GjLMTy5LAd2H4oVCWQ4JgXAAo7jeOfx3/A8v1J6kJkc\n8d+nXYIJy37G0VkXmVamH74DszwQgQP64ETnrihK6+LaYjYTEcFtRoo339nW9jX+urB+2qUAgH8Z\n0BEHzOsv7Q31za0IDbRZGih8pgWos/SVM+uO/TCCv+vYYjVa7Txu/jEbgTYO867pD5sPjTM/7S0B\nAOSU1qNnknqwrCegaojzPJ8PwIJsPfLYOWoijnfpjozhnlH1Xj/1Igzc9gcqL7zAI9fzwyQEBuC7\nOx8FADxt8aW0UrjMRKsPrdz1wJc8D+0FO45X4+nlubiwTyLuHd3Z9PJbAgMR2NKCgKR408v2ww8t\nOF7VgKTIYAT7UKZDT8GH7FNT0dBix+lGh6pZq52HLcD3brTZhzxcpvV8M3XEeZsNpzplwO4h6sH2\ncybjs0deRGt0lEeu93eHEBihhLU55ThcWqd8kMX2HWk/evOVbWnnWs9Gq8/SXzyJpQdK8dexat3n\n/7j7FF5YlYdWhYZZdrAMdh5YmF2q+zpK+ODpOfjPM3PAhWjINNsO4Gt9xQ9lrMurwM0/7sdLq/MN\nl9Vq5/Hx1uPYeeI08zlW9Ree55F9qha1TcYldtujsU46X7zth9lxvBpf/nXSzZlW5UO0GZ9egnr7\nAfrhHRwqrcNrvx/Bvb8cVDyO12iJLztYhvl7ivVVyot90d7ODXGtz4nE97tO4b2NRxU5lJ7E8aoG\nvLPhKJ5anqu7jP9tO4GNR6qw66S8wWDlVu76/Aq0BAejMSzcqwtMI8gtq8P/rS9st/ETVkFpcWcl\nKuqaMS+rCJUan8fanAoAwNaj+he2AtbklGP+nmI8sTTHcFlGsaWwGg8tPoR7fzmgeBzLW94O7XCR\n88Xbs9eTy3Lx9c4itz5WWus7Y4dphrgVOuKeHlO83WHaO1gnATVe3qnTTWZUxw1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2AAAg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\nk5s0v0AVhcCyGnn67An6XFern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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import pymc3 as pm\n", + "\n", + "with pm.Model() as model:\n", + " x = pm.Normal(\"x\", mu=4, tau=10)\n", + " y = pm.Deterministic(\"y\", 10 - x)\n", + "\n", + " trace_2 = pm.sample(10000, pm.Metropolis())\n", + "\n", + "plt.plot(trace_2[\"x\"])\n", + "plt.plot(trace_2[\"y\"])\n", + "plt.title(\"Displaying (extreme) case of dependence between unknowns\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, the two variables are not unrelated, and it would be wrong to add the $i$th sample of $x$ to the $j$th sample of $y$, unless $i = j$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Returning to Clustering: Prediction\n", + "The above clustering can be generalized to $k$ clusters. Choosing $k=2$ allowed us to visualize the MCMC better, and examine some very interesting plots. \n", + "\n", + "What about prediction? Suppose we observe a new data point, say $x = 175$, and we wish to label it to a cluster. It is foolish to simply assign it to the *closer* cluster center, as this ignores the standard deviation of the clusters, and we have seen from the plots above that this consideration is very important. More formally: we are interested in the *probability* (as we cannot be certain about labels) of assigning $x=175$ to cluster 1. Denote the assignment of $x$ as $L_x$, which is equal to 0 or 1, and we are interested in $P(L_x = 1 \\;|\\; x = 175 )$. \n", + "\n", + "A naive method to compute this is to re-run the above MCMC with the additional data point appended. The disadvantage with this method is that it will be slow to infer for each novel data point. Alternatively, we can try a *less precise*, but much quicker method. \n", + "\n", + "We will use Bayes Theorem for this. If you recall, Bayes Theorem looks like:\n", + "\n", + "$$ P( A | X ) = \\frac{ P( X | A )P(A) }{P(X) }$$\n", + "\n", + "In our case, $A$ represents $L_x = 1$ and $X$ is the evidence we have: we observe that $x = 175$. For a particular sample set of parameters for our posterior distribution, $( \\mu_0, \\sigma_0, \\mu_1, \\sigma_1, p)$, we are interested in asking \"Is the probability that $x$ is in cluster 1 *greater* than the probability it is in cluster 0?\", where the probability is dependent on the chosen parameters.\n", + "\n", + "\\begin{align}\n", + "& P(L_x = 1| x = 175 ) \\gt P(L_x = 0| x = 175 ) \\\\\\\\[5pt]\n", + "& \\frac{ P( x=175 | L_x = 1 )P( L_x = 1 ) }{P(x = 175) } \\gt \\frac{ P( x=175 | L_x = 0 )P( L_x = 0 )}{P(x = 175) }\n", + "\\end{align}\n", + "\n", + "As the denominators are equal, they can be ignored (and good riddance, because computing the quantity $P(x = 175)$ can be difficult). \n", + "\n", + "$$ P( x=175 | L_x = 1 )P( L_x = 1 ) \\gt P( x=175 | L_x = 0 )P( L_x = 0 ) $$\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Probability of belonging to cluster 1: 0.01062\n" + ] + } + ], + "source": [ + "norm_pdf = stats.norm.pdf\n", + "p_trace = trace[\"p\"][25000:]\n", + "prev_p_trace = trace[\"p\"][:25000]\n", + "x = 175\n", + "\n", + "v = p_trace * norm_pdf(x, loc=center_trace[:, 0], scale=std_trace[:, 0]) > \\\n", + " (1 - p_trace) * norm_pdf(x, loc=center_trace[:, 1], scale=std_trace[:, 1])\n", + "\n", + "print(\"Probability of belonging to cluster 1:\", v.mean())\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Giving us a probability instead of a label is a very useful thing. Instead of the naive \n", + "\n", + " L = 1 if prob > 0.5 else 0\n", + "\n", + "we can optimize our guesses using a *loss function*, which the entire fifth chapter is devoted to. \n", + "\n", + "\n", + "### Using `MAP` to improve convergence\n", + "\n", + "If you ran the above example yourself, you may have noticed that our results were not consistent: perhaps your cluster division was more scattered, or perhaps less scattered. The problem is that our traces are a function of the *starting values* of the MCMC algorithm. \n", + "\n", + "It can be mathematically shown that letting the MCMC run long enough, by performing many steps, the algorithm *should forget its initial position*. In fact, this is what it means to say the MCMC converged (in practice though we can never achieve total convergence). Hence if we observe different posterior analysis, it is likely because our MCMC has not fully converged yet, and we should not use samples from it yet (we should use a larger burn-in period ).\n", + "\n", + "In fact, poor starting values can prevent any convergence, or significantly slow it down. Ideally, we would like to have the chain start at the *peak* of our landscape, as this is exactly where the posterior distributions exist. Hence, if we started at the \"peak\", we could avoid a lengthy burn-in period and incorrect inference. Generally, we call this \"peak\" the *maximum a posterior* or, more simply, the *MAP*.\n", + "\n", + "Of course, we do not know where the MAP is. PyMC3 provides a function that will approximate, if not find, the MAP location. In the PyMC3 main namespace is the `find_MAP` function. If you call this function within the context of `Model()`, it will calculate the MAP which you can then pass to `pm.sample()` as a `start` parameter.\n", + "\n", + " start = pm.find_MAP()\n", + " trace = pm.sample(2000, step=pm.Metropolis, start=start)\n", + "\n", + "The `find_MAP()` function has the flexibility of allowing the user to choose which optimization algorithm to use (after all, this is a optimization problem: we are looking for the values that maximize our landscape), as not all optimization algorithms are created equal. The default optimization algorithm in function call is the Broyden-Fletcher-Goldfarb-Shanno ([BFGS](https://en.wikipedia.org/wiki/Broyden-Fletcher-Goldfarb-Shanno_algorithm)) algorithm to find the maximum of the log-posterior. As an alternative, you can use other optimization algorithms from the `scipy.optimize` module. For example, you can use Powell's Method, a favourite of PyMC blogger [Abraham Flaxman](http://healthyalgorithms.com/) [1], by calling `find_MAP(fmin=scipy.optimize.fmin_powell)`. The default works well enough, but if convergence is slow or not guaranteed, feel free to experiment with Powell's method or the other algorithms available. \n", + "\n", + "The MAP can also be used as a solution to the inference problem, as mathematically it is the *most likely* value for the unknowns. But as mentioned earlier in this chapter, this location ignores the uncertainty and doesn't return a distribution.\n", + "\n", + "#### Speaking of the burn-in period\n", + "\n", + "It is still a good idea to decide on a burn-in period, even if we are using `find_MAP()` prior to sampling, just to be safe. We can no longer automatically discard sample with a `burn` parameter in the `sample()` function as we could in PyMC2, but it is easy enough to simply discard the beginning section of the trace just through array slicing. As one does not know when the chain has fully converged, a good rule of thumb is to discard the first *half* of your samples, sometimes up to 90% of the samples for longer runs. To continue the clustering example from above, the new code would look something like:\n", + "\n", + " with pm.Model() as model:\n", + " start = pm.find_MAP()\n", + " \n", + " step = pm.Metropolis()\n", + " trace = pm.sample(100000, step=step, start=start)\n", + " \n", + " burned_trace = trace[50000:]\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Diagnosing Convergence\n", + "\n", + "### Autocorrelation\n", + "\n", + "Autocorrelation is a measure of how related a series of numbers is with itself. A measurement of 1.0 is perfect positive autocorrelation, 0 no autocorrelation, and -1 is perfect negative correlation. If you are familiar with standard *correlation*, then autocorrelation is just how correlated a series, $x_\\tau$, at time $t$ is with the series at time $t-k$:\n", + "\n", + "$$R(k) = Corr( x_t, x_{t-k} ) $$\n", + "\n", + "For example, consider the two series:\n", + "\n", + "$$x_t \\sim \\text{Normal}(0,1), \\;\\; x_0 = 0$$\n", + "$$y_t \\sim \\text{Normal}(y_{t-1}, 1 ), \\;\\; y_0 = 0$$\n", + "\n", + "which have example paths like:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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0zDT0eBV9znwIncZd0HjKo55f0quID60ddnrUgyfLE3ntwcIuJ3qu9btZjzpl\nKE2UDCWVrw/iLzmbvF/dj1I41unBLksflDYSs//6GONffgAz1v0bglqtOKbTGCpqiYHlGxOJ5Jsv\nRWSn4waiiIO3P+m2gA/gXioUAEwKUSPacx57wRnymOxwdJs0qFWoqmFt1cJu6r18RAnR4UDVV+6/\nS8vOLMViDk7oCJazFCIgG+h0DXWf8BCEUpNB1xVKRYcD2Ssfxebx5+LQ6uf6FMGkI0u0Rx1gdep0\nRNk/WY68+Ea569SVcgF6KtFIP19DpqbBOyQIcUvPlD9PeZZFixXV30r5UbYOveJvrfWwWkzNN7+T\n6kaapHgkXikvLOXqUW/ZdQA13/55zNp1XS47OQ+ZOp5sO3XqBQ+/CofRDNFuR3U/y99ONJwRQ6Xf\n8VgYdEN9ypQp+LtUNtSXTYiCj1rAsHL5pgufJenYw2ZQhvr+PMWHScOGHSh5+UO3gvvVX//BlEVM\nunE5Zv3yHgIoY4xGM4wqmUikL5RGXUH6ArAlGqu17EDqsNkYrx/rUaekNtW986iLooj8R14lA4BP\nZBhS77qGOYYJSXnoUa/64mccvONpZN/4MAqffpu8rzPbyIJPAFDSZITWJP0WdGIXPXi3788jEy91\noD95v3jNe24Z4naTGe3ZBaj84meUrf1yQBYocVL/21aiVwyeNJb0h+AJozFn4ycYcfuVJARuN5pQ\nvvYr8tn+1qg7rDZkr3yUJCypNX7wH5HIfF+1P22Sj7dYkX3zY2jddYDUcHZC/w7HA1dDvfrbPxkP\nZPDkseTvcJgsbguLuULfJ75UonVH8VHGOxS58FTFzzhp2rKHvE645BzM+v19st3faxZ0h8NidQv3\n9xRZEO12NKzfTrZjlswnrzVJcWT1S2tLu8dJbgAwXi2vmun0qPvFRJLv2W40MbISGjrMDUjVSES7\nHQ6rDbrDcrWDoPGyRzPxctlgqP9zm8cewp5gnR7D3fYHjkzGsKsuJN9TT84QPaVPDxiVDEEQMOG1\nh+AdLpXgNdc14dA9z7sZkUpVNVx/W8PRamLQq/01CD1lAiLmy4unuN4/NB1dGGrmhr7X2aZp3r6P\nPOO8w4KZqmfdedVp6UvodNlAI4Y67VGPDEXYTPn53bIrm/FWV6/7DfW//Q1AMjhp+aST7sZbh43t\nf8HjWUPdhzLU6eRHDeXMomupmxubmf9peppgs4a6NBlLumEZkyeh8pXth7qfNkl11/fnKSZi6xSq\nqijhrBYxdpTfAAAgAElEQVQDAMk3r4D/8ESyTSfPavOKsffiO3DwjqdR/p9jq8ZES3yCJ45G6LQ0\nZl/td+sZe6N1Tw7UajUMhhNbytlbRFFEXdlRdOyVEsN1/Vzi2avnQwYeZ5JmoI8a18+Ix6S4IBx+\nWx6cwk+bCgDQJMbCLz4appoG2A1G6PJKEEJ5ghrWb0fWtQ8AkG6W6V+8AkD6Equ++JkcN/qRW5Fy\n59XdtokxnKucHnXZGIoNVF6GmvWos9IXY0UtMQp9YyKZJaA1iX33qJe/+xWqKY/IqIdWuS1hHTgm\nBSo/HzhMFpiq62FubGFqxypR97OclFq+9kv4RoVjxG1XoKSJTfITAeTUdmDuiFCmQsKYx25D7U+b\nUP/rFvJeyNQ0TPv0JWRd+4A047bZkXPr40i69mJo84qgyy2GvqSC0bK27DyA6Z/9i7lm6ZufoXlb\nJkY9tAqh08Yz+4xVdegoKkfEvFOg8uq+i9MPhLiLz2T2qTW+GPPY7QhPn479l98LgDUOPMFuNMOm\n62DCkF1R+NSbciKfIGDKh88j6vRZaNy0C/uvvA+AtHrumMdug6BSoeHP7SREC0h9yqlddTWoBhKH\nxYqWXazW0t5hQPEL75LtkCnjYNN2EAPQXNvAPDxdoaUv0WfOISHdlh37yT3kExGK4Ilj5M+UV0F0\nOCCoZP9DE1W/O3LhqQiZmkbuA5tOD6u247gsxa49VOg2merJM9e69yAxdnxjIpl+LggCgsaPJCs3\na3OLmepOTho37ULZ218gbukiDLv6Irfr+sVGktchk8eioXNfe3aBnBPUicNiZaQhQKdRf6QSot1O\nfhe/hBjmtw0am4KQaeOl+91qQ8136zF81WXd/u09ITocTFsCRiZ3czRIu5woyQvpRNLA0SOkz8RG\nYeLrjyDr6n8AABo3ZKDiw2+RfNMl8rkUZAWuE6cmKmE0fPYUqHy8ETl/Jkr//Ym0/++udepdeVTN\n9U1M1LSvVH35C3kdv/xsRC9OJ4tCVf/vD4x+5BZ4BQa4fY6uWhQyfTxZfdMpfaGrC3mHh8I/ZRj8\nRyTCUFYFu96A3HtfwLTP/gVrSzsKn3mbOffhx15H5IJZ3Y4RTFtKKsj95RcfDZ+IUGY/LX2hF2Fi\nPeoK0pe+eNQpw9TpIAueMBpTP16D1r05CJs5CeGzp+LvaRfBptPDWFEDbc5hpuy0OtCftNMTaZvD\namOOi794MRP9ovto0+bdxGnWvG0fUu5knXq9QeviUfeJDIMmKR7Giho4zBbkPfgyc7ypuh5BZjt0\n0KGtzT065aSi1YQ2s+T8Swz2Rbi/d5/b6ERntqOs1b1sqspuR3xF53clCAibOQnaQ0WkmIEmMRaa\nYcr3mfZgIaw6PewGI4KDg9H+uWSH6Qr6t0TjoHvU6Trqc4aHwEetwtQwNWJqJO+YKAgImC6HzEKp\nWXnrXrl8o6WpFbn3rSHbjZt2kYod2pzDRDOr0vhiGLVccFewixDVSTXU9bJGPSrQveOIooiwhlp4\nmyUDvbrdzHhfugvV+tHJq9WeFdYHgIYNGYy3O/6Sc5B4xflux6m8vRijhl7WXQmH2eKmqS18+i1U\n/+8PFDe5z4YPVOvc9Onhs6diwisPkr81Yu4pmPG/1+EbFY7Ja58ikwnj0RoUPv0War/bgI7CMreE\ns9bd2cz30VFcjqLn1qJ5+z7k/eMl5lhLcxt2nnUD9l9xL/O9KGGqb5JDzoKAuAsXKR4Xcdo04lU3\nVdeTigVOzWTVl7/g8FNvuXkKLS3t2HrKUmyZfAEKnni920S6mu/W4+gHctWFUQ+tQtTpUtg9Yt4M\nEro1VddLSYkAKr/4iRyfes91mLfrG6J71ZdW9VtovCfasvLcKrQArIY1ZMo4+MXJhmR3iUUOm435\nbNQi2cNHl2zVJCfAJyyYaKAdJgvzELU0t8lhbpUKEXNPgSAI8IsfuJWAu0Jp7YeeHvh0JaLoxXOZ\nCQjgIn/Jc/e6mWoakL3yUbTszEL+Q6+QBLn95bLh5xsrRysYeZxC1E1fWukmawOkh7WrZ80VOgxf\n+dmPx5xUaqyqJ5W6vMND4eNcXbUbmAIBClHLjsJy8prWvEefOQfJN19Ktg8//RZjoCglN7smCjdT\nspeI+ZKON3T6BKgDpCiTsaJGMTlTFEWm4kvwJNkx1R8JpZaWdqafJV5xPsLnTCdjtr2j60oldA31\n0GkTqHO611H3iQiFIAgY/9I/yXuNG3ei6stfUPjM28yCVID0PC96lh2/u9Oo0xKMIBdvOsAa6jS0\nR50t0didoS6PXcbKWmSvegzFL74Ph9UGW4delgupVMwzN/qsORjz6G2IPisdXkEBiD57HtlX9/Nm\ntFG6/YRLz6X+tp4NdX3JUXaiHB7C/G209IXuT13lGXiCaLcz9f2DOu/7EMqr7royLSDJnmJiYhAf\nH9/lvw8LzHg1S49Xs/RQB0d2e6yn/0YNT8S6Eis571s5BuR3+OGHdXtQdftzqLr9Oeg+/AEJiYkI\nNTvIe0dW3IegdqPiOWsf+jeq73wedQ+8huiJY+UE9LKqLtdS6AsDbqgLgnC2IAiHBUEoEgThge6O\nXZgqzWgNecVQdYaAmqLj0KyW5SS0/KX6q99gbmiGKIrIe+BfboaSc3Uu2mMQe/4ZHnnQfKPDia7W\n0tyGphYdbJ013kP8vKDxVjPHG6vqsHfpbTh01rVY9eLDOP3nddBUVaHVKMtz6OongS4eIO/gQGK4\nOoxmxhvRFbr8EuTc+iSZHYfOnIQJLz9AdKyu9PQgpmnbn+fmAQSA3HueR+u6n+FlYY3AAzU6Rp8e\nODYFPpFh8A4Jwuw/P8RpG/+LU77+N/HM+CfHY/y//ul2fgCAIMA/ZRgJD9p0eqZSBb06oy6vmDH6\n6v/cRpawbtzQffJR3c+bSKgxfPZUppY9jcrXR/ZcudQObsvKQ+69L6B87Zdui9g0rN8ueURFEUff\n+xr7r/4nrArlzACg5JWPyOuYJQuYiI/K2wsxSxaQ7dofN8JwtEYu6yYISLzifKj9/eRqFw5Hr+tr\n95XmbfLiGjHnLWTWPHAiGeqerRVgrKwj/cg3LgrBk2TDjzYUnSsP+o+QQ7wGaoXS5u1yVafQ6ePJ\nw5r2PHc3YTAcrUH2LY/j0N3PofbHvxT1yZ7SppA8193COKIoMvr0mHPnuR0TTMlLlEqkHX7yTTKB\nEm12tGUeguhwMEaRb4xsnDA6dYWE0q70ytpDRW6eNVfiLjyDGKX6kgpUf80uQlT9zR/Yd/k9aNzs\n2QqmdN8OHN2zNx0A/OiopUIJXDY5dQSzb8wjt5IJiGixMvlAShU16Oogot2Olh2yBt1ZslLl402i\nxQBQ+fnPbmULjRW1xNjxDg9higJ4WkvdYbNBl1+iWDmq5rs/iYEXMmUcgsalQhAEJF17MTmm4qNv\n3ZL+re06Ms6q/HwQlCZHX6ytUq1yWrLo0ykfiph7ChONKHj0NUa3nHSdfN2qL37ptgIRDd3/lfqf\nt4JnXlCrmUk7LX1xJoxaepC+FL/4Pup+2oQjr32MwmffhvZgkVwicswIJu/NlbgLzyCva3/ayFSy\nS7pmKXG6dJQc7bGcJXP/dfZTv7gokpdjaW4jYw1tqBur6+GwWNEX9GVVZHzxiQqHX6eMzjXCDbAy\n2BbK2aKE1e5g1AjJoX7dHO05KkHA5VOkyboA4O70JCweHY74o3LkwZnwHHv+QpLn4DBbkHPrE26/\ngSiKjM2piY+RpdSiiI7D/edVH1BDXRAEFYC3ACwGMB7A5YIgjKWPcdZRD9N4YXKcVGmjg9JHNsYm\noIZK4oyYP4PMWnT5Jdi5+AYUr3mP6Nto6n7dAm1eMWq+lz0Cw666wLO2q9WMB7CmRJ55xrro02t/\n2oQdZ1xLwtA+FjOm7N2Oa998DtmX3U1m57RGPkBBU9lTspMrh+55npQV1AyLw7SPXmC0b670JqG0\nmXqwxF5wBqmuIdrsSP74Y6x68WGc8dNXiKyTvpdqrRmVf8sGG13uzSvAH8ETRrt5BOMuOhPjnr0H\nEfNmIPHqC5G25n6c+ut7WFTyF+bt/BrBk2RvBB2WdjUYmv6WdchNVGKosbKu21rAjRt2yG1xkb24\n4p8i5zI4Q+7p6elopSQfrpMf1xJNTZt3Yc95q5hkSEAqxehMhBS8vTDx9UfcJltxF8ne/rpfNqPy\nc9mbHrngVBKaI2U44Z74N1A0b5fD+rHnn47YC9jIhFdQAAJSk1gDuZsSjXR98YCUYfCNiSRGHo1z\nUhIwQl7kRl8qT6IaN8v9gk46ZbTKNcr3mSiKyL75UdT9uBHV635Dzi1PYPOEJdh17kpm1T9PEEWR\niQTQSa1d6V2btuwhumGv4EDmfnJCJ8y51tlu2pYpTUQpWvfkwNLUinGQHnzeYcFQ+8lSvZDJ8vig\nzS9xe4DT9x1d/lDn4lF3TeQDAK/AAIy47QqyXfzSf4jh0Lh5Nw7d9QyatuzBgRseZGqzdwUTnfRA\n9gIAmgQ6Ssr+7qLDwejyaY86IE3WJ74plx1t2Z1NxhZmISfnfetwwNKpIdceKiI5Gb6xkQgcI08C\nIufLVTLK3vocmycuwcG7niWGF714SlDaSJJTAHjuUS94+DXsOP0a7D53JbP+iMNmY6qEJFCR2PgV\n50DtLxmZHYVljHQUYD2x/skJUPv5EkeTaLfD2qZjnE10xGP0I7cRj72DMn5ilixA2pr7EX22vFJu\n3v1r0JyxD3aTuVuNOrMiqUL/U/Ko+8VHQ0Xdi7QU1Kmf70n60kY9R4++9zWKX5JzYEKpvDAlIubN\nINXFTNX15FnuGxeFgNHDEZDaOa45HD0afVqFiIKgVjNjnbGyFnaTmaxH4Tx3Xxcic00kdUJ71AHJ\nNklbcz/ZbuuhYl9Vu5ksLBkT6AN/H7XicQ6rrdeRucWjI/DqeaPwztIxWDQqHMPDNUg4SuU2nCJF\nhgS1GpPffpI4nToOl7rJs2w6PakeqA7wh9rfD0HjR5L9/ZlQOtAe9ZkAikVRPCqKohXAOgAXuh4U\nWVeNeSNCoVZ1hu0po6w5Og61VOJi4MhkjHt6NTHWzbWNKH39U7J/2DUXyQlmDgeyrvkn8UgEjEpm\nMs97gpajNB6RByZnxRdRFJH/4MvIWfUYWQTEFcveA8i99wUA0syY/B0uDwLANdmp+4RSW4eeeL0E\nLzWmffoSUwdWCSahNKegW3lNC5UIGHPuPJzy1avMrNjXbMLkzAxctfZFDC+SPAH122XjnvYUdUfy\nTZdgxjevY8K/HkDSdRcj7JSJ8Oo0yujviDbUXR/kTi+cw2xhtKCi3d7tIERHOMLnTO+2nc4awAAY\nbSzdFtdrKV27o6gM+y69m8m2p71BQWNTFPWg4bOnEo+PpbGFWZKdlhUEUYa6JwbPsWLT6dFOJQNH\npE9H0rUXMccETxoDQaViZBbdedSZhOvUJAiCID+0KJz9kV6N0jnhEUURzdQEjk46pb1oXU2IGzfu\ndPcqiyLas/KQecldKHjs3x4v2mIoqyLeeK+QIGbCrPQ9tB/IR/bKR8l29OK5UPm4S+0CRw8nCWqG\nsipihDksVhQ8/Irb8a17cmCiIlP07wGgM1wufaeixeqms6TzHuKWLSavtblFjKGk5NEEgOG3XE4M\nTXNdE8rfWwdTfRMO3fk0OcZh6vRe9SDb6imRVInuHCGm6nriHfQOD1EcS4PGppAJscNohvZQERwW\nqxyVEQRmzHL+trQRFXbqZGYSHrNkATMJtXcYUPPN79h17kq07DrALEcuGeqUPMMDQ93c0Ewm9R2F\nZSh98zOyr3rdb2Ryog70Z5wB3sGBGL5KlvsUPruWOJwAtuKLM6LlTRnjhvIqYkR5BQUwDiS1xheT\n3niMSa5UB/hj3DN3AwDGPXcvE33JXH4XNo1djMzL7lZc/0AUxR4jOkqGOl2aEQDzm1uaWmA3mBSr\nbznvIbvJ7LZ2A71YmDORtCtUPt6IPme+2/thMyZ15qC4L2rm/Ftdy3nqmIiC/DlaW22sqIW+uNzN\nuO1q/Yme0B6kvnMq6hk8YTTjjBj10CqEz5pC3usoKuu2QEQ5Vap7eJiyN72jqBx/T70Qf0+9iMml\n84QJsYFIjZD6l5/dhpga+XneMVp2DgaOGYGxT60m2xUffYsGyrlHe9OdORHBlKHeVRJ4XxhoQz0B\nAF2KoarzPUJ2djZmbfkdC1Llm4Q2oFqiY1GrYyUYyTddgulfvAyvkCDmfU1yPMY8cQdG3CHLBmjP\nSeIV53cpC1GCNpx1VDJGdKeh3rwtk8mK90uMxak/v4v2NU+hcIJsqDb+tQPtB/IZj42rRh1wTWCV\nDXWl6jbMQDk8wS3xSwn/EYnkO7O2tHe5CILdaEZblhyGCz9tGvxio3DaXx8j4K4b0RIpe0ZVdjvO\n/u5ThDQ3QixgH0jHCh1+pvuEa6Jk87ZMOGw2tOzJIV4JJ10NQjadnjzoBG8vpsqPEgGUMegsHZiR\nkcF4OiyNLcwKhvRvmHjl+eRhZSivRus+edlw1hukbOQIajViLzidbJOEysgwRJ8le5oCxxxfj3rL\nrgNk4A+eOBo+EaEImTaeecg4DVNGo96doU5NhJxGuFJ1JmciWECKLH1xGvm6/BLiFfMOC2aSzhkJ\nRLV7O0RRxBFKihQ2awpCT5lAnAOAVFd751nXe1RBifamh82Y6BJZYD3qusOl2HfFvbJ3LTYSox5Y\nqXhetZ8vM444jbry99YRrxltBGoPFcFQWoF8h2R80ImkTrqTx9H3XfSi00hdcmurlpTA9A4LZgxi\nGq8ADUb+8yayXfb2F8i5+TE3SVFHwREUPf+u68cZmLHUQ4+6b0wEMQ4tjS3MZICRJSo4UZyEncrm\nSBmr6ojUwS8+GhoqOdH527oa2zR+cVFI3/o5Rt5/IzPhFC1WHLjhIWYNgKC0kfCNln8zkweGeu1P\nG5lKIuXvroOhohY2vQHFL8re35Q7rnKThKbcdS2JnNjadSh86k2yj5b/OauLOOUtAPt9eivkD4RM\nTUPqfTeQ7VEPriT3hSYhBmOfvIM53mGyYPvmLche+aibDMdU00DkXF5BAYw2m7RBQfrin8Qa6qxG\nvZWp+EJX3jLXNkIURSmq0806ICE9eNQBMGO6k9CZkjORXX1YekYcfuzf2LnoOuw86wYio5SMd+WJ\nMqNTr6xV9PLqu1i4qie6mhyp/XyRdMMyAEDUGbMRd9EiqP39mAg5nV/oSjmV8NmVoV7x8XewNLXC\n3NCM7JsfRf5Dr/Sp1GR7TgHUnc+vlshoVIAtEjLsmouYCM+hu5+TV96lDfXOSR69EJ2nZTU9YdCT\nSbdu3Yr1BZvwy8dvYc2aNVi7di12H5JnpcXGFuzbLQ9WGRkZyMjIQNTCWZj954coiw9GvkMPQa3G\npDcew+4DWch36BHSqZPKd+il/d5eiF9+Nvm86/mUtv0SY8jnDZ2aRu2RbLQWS5VNWnfnkP0R82Zg\nzuZPkWfRosHfht8uuwmHJ04n+/MfegU2bQfyHXoc9rUTz1JX13NqKNfd8RBeT5qJvH++xBzvDPHn\nO/QoDvZSbL/rtiAIKE8KJQ/q9gMF2PrXRvzw1L9Q9/NmiKKIjIwMrP/4c2IIlsYHIbNIemB7hwRh\nc3wU3jjvAnx9492whYUh36FHua4el3z0OgS7HfkOPQpig3DDxhrc/uNhrN+81ePv23U7YPRw8n04\nVwzcunET9pfJg1K+Q4+DbfVoz8pH46ad5HjSvzZuVDy/0xjMd+hxJEpDqsN01R6noZjv0GP3AUn6\n4LDbsSc/l7ne5p9+JZ83VtaS9gy/9QrErziHbLdn5ZLzb90oSxSK/Bxdfh9xF53p9vfVnzYOO/fK\nnuNDhhayX3e4tFffd1+2//rqf+R6EXNnICMjAzt27EDqPddJ35doRHmSFAnwi48i7XdWxVA6/679\nclQk19ju9v07r+c/PAEZGRk42C4bu3tyc5CRkUHKMuY79KgcG08MtIyMDOS0yBOoPXkH3a7/25vv\nEyO1QG2B/oZzMevX/2DBgR9RMy2FXF9fXI4PF1+OT1asIh5apb9ny8+yBvdIlAb5dvn327FzJzne\ncLQG/73oOuQ0S04B7/AQ2B64mkn+dD3/kSgNaY82txjrP/kKP7/0Btnfvnw+yhIlQ0m027H+v1+h\n3CFNJn1jo9zOVxysls+Xc5jsl7yH1dL3LxoQMHoEgsaPcuuPZQnB2LFD9jq5nr98WCjKEiSjya43\nYMcu6Z6FICDh0nPJ+Y7+52s0bt7dZf9zygjzHXrktDV0eT16W+XlheIQL9JeU00D2d9Bna84UNXl\n+YrDfMnn2/YexN+//0m2NcPiUOAwyOeva5Tuh13y8yvfYXRr3/7yEoy8/0bM3bEOeP5WFAVLfdXa\nqsWu/ZnkfEFpI3GgVp5omeube7w/13/8BfP75Bpb8c3qR1D2zpewNEpjRXGYN4bffJnb59UaX2iv\nPJN8vubb9fh97YfIyMggDpB8hx55dslg9AkPkcfrzuhxvkOPw16yo4k+f+o918Fyz2Ww3H8Fkm9a\nwewfdvVFmPn922g6azqOxMoTiAPV5djw2TrmfBu/+Y5sd9X/nB51ur9qkuOZ9niHBaMAJuQ79LC1\n65jxO3BkMlQa6bc/1NEEm06PjsOl8v5xqWR/vkMPlcYXgWNSevx9CgQzigJk52G+Q49Cb+n7Cpow\nmpxPl1eMpm2Z+OM//0W+Q6oU07hBOtfmH34mEf1CjYh91HiRT/VHY0UNtv61kekP+Q59t/drV9ui\nwwHtwcOkfU5dvHP/uKdW4/T8P2C45SLs2Cn1/7CZk8nxTpmw0vl3UNsdpTmK13eOz87zVXz8HXaf\nvwobv/uxV8+vjd98J/fvpFRs+nsbs3/Hjh1oX7EQvp1OjZymavz2hrRKsaW5lVzf6VE/pG8m7320\nbxtuu/VW3HbbbUzRlL4w0OUZqwHQrrDEzvcIq1evRsP6Ypx+863wCQ+BVduBTU9J4Tmb2gvqyfOg\nipClALROLWBEIlZu/x51P29G4JgUhE5Lg3NvfYcDB65/CGkq6bPRi+fCNyoc6VGszs1V90ZvaxJj\nyedra+uBqUBw6hQsmCd5LXUFJWR/wopz4B0ciPT0dMQ0GfDLj4XYvfAcXJubBaFzyWAASFMFICQt\njXj2meslxJDzGavrYaioRej32xHq8EPlpz9i5P03kuOPvPYxOd/wGbLOsbu/BwDmnb4QpYckr2PZ\n2i9hq6yDpqUN2fgBY5+6C+mrLkPR9lw4fWcLzjoTadQ5hMSJCLa1oRqA+vH7kHbvY5JHqb2VtCd7\n+DQ06q1o1FtRGT8SN82UvUw9tY/eDhw9gnwfHYWlEEURUyLjYVTJ/cG5v2nLbjRu3EW26f10+53n\nr/luPdkfPXmq237XbWd4O00VAO8mydCZFp8Mg90HUMlh3SnRCYhKnw2HzQZzbSNpjyYhFqHTxiPt\nM2nbWbklPT0deOw9OFNMT7/ofCYaQbcndPp4TBuWwkSJLnhwNePtX7R8KcQH3oJotcFUVYdFk6cy\npTp78/17sp18pAkRnX9jxLxTMCZdlpjM+ftzzNP4Es+3X2wU+T6c3kal89taX4EzLnH6BeciIDUJ\ntZ0lQZ2fF3y84RsbifT4aNgm67HxgbcAAKlNJsyZPRuZr60jx0+4dBlz/o6oBGQ8918AwBgD24Y5\nc+Zg9wufwBmYXXztFUi74Dyp/TGRuP63z6QqP4+9DrvBiDTBH9h2CNvnXIrkm1Zg1upr3b5v8cG3\n4Hw0Lrp0GbQ5h3H4V0muNcEvlPTPgkdexag2G6AKgDrAH6d88YqbV07pfi7cLkW/qr78GcKRCoy1\nSjKZwHGpOOu5h1AgvobKT38AACTklCPWK6Lz94jERJfznb70AmR+LuX0tGcXIP3VhwBIJeJEux1p\nqgBokuPhFaBB8MTRSNt1gPl8evpcjFW435zMnTcPY1/0wv6rJM2q8/dMvfs6jPznTbA0txEv8qHV\nzyJ9y2eMJCE9PR2WlnZs7vTCTwgIxxlLz2f2d/d9zRg1Fq0tkpFgqq5H+lxpf+73L5D2jF0wv8vP\nn3XFJdjxvqTXbt2Tg4nzZ0LtvMeT4jE7JRHFGyXZoLmmEXNuvATmumfhVPsvWn4hI0egzy8IAs6+\n4WrMmjINey++HQ6TRe7vajUCRw/H/JgIiA9Inm1zfRPO6Obv1R+pQHJpE6AKgKBWk98Puw6jLKuU\n/L0THv8H1P5+in/veXfejOzcStR1rt8Q+MmfiFkmoqYzNydNFYBTzpQkM97hoaS9zolUmioAUSPk\nKILr33vBA3d12f7w06biqtOkvzXn9ieBzuozI1stzPEle4rgNE3T587FOIX+56zMQz8f/JPj2fao\nVJgSk0girbr8I+R435gIWNt1SCuTojDm2kboCstk++KsOQgcPQKO25+S2j57GlTeXj0/jxfMR/jS\n81H1udSnJgZG4owrpUlL8ITR5Py6vBLk/eNFpv0NG3ci/d2nUf/nNjjvwtlTp2PmXNkDnD5vLg5+\nJf12xspajNLayHjt/D6iLLIZ6On4r80rhrVNhzRVgFSSsXOMp4/3CQ/BXKot4bMmI22tdG1nFSyl\n839Qkw90yp3PO3MBkak49zssVmzMf5S034n2YCEC3/oO6Vs+Y47v7u9JbTAiuPMc1ckp0AybgPR0\n9/5acrgWJS+9jzRVAJJFyetuaWol13eOUQvPX4LwpXvgPzwBl6eNQsyS+VB5eSEr69jWNRloj3om\ngJGCICQLguAD4DIAPysdqD0o6UHphMvWyGiIajVqdWY4utBTewX4I/Hy85hC+4BkmNMJm7SO11Po\nEK6qQQ4zOhc76iqkmRAs/ZAt0XEonHSK23kDRg1Hm9HK1GV3vZ6puh5HP/yGCa3RmmM6aY4OmfYE\n/eDX5hwmmfuAlMFuqmlg9Onhc9gkNro04+izZiHlLvd69JUj5PDPH4XNMNm6Dg92h198NAndW9t0\nsE1E3SAAACAASURBVDS1Mt8BHY6sWvcbk4ToxEB9TzR0Qk1Xi17R+MZGkmWgra1aWFra0VHgLi1x\n6tLNtY1EEuIbHQG1xheh0+USZm37pVXb7CYziRYA7qFxGkGlQuwFcqWA8NOmMUY6IOke6b+H1vb3\nN6a6RnJ+wcebWSIckDS9dJ1i74hQCJ1aa5u2g0lsc2I3mMhERFCriWba9TfyT4ojycleQQFEvy9a\nrNg6cznTh+llrQHAL4GVntCh9Oate6XFuTr/ppQ7rmI+KwgChl15AeZs/gRRi04j7ztMFpS99Tm2\nz7uCVGsRRRHNO7JIXxO8vRAyeZyiBEiqDCK3edonazwKnTMlGnOLSXKeV3AgJr72MFReXoxcw26U\npVl0YqKTkElj5GoThWVEykUnkjrlVUpaYKXSjK5EnjEb4elyTkjYqZORet/1nQsMPczkYhQ88brb\n55lE0tQktyT17qBlT7Q0TamGuhKBY0YQ+aCluY1JZPdPjmfzMOoaYa5rYmQZdN5TV4ROG4+Jrz/G\nvBcwMglqP1/4RoYRCZa1pb3bih10WcWoM09DLFVlxCkTCByXioQV53TbnrFP3UUmn4byahx55SNG\nNkmkL1TtcroghGtN874Qdfps8ppexAxwkQ4qlGYElKUvGhfpCwD4ULXU6QRpn+gIt9+WlhYGjklB\n/LLFmPLBc0i+6RImebIn4paeRV6HzZpCoru+UeFEjmM3mtxWwG3asgcOm41N5J7I/v30pNBQUeOW\ndA7ArbiBJ9AL6oWfNs0jSXEoVbFPe/CwYsUrk81BchJVAhBSVuZW+EJ3uJT0X82wOIx7/j55zCo4\n4nHukFXbgTYq56E6ORVlLSbFY2k5nL5I6tvsgl5SvxEEAVPeewajH7oFcRee0eM6Lp4yoIa6KIp2\nAHcA2AAgD8A6URQZ4aMzJOCsd0zXstXFSp3MahfRYuhdCSFBpcLUD59H1BmzMerBm5mqD55CVwnw\na5H1ajGBPmShAkBK5qR1kv4+aoT7Sz/QrgXnMNpWALAkxOO6b/Jxzdd52HVUTqqg6/wayipR9cUv\nzOdojShdhk4p0a4raA2qK3aDEXn/eJHRptLVJtpNNrI6q7daQHKYBiPvvwmOtDHMeaqGy8amzmzH\n5pK+raAnuCRndRSWMQZD4uXnEUkDvcAInSREf080+tLeGeqCSgX/VFqnXoG/17vXF3Ya6rQR4Hw4\nB4xMkh/yTa0wVtSi43ApMej9RyS6LVTlSvJNl5BJQ1fa5cBjTCit/uYP7L34jm6TdBxmC0rfkD0X\nYTMmEq9cVwiC4FKi0b3iCa191STHk6oMdNUdgF2oBGBzCOiIQ/CkMfBzSZr0Cgwgv4PDbCEDriiK\nTJnMxMvPU1xECJCMk+mfv4wZ377J1raubcSBGx7C/ivvw+5zVyJzmay1DZ40BmqNL7PSqvM7MByt\nIUa0T1Q4ItLdJ/hKBCtM7PxThmHW7++Te51eERKArFFXKEfqFRRAEqdFu50sokKPPc6EZSWjvKtE\nUhpBEDDhlQcRMjUN4adNw+R3n2aMk4mvPUyOrf1uAxq3sCUb+1LxxYlS5RdRFFmNejfJqYJKhTCq\nIAGtIdckxbmV/qQTcgM7Sx96QtyFZ2DUgzeTbefERlCrFauTuCKKImq++5Nsxy9bjDGP3uZWFWzM\n47czSZ1K+MVGYfTDtyjuCxiVDE3nxNcngk4mlY0/7/BjN9Qj589Evig5idr25TIrj/dUwx+Q+rXr\n3+mqUQcA3yhZp05PAHyjI9zGLvpZ5LwnYs9biHHP3tOrhagi5kzD6EdvQ8ySBRj71J3MPqWJh/Pv\nsLXr0L4/j03kHs/+/fTf2FFYRirxqDSyFttwtKbX1VPohQ09LRzhEx5CJsGizY72A3lux1S0meB0\nyU6rLMS+81Zi1zk3MWVbtTnUglJTxiH5hmU9rpHgit1oRtY1/yTVmPRBwWiLiEazwYp2k3tOID0m\nOGVySsmkA8WAa9RFUfxTFMUxoiiOEkVxTVfHOWtj09n8tmFykliNtveJAoGjh2P6F68g9e7repVE\n6oT2cAe2twIOB4J91dB4q5kBOGDUcLeqDInBktHSGhUDn7MXMvu22gNgsDogAthEGbG+sZGyt6RN\n57ZYQAfjUZcNUP8RnhvqfrFRiOj0MPrGRiJtzf045RvZa9W4aZdcC31cKtMBaW96argGXioBKm8v\njHvjcZg0kne7PHUspqUl4rrp8kD1U16jxws4ucJWfilnvoOwGZMQQi1d7ST5huXkdVclGnu7qiEA\nBLiUaFRaOty5AhxdmtGZqCqoVEzkpy0rl1lNzhMjR5MQg/n7vsfpBX90mbAb1E2JRtFuR3PGfuTe\nvwY7Fl2LI//+LzNIl7//NQ7d9Qxadmbh4OpnFKseNGfsR8bp16Dio2/Je55OhGlvMl0b34nepTSj\nE68ADWMEaVwM9dBTJjDbKl8fhM2eyiywwrSDNqg6DTZdfgmpdy54e/W4ejEgVbmZ/ecHmPTW44xE\no3HTLtYTJAhIvl6S4NAPfOcEk/UKdh1VccW5EiBpz7wZmP37+8w6DX6dKzq7ouRRB8Ak3rZ3PhRZ\nj7r0sA0YlczUzFdpfJnqSN3hn5yA2X98gJnfv+U2YYhadBrilsrlUvP/+S/G+9bdehQ9oVT5xVzf\nRJJhvYICiB61K+gIhUiNLf5J8cyk0FzXyHgwg8b2nPBPk7L6Wkx6+wmk3ncDRv1DTsJVqvwiOhxo\n259LEt3as/KIB9YrKABRZ86BZlgcht96OflsxPwZiFo4y6O2DLvuYkx6+wmMuPNqpN57A0Y9eDPG\nPXcvZvzvDWI4MgY5FaXqDyPGJzKMRI5Fu52USDUcrSbOEcHbq8tJliAITPEJtb8G3grtomup07aI\nb0wk89saSitlR51a7ZGzpztS7rgKUz983q39rqUmw2ZPRcJl8mJIDRt3djtR8YkKJ0Y53Vedq4g6\n3+9uPQlXRIcDrZTkzTXq3h1hs+RnllOnTnOUSiSduGc7eU2vvN5OVeNyrv3AqBEUVh2mcVhtyL75\nUaZCT9GyFcQrX9bi7un3H5FI+rmpqg42vQFmylD37aHi3rEy0Br1HpkyZQoaIH/5dGlGrxR5EK7V\nmTEpbuCX+qbxCtDAOzwE1pZ2qO12BHRoERMtGaDManEKD9aEEF8crJMGf+2KZdCs/5sYRHtU8gBx\nlCpFpPLygl9cVJerJTofltY2rTwz9vPpcqGerpj++cvoKCyTEmQ6PSzxK85FzTe/M8cFzpqKjzNr\noFYJWDIuEkWNlOwlSpadjJgwAn+9+QrKNuzC2Avm49HTR8BotWNdTj1MNgfKWk04WNuByfFslR5P\noMPQ+qIyNkQ9NgVRC09Fm8uqjzFLFqDs3a+I/MRYWcsYfaLDAcMRtgSgJ9DH6Y9UYGSjEa5LiCh5\n1OnZfsi08SR027YvF7DLDzSl+r9KqLy8gG5Cakq11EWHA6Wvf4KK//7AlHXT5Rajeds+TFr7JBr+\n3I7Dj8mTNofRjIYNGYinSvGVvPwhSl7+kLle6MxJJBmsJxivlMLDgan44hIpCkhNIp+h63gDwMj7\nbiQGVuj0CQieMFqxpKETTUIMOjon26aaBoRMGccY1tFnzmF+t+4QVCrELz8bUYtOQ+Fza1H1mVzj\nXvDxRsLys5G8cgWpzOQbEyk9FEQR5sYWOKw21qAb57mhDgBpa+7Hkdc+RsS8GUi95zq3cKsgCAid\nOQl1P26UjnfqbrswSIOnjEPNt1IOh7YzusaG+aV7UuXlhaCxqSQCFzQ2tUfvrKeMfXo1mrbshrVN\nSuo78spHGPP47QBcV3ge3qvzalzkhYBLBZnRw3t06rhKvMi5k+NJaVlAkkfoCqjfNa13hrogCMy9\n50SaYEmOLWed77wH/oWqz36CSuOLpOuWwUKVUoxZsoDUy0+9+zrY2nQwN7Zg3HP3HHNbaLpaHdan\nHzzqAHDGRefjyGv/BSDlJMWetxBl73xJ9kekT+/2nvcOCyZST01yvOLv7EtJX2jD1jc6HA6L7Cxs\nolaa9U9J7Hb9kmMhmPKoq3x9MOHlB9BRXE6i7XU/bpSlgj7ebk4nQRCgSYxjJMWALLF0eoUN5dWM\nTMaJvrQSVV/+gqgzZiN8tuQ51+WXEE+0T1R4r6JaYadOJrX7lVZrLu+UnnibTQjNlSujNXVWdlN5\neTERf2fUUJMYC6fZrFRy1240w1TbAFNNPSo//QmNf8kJtGMeux15E9OBIumeKWsxYoqLraLy8Yb/\niAQiY9SXVMCqIH0ZKAbdUHdiqqqDpbmN8ZYEjR4OdH4XdC3144kmMZYYxcFtLYgJHA7ARZ+u8GBN\nDJFDS9us/rjlnutQ+vKHaJg2HW0RsrFS1W6Cxe6Aj1rypPslxDCGujrAn5Rq6ygsk8pC0fr0EcN6\npdEEpAdssEtIbcxjt6Fxw3ZyAwLAZ2IUDuVIbfn6YD2CfOWH8OhIdgGam8+bDHHJJDL4Bfp6YdGo\ncPxaIBmFP+Y19slQD6A86m37c+VBydsL/iMSEblwFlNmLHBcKjSJsQgYMYx4Kw1lVaw0oraRyAy8\nw4I9Wn4cYCVGutwixaXDiaFO1VCnB0Bap96+P4+pN+uJR90TlGqpl775GfM90bTszMKO+Vcyv72T\nup83kQe0obyKMdK9ggIw+uFbMOyaizw20Lor0Wg3mJhVCgNS2QdA5IJTiSfN1Yuj9vfD8JWXwlPY\nWurSpIqpC9yNRKwrvEODMeFfDyDhknNQ+ekP8E9JwrCrL2SkCoC00qxvVLgkWxBFmOubmLJpShP/\n7og6fRaiTu/eMxo2czIx1KVGqNza5YRe+KhlVzZ0h0vlvq5SMQ/moImjyYPTE326p/hGhWPM43ci\n997nAUglJ+OWLkLwxDHsqqQKZW67Q8mjzkQLutGnOwmePBaCjzepjAVIRpRvdAQElQrqQH/YOwxw\nmCzMgmielND1BNqjbqprgt1kRs23kszFYTSjfO2XzPHxy2UDW+3n2yv9dG/wiVA2Vnwi+8dQj1w4\nizLU98Dc2ILqr+XxYsRtV3bfvrBg4ljpSppCl2hk349kVkWmV8f2pM/0lahFs6EZFgdjZS3GPHEn\nAlKT4BsbSfof/ZwJGpvCLODkRDNMwVAfPwp2g4lEEPVlVYiYy8rtdIdLsXfpbbC2anH0g28wd8fX\n0CTEuMleeqNWoKPArXtzoCs4wtwXzhrqI4ryIFjl+8vWrkN7Vj6CJ45hnAbOko90eWVXj3rhM2+j\n/N11ivKelLuuwYjbr8SIXPlZ1JVOPWDUcNlQLy5nPOpDXvrSE3TZmtY9OcQTKajViBoznOxzraV+\nvKAH9qD2VsQESjN2esW4QAVPybQE2SjNrdfjj1lnInrnz/h86fXy6nUA7CJQ3S5PQjQuNYiTV15C\nVi+z6fQw1TTAUKosDzgWfKPCMerhW8m2KAgoSpANPilPQPYwjHIx1AG43bAXpskeu10V7ajT9X6y\nRQ+CdIgvYGQyVN5eCJ40hgm5OhP8/EfIHle9i06dkVf0ImRJH9ucsR/5nWXJ/FOGuS3VzBjqlGeW\nlr5oc4uYhSo89aj3hCYpnoQ7LY0t6CgqZxY68YkIRdL1yzDi9itJX6SNdHrlxMYte4j8pZLyFIdM\nTUP69i+RdP2yXnlRfeNpjzqrUS968T2ibfUKDkTMOfOY/ckrV2DSO09i5vdvu000ewuTUNpZS117\nSH74HovRGTZzEia99QRG3nt9l8Ywo1Ova/w/9s47zI3qbPv3qPftvXt3bW+xd927sTHYFFNMN/Wl\nBhIIIaQBSQjJm5AAIV8gb4CQhBp6L6Ea22CMDe5ed2/vvWvV5/tD0swZabSSdlW953ddvi6NNDMa\na49Gz3nO/dxPQAVxk4GUaxx2jEKZnuzz72aoKOWXeVs78fWqqzmvcE1RrqCbKdkGnSx0DgU5G8/l\namRYux37bvkVRk40wOjuacEwQRXSA8Lvoqm1AyzLClYzxvNQdyNVKb1qfdREcbOvVSNypWsykF7q\n5q4eDOw6KOjwKdg3M5XLhIYbMb/08Z4PloNj/Zx3v6mtC4d//jAcJmdcYJg9U1CgLHodRNMjT+mc\nG4Wv72t6snDlmpByhurvKoZMp8Xyr17C6oMfoMDlTS7TapC8pNprX1+JHrFJib68WLAqOdYgLCg1\nNrZi1+U/4gqhHSYLGp9+DQDQR3Qt99co0BN1biaXzXeYLNh99U9gcnVnZlkW9S7pS8lhb1lM9xff\nYPjwCW7CpC3J57z/ySJtUnZq6R1A/d9fEg3S8669EKX3fA8AUJSs5p6v7/eWvgDeOnWhj7r4uAkV\nUQ/USdre/IT4QchBdipfWBeKjPqY1Y72IINFMnA2DPQhQ68E63BgmHD8EAsailM0uI7QaX94tBcP\nbm8XBOluSIN/cmLAyGXIv/5iYRObY/UeGXVexz9Zsq88D61znF+8fYtWwqzWIFUjx4w0YVCulEmQ\nnzh+4SAAFCSpuQmLg3Vq1YNFnZfJua2QuINJRiJB5npXDQDDIPM8ZwMJUrfv6fwSrOOLG0FDEmJZ\nVF9e4tWqmZzVkxl1eaKBa1LD2uyCAkKVD81wsDASiWCCc+D23xLdeQuxat97KH/wbsz41Q+w4LW/\nCpbtDLOmY9G7T3CBKmuxouuTr+AwW9DyMp+9Kv7x9V5FmoEgyKh38OOh/7uDaPzHa9z2zAd+6J2J\nVsiRfdHagIuXxkMggWjrgsNmE8gUQrW64QvyR3/kaJ1gpSjYAslA0M+cJihUHu9vJ9WokHfthaKv\n6WcIs4cpy+dj2eYXsGzzC0jxEygFC8MwqHj4Z3yjsPoW7DjnZk7/rM7PEkwaAkGmJwqJTRaMHK1D\n+9ufca8HOkHzLNBV5/F1AuQY557LyYA8IfgVRTFIyZK5o0fQjTl56VxB4Jh39QUhkyP5w5fExVem\nPVgkUqkg6+t2VwKAaXdc7TezK0/iJwxiTZEA+J5YpyV7dfJ1o58RvkAdcE4MPa+LdJzirsPHBF/M\n3UZfViyIHcgiflNHN7679E6vzrfNL74LS/8Q+ght+UTuxbMe/xXn5mZq7cSea38G26gRx3uM6Bm1\nQmq1YtqxGq/jer7YgcF93vp0QHg/J2Wno7VNXEwpUSuRuHA2sjacicq/3IvyB+/mxkwR0VipoW8M\ndod3TR3ZXG7keAOntAB8y75CRdQD9epqfmbYReiGtKWFyNTzN+HJZtRHzDZc//phXPfqYbx3OPCA\nkZypOaUvCow1t3NyFEVKos9Z+JXVGVhNdFx1VxPLJIzg+QZiqYXMZmZtWAtVRqrguZGjdULHlxBl\n1AFgS/0gXr3oevzffQ9j8/rLcPaMFDx9SRkeO386/nh2MaqydFDKJLhmTiakksCWuy4o529ubx/q\nxvbGgXH29oaRSER1qKS8Y/ovb8P0X34fc5/7k9NeDsLPxbM76Wgt6RoReKAuT9ALglq31ldfViy4\nGY41tQl0cp6WbIlzvQtgQx0Ykp+P2/oUAGb88jbB8mjKivlYuuk55N9wCfKvvxjzX/0r5IkGZJzH\nd8zreP8LdHy4hdN3qnIy/EotfCEspHRmG+1jZtTc9Xvuhpq6ehFyrjh3QucP+Do8pC+jJxq57Jwq\nO93nD3bI3p8I5noIRwPd9CLR5evJwkilSJzvdCspl/gvmCz7w4+x4I3HvLKU5I+jG31ZcchkHZ5o\ni/NR9eQDvK0nUdw8njvLeJA/6ofv+TM3WdaXlwhcrsbDM1Ans5ZiAV0oPx+VoJi0F71EoF5w86VY\n9sXzmPvCw5j1+K8w7YfXhux9/SFP0Hk5nAGhkwUsX74cqSL3Hc20PGScc5rIEUKyLjoTjEwKWYKe\nS+h4IqY1licZOGmTWKJNNyN80hdfpK3xDtQNPlZkPSclmsIcyLQaQUbdvZJpGxnFrst+xBXKSlQK\nrhDdPmLE4V88zDVXUqanTKiI1lBRiuqn/5ebQA4dOIb9t96PDw45fw/ya49CYXEmVFU5GWBk/H7d\nn/MxIrmqpcr1dnMChKvn6WuXY/F7T6LqiQcEjnEAkKiWc059ZjsrmtAlk18D3x3ksvQygy5sNQpu\noh6ok5CaP930QqRq5ZBLnV+MQZMNo5bgLIRIdjYPcdKNV/Z3+vRl94S0N8qtP450rRzDh8gCoRKf\nM3mGYXD3inzM9MhInzMzBYvy+GW4BqKgNPO805F37YXI2nAmZj7gbAYhzKjXcS3sgeA81MfDwbJ4\n9UAnwDAwqzW4ek4m7lqRD61CCoZhMDfHgIfPLcV7183GZVXiLcLFWJhnQFm6xvUewB++aMChzhE/\nRwkRW44mb45ygw7Tbr8a6Wv5ZgaCbIGH9MVYRxaSBpe9FAvs9WXFAo3cwK4aLuMuT06ETKsW7J8w\nT+hQAoRO9uJGbDk2aVEV0ojPyI0qIxXlf/gxyh+8m8sMkD9k3Zt3ouFJvhtg3jUTz9IJMuouWcDJ\nh//Jt7zXaVDx8M8n5NIU1HV4ZNQFXsRhzqYDQukLmREdz0d/spCOC6qc8b/DDMMgZfl8LHzjcSz+\n8B/IvmQdsi87B/nXbQjb9fki4+zTMP+lRwV9E4DgrRndkP930vmh5Gc3BVzv4570uCEtYVVZ3pOg\nUP5dSbeekeP1nGSLkUqRvGweGIkE6WcuQ86lZ49bXBlqGKlUIC8BnCtE/ixng0HMXaroto0B3Y/S\nVi/Gqr3vYvXed32uXopp1N3PuWtLSBi5LGS/wcGgnZbn9b6+3KI8i0TdmXe3/z3gTGaxLIumZ9/m\ne2PIpKh++vco+QnvOORufAU464Qmep9OO30xyv94N7fd/dnXsP/1aYBlUUrIXrIuPEPwXSM99Mla\nGoHtansXF0ST7njaaeNPKoqS+N/pOhHnF/J+I5S9hLeQFIiBQH3fvn2isxHd9CJIGAaZOv61iWic\n3ZDWgj2jVhzq9LadEyNpxTxYFM7MfmpXB9RHjwkdGvzcgBUyCX5z5jSkaZ03TLVcgo1VmSgkBgUp\nfZGqlKh46GeoeuIBKFxNGsigdDhMGfWdTUOcA41aLsGGSvFlvmC/mFIJg9+cOQ3ZBuff0WJn8etP\n69A0IF6wIYaOqFXgnxt/uZH02fa0aJyo9AUQftndftS6smLBzZBsBkEG8G4SRSwlQ51RF/t8Zvz6\nBwH//bRFuQL5izsrz8ikyNm4fsLXRWqjLb0DqHv8BdT//T/ENd4esNvKZFBlpXHZMXNnr8DxJZRF\nkeO+vwv36hwQnDVjsORdcyF0ZcU4maxE3jXi0hYxEudVYvbf7sfsx37pFYhFipTl87Dwzb8J6lEM\nVTPGOcI3nnVAznPNRPq6FSJ7i0N6QgNCeYGY9EVXFjp5BBmom1o7uZWohDllnGY3WnhmzxXJiSGb\ndG/btg3qnAzB76EiLRnZl47fsIlEmZY8br8HeZLBK+gnP2/P1RJtcX5YVsACIW0N3wRKU5QLmU58\nQuQpfXGv7siTDJwMzD5mgrmjB80vvMPtN/OBO5F+5jJkX7xW1Mp1shLEvGsuRBHRUG72N1sw7+tN\nKD3GNyHKOHcV0taIrN5KJILfTKlaydtN2uwwuax/hUm58WOl4hQ+JiMd7tzItGrRBEe4C0mBGAjU\nAfFg1y13yDLw8peJeKm7OdEjnCFtru33saeQEakSR4nuot0vvyvwUA8kU5KskeOxC2bgxgXZ+PO5\npUjRypGbqIRbPdIxbMGY1fdqgcDF49AJbvlXqtX4lN0EA8uyeHU/v1x07sxU6JWhu/kkqeX4w1kl\nSFA5zzlstuPej08GvELiWVUvUSmgKfDW3ZFINSoua+m2aAScMgtOwyaReNn8+cMzsJeqVdAUZAsC\nddI+Sizo1M0oglQjzLL7WracKHqPjHrGuasEjjOBkHm+9/Jw+roVk9LSM1KpwLXi+O+f4B6nrFyA\nvKvPn/C5g0GikPPZMYdDILtzy6fCiS9L1ckWyY6HIjkByze/gKqnfus1PuKBhKqZWPz+k8i8YA3y\nb7jEp3zBH2I/tqU/vyXogNKt41ekJgm002J/22A91MdDkZYkKsFIWblQZO/IQjY9AkJXSEpCTqgK\nb7k86DqF8WAkEq8MqTKd/431XC0JZyGpPzLOXcU9TlrsXVzqRp6oF6xquJMBDMMIElpNz73Fee/L\nE/XIvdLZzV2iVKDgpku9zhuoTGw8pt97q+B35rSP34Zy1LnirsxKQ0J1GVJFvP6dv6HCCZeYl7qg\n34yfjPrMdP4zOtrlHagD4qv7UyKjXl1dLWiwAQBgGK6RRZZAp+6dUXewLGo6RtA14juId7AsanuF\nH/xX9QOiBQMAMGqx462aLjy8tRH3fVKLAwt5uUDnB1s4SyMgcG/cFI0cl1dloMTllqKQSpDjmoSw\nAJoHfK8WKFKTuFkbaRGlLc4LSbbiYMcoDnc5g3+5hMHFleLdGCdDtkGJ368rhkrmHHJdI1ZsrQts\nsqT1CNR1pYUBLXVqi7x16saGFr5gOT8raG0Z6e1dLtFCN6MIjEQiyFqQfyMxb1qJTIaEOfyynVSr\nCWlRMOC8ybl1yIxU6rOz4HiIBUJ5IZA+iGl4kxZVYc6//hC01ehk8NUkIxLSF7GsKxBaLbMvVqwI\nPHMca2iL81H91O9Q/ocfT7g9typXGKgnLpyN1NXBd64uuOlSrPj6Fazc+bogk+05vkNdICyRyUSD\ng9RVMRCoexSUhjLbuHy583e46ParkXfdBhTdfjUKb93o56jgUaR5Buq+M+qexdWRJHlxNSr+/AsU\n3HI5prvcS8RgGIazMWTkMiTM4Z3HSHe0hqd4eWP25edASnQvzbv2Qq4AFHAWNIdC8sNIJJDeexda\n870nPBlnrQQjkUBfUeolSRLrsC7sTtrp7JciUB+M/xtblsYH6sd6jD4KSgu9npsyGXWyBTfgDG7c\ns6UsAx9IiTm//GdvB378wQnc9vZRtA6KyylaB80wWh2C5wZNNuxt8/aNBoD/91UTntzRis9OY7Hg\nOAAAIABJREFU9KG2dwxd2fnoyHHOxhxmC9e2mZFKJ+WhWpgsLn8RQ0zKEKrg7pX9fJByRmkyUrTh\n0TVOT9PgCkLfTsqRxsMzoPYne+GOE7FoJD2Y/c2wxfDMqOtcgZWYxAUQz6gDQj91fUVJyANUhmEw\n67FfIX3dclQ98cCEin40hbkCGYimKDckzh6eGceUFfMx76VHQ6plDeg6RLp1ypMTRZ8PNWKTFWVG\nakSyM1Mdda5w8lz6s5snnPDQFucLmhwB3uNKV1oYcnkEuSoFOGs7yAAsWnhm0EPV7EjwHgYdKv70\nU8z45ffDIjtRpgk/W4Ugoy783kYzow4AeVedj7Lf3unT/91N+R/uRu5V56Hq/34jcHwiV5RJi8/8\na4UJGXmCHnnXXMBtJy+duD7dkw/rh/HuVd9Df4rws80411kgzDCM10TaK7kLj0C9pcPp5uUyCFCk\nJPqV7aVo5ZxE2WxziMZkYn0bpkRGfd++fV5aQ3J5gcyoe0pfLDYH3qpxteA22/Gv77wb0ADAcR8B\noZj8xWxzYHvToNfzDctXeT2nLcmfVLVvIWkJ1D++ZlvshhAKfXptrxG7WpwTFgkDXDY7vEEKafV4\nsnf8yYkbRioVZKQCrbIXs2gUeKgH4fjCnbMgh8vmH3aM8t0m01M4ZwoSXzZgaWcu4x6nnhaeTFjq\nygWY+9xDohKWQCH1n/k3XBySCYWBkJakrVmCuc8/7FVwGwnEJBCG2dPDXsgKOPWOMg+7vnAWkpJs\n27YtIu8Tq+jLi7neFGlrloTcVlKRkihoZBZsR9JA8JSfpSybGzWtNEk4M+qRGreeclJyUuQ5wQ40\naRRtdDOKUPnne7x+C8iCUjcpKxeIJnam/fBaJC6YBU1RLqbdcU1IrmvQZMNXDQMwaXV4+5rvQ+K6\nJ6rzswVyntTTlwiOE8uoqzyaHgllL4HFSmWE/OWIiPxFNKMegUA9+t9suApHlQo4zM5AnPwwsg2+\ni0m/bR4S6Jy3NQziUMcIKjKFBTVk5nZ+rp4LTL9uGMCdy/KgkPHBR03HCKx255JHpl6BH6/IR36i\nCnrHdGz58A3OjxqY/A+rr4JSMcSCUzIQnShv1/BWlSsKE5GT4N8ffTKUEI2S6vrGYHOwkAVg9Zg4\nv5JrCuNpjeYLofOLK1CfRCEp4NQ2q/OzuPO5A3VGIoE6N1NQvAKIS18AIGnBLMx59o8wtXUjdxLF\nmeEm/4aL4TCbwchkKLjhkpCcs+DGS2AfM0GeoEfBDZeE3drKF6JFhRGQvbhRZaZiZJBf1QtnISmF\nR6bVYPFH/8LAroMB2foFCyORQJmRysmpdCHUp7vxLO6LBX064B2Yh0OjHm6U40hfyIx6ILVSsY7Y\nqrwveaMiOQGL338qpO//0r4OLt7KKCvEik3PofPDLUhbu1wgbUs9bQEYmRSszQ6JWikqERT2MumA\nkUzKBRioz0zT4Mt6pw3x0a5RrC/zqEkQUVBMCelLdXU1JHKZwKyfzKiTXuqdIxbYCN3QppN9Xud7\namcrWA/rRbKQdH1ZKhf8G60OfNsyJNh3dyv/w7koLwHV2Xoka+SQ67RcK3U3kw/USZP98TPqYsVf\n/qqY/TFstmELoRO/aFb4l/wTVDKku7q7Wu0sGv1MUNyU/ORGFNxyOcofvFvQhng8hF7qLumLoAo8\n+EAdAOfxPb+0TDBpEJO/jOdgknHWShTccLFACxhrSGQyTLvjWhTddmXIGqfIdFpM/8X3UHTblVEL\n0gFx6YthVvgLSX29f6Qy6m6t71RGW5SLnEvP9pKthAryex+Ov6un9CXltAUhf4+J4CV9CVGzIyBy\n49ZTRkIWk5L1UQnV5RFrJhUuPM0UlJmpSF8Xmc95b+uwIFF4YUUa1LmZKPzeFdB6TCDkiQaU/e9d\n0M0oQtn/3iX6u6H28FIXZNQD/K0XZtS9nQEVyQlegbkyzF1JgRgI1N3kXHoWAKfWjuy6pZRJkKJx\nBnYOFuh2FY0Om234tpkPst1Z2aPdRm5G5DxGWEhamqrBadP4m8cWD/nLHiJQd3fVdOPZrW+yN+Bs\ng5Lzie8xWjFstvncNxwZ9c9P9MHims2WpKi9/N7DRUlK8PIXZVoyyn57J/Kvvzjg9xGzaJys9AUA\niu+8Dit3vo7lm18Q3DA8bbA8q+0psYW49CVygbpXYVqEAnVK+Cm89QrI9FokL5+HlJXz/R8QJGRG\nXZWTMeGkQ6gJp/QlUnhLX4jPOjsdFY/8HFkbzkT5g3d7Hhp3KDNSISESRblXnT/hIu1gGDHb8PCX\nfL3YglwDTi8ef1KX/z8XYfnW/yDvKnFnMBVRezLW0iFcPQ8wo16SqoErJEPzoFk0JvOUv0wZjToA\n5P3PRVi2+QWc9u2bXk0FsvR8MLStwRmEf1U/AKsruz4jTYMLK/gfvX991waL3Vk8ShaSJqpkSNXI\nBV1BdzQNcvKZfqOVM7qXMkBVllBCY6goRdISp3eoVKOedPGOVMIgj5CaNI6jU5cnGgQ3DHmiflJt\na1mWxQdH+BbB55alRkSbCzgnS25OBlhQOhE8LRq/qDiH66om1WpEvWEDRVOQg+3f7hQ85ylz8exI\nSoktPAN1qU4T0aVs0vmFUcgnPHEMlqmuUY8EGWetxOlHPsLCNx4PS+BDFtNlnLsqYvduf3j+Jnna\nNU6GSI1bMv6QqBReyZbcjetR9cQDEXFoCjcMwyDJ1VBIolYi7+oL/BwRGv62vQU9o84GlwalFD9e\nmT/pMSxP1HO2x3bjGAb38b0xAp3IKmUSTCP81I+J+Kl7WjROCemLG4ZhoC8rFg0+lxTwzz27ux1N\n/SZsOslnwk8vTsLG6gzolc5lqI5hC94/7AxCSX16aaoGDMOgMEmNIpfsxGJn8clxp4sL6QJTlq6F\nRuG9rFX91G9Reu+tmP/a/5tUoOwmuIJSPqs+EccSkoMdI2gedGr+NXIJVk+LnNtEaSr/RfD0tw81\nOqII1TbEd0TVlkz+xuCJp/TFlz6dEhso05IFRX+GyumRtYckPJn1M4oiksmiRI5w/j0T5pRj9t9+\njZKf3YzSn93k/4AIIfeQuoRS+hIp3La2gHMyHSuToHBR+Zd7UfzjGzD/5b/47O8QSrbW9eMLQsnw\no+X5nGpiMjAMI5C/WPt5xYVY0awvygR+6t7yF62H80sk6jCiHqhXV/s26nezoTIdJa5ZjtXO4neb\n6nGwwxl0SRhg1bQk6JUyXD2H/yO9tK8DQyabR6DOB4jnlfMD8q2aLtgcrFD2kitu5aNMT0HxD6/l\nZqGTpTCZzKgHbtHozxPUH+8T2fTTS5JFJyXhgpS+1PaN+fSzDwVFd1zjtTQlUSpQeOsVkz63p2bS\nMzCPRIdNysRhJBKBVVkkZS+AsA19ikhr9HBBNeqnBtmXnIWSH1/vsyNlNAhnw6NIjVttSQHS1i4H\nI5eh8JbLI/Ke0USdm4nSn92E5HGaJoWK+r4x/OUrXpJyZmkylheFLiMttoqtyskIqg5sZtr4zi86\nQvoiTzJEJMESFykcmYTBT08rwO3vHIPVwaKRaD8/N0ePJNdsbH1ZKt493I22IQuGzXa8vK9DkLEl\nJRdnlibjud3tGDTZ0DVixZbafkEh6TwPfXq4EDq/jJ9RT1uzBI3/eBXA5Kr8+41WfN3AW1Cunzlx\nCchESNbIkayRoc9og9nmQOugGflJ4XGbSV25AKsPvA/7mBkOswUOiwUyvTYsRWQaD406zajHPqqc\nDK5rLekZHwn0ZcWY9+IjGG1oiWnnHwolUKQaNRQpibD0DkCq04TFRz3cMAyDec8/BPuYOaYL/eON\nXqMVv/yklpMiZ+gU+P6S0Db6E0uOBVu/UZbOxwZHu0fBsqxgVcVQOR0SlQIOkyVi9pxRz6i7Ner+\nKEpW49p53oHP6cW8nkwuleDGBXwB4buHe3Csm1+6mE4USyplElxA6Nr/+V0reo1OzZRWIcX01MgU\nVpLSl/q+MS/HGpLU0xZi3kuPovpff0D2xWsn/J6fnOjl3HPK07UCTVakKCWy6id6w6dTB5yZU5lW\nDUVyAlSZaSEL0j01k4q0ZEhURHGpjyZIlNgh+xKnk5MiNQnphLd9pEg7YykKb7osbO4jYlCNOiVc\nMAyD8j/9FEmLq1Dxp5+G1Ns90uOWBumhY8xqx/2f1qHbpUvXyCX47dpp0IZ4Jd+z6zAQfL+ZbIOS\nk1EPm+1o82i0qUhNQtUTDyD36vNR/sefTPxigyDqgXowXDIrXTDbUcokWFYoXFpbXpiAcpfGyOZg\nYXa5mrgLSUnOL0uF0uWh3mfkq3urs3SQBuDtHQrSdQqo5c5rGDLb8cr+znH3Tzt9MTLPXTVhWygH\ny+LDI73ctqdPaKQoiVBBaSRhGEbgNBOMLo4SHfKuvgArd76OlTvf8Nu5jkKh+Cdz/WoseucJLztj\nytTE7mDx0JZGrvGkhAF+uaYIRcmhTxCKZdQ1QdpYMwzjt/FRxtmnofKRX4jaZoeDqAfqgWjU3Uhd\nEhj3bOe8slSo5cKAlWEY3LIox+tYdyEpiUElw1nTvVvvetoyhhMJwwiu4Zld7dhc6+0PHwh1vWM+\nu7C62d0yjE6XxaVeKcWKEOrDgqGEyOIHatEYa4hpJqfdeR1kCXpkbTgz6u2lKYGhKciJSmfUaEE1\n6pR4hI7b+KNrxIKffHgCXzfyUtvbl+Zhvo8awMkiKn2ZgI01aVUt5qceaeJCo06Sm6DCUxfNRMug\nGbM8OpC6Kc/QYmVRosBPnSwkJbl4VhreP9INsp5xXpgGkS9uWpiNur4x7G93Fsg+srUJqVqFz/+f\nGPvbhvHT/54EADxw5jSBUw4Jacm4tjSZW1GINGS9wIkeIxwsC8kpUF2ffdFaZF14RkTdQygUCoVC\niSW+bhjAo181YdjMd4+/uDItrKv44hn14B3yZhIZ9QMdI1469UgT9WgiUI06SapWgeps/bjylBsW\nZAta05f60Jxn6pWCBkiZegWyDZHVpsmlEtx/RhEKEp16dauDxW8+qwu4aycAfE50af3waI/oPl0j\nFuxs5me250S4iJQkTSuHwbUyYrQ60D5kidq1TBRfmkkapFNiGapRp8QjdNzGDy/v68ADn9dzQbqE\nAa6fn4WbRdQOoUSZkQJGxqssGJl0QrViZelarhllY78JO5qG/BwRXk7ZiCLboMSVLrvGNK18XDnL\nFVUZ3B/FX3escKFTyvC7ddOQpHYucgyb7fjZf0+iyY8TjBu3XSXgbM1rtNi99vn4WC+3clCdrUNe\nYnicVgKBYRhh46MwF5RSKBQKhUIJLyzL4lWi1i5dJ8ef15diY3Vm2FfNGalU0EhOU5gzIftErUIq\ncMN7bnc7HOMYfYSbqAfqwWjUg+Wq6gz8+9Iy/POSMi8tO0lRshqPnz8D959RhKvnRs9SL1OvxO/W\nFnPFpf1jNvz0vyf8Bus9oxa0ERlpq4PFrlbhDNDmYPHfY3ymPdKWjGLEe0Ep1UxS4hE6binxCB23\n8cGAycZZMKrlEvz9wpmoyAhcxjtZSC/1yTSGvLwqg5MG1/WNYRshpY40UQ/UwwnDMMhNUI0bpLuZ\nlqLGssJEgVwmGkxP0+D364IL1slsupvthE86AOxoGuScbZLVMiwtjL6/bSlRULq1fgB7W4fHtads\nHzZjVGSlgEKhUCgUSvTpGOaThll6JQyqyJZCkjr1YK0ZSZI1clxYLsyqh7M543hEPVCfiEb9VKcy\nU+cVrP/6s1qfg+RAu3egvrN5iPNKB4APiSLSdTNSoj4hAYS+9h3DFvz8o5O4+8MTXhMPlmXxj52t\nuO7Vw/if1w6jZzQ29OxUM0mJR+i4pcQjdNzGBx3DvO94ll4xzp7hIWnRbO5x8tK5kzrXpbMzoHHF\nYc2DZmyu7Z/U+SZK1AN1ijiVmTr8YV0xVK6ll7Yhi2hADggDdZfUHqMWOw60D7uONXNdVxkA58yI\nvuwFcEp9rpmbKZg01HSM4u4PTuCJHS2w2B1wsCwe/7oFbxzsAgAMmmz46Fivr1NSKBQKhUKJEmRG\nPTMKgXrO5eei8tF7MPuJ3yDtzKWTOpdBJcPFs3jN+wt72gUJ0EgR9UA9nBr1eKc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Nod+O3n9WgftgiOMVodtPiUIkqg43anQJ+eMM6eviHlL3tjRKfuT/riRiGV4L7TC7l+Bm1DZjz2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\nIiIiMiEW6kREREREJvT/YvXijE994isAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "import pymc3 as pm\n", + "x_t = np.random.normal(0, 1, 200)\n", + "x_t[0] = 0\n", + "y_t = np.zeros(200)\n", + "for i in range(1, 200):\n", + " y_t[i] = np.random.normal(y_t[i - 1], 1)\n", + "\n", + "plt.plot(y_t, label=\"$y_t$\", lw=3)\n", + "plt.plot(x_t, label=\"$x_t$\", lw=3)\n", + "plt.xlabel(\"time, $t$\")\n", + "plt.legend();\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One way to think of autocorrelation is \"If I know the position of the series at time $s$, can it help me know where I am at time $t$?\" In the series $x_t$, the answer is No. By construction, $x_t$ are random variables. If I told you that $x_2 = 0.5$, could you give me a better guess about $x_3$? No.\n", + "\n", + "On the other hand, $y_t$ is autocorrelated. By construction, if I knew that $y_2 = 10$, I can be very confident that $y_3$ will not be very far from 10. Similarly, I can even make a (less confident guess) about $y_4$: it will probably not be near 0 or 20, but a value of 5 is not too unlikely. I can make a similar argument about $y_5$, but again, I am less confident. Taking this to it's logical conclusion, we must concede that as $k$, the lag between time points, increases the autocorrelation decreases. We can visualize this:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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2958Vq2Aikh+NPSEiIkkzYMAAVqxYwerVHU65lZROnToxYMCAoq0/W0tEeNi8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\nD0qv2kYmz1cpuo6V61hXXRABjAbmuvt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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def autocorr(x):\n", + " # from http://tinyurl.com/afz57c4\n", + " result = np.correlate(x, x, mode='full')\n", + " result = result / np.max(result)\n", + " return result[result.size // 2:]\n", + "\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", + "\n", + "x = np.arange(1, 200)\n", + "plt.bar(x, autocorr(y_t)[1:], width=1, label=\"$y_t$\",\n", + " edgecolor=colors[0], color=colors[0])\n", + "plt.bar(x, autocorr(x_t)[1:], width=1, label=\"$x_t$\",\n", + " color=colors[1], edgecolor=colors[1])\n", + "\n", + "plt.legend(title=\"Autocorrelation\")\n", + "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", + "plt.xlabel(\"k (lag)\")\n", + "plt.title(\"Autocorrelation plot of $y_t$ and $x_t$ for differing $k$ lags.\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that as $k$ increases, the autocorrelation of $y_t$ decreases from a very high point. Compare with the autocorrelation of $x_t$ which looks like noise (which it really is), hence we can conclude no autocorrelation exists in this series. \n", + "\n", + "\n", + "#### How does this relate to MCMC convergence?\n", + "\n", + "By the nature of the MCMC algorithm, we will always be returned samples that exhibit autocorrelation (this is because of the step `from your current position, move to a position near you`).\n", + "\n", + "A chain that is [Isn't meandering exploring?] exploring the space well will exhibit very high autocorrelation. Visually, if the trace seems to meander like a river, and not settle down, the chain will have high autocorrelation.\n", + "\n", + "This does not imply that a converged MCMC has low autocorrelation. Hence low autocorrelation is not necessary for convergence, but it is sufficient. PyMC3 has a built-in autocorrelation plotting function in the `plots` module. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thinning\n", + "\n", + "Another issue can arise if there is high-autocorrelation between posterior samples. Many post-processing algorithms require samples to be *independent* of each other. This can be solved, or at least reduced, by only returning to the user every $n$th sample, thus removing some autocorrelation. Below we perform an autocorrelation plot for $y_t$ with differing levels of thinning:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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3v2dYj+SYcv7zJ3Rw8Myqd9jjvSkt0KLSkYvxAXHKUy5lilPhK/UYxWVWIuX8\nZy+k87+8/nFmthGZLcw1HTgDuCFp30+BGRmUEao1MBj4AdABeMXMXnH3sKRckSIXOjh45Zef5r4x\nJUbjA0Qk7ooxlajUhHT+HwLuNrOfAZhZV6IBt2MzqOcU4J9mdgEwm+gK/krgkMyay2yi8QK1uif2\nJasGvnD3pcBSM5sEbEf0BWQN48aN4+Xn36fjuhsBUFHenk027E2vblsBMHP2BwD03qjvGtv1H0/e\ntpXL665ohxwfsh1c/9xpeOvyrOtrifp7dR3AZ819PgPrz1k8811/M8cT4IPVNWxV1qHudyDr7c2o\nCDp+2srFtFm9vFnrX7FyRd0MRs1Vf+jrybT+eXM+ZvANv2Kz9tGwpRlLogzG+tsb996ap3ptyzcz\nors0620WvV9SbS9vXVZ3ZTPk+JDt9gMGBx2/cPoUlq5cnXV9TX09+a6/dl9znc98xzPf9ecinhWt\ny6hV6O+n0PrzHc/qdkM4/4mPmDv1LQC6brkDQMrtjTqUc/3oQ4Ho6j58n9+fvD1ixIhGHy/V7Xff\nfZdFixYBMGvWLIYMGUJlZSWpmHvjwy7NrBy4CjgVaA8sAW4HLnT35Y0+ec1y2gA7A12BucAr7r4i\n9PmJMloBHxIN+J0LvE40lmBq0jEDgL8A+wBtgdeAI939g/rlTZw40Z8f93n6epcvxcsrwtoYeGxc\nysx3/XEpM9/156LMivmz6DfhrqAyl7WtoO2ysMHBoceWcpmZHDunz+aMPfncoDLbtykLGtAYelwx\nlpnv+uNSZr7rj0uZ+a4/LmUCrN+uNd07tk17nMYchJk8eTKVlZUpbyE3euU/MbvOCOAid/9ZIt3n\nC0/3jSGFREd/UqbPq1fGKjM7E3iG76f6nGpmp0UP+23uPs3MngbeAVYBt6Xq+Et+Kee/8H1U8zll\nWjis4E1fojkN4qDU88njQDHKr9B0onfefJXqRcOCytQXhdQa7fy7++rEVJrrJrYXNKWSxN2DHwOD\niAbhJtcR1rv4/vingC3q7bu13vafgD81pa0iktCqdbMvHCbNb52FX+d1kTERkZa0YpVrzEGWQnL+\nJ5nZMHd/NYt67ibKu38cmJ9FOVIkNM9/4VOM4mFrKmirQcQFrxjnkC82ilE8ZBInTV+aWkjnfybw\npJk9SjTNZl1/IIPVefcB+rj7wsybKCIiIiKSmbhMX9rSQjr/7YBHEr93T9qfyUXBWUSDb0UA5fzH\nQSYxCl34pOofAAAgAElEQVQ7ADQ+oLlNW7m4bgahdELXGVB6UPNTPnnhU4ziIRdxKrXpS0MG/P4d\neNndl2VRzz3Ao2Z2PfXSftz9+SzKFZECELp2AGh8QD6FrjOg9CARkdSKIZUoowG/WTgz8e8V9asA\n+mZZtsSQ8skLn2IUDwNarwurwqYPlfxRPnnhU4ziId9xKoZUohYZ8OvufZr6XBERaVmh6UGgFCER\nkVQKOZWopQb8YmabAEOBDYG6e8rufmdwa6VoKOe/8ClG8ZBJzn+o0PQgUIpQKOWTFz7FKB6KMU4t\nfZegRQb8mtlBwL3Ax8DWwPvAQOAlQJ1/kRISOjhYA4NFRKQUtPRdgrSdf3c/sRnquQw40d0fMrOv\n3X17MzuR6IuAlCDlkxe+XMUodHCwBgaHyXfOv2YQCpPvPGVJTzGKh1KPU+hdgmM2bfixkCv/mNnm\nwNFAN2A2cL+7fxzUykhPd3+o3r67gXnAzzMoR0RECohmEBIRaTnBdwka6fyXpXuumR0AvAUMAL4C\ntgDeNLMDA9sJ8Hki5x/gMzPbGdgMaJVBGVJEZs6dlu8mSBqKUTxMW7k4302QAAunT8l3EyQNxSge\nFKfshVz5vwL4kbu/ULvDzHYHxgChCbm3AyOA8cC1wAvAauCaTBorIiLxpBmEREQKQ0jnvzvwYr19\nL7Hm4N9GuftVSb/fY2b/Bjq4+9TQMqS4KOe/8ClG8ZDvnP9QpT6DUKnnKceBYhQPilP2Qjr/U4Dz\ngauS9p2X2N8k7q6RfCLSqNBZgUAzA4mIiIQK6fz/FHjczM4hmue/B7AEOCCXDZPipjnkC1++YxQ6\nKxCU9sxAuZjnX5pfMc5NXmwUo3hQnLIXMtXnNDPbEhhGNHZ4DvCau6/IdeNERKT0aPpQEZHcSdv5\nN7NBwJfu/lLSvh5mtoG7v53T1knRUj554VOM4iEuOf+ZKMbpQ5WnXPgUo3hQnLKXdqpPopV5699T\nLgf+3vzNERERERGRXAnJ+e/p7p8k73D3GWbWuykVmtkm7j7fzIa5+6tm1gMoc/eZTSlP4inf+eSS\nXpxiFDo4uBgHBivnPx6Up1z4FKN4UJyyF9L5rzazwe4+uXaHmQ0myv1vilFm1h/olZjy82WgK6DO\nv4g0Sejg4FIeGFyMtHaAiEjmQjr/1wKPmtnVwAyilXl/DlzelArd/VoAMxtBNHvQcCBgnWIpJson\nL3yKUTwUY85/qDitHaA85cKnGMWD4pS9kNl+bjezhcDJRNN8VgHnu/u4TCszs2eBz4BngOfc/Wt0\nxV9EREREpEWEDPjF3R9y933cfevEvxl3/BP2IxooPBB4zMxeMbOjm1iWxNjMudPy3QRJQzGKh2kr\nF+e7CRJg4fQmr4spLUQxigfFKXshaT/NJrE2wKTEz+/M7Gygv5kd5e5jW7ItIiJSOjQ+QEQk0qKd\nfzO7n2ihsPuAl4AKd/+9mR3bku2Q/FM+eeErxhiFzgoE8ZkZqJRz/jOR7/EBylMufIpRPChO2WvR\nzj/wEPA6cAJwJfCImV0BfNzC7RCREhQ6KxBoZiARESlOQTn/zeh1YIC7X+7uB7r7ncBzwOQ0z5Mi\no3zywqcYxYNy/uNBecqFTzGKB8Upeymv/JvZpSFPdvffZlKZu1cD1fX2PZ9JGSIiIrkUOj5AYwNE\nJI4aSvvpkfR7BXAo8AbRtJw9gaHA+Nw2TYpZMeaTFxvFKB6U89/8QscHZDI2QHnKhU8xigfFKXsp\nO//ufmLt72Y2Fjja3ccn7TsEODz3zRMRERERkeYSMuB3X+CYevseA/7W/M2RUjFz7jR69hqU72ZI\nI0o9RqEzA+V7VqBpKxezHW3yVr+EWTh9CuW9ts13M6QRilE8KE7ZC+n8TwfOAG5I2vdTYEZoJWZW\nDvwYGASsk/yYu4fNuyci0oJCZwbSrEClK5O1A94tX82049VhEZH8C+n8nwL808wuAGYD3YCVwCEZ\n1HM3sB3wODA/00ZK8VE+eeFTjOJBOf/5k8naAa36bI7mzypsyiWPB8Upe2k7/+7+PzPbHBhGtEDX\nXOCVxGq9ofYB+rj7wqY1U0REREREspXxIl/uPsnMOphZubvXBD5tFtA207qkeJV6PnkcKEZh8r1q\nsHL+42HenI81fWiBUy55PChO2Uvb+TezbYgG+C4DugMPALsRrdJ7ZGA99wCPmtn11Ev70Tz/IhJn\nWjVYQrRauaLZpw8VEWmKkBV+bwZ+6+4DgNpUn/8AIzKo50xgE+AK4I6kn79mUAYAZraPmU0zs4/M\n7MJGjtvRzFYkpiWVAtOr64B8N0HSUIziYUDrdfPdBAmgOBW+Tv10pzMOFKfshaT9bA3cm/jdAdy9\nxszahVbi7n2a0La1mFkZMAaoBOYAb5jZo+4+LcVxVwJPN0e9IiIiIiLFIKTz/xmwA/Bm7Q4zG0o0\nBWhLGwp87O4zE+0YC/wI1ppE4SxgHLBjyzZPQimfvPApRvGgnP94CI1TJtOHanxA81IueTwoTtkL\n6fz/BphgZrcA5Wb2S+B04NRMKjKzvYCjgY3c/QAzGwKsl2HOfzegKmm7mugLQXI9mwIHufseiS8p\nIiIisZDJ9KEaHyAiTREy1ecTZrYPUWf/P0Av4BB3fyu0EjM7CziHKMf/0MTu74gWDtsl00ancR2Q\nPBZAn44FSHPIFz7FqPnlYmYgzfMfD4pT4dP88fGgOGWv0c6/mbUC7gR+4u6js6jnXKDS3T9LGqQ7\nDdgiw3JmAz2Ttrsn9iUbAow1MwM2BPY1sxXuvtb/ouPGjePl59+n47obAVBR3p5NNuxNr25bATBz\n9gcA9N6o7xrb9R9P3raVy+tSJUKOD9kOrn/uNLx1edb1FVL9GZ3PwPpzFs981x+DeOa7/jjFc+57\nL/Dt6hq2KusAwAero5mV629vRkWjjydvr1i5oi71JOT4kO3Q+qetXEyb1cuzrq+prycu9WcSzy+W\nfEGtb2ZMAWC9zQZltd1+wODg45e3LqtLv2jp+hdOn8LSlauzrq+prycu9cclnvmuPy7xbGx7yZzp\nrPou+pxY9vU8ppTtTWVlJamYe+PX9sxsLtAzw0W96pfxOdDV3VeZ2VfuvoGZVQCfunvXDMppBXxI\nNOB3LvA6cLS7T23g+L8Bj7v7w6kenzhxoj8/7vP09S5fipdXhLUx8Ni4lJmr+mfNnBKUT57vdsal\n/lyUGRqjXNVfymVCNC1ovwl3pT3u7VYr2G5VWM7/srYVtF2W/upz6HHFWGau6g+NUyZl1qyzHl9t\nuHHa4zIZG9C+TVnwVdXQY+NS5vKZ7wTnksflNcWlzEyOzUWcivE8XTnYqaysTJn9EpLzfy3wezP7\nXRZfACYBFwGXJ+07G3ghk0ISXx7OBJ4hmqb0DnefamanRQ/7bfWf0sT2ioiIFLTQ8QEaGyAiyUI6\n/2cBXYDzzGwBSR1qd+/Z4LPWLuNxMzsVWNfMPgQWA/tn2F7c/SnqpQu5+60NHHtSpuXX6rdNR7p0\nX4eyMgNfDRayJALhx8alzJzVv6nOU8GX2XCMVq925lV/y/R3F4XVKTmjXPJ4UJwKn3LJ40Fxyl5I\n5//YbCtx97lmtiPR1Ju9iGbsed3dCzJ6nbu0ZYddetGj16b5bopIwaqaOYevF3zIl/OW5bspIiIi\nEihktp//NFNdewJHAZu4+/5mNsTMMp3qs0X0G7g+3XsGD0UQKUnde3al38DP+XLevHw3pSiFzgw0\ns+od9nhvSgu0SLKRz/UYtHZAGM0fHw+KU/bSdv7N7NKGHnP334ZUUm+qz8MSu3M11WfWystbY8qR\nFGmUmVFe3irfzSha3roNS7r2Tnvcyi8/zX1jJNa0doCIJAtJEu5R72dH4OfAZhnUcy6wp7tfCdSm\n+jRlqs8Woc8+kTD6kpx/fTbK5KNY8mVA63Xz3QRJo1M/rWgeB4pT9kLSfk6svy+x6NfRGdSzLt+v\nzFs7YLgNsDyDMkREREREJAshA35TeQZ4IIPjm2WqTxERWdOnC2bQL9+NkLTymfOfiVIeH6Bc8nhQ\nnLIXkvPft96u9sAovr+SH6LZpvoUERGR3ND4AJHiF5LzPx34OPHvdOBVYCRwQmgl7j6XaKzAkURf\nHE4Ahrq7pglpggkTJtC5c2emT0//Af3NN99w5513tkCrwvXs2fjyEKnavO++++aySU1qU7Jbb72V\nYcOGcfrppzd300QapZz/eFDOf+FTLnk8KE7ZC8n5D1w5qGFmtq27vwO8lviRLDz88MPsvPPOjB8/\nngsvvLDRYxcuXMgdd9zBSSc1eb2ztNx9jYGf9bczlarNTz75ZFZtzFa683jnnXfyyCOP0LVr+BSx\n2Z4nEQifEhSg9bcL6fniYzlukYiIFLKMO/ZmtoeZ7Zbh054wsy/N7BEz+5mZDTb1epqkpqaG1157\njRtuuIGHH34YgKqqKoYPH153zJgxY7j66qsBuPTSS5k5cya77747l1xyCQA33ngjw4cPZ8SIEdxy\nyy11zxs7diy77roru+22G6NHj27w2KqqKnbaaSdGjx7N8OHDeeWVV9bYnj17NgAPPfQQe+65J7vv\nvjvnn38+7nWLQwNw3HHHUVlZyfDhw7nnnnvq9qdqc+2V+YbaM2zYMM4991x22WUXDjvsMJYtW3vh\nqdp2n3baaQwbNowTTzyRpUvXXnEzuY5bb721wTbVOv/885k5cyZHHHFEXZtCzlvteRLJxmcLZrCk\na++gn+XrbZDv5pasaSsX57sJksbC6VovIw4Up+yF5Pz/B7jY3V82swuB84CVZnaju18RUom790yM\nHRgJ7AacCXQ2s5fcXXn/GXjyySeprKykb9++bLDBBrzzzjusv/76DV5B/t3vfse0adP497//DcDb\nb7/N2LFjmThxIqtWrWKvvfZixIgRtG7dmmuvvZann36aTp06sWjRogaP7dixI5988gk333wzgwcP\npqqqao1tgI8++oh//vOfPP3007Rq1Ypf/OIXPPTQQxxxxBF1bRszZgwdO3Zk6dKlVFZWcuCBB9Kp\nU6e12lyrsfZ8+umn3HnnnVx33XWcdNJJPP744xx22GHUN336dMaMGcOOO+7IWWedxR133MEZZ5xR\n9/iUKVPWqmP48OENtgngmmuu4fnnn+fxxx+nU6dOwect2dSpU5kwYQK77747Q4YM4eSTT+aOO+4I\neUuIiORF6ODgYhsYLBJ3IVf+BxLl+QOcCuwBDAMySm5290+A/wKvJMpbBWycSRkC48eP55BDDgHg\n4IMPZty4cRk9/9VXX+WHP/whFRUVdOjQgQMOOID//ve/vPjii3Wdb4COHTuudez+++/PK6+8AkCP\nHj3W6MDW3540aRJvv/02lZWV7LbbbkyaNImZM2eu0Zabb76ZkSNHsvfeezNnzhxmzJjRaNtfe+21\nBtvTq1cvttpqKwAGDRrErFmzUpbRvXt3dtxxRwCOOOIIXnttzSy0xupojLvX3dnI5LzV+vbbb2nT\npg3uzieffEKHDh0AeOutt9LWLaWtV9cB+W6CBCjGnP/awcHpfjot+DzfTQ2iXPJ4UJyyFzLVZxng\nZrYZYO7+AYCZrR9aiZk9AOwMzAH+DdwHnO7uug+agYULF/Liiy8ydepUzIxVq1ZhZpx22mmsWrWq\n7rhUKS8Nqc07zzQLq3379o1uuztHH300v/71r1M+/+WXX2bSpEk8++yztG3blgMPPDCo3fVTh2qV\nl5fX/V5WVsbKlSvTlpUP9c9TrR133JGbb76Zc845hwcffJChQ4cC8Oyzz7LDDju0ZBNFRESkiIVc\n+X8JGAP8CfgnQOKLwBcZ1DOYaGXftxM/U9Txz9wjjzzCkUceyZQpU/jf//7HO++8Q69evZg5cyZf\nfvklCxcuZNmyZTz99NN1z1lnnXX49ttv67Z33nln/vWvf7F06VJqamqYMGECO++8MyNGjOCxxx7j\n66+/BqIvGg0dC2t3wutvjxw5kscee4wvvviirrzq6uq6xxcvXsz6669P27Zt+eijj3jzzTcbbHO6\ntqeqvyHV1dV1dY0bN67u+enqaKhNqTS1nbVfDN544w122mknnn32WcyMb775JqheKU0z507LdxMk\ngHL+C59yyeNBccpeyJX/HwPnAwuA/5fYNwC4PrQSd9/czLoS5fyPBC4ys3bAJHc/JaMWl7BHHnmE\ns88+e419BxxwAP/85z/5xS9+QWVlJZtuuin9+/eve3z99ddnp512YsSIEey5555ccsklHHXUUVRW\nVmJmnHDCCQwcOBCA8847j/3335/WrVuzzTbbMGbMmJTHVlVVrXWnoP72FltswcUXX8yhhx7K6tWr\nKS8v5+qrr6Z79+4AVFZWcuedd7Lzzjuz+eab16XiNNRmgG222Yajjz46qD0N6devH3fccQdnnnkm\nAwYM4MQT11zAetttt01ZB5CyTalef0NlpGtn9+7deeSRR5g0aRL/7//9PyZPnsyoUaPqUoBEshU6\nM5BmBZLmVMoLh4kUIgu9YtoslZkNIhozsHvi38Xu3q3FGlDPxIkT/flxa+cijvxhd4YOH5iHFkku\nVVVVcdRRR/Hyyy/nuylrueeee+jbty9dunTh3nvv5ZJLLuGee+6hf//+7LDDDrRpU5grg77+8ntM\nmlCNLV+Kl1cEPSf02FIuM9/1V8yfRb8JdwWVuaxtBW2XrT1rVlOPy3eZ+a4/LmXmqv45fTZn7Mnn\npj2ufZsylqxYHVRm6LG5KDPf9celzHzXH5cyMzn2ysFOZWVlyiuOIVf+azvtuwIbAnUFuftvA5//\nGDCCaFXf/wCPAz93949Dni/SXAp1htnevXvz7bff8vTTT3PxxRcDcPzxYXO3i4iIiIQKmerzJ8C1\nwDPAvsCTwN7AoxnU8xJwjrt/Wq/s89z9zxmUI9JkPXr04KWXXsp3M1IaOXJkvpsgMTVz7jR69tLs\nF4Vu2srFbEdh3sGTyMLpUyjvtW2+myFpKE7ZC7nyfwGwj7u/aGZfu/vBZrYvcFQG9fza3a9OtR9Q\n519ERES0doBICwjp/G/s7i8mfl9tZmXu/qSZ3ZfuiWb2g9p6zGwPklKGgL5EaUAiItJEvboOoOVG\nbklTDWi9LqwKy3svZbVrB6QzJwcpnJ36DQrOu5b8UZyyF9L5rzaz3u7+GfAR8CMz+wJYHvDc2iVK\n2wJ3Ju13YB5wVgZtFRERERGRLIR0/q8GtgQ+Ay4FxgHlwNmNPAcAd+8DYGb3uLtGL4qINLNc5PyH\nTgkKmhY0lHL+C59yyeNBccpe2s6/u9+V9PuTiZV9y909bMWj6Hnq+IuIxIS3bsOSrr2Djq2YPyu3\njRFJQWsHiDRd6FSfnYH9gK7ufrWZbWhmndy9Ot1zk8rYCzga2MjdDzCzIcB67v58k1ouIiLK+Y8J\n5fw3r9CxARA+PkC55PGgOGWvLN0BZrYb8CFwDPCbxO7NgZtDKzGzsxLHf0S0wi/Ad8BlmTRWRERE\nRESaLm3nH7gOONLd9wFWJva9BgzNoJ5zgT3d/Uqg9uvaNGCLDMqQHLv//vvZb7/9Gnz8iCOO4IEH\nHsi6nurqanr27ElLri4tUqxmzp2W7yZIgGkrNbldoVs4fUq+myABFKfshaT99Hb3iYnfa3trywOf\nW2tdoKpeGW0ImzEo7659cRbVi3J3u7Z7xwp+tmvPnJWfSlVVFYMGDWLBggWUlX3/HbCxFXAffPDB\nZqm7e/fuzJqlPGERERGRlhbSgf/AzP7P3Z9O2rcn8G4G9UwCLgIuT9p3NvBCBmXkTfWipbw7rybf\nzWhW7o6Z6eq7SMwp5z8elPOfPxktHKZZZAqecv6zF9L5Px94wswmAO3M7FbgAOBHGdRzFvC4mZ0K\nrGtmHxIt8LV/pg0udYMGDeKUU07hgQceoLq6msrKSm666SbKy8sBuPvuu/nLX/7CwoULGTZsGH/6\n05/o0qXLWuXsv3906vv06QPAww8/DERfCn77299y77330qlTJ66++mr23HNPAA488ECOOOIIjj32\nWO6//37+/ve/M2TIkAaPHTZsGC+++CLvv/8+Q4cO5fbbb2f99ddf665DY8cCjB07lj/+8Y8sWbKE\n0047jXvvvZcbbriBkSNH1n9ZItLCQqcF1ZSgki/5XDhMpBClzfl391eB7YD3iRbq+hQY6u5vhFbi\n7nOBHYEjiGb8OT5RxrymNLrUPfroo4wfP54pU6bw3nvv8Y9//AOASZMmcdlll3HXXXcxdepUunfv\nzimnnJKyjAkTJgAwc+ZMZs2axZAhQwB466236N+/PzNmzOCss87inHPOabAdkydPbvTYhx9+mJtu\nuomPP/6Y5cuXM2bMmLrH6qcXNXTstGnTuOCCC7j99tuZOnUq33zzDfPm6W0jUivfOf+104Km+1m+\n3gZ5bWe+Kee/8E1f8kW+myABlPOfvZABv7j7bHe/2t3PcPcrM5niE8DMyoHfA/cBdwP3Ar83s4qM\nWyycfvrpbLzxxnTs2JF99tmH9957D4B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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "max_x = 200 // 3 + 1\n", + "x = np.arange(1, max_x)\n", + "\n", + "plt.bar(x, autocorr(y_t)[1:max_x], edgecolor=colors[0],\n", + " label=\"no thinning\", color=colors[0], width=1)\n", + "plt.bar(x, autocorr(y_t[::2])[1:max_x], edgecolor=colors[1],\n", + " label=\"keeping every 2nd sample\", color=colors[1], width=1)\n", + "plt.bar(x, autocorr(y_t[::3])[1:max_x], width=1, edgecolor=colors[2],\n", + " label=\"keeping every 3rd sample\", color=colors[2])\n", + "\n", + "plt.autoscale(tight=True)\n", + "plt.legend(title=\"Autocorrelation plot for $y_t$\", loc=\"lower left\")\n", + "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", + "plt.xlabel(\"k (lag)\")\n", + "plt.title(\"Autocorrelation of $y_t$ (no thinning vs. thinning) \\\n", + "at differing $k$ lags.\");\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With more thinning, the autocorrelation drops quicker. There is a tradeoff though: higher thinning requires more MCMC iterations to achieve the same number of returned samples. For example, 10 000 samples unthinned is 100 000 with a thinning of 10 (though the latter has less autocorrelation). \n", + "\n", + "What is a good amount of thinning? The returned samples will always exhibit some autocorrelation, regardless of how much thinning is done. So long as the autocorrelation tends to zero, you are probably ok. Typically thinning of more than 10 is not necessary." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### `pymc3.plots`\n", + "\n", + "It seems silly to have to manually create histograms, autocorrelation plots and trace plots each time we perform MCMC. The authors of PyMC3 have included a visualization tool for just this purpose. \n", + "\n", + "The `pymc3.plots` module contains a few different plotting functions that you might find useful. For each different plotting function contained therein, you simply pass a `trace` returned from sampling as well as a list, `varnames`, of the variables that you are interested in. This module can provide you with plots of autocorrelation and the posterior distributions of each variable and their traces, among others.\n", + "\n", + "Below we use the tool to plot the centers of the clusters." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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VWEq7ZFgDek+PnYIFs1GfL0wBCDzf7q6e4L0F6Dlyip7jZwadd/6cCrJKCsks\nKrD6WWlZ/N2d3WTk52HLzqJ41RJaXnoLj93O5A1rwhX3m9bjau0A/8B/+nutgXpWcSFlV1Viy8lG\nRCi/aT0+Zz+ebnvYdSxYMAdfv4u8WdPJnTbFepZbO8ibNZ28WdOx5eYEv5/2s3U4ztZRds3leLp7\n6Tp4jKySYiatuYTMgjwyC6zfeFt2NqhSuHQ+7vYuJq29FBGhaIVljbLl5uA4V0+BczYFC+dSvHJR\n2AK86vNZ1zrkuubPn0X34RPB+xd4/nNnTKVia0TWvKxMJq0eHB9ctu5yEEuBLF1rZbz12PtwtVmT\nRKHfqeyyEjr2hGfDzZk+henzZ1Es/eRMmUx/SxvZZZOs9pMnMXn9FThqGiipXD7Iq2PK9VfRdeAo\nJauWBhNb5M2uILOkiMzC/EFKZLqQcHZBEdkMfBTLCrUH+CVQC9yPtWjjtTH2+3PgZlX9tL/8UWCt\nqg6KrxKRrwM9qvrtiPpC4FXg/w9JrxuGyS5oMBjGE69ecSfO+mY2vP4rCpfMi9lOVdm+9GY83b1s\neudPo5JBaTyQrCxO/sm9YV9gqhp92jVFbN++XafXtA7p8uXq6Mbd2U3B/JFnIWx4ZiAkLHAsVcXV\n2kHWpOIhXVWHwtlwgaxJxWEKXl99Mx27DoQdy9vXj3o9cbnc2U/X0nvyHFOuWxvW72jidTi5sK2K\ngkVzKL5kCa62Tmy52WQW5Me1v7u7l4zcHGzZsd04U4G7q4fM4sKokzBtVXvob2mnaNnCIeM/1evF\n0+sIKkb9Le20Ve0Jbg/eU2d/StwCI2UomDeL3FnTw5Sl4VCfD/X6Yj7nkcreULS/tR9nUwu5FVMp\nW5f8mMpoSlIy8LncIDLi73oiqNdL6+u7ya2YSs/RUwBMu+X6sIkEj72PjLyctFCQRiu7YNx3QkT+\nGfgQ0AU8AfxfVa0P2b4T6Biii3og9GUXdU2RIY4fbf2SQVRXV7Nt28DLZsOGDcH8+AaDwZBKXO1d\nOOubycjPo2Dh0K4yIkL+vJl0HzyOo6Z+wihZVVVVYWuTTJ06NVnrkXw0GZ2MB7JLi4NWn2QiIgkN\nVKORO2NwfFFuRTm508vJmTaQC8saXMU3IC9YOIeChanVfTPyc4PWOLBm1hMhq7hwNMRKmIBiFI3S\ndZW42jqHveeSkRHWT055GeWbr6Fl+5thsYCpUrCCMmxcR0ZB/oiUBLHZhhzMJzLQL11Xibuje9SS\nLIyW0pEQt/aIAAAgAElEQVTKCQDJyKB84zrAUrh8zv5BltpQy/S7lUSe5FzgTlXdHW2jqrpFZKho\n3N3AIhGZCzRiKWx3DdE+UqP8GXBEVb87lJCVlZUYS5bBYBgP9Bw5CUDh8gVh7h6xyJszw1KyahuY\ndEX8iRLGM5ETXfv27UtKv6r6WlI6GmWqq6tJx3WyqqqqYk5Qis1G2dWXp1ii4RlKZhifQfPDyZwI\ntsxMcqeNLAl0VnGhFU8VxzVKpsxhMgyTIOFiSERmEbHcRMeY0brOyabY78IZIF3kTgWJKFnfBByh\nFSJSCuSpagOAqh6LtbOqekXkPqy1S2zA46p6VETusTbrj0VkGpYLYhHgE5H7gRXAZVjrlxwSkf1Y\nLiIPqeoLCchvMBgMKaX7HUvJinwJxSJ3pmU1cNZfGDWZJioiUomVUXAKIZN0qvq1OPd/HHgv0Kyq\nl/rrLgP+DWuS0Y21FtYe/7avAJ/EStR0f6wU7jCybICJUrr2Mjp2HRiUZcxgiJd4JoIMBkP8JKJk\n/TfWCyXUJXAW8FOsFe+Hxa8ULY2oeyzkczMQzadmB2C+/QaDIa3oOXIaIBjQPBx5M6YB4KxvHjWZ\nJiIi8mngO1iTeLdiZcHdAsR0LY/Cz4F/xXKHD/Ao8HVV3SYit2ItL7JRRFYAHwCWY70HXxKRxdEW\nI66srLxol714yJs5jbwkpvpOx5loI3NqMDKnhnSUGdJX7tEgEcfQpaoalkrEXzbrVRkMBkMU7P6s\nXYXLFsTVPnemX8lqMEpWgvw1cIuq3gn0+f+/H8v6FBeqWsXguGIfEPAbmsRAHPHtwFOq6lHVc1hr\ndCWcLddgMBgME5dElKwLIhI2HesvtyVXJIPBYEh/VBX76VqAuIP8cwOWrAbjLpggU1X1Df9nn4jY\nVPV54H0X2e8XgH8WkVosq9ZX/PWRS5LUE2Ptxurq6mjV457QZCXpgpE5NRiZU0M6ygzpK/dokIiS\n9TPgtyLyXhFZISLvw8r299N4OxCRW0TkmIicEJEvR9m+VETeFBGniHwxkX0NBoNhPOFqacfTYyez\npCjuTIGBmKw+E5OVKHX+NRQBTgBbReRawHWR/X4GK95qDpbC9bOL7M9gMBgM7xISicl6GMv14p+x\n4qbOYylY3x5qpwBiLVX9fWAz0ADsFpFnI5JltAGfA+4Ywb4Gg8Ewbgi1YsWb1SynvAzJzsLd3onH\n3mdS4MbPo1jxUeeAv8OaAMwGBq3DmCAfV9X7AVT1aREJTCrWEx4/HHNJklOnTnHvvfcyZ45lzSwp\nKWHVqlXBuIXArK8pX3x5w4YN40qeeMqBuvEiT7zlUNnHgzwTsZyOz3O6PB+Bz7W11nt6zZo1yVpa\nJIyEFyMe8YFE1mEFEN/qLz+IlVXwkShtwxYjTmRfsxixwWAYD5x/8vccfuBhZrz/Fi79flwJ7gB4\nff2HcJyuZf2r/0FRnLFc6cRoLfoYiohkA9mq2pvgfvOAP6jqKn/5MFZGwddEZDPwsKpe6U988SRW\n0qeZwItA1MQX5p1kMBgM45vRei8ltCKa353vAyLyydC/OHeP9GGvI4YPe5L3NRgMhpTjOFsHQP78\nxNZIyp8zA4C+2oakyzRREZF/EZErA2VVdY1AwfoV8CawRERqReRu4FPAt/xLh/w98Gl//0eA3wBH\ngOewFLGoM5YmJit1GJlTg5E5NaSjzJC+co8GcbsLishDwNeAA4Svl6UYP3WDwWAIw3HO8h5LWMma\nOyNsf0NcCPCsiNiBXwG/UtXjiXSgqh+OsSnqIleq+k2s9SMNBoPBYBhEIjFZfwWsVdWDIzxWPRCa\nYiumD/vF7FtdXc22bQNrQgb8Wg0GgyGV9NX4lax5iRnd8/ztHTUTQ8mqqqoKm9mcOnVq0n3fVfV+\nEfkCVtzuXcBOETkDPBlwOx8rKisrx/LwIyYd35tG5tRgZE4N6SgzpK/co0EiSlYfcDGJJnYDi0Rk\nLtAIfAjrZRiLUN/IuPetrKzE+L8bDIaxRFUHLFlzE1OygpassxNDyYqc6Nq3b9+oHEdVfVixUS+K\nyFexFhf+J+JMzmQwGAwGQzJJJCbrq8C/ikiFiNhC/+LZWVW9wH3ANuAw1kKOR0XkHhH5NICITBOR\n81ipcv/G7xdfGGvfBGQ3GAyGlOFu77LStxcVkFVWMvwOIRQumQ9A7/EzoyHahEVECkTkoyLyJ6w0\n7h7g42MslonJSiFG5tRgZE4N6SgzpK/co0Eilqxf+P//n5A6wYrJyoinA1V9AVgaUfdYyOdmwtPi\nDrmvwWAwjEccNVbSiry5M+JO3x4gf95MbHk5OOubcXd2kzWpeDREnFCIyH8BtwL7gP/ESr3eOrZS\nGQwGg+HdTCJK1vxRk8JgMBgmEIHMgIm6CgJIRgZFSxfQVX2UniOnKbvm8mSLNxHZDTygqrVjLUgk\nJiYrdRiZU4OROTWko8yQvnKPBnG7C6pqjarWYKVSdwXK/jqDwWAw+HH4lay82RUj2r9oxSIAuo+c\nTJpMExlVfXQ8KlgGg8FgePcSt5IlIpP864g4gVP+uttF5O9HSziDwWBIRwKWrDz/mleJElCyeo+e\nTppMhrHBxGSlDiNzajAyp4Z0lBnSV+7RIJHEF/8GdAFzAZe/7i3gg/F2ICK3iMgxETkhIl+O0eZ7\nInJSRKpFpDKk/gsi8o6IHBSRJ0UkOwHZDQaDIWX01QTcBS9Oyeo5YpSsVCEij4tIs4gcjKj/nIgc\nFZFDIvJwSP1X/O+qoyKyJfUSGwwGg2E8k4iStRn4vKo2YiW7QFVbgKnx7OzPQvh94GZgJXCXiCyL\naHMrsFBVFwP3YCl2iMgM4HPAalW9FCuW7EMJyG4wGAwpI+guOGdk7oKFyxcC0HvsDOr1Jk0uw5D8\nHOv9FEREbgDeB6xS1VXAP/vrlwMfAJZjJdz4ocTIcGJislKHkTk1GJlTQzrKDOkr92iQiJLVBUwJ\nrRCROVjrVsXDWuCkP47LDTwFbI1osxV4AkBV3wZKRGSaf1sGUCAimUA+0JCA7AaDwZAS1OvFWd8M\nQN6skSlZ2aXF5FSU4+1zBjMVGoZGRCaLyF+IyF/7yzNEZFa8+6tqFdARUf0Z4GFV9fjbBDIWbsVa\nSsSjqueAk1jvOIPBYDAYgMSUrJ8CvxWRjYBNRK4Gfonf2hQHM7GSZgSo89cN1aYemKmqDcC3gFp/\nXaeqvpSA7AaDwZASnA0XUI+XnKmTycjLGXE/hUvmAWA/eS45gk1gROR64DjwEaw1HQEWAz+6yK6X\nANeJyE4ReUVErvDXR31XRevAxGSlDiNzajAyp4Z0lBnSV+7RIBEl6xHg18APgCzgZ8CzwHdHQa4w\nRGQS1szhXGAGUCgiHx7t4xoMBkOiOGot4/5IXQUDFC6eB0DviXMXKdG7gn8BPqiqt2AtQgzwNhdv\nXcoESlV1HfDXwH9dZH8Gg8FgeJcQ9zpZqqpYCtVIlap6YE5IeZa/LrLN7ChtbgTOqGo7gIj8DrgG\n+FXkQaqrq9m2bVuwvGHDhgnjH+r1KbvrulGF+WW5TC8a+Sy5wWAYHS42s2CAgoCSdTK9V8moqqoK\nm9mcOnUqmzdvTvZh5qnqdv9n9f93kdhakNE4D/wOQFV3i4hXRCYT3/sMgFOnTnHvvfcyZ47VvKSk\nhFWrVgXfS4FrY8oXX96wYcO4kieecqBuvMgTbzlU9vEgz0Qsp+PznC7PR+Bzba218seaNWtG472E\nWLpTHA1FNsXapqovx7F/BpY7x2asOK5dwF2qejSkzW3AZ1X1PSKyDvgXVV0nImuBx4ErgX6sAOXd\nqvqDyONs375dV69eHdc5pRMHGnr43o7znO/qB8AmcMvSyXxyzQyKcy92HGEwGJLFyUd/yulv/4wF\nf/Vxljx4z4j7aX9zP7v+7LOUXL6Cq5//aRIlHFv27dvH5s2boyaJGCkisgP4O1X9HxFpV9Uyf8a/\nh1T1hgT6mQf8wZ/kAhH5NJbL+tdFZAnwoqrOFZEVwJPAVVhugi8CizXKC3WivpMMBoNhojAa7yVI\nzF3w8Yi/3wMvYMVqDYuqeoH7gG3AYayg4aMico//RYaqPgecFZFTwGPAvf76XcDTwH7gACDAjxOQ\nPa157lgrX37+FOe7+plRnM0VM4sQ4Lljbdz37HHOtveNtYgGg8GPo6YOgPw5UUN04qZg8VwAek+e\nI97JsHcxDwBPisgvgTwReQz4BfCleDvwrwP5JrBERGpF5G4st/gFInIIy3PiYwCqegT4DXAEeA64\nN5qCBSYmK5UYmVODkTk1pKPMkL5yjwaJuAvODy37LVP/F+hJoI8XgKURdY9FlO+Lse/fAn8b77Em\nAqrKr6qb+eVeK8bjf62ayifWVJCVYaO208kjr57jZGsfD/zxJN/buoRZJbljLLHBYHCcs7zG8udd\nnJKVPaWUrNJi3B3d9De3kju9PBniTUhUdaeIXIaV+OJnWG5+a1W1LoE+YsX5/kWM9t8EvpmorAaD\nwWB4d5CIJSsMv2XqH7CCgQ2jwFMHLAVLgPs3zOZTV80kK8O6ZXMm5fLt9y7hqtnF9Lq8fG3bGXr7\nPUN3aDAYRp2+JClZIhKMy7KneVxWKlDVelV9VFU/q6oPJ6JgjSZmnazUYWRODUbm1JCOMkP6yj0a\nXGwwz02ALxmCGMJ5s6aTn++xFKyvbJzHDQtLB7XJybTx0KZ5fOEPJzjT7uQHb9Xx5RvmpVpUg8Hg\nx9Nrx9XWiS0nm5zpU4bfYRgKF82lc9dBek+cY/K1a5Ig4cRBRP6dgSQXMVHVj6VAHIPBYDAYwojb\nkiUi5/1+6oG/Vqx0tg+OnnjvTuq7+nn0VWvm+u4rK6IqWAHysjL46uYF5GQI20918GZNZ6rENBgM\nEQQWDs6bMwOxjdhRIEggLsuslRWVU8DpOP7GFBOTlTqMzKnByJwa0lFmSF+5R4NELFkfjSjbgROq\n2h1vByJyC9Z6JjbgcVV9JEqb7wG3+vv/hKpW++tLsJJsXIJlPfukqr6dgPxpgcvr4x9ePovD7WPD\nvEl88NJpw+4zsySHT145gx/trOc7b5xnWXkBZflZKZDWYDCE4jhtrU+bP39WUvoLrJVlP12blP4m\nEv44XYPBYDAYxiVxT7Wq6msRf3sSVLBswPeBm4GVwF0isiyiza3AQlVdDNwD/FvI5u8Cz6nqcuAy\n4CgTDK9P+afXajjV1sf0omweuG4OIvFllNy6spzKGYV0OT3802s1+Ew2MoMh5djPWMpQwcI5w7SM\nj2CGwVMmJms4RGSTiPxERP7k/5/8RU9GgInJSh2jLfOFXhd76rpxepIXJWGuc2oYbZk9vuSPudLx\nOkP6yj0axG3JSoL/+1rgpKrW+Pt7CtgKHAtpsxV4wt/P2yJSIiLTgD7gWlX9hH+bB4hbwUsXfrSz\njtfOdJKfZeNrm+dTkJ0R9742Eb58/Tzu+d1R9tb38NNdDXz6qosLvDcYDIlhP+VXshYlR8nKmzUd\nW042/Y0teHrtZBYWJKXfiYaIPAB8GWsNxf1YCwX/SkQeVdVvjalwaYjL6yM74+LdXScah5t7ATjR\nYufSiqIxlsYwXjjd5qC208nMklyWTMkfa3EM44hEfkU7gTuADKDOv+9Wf308/u8zsdLqBqjz1w3V\npt5fNx9oFZGfi8g+EfmxiOQlIPu45w9HWvj9kVayMoS/27KARSP4ok4uyOKhTfPItAlPH7rArw80\nj4KkBoMhFgG3voIFs5PSn2RkkO/vy2QYHJIvAptU9cuq+kNVfRDYhLV+1piSbjFZF3pd7DjXyW+e\ne2msRUmYVMWCJNNRJF6Zu50evKNgLRkJ6RhzM5oy13Y6Aajvcia133S8zpC+co8GiShZS4D3qOpH\nVPUhVf0o8B5gqar+beBvdMQkE1gN/EBVVwMOJlDCjVOtDn74lpVt+Asb5lzUDNnqmcV86XprFv3x\n3Q08e7glKTIaDIahUdUBJWvR3KT1G4jL6jVK1nCciiifIQ7viwAi8riINIvIwSjbHhARn4iUhdR9\nRUROishREdkycrHHFzUd1kCxudc1xpKMXzJs8bnxJ4tWu4u99d3srZ9wDjxD0tzjorPPPdZiGAwj\nJpHEF+uAnRF1bwNXx7l/PZYLR4BZ/rrINrNjtDmvqnv8n5/Gcg0ZRHV1Ndu2bQuWN2zYMK79Q1WV\nH++qx6vwvuVTuHFx2fA7DcPGhWXYXT6+t+M8P3irjoribNbOLkmCtAaDIRbOuiY83b1kT55E9pTY\nGUETpXCptQ587/EzSeszlVRVVYXNbE6dOpXNm5MeLvUN4HER+QaWl8Rs4KvA1/3xwACo6lDBND8H\n/hW/y3oAEZmFtVxJTUjdcuADwHKs99RLIrJYdbCNI91isgJhwJdcsW5sBRkB4/ldH4t4ZG6xW4qG\n3eUdbXHiIhXX2eHycuSC5Z65ceHFj4sm6rMxHklXuUeDRJSs/cA/isjXVLXP7673t0C8vhC7gUUi\nMhdoBD4E3BXR5vfAZ4Ffi8g6oFNVmyGYQn6Jqp4ANgNHoh2ksrKS1atXJ3BaY8vuum6qG3opzM7g\n41dUJK3f9y6fQpfTwy/3NvLIqzV8/46lVBTlJK1/g8EQTs8Ry5BStHJx3Alr4qFwyTwAeo+fTVqf\nqSRyomvfvn2jcZjH/P/vwrJeBW7AR/zbxF8fM9BVVav876dIvgN8Cev9FGAr8JQ/PviciJzEijtO\n+4y3Lu/oLX2pqrh9mvbxXql22mvq6U/xEYfnUFMvqnBpReGo9G8sqaNPn9tLhk3S/vs4nknkyn4C\nWA90iUgz0AVsAD4ez86q6gXuA7YBh7FeUEdF5B4R+bS/zXPAWRE5hfVivDeki88DT4pINVZ2wX9M\nQPZxiU+Vn+1uBODDldMozr3YtaHDuatyGuvmFNPT7+WRV2rGjT+3wTAR6T7sV7JWLEpqv4VLFwDp\nq2SliPkhfwtilBck2qmI3I7lRXEoYlOs+OFBjDQmy+NT2h1uohjHLpo+d2yLSL8/c947eyMdVy6e\n6sZedpzrHLFFZrisuamKBWm1J08BGErmV06388rp9qQdK1m88trrtNpdtDlcuEdRKQ+QjGzJ6Rgn\nNJoye3zKrvPd7KvvGdH+HX3umL8jicrd2++hoXv8TSQkg7hH9ap6DrhGRGYDM4BGVU1o8RZVfQFY\nGlH3WET5vhj7HgCuTOR4450d57o4097HlPwsbl9RnvT+bSJ86fq53PPbYxy5YOepA8185PLpST+O\nwWCAnndOAMlXsvLnz0Kys+g734inx05mkckwGEkga20y8XtrPITlKphy9tV3Y3d5WTKlgJklF+eF\nYHd58fqU4txMznX0cba9j7mT8lgwOXX5o1Q1GF9zodfF/LLEjt3Q3c/xFjvLyguoKJ74XhntjvEb\ni1TX1c8s/1KAnU4P5QXZST9G6KSwhtqmI3B5fGRnGktMovR7fPhUh5xwiYXD5aW6wVLOkuHKubvO\nijXMybQxeYKt8ZqQ6UREJgM3ABWq+qiIzABsqlo3GsJNZHyq/Mc+y4r1ocppo/YjUZSTyZeun8uX\nnz/Fv+9rZNX0wlEz7xsM71ZUlc69hwEoWb0iqX3bsjIpXDKPnndO0nP0NKVrL01q/xMB/2L1nwcu\nB8J+4FR1pEkpFgLzgANi+X/OAvaJyFriizEG4NSpU3zqLz/DwnmWJ2JJSQmrVq1i/fr1HGzs5dSB\n3Uwryg66VAZmgd0V1nP00quvs3By3qDtiZT3N3RzyRXruG5+KX948RVLsCvWsWByHv/9P6/Q7nDx\nsa1byLRJ0IIViMkayfGilVeuvgqwLGTvAPf9r1sRkZjtL197NTaBvW+/FXY9nn5hO5fPKI56vA0b\nNiRN3ljlwPXZuPC2EffndPu44fpryfQn0KiqqhrUfknl2rDjXcz96Ohzs2rNOuaV5iXleoRaIne+\nuYPSvKykX+/A/X5n705s9UVcf921g9ofabaz/bXXWFiWz2033pDU4ydSfsf//Yq2/fXX36DF7uKW\nzTdgd3k5vHcnWRm2uPoPPM9un4+N112XVPkrr1wXvL5ZjdG/T7HK7Q43RQsvG7J9gESuX5/bS1XV\n22Hbn3vpVbqcHj74ns3Yhvi9SLQc+Fxba9mK1qxZMxqxwki8rggicj3wW2APsF5Vi/x1/5+qvi/p\nko2Q7du3azrEZG070cY/v15LeUEWP//AilH3iX18dwO/PtBMaV4mP7xjGZMLJtZsgcEwlvTVN/Pa\nFXeSWVLE5qPPI7bkfp8Pfv7vafjNc6z45gPMufvPk9p3qtm3bx+bN29Oano2EdmGFW/1DNa6ikFU\n9fEE+pkH/EFVV0XZdhZYraodIrICeBK4CstN8EUgauKL7du3a1fJvEEzvq12F4eaYgf2B9zEphRk\ns2r6xU2MBfq6tKKIg40D7kEbF5YFt80vy2NeaR47a7uCs9vJmKUO0O5wcyDk2JdWFDEpNzNqpr4O\nh5vqxvCZ8lC3uY0Ly3B6fGTZBK9PkzZJ6fXpkJkDQ2VYUJaHw+1j+dTELMt2l5dd57vItNm4dv6k\nmO26nZ6o2QTjuSd9bi91Xf3MnpRLbqYtKHdlRRHZmbaE1uCMRqQL4yXTC5NqzfKp8tqZjmD52vml\nQYU0mhzlBdlcksB3xOV3iQ19blxe63kaSTxt5LMZytn2Ps51DPwk5WTauGZu7PseSX2XkxOtDhaU\n5TG3NLb1V1XxKlGvUzR6+z1BC1Ki3/Pqhh46/FbpwL6n2xwU5WQytXD458Dl8fH2+W5mFGezcHJ+\n8PotnpLPrJLcsLaBbYsm5zN7Uu6gvpLFaLyXILGYrH8BPqiqtwAef93bWMG+cSEit4jIMRE5ISJR\nswOKyPf8aXGrRaQyYpvNv07W76Ptmy70ub38bHcDAHevmZGSoMNPXFFB5YxCOvo8PPzqOROfZTAk\nka79Vh6eksuXJ13BAiheabkgdh+JzFJu8LMOuFVVv6+qj4f+xduBiPwKeBNYIiK1InJ3RJOg05Kq\nHgF+g5WA6Tng3mgKFsSOyRqLn+Chklp09Fmv9YCCleyYrMjRy5FmO6+f7cAREZ/V7fQEFSywXAsj\n5T7V6uCtmk5eP9vBjprO4PaLiWE5297H62c7osaGOFxe2iLc986099HU059QfNnh5l52ne8CwOPz\n4fT4Ysp8MVniDzb2Utfl5J2m3rB4purGHnad77roLIWRz0Yg7X+i2F3eqDGHkffAN8yXpcXuQlXp\n7ffwVk0XF6IkzQi9zjtqOtlR04mqcqHXRdW5Tnac6+RQk31E5zEUnU5PWDngpney1TGsS2hVVRUn\nWh2A9byF4vEpPf0Dfb96poM3znYEFcjhCL2iiboMRsbIdfa5qe10cri5l/OdTn7z3Et4fRoznrS+\nux+Pz0dtpzPumNPRTMgzmiQyGpinqtv9nwNXxUWcLof+NLrfB24GVgJ3iciyiDa3AgtVdTFwD/Bv\nEd3cT4ysgunEUweaae/zsLQ8n02LkpfqeSgybMJXbphHaV4mBxp7eXJ/U0qOazC8G+g6cAyAksrl\no9J/IM6r9+hQ672/q6kClg3baghU9cOqOkNVc1R1jqr+PGL7AlVtDyl/U1UXqepyVd02uMf4ebu2\na8iJL1WNe2LM5fHR2++Jum2ocXsyEhg4XF5eP9vB+c7hB90en3W8xojMeZGD0sPNVrKMUM5HLPqa\njPilgLXheIt90CD97fNdYRbAUEIHnI09/bxV0xWMV4kkst89dbHXvYqVXa+mo48DDT2DBqf9Hh/N\nPZay4fAPmnv6oy9g3B3j+YhGi93FO029Qz5/nijbAu3rupy8crodu8tLn3tAqartdLLrfFdQiQjF\n4Qp/FgMW36Fo6nFxrMWB0+PlcHPs9qFKiGI9X4Fnv80x+JrXdPSx63xX1HOMh2jrfDX1uKjrcgYt\nu3VdzuCCxhA70YdPlY4+KxnO3rpu9tR10+Fwh92buq74EkiEHmJnbVcw4U08RF4Kb0j5VJuD5l4X\nr5/tYGft8Ou6hfYV+vvU2N0fdu3sromvZB0RkZsj6m4EIrMuxWItcFJVa1TVDTyFlQY3lK341yhR\n1beBEhGZBsG1Sm4DfpqAzOOOxu5+nj50AYDPrJuFLYmpnoejND+LBzfOQ4D/rG7idNvgHzeDwZA4\n3Qf9StalFzXOj0nhMisxXs+xM6OSbW4C8AngZyLyAxH5WujfWAsWWCcr0mJzKuT31+H2ctA/kLS7\nvBxpHphRb7W7ePVMB6+f7eBwcy8dfW7qhxhI7ajpZHddd3B2OvR5kSHUrMhtl1yxjkNNvbxyuj2m\n0hbJ2fY+vD4NO7eQA0SlttMZNiM/kjfi0QvW9YpnfZ5XT3cMcneLHNQevWDnYGNPmFyxCCgAZ9v7\nOHbBjtPjpaPPHZfS6vb6WL128FKj7Q532KA7lDPtfbT3uWlzuDnbbikAXn+muCMXemnoDlcUDjQO\nr6AMxTtNvbTYXWGKbeQaan1ub5gScq7Dsgq22F2c9CtRu853sbO2i1fPdOBT5azfMhNPVrlIpdDl\n9Q26Z70ub0zlxOvT4LOxo6Yzapto+FQ5096H3eXlfKeTxu7+EStboURaZU62Ojjd5sCnVkbR1850\nUN/lHPQ8v3amg+qGHnbXdQcV6VaHO+w5jfXM9vZ7gkp+Q3f/IFfUN2s6OXbBHpeVc7jvReD5cHq8\nI0qs0dPv4ViLnf0hkxVtDldSskymmkSUrAewUqj/EsgTkceAX2CtHxIPkSlv6xic8naotLiBtUrS\n7yqH8OO363F7lc2LSlkxLfVZwi6fUcTtK6bgVfjOG+eN26DBcJGoKt0HjwNQfOnSYVqPjJzyMrKn\nlOLtdeCsM1boKPwD1gLE04DFIX/JTfV4Ebx9vov6kIFq5Mxxp39gvut8F8290QeeF3pdVDf0cKLV\nPuxAZ2et5ZYW+gs/1AAq2nxfIFX5mXZL7m6nh26nJ6aif8EeOvMc/+Aq1KIz2uMo9V+RWr+Lm0bE\n/8ACoj4AACAASURBVIA1uG5zuNlX3zPsILHf46PD4Q6Lu7H6sOJJ3jjbSZ/bG9Nqtb+hB7vLy6lW\nR1Axi0e5a+h2ca7DUgCaelxBy2CnM9xyErWvOK5xR5+btpD76fEOvdMbZzuo8z/fAQXqTFtf1LZV\n5zqHHDA7olzzV0634/UpLo+PHec6eaumK2x7Y3e466bT//063+nk9bMdNPcMtlINN/wJ/Y6e6+jj\nWIudd/xK9YGGnqCFNTNBF/HQr1rod0kVjrdYSmk0C1+A0POs63JGvZ0N3f28HWKh2l3XzeHmXrqd\nHo63RHeLbOzpDyrtiTCUFex0W1/wXgQIvfehrqYBK3as/tJxvBr3k6GqO4FLsda4+hlwFlirqrtH\nSbYgIvIeoFlVq7Gez9SZf5LI0Qt2dtR0kZtp4/9cGXVJlZRw95oZTCnI4kSrg/861DxmchgME4G+\n8024O7rJKptE7sxpo3acouULAeg5embUjpHGfAioVNX3q+pfhPx9bKwFC43JOtvuZH99TzAuJ5JY\n1otoNEYZNEYjdFxS0xl90AtWQH4ooXE3Hp8Pu8vL3vpu9tZ38+qZjqD1KJyBg8U6x1icaeujttPJ\n6faRe1iExt1c6HVxus0RZkHsCHErDFhbaoa45j7VoLI6FNVRXAkDFhqPz8fO2q6YitO+XW9yoLGH\n811OTrQ4aLW7BsXfRCPUtS3RGX73EIPVs+19nG5zUN3Qw8GmgfMK3SNWvN7JCMUgmrIEgwfLodah\n2k5nMKlCJE09ruBAPNIa5I24BgH3zoBV9TfPvzToOr1xNly5Bkt5Cii7TVG+Yx19luWovc+Ny+uj\n1T6g4EbSEmM9tdD7G3opOvrcOD0D12wkMYY+tRSv4y12HG5vUCkMEC2ZSiSR7rkdfW4ON/XGjIuK\ntO6FPh8tdhdv1XSGuWmGenCF/iZd6HXR0ecOxodOBOKNp8oAtgM3q+qjIzxWPClv67FmIyPbvB+4\nXURuA/KAIhF5ItoLtLq6mm3bBtzjA2kwxwO/2GMlu7hzZfmYZvfLz87gi9fO4aEXTvPE3iaunFXM\nwsn5YyaPwZDOdB84CkDJZctGlJkqXgqXL6TtjT30HDvN1C3rR+04yaaqqipssDB16tTRSJV7Bhi/\nCwv5cft8dDpjz/omomTVdzlZMmXgd1tVaY8YnNR3OQcpT7GYWpAdc6ZYFToj+m7q6ac4J4NWu5tV\nFYVRXd9PtDhwenyU5GZQkjv0cGMoBTBefD7lVKuD0vysYFxObaeTjQvL8Po0TBnyqoIOWF2STaR7\n6FAEZu67+j1cGMFCx6F3bTiLE1iZ4Ob4M7V1ONx0Oj3BdcsiLXIBGnssV7nQZy5ZvHG2g/KC7JhK\nSQCvKhe64rs+dpd3kJtrNKUpkvY+N2c7rO9WrLi4UKtkiz38ZyfwPM0vy+NU6/DPVujd6ukPf2bi\ncTnN+X/tnXl4XGd18H/nzqYZaTTaJVuyLFnx7tiKHRxnIWuzl0CBNKR5WggtzUeA5oF+LQS+Frqx\ntKVQKBRSIKUpJECh2RqCEyekOKsTx47jJd7jXd5lS7K20fn+uHfGV6MZaSTNKr+/55ln7n3nzr3n\n3PU99yyv1xp27Z3sHRjmzTzVNzgi73Esoqq8+HYndWU+WiqD8RxDy5IR1TRVNa3Uk7UHTrOovpSy\nwOj3gXUHTlMdSl6hsPj8WGkaWaoaFZFWxhdemMga4DwRmQkcxH7zeHvCMo8CHwN+IiIrgJOq2oE9\nIORnIV5K/k9TvaFsb2+nEEu4v3HwNK8f6KLU7+H9i+vyLQ4XNpXzrvk1PLb5KH+7ajffePccwmOc\n/AaDYSSdsVDBJdkJFYwRdvKyurYUlycr8UXX2rVrs7GZB4BHReSbwDD3vKo+k40Npkt7ezvj8+mk\nz7M7jtMYKWFOTYi1+0+PyF3ZerSH9unhtNZ1ZjDKi2+f7Sy5826U5NXuYiFN24+eoSE8smO0/5Rt\nNB7rIWXHKZNEGxeyt7N3RGGMPSd7c56DnK6x5N7P4yk+4MbjOjbHU3iBUhEzPEt8FhWjGMLRIeXQ\n6T6EkTlZmWAsAwvs8uQDKbxGyVjjMoYWLVuRtOpgMnoH7G2kk090KMGAiRmpdWX+YV6pVLzgyhFL\nNHBXXHLpmJ5UVfCNUYpyS1Kv8+j0DkbZczI67MXPQBIDfneSypLJzo8zA1HW7DvFVW1VY3pekxUg\nATjaPcD0IhuIfDy96r8C/lVEPo+dTxXfS6o65lnvGGofB1ZiG2vfV9XNInKX/bPep6pPiMhNIrId\n6AYSS+gWLQ+tt5/7711UWzDGzEcuamRjRzc7j5/hS8/u5m+uaxt1jBCDwTCSePn2LBW9iFE2LxYu\naCoMJuFjzvcXE9oVmJVjWXJKzKOVqmJcunf00Tw6diJ66hCe/ad64wZVKlJ1nDJFYmfXzVQv8pTo\nwUwXd2c33Y74WF6RdIukTASR8eX6JZIqDDGRYz0jhw0YL+mGy46WZ5ROCpIdspgbJ/6xnn7WJoQb\npvJ8pmLb0Z547t54eetId9EZWePxTH0P+APsXKx+7NCMQcYRoqGqT6rqXFWdrapfdtq+q6r3uZb5\nuFMWd4mqjnjlqarPqeot45A77+w6foZX950m4LV494LafIsTp8Rr8YVrW4mUeHl132nud8IZDQZD\nekR7+zj5ql1gteIdI8avzShlc1sA6N7+NkP9BR8Zl1NUtTXFJ20DS0S+LyIdIvKGq+3vRWSzM27j\nz0Wk3PXbvc6YjptF5LpU6001TlaueD1FOXEYPRwp0+NkZZvNh7uLTmbIzH4+OoEQw87eQbYcnpjx\nOZrMa0YpSz9ZJvMKeLz7OTEvKR/84OFfpbXcZPIYx0tn79hG9Gj7eqIGVrEyppElIg3OZKvrM8v5\nxKYNo/Azp2T7DXOqKR8jLj3XNIQD/L+rW7AEfvrG4RGlbQ0GQ2pOrtnAUG8/4YWzCdRWZXVb3tIQ\noZZGdGCQ7u1vZ3Vb5yj3Y4/j6GYlsFBV24FtwL0AIrIA+F1gPnAj8G3JZkLeGEy06tbqAuhIGvLD\n2v2nUlaxLFQS8wINhkInHU/WVgBnfKu3ga/Fpl1thhQc7urn2e3HsQTee37heLHcLJke5u6LmwD4\n6v/uGbV0qMFgOMvhp58HoPryd+Rke+FFcwA4tWFrTrZXLIhIuYj8k4i8JiJvi8ie2CfddajqauBE\nQtvTrnD4l7CLMQHcAjykqoOquhvbAFuebL2xcbKyyf8mqZI2WbKRd5NtjMy5IV8yj7eAgxuzn3NH\nNuVOLAdf6KRjZCW+nbsyC3JMWR7eeISowjtbK5gWLtxY0nfNr+HGudX0R5XPr9w56mCXBoPBrqrU\n8fivAai/6YqcbLP8/JiR9VZOtldEfBtYCvw1UAV8AtiDPb5ipvgw8IQzPdqYjgaDwWDIAv1T0MjK\nWNVEEblBRLaIyFYR+XSKZb7hxLmvE5F2p61JRJ4RkY0iskFE/iRTMmWT7v4oT2w5CsCti7M3fk4m\nEBE+dkkTixvKONYzwJ89se2ci501GMbDqfVb6N3fQWBaLRXLFuZkm+XGk5WK64D3qeojQNT5vg34\n/UysXEQ+Bwyo6oPj/W++c7Imyrma35RrjMy5wcicO7Ipd/6CsidGOglCXhG5irMercT5tErkiogF\n/AtwDXAAWCMij6jqFtcyNwJtqjpbRC4CvgOswC6w8SlVXSciZcBrIrLS/d9C5BdvHqZnYIgl08qy\nMrZEpvF7LP7m+ll89skdbOzo5p5Ht/JX185iUUNZvkUzGAqOwyvtUMG66y5DrMmMbpE+kQsWANC5\nfjNDff1YgeyXxS4SLIhXSu8SkQj2UCHnTXbFIvIh4CbgaldzqjEdR/Dcc8/x+LPPUzfdjjQMlYVp\nnbsgHlIT65AU2nyMQpFnqs7vemtTQcmTzvyutzYVlDzpzMcoFHmm8nw2z48XX3iekM8THxYkNgbj\neOdj03v22BHlF154YTbGb0R0jHr1IrKb0b1Zmk4FJ2fcq8+r6o3O/Gec/37Ftcx3gGdV9SfO/Gbg\nSmesLPe6Hga+qaqrErezatUqLYRxsk71DvIHP9lIz8AQ/3jzbBZPKx5D5cxAlC8+s5uX954i4BH+\n+vo2LkhzrBWD4VzhhWs/xKkNW1n2o69Se83FOdvu6svvoGvrLi567LtUZrmiYTZYu3Yt11xzTUbf\nR4rIKuCLqrpKRB4EhoAuYJmqXjiO9bQAj6nq+c78DcBXgctV9ZhruQXAj4CLsMMEnwJma5IH6qpV\nq7Qz0jJBzQwGg8EQo31amMqQL+PrzcZzCdIIF1TVllHK446nRG5iDPs+Rsawjxnn7jwE24GX09xu\nXvjZGx30DAyxtDFcVAYWQNDn4QvXzuL6OVX0RZW/+NWOUcsAGwznGr0HDnNqw1Y8wRKqLs3tS53K\nFUsAOP78azndboHzEWC3M30P0AtUYA87khYi8mPgBWCOUzTjTuCbQBnwlIisFZFvA6jqJuCnwCbs\nPK27kxlYBoPBYMgcAxOspJovchPjkiGcUMH/Au5R1a58y5OK/Z19/OLNIwB8cNm0PEszMTyW8Ml3\nNseLYfzlyp28cbBgd7nBkFMOr7RDDqqvXI6nJLcFbWp/6xIADj4ywpF/zqKqO1V1hzN9WFX/UFVv\nc4yhdNfxe6o6XVUDqtqsqvc7YzrOVNWlzudu1/JfcsZ0nK+qK1Ot1+Rk5Q4jc24wMueGYpQZsit3\nZbCwhkEai1xKux9ods0ni2FPGecuIl5sA+sBJ6k5KevWrWPlyrPPu8suuywei5kLVJXvvLSPgSHl\n2tlVzK8rzdm2M40lwj2XzSA6pKzcdpx7n9zOp6+cyeWtlfkWzWDIKx3/82vAzsfKNTVXXoSvspyu\nzTvoXLeZSPv8nMswHlavXj0sDr6uri5jse8isgzoU9U3nfla4OvAIuBF4P8W8gs5w7mMkMG6YlOS\nUr+H7v5ovsUwZJkVzRFe2tM59oLY/dJiYsycrIxtSMQDvIVd+OIg8Apwu6pudi1zE/AxVb3ZyeH6\nuqqucH77D+Coqn5qtO3kOyfr8c1H+cbzewn5LO6/dUFWYkdzTXRI+daL+3h8s10p8Y4LGvj9pQ1F\nd7IbDJmg78hxnl1yC+KxuHrD4/gqynMuw5YvfJPd33mQ+t++igu+93c53/5kyGTsu4j8BvgrVX3a\nmX8EmA78O3A78Ibb+5QPVq1apZUt8+nuj3Kkuz+fohQNPo/FQLTwSzV7LJnwQNCza0JsS3NMyoZw\ngEOTGCOqWKkO+TnWY66ZbLJ8RoRX9qZn4GSL8RhZV7VVZUWGvOVkZQpVjQIfB1YCG7EHctwsIneJ\nyB87yzwB7BKR7cB3gY8CiMilwB3A1SLyuhMbf0OuZE+XjR1d/OuL+wD4xKUzpoSBBfaD5BOXNPFH\ny6djCfzo9UP8xa92cqrXjL5uOPc4+N9PwdAQNVcsz4uBBdDyfz6A+Lx0PPEcZ/YezIsMBcJ84DcA\nIlIB3Ajcoarfwjay3pVH2eK0VgWpK0u/EuRFMyJZlKZw8VkWy2dEuKylIt+iJJC873XpzAoaJjD+\n5ZyaEI3lY/+vfVqY5TMizKsdf3XipY0j703jOQfTIejzZHR9iVgCC+uzn9N+xaz0o3MCXrvb3Fhe\nktbyc2sLO5rJ78n/y/LYPk1FbamfOTUhliU5pwudnOZkqeqTqjrXiXP/stP2XVW9z7XMx5049yWq\n+rrT9ryqelS1XVUvcGLjn8yl7GOx7sBpPvvkDgaGlHfNr+Ga87JjbecLEeF3F9fzd9e3EQ54WLPv\nFB97+C22HO7Ot2gGQ85QVfY9+DgAjR+4OW9ylDTU0nDL1TA0xJ5//0Xe5CgAvEDsVfcK4JCqbgVQ\n1b3YxS/ySiwna6yORIx5daV4rNE7Po2REubUpO68VYdGdqZXNI/PcMtHPshlrRWU+u2Oe3PF2J3Y\nWVXBYfPpyBwpGZ4lkY6hsDhhGJPygJf5znFKTAmoKBn95eqsqiCNkRLEiQQZTebKkI9SvwcRITRO\ng6Y84BlmoAS81oQNFr9n+Ln75msvEfBarGiOjHler2iOxPd5W9X4jEXFNgyXTJt8dWP3fvZ5bNmX\nz4hw8cyKcUXlLJ8R4cKmclqq0jOyvJbgNtKvHIdBN55rcEYkPXkSmUhE0lgvgcZ770glw6yqIJfO\nrGBhfSmNkRLKS4orHwuKrPBFofLsjhN87skdnBkY4qq2Sj56cVO+Rcoay5rK+dZ75jK7JkhHVz+f\nfGwr331pH53Gq2U4Bzj2v2vo2rwDf01lXvKx3DTf+T4A9j/0Pwz1D+RVljyyEbjVmf4A8HTsBxFp\n5OzYWQWLu4Mxv66UaeEAAa/F7JrQsI71tHCAUr+HmRVB2xMSSe0JSVbR1m1MeESYl/CGvTLow+fq\nTAe9nqRv61sqgyPaRqM84B2mR0XwrBES0wlGdrRaKoPUlPqZX1fK+Q1lBH2eEZ3taWN4g2pLRxqb\nF0wPI65Or9v4nFNTysUzh9vlpX4P6sqdKvF6WNZUPsyDtdiRqyEcYGFDauP3kpkVzBxl/402VEo4\ncLaDeUmCjA3hwAgjWkSoKT27r8dr4LhZ0RwZcdwvbLK9Chc3R1J6yBbU2cdtaWM5V7VVMa185HKW\nCB5LsERY3DBc/xonGqgq5OOdSXLBL2+tpKUyyPIUnf4yf/JO+dLpYYI+D6V+DyVpvvwAez97LSEc\n8OL3WEllSsTnEWpdx0FEaAgHUnpAx3q50FxRklSv82pC8WvJ3u5IvbyWRanfM+zaT/U+Z94o9QRC\n/vEZ/InGfTL5S7wj1zmzMojfa8VfSBQjxWcWFhCqys83HOa+Vw4AcMuCGu6+uGnK5yo1hAN87V1z\n+N4rB3h44xF+/uYRHtl0lAubwlw7u5oVzeVJL3CDoZhRVXb80/0AzPzj27D8+Q0Hrli2iLL5bXRt\n3sGhR1cx/f0FF0GdCz4NPOaMsRgF3JbvbcDzeZHKRXt7O8CwDpCbZY3heKfF/exoipTQFCnh2R3H\nAdsTsbwufW9US2WQ3SfODGurK/VzuLuf2TUhppUH2HLEjkTwWRbt08Oc6Blg3UF7uI4/eu/1ADRX\nlvDi2ycBWNwQprrUN2y9TZES9nX2xucT84fObyjD77XierhzrcIBD7NrQvQMRIcZEWCHqZ/v8iDV\nOAbTssZyXtt/iqWN5fg9FjMiJex1tn/X+25g+9EzdHTZ219YX8qZgSAvu3JORIR3tlaw7sBpKpxK\nZYunhTna3c+0cj+WCFfOqkREODMQJeC1OHnm7EvEi2eOPAbVIR+XtVTEn3tt1SEGokMMRJWZlSVs\nPdJDg2M8u7FE4oOsVod8wwzQRNyGnjehZ5yqwJb7fKotS77umGHzxqGRw7QsnxHB77GNoNaqs+fT\nomUr4t4tEWFhfRnzapU9J3tpigRYvds+X7wJoWg+jx0O6rWE7cd6mBYOUF7iHaZPXZmfw122c7oh\nfNYo81rCVW1VnOgZYMfxMyxwPImtCd7MaeEAB53zb1lTmOd2nojLHKPEN77+iUeEkN8zYj97LaEx\nUsL+zl7m1ISIDkFZwMOQKhsO2fV2KoM+Sn0ePJbEQ0Rj6znVO0jPQJQZkRIGh5SDp/uYXh5gz8ne\nETKD7VFsriihrdpicEj5za4Tw353FwlpigRoLA9w8FQ/JT6L2lJf3FhR1fi1LyLDciB9HotF9aVU\nBH3DIpW8lsXg0NlrtyLo4+SZ5C/3EuV2G5kN4QBzakJs7OjiWM8AMS9f7Lo6cKqPt45MnQgpY2RN\nkMEh5bsv7eeRTXap9o8sn877z68raot7PPg9Fndf3MS1s6v44WsHeXXfKV7aY39qQj7es6iWG+ZU\nF6V712BIxpGVqznx8np8VRFmOl6kfCIitHzkNt781BfZ/k/3U3/TlXhCEwsZKVZUdbWINANzgK2q\n6u4p/g/wUH4kG4nXEi5rqcBjCad6Bwn67M7YWOFqS6aFOXS6P+kb7oX1ZWzs6OK86hC7T/QO6wQ1\nV5RwpLuf7v4oVU7nfUF9KS0DwREGX1nAnk9WwqHEa3HxzAr6BofiYV/hgJfTfbbhMbsmNMzImlcb\nihtZ08sD+BMMi+7+KCuaIxzvGWR6uR8RGWFgjUZ5iXdY8rv7v36Pxfy6EKpKJOi1w+z8HtqnhVl3\n8HR8WY8lLGs6m99RHfJRHRrubYCz3r/KoJeGcICKUZ5n7heLicdqSQoPVVXIx9HufiqCvrg3LEai\nwVUTso2PUr/dYT+vOsT2Yz3D/nfB9DCvHzg9zBhYWF+G6lmDK+jzcGYgysL6MgaiSnWpj97B4UVG\nLmupiHuY3KxojrDuQFfSczGZwVOW5MVC7NxLFbo4pybEYFSZHgkk7U9VhnxcOEq+e32Zn4DXYkgV\nS4QLpoc5cWaQvZ29RIeUpkhJ0hfhMeO9viwQN9LByQeqDY0ImXTLO6dmpJfwna2VcePR77WSGsLL\nZ5QzpMT385zaEJacPbYxGstLaAj7h/WnvJawZFqYA6f64h5ddyGWxvIAPo9Fc+XIYyUiXDKzIu7P\nXdYY5uCpfpoiAXweie93v8eiPzpE0OdBAPdpsrCulOffPhlfBiDk8xAOeOno6sNrWTSWB6gP29f4\n5a2ViJw9D+fWlrLz+BlmJHjk68v8HDzVR22G8wfzRU7dDSJyg4hsEZGtIvLpFMt8Q0S2icg6EWkf\nz39zRcfpfu795XYe2XQEryXce1ULty6uP2cMLDeza0L87fVtPHj7Iv7PikaaK0o42jPA9145wO0P\nvskXntrJU9uOcbznnA1nMkwBeg8dYdPnvgZA26fuxBsujGTm6bfeQKitmZ6de3n1jj+l99CRfIuU\nc1T1tKq+lmBgoapvqeqBdNcjIt8XkQ4RecPVVikiK0XkLRH5lYhEXL/d6zyrNovIdanW6x4ny+ex\nsESoCPoIeK208oGqQj4W1CfP06or83NVWxUzKkpGeDc8lrB8RoRljeUscjxCIpLUoxb7pzt0yl12\nv8RrDctlakoRqnhedWjM56DPsvVuTNGJHi8xAxFsmUWEhQ1lNLlyVCpDPi6dWcGyxonl9ojYuVdj\nhSeOl3m1ITq3r2Nh/dn7SXnAS4nXQ3tCyGd92M/SxvJ4QYsZFSVc1VY1zDisCPq4qq1qWChaXZmf\nepdHaEVzhCtnVVJX5o+HnJYknIs+j5X0fAv6PFw8M8KuDWtG1euylgoumjF2vlYyfB6LJdPDSUM9\nR2N6uR16Ggl6aa0K0lZtGz4VQR+tVUGiezYwr66Uturk4Zox431B/fB7+6KGspQG1mgkXo/JkARD\nNmaAzKgoYW5taTy3aU5tKOkL66qQj0UNZfFzIOgdPVzQTcBrxV+ABH0eZlWPDM1rd47D+Q1lJF6q\nfq/FpS0Vwzy7FUEvc2pDdO1Yz6UtEWZVn32hEwsJdW9/fl0pZUk82MuaytPKySwGcmZkiYgF/Atw\nPbAQuF1E5iUscyPQpqqzgbuA76T73xjZHPjxWM8AP3ztIB/5+WbWH+yiKujlH24+j6va8jdulPtB\nmE8qQz7eu6iO+943j7+5bhbLZ5QzGFVeeLuTf3huDx/48Zv84c828Y3n97J610m6+iaWw1Uo+uaK\nc01fKDydD698nheu+SC9+w5RvngezR96b0bXPxl9LZ+XpT/4Ev7qCk68+DovXHsnpzfvyKB0maeA\nB+e9H/sZ4+YzwNOqOhd4BrgXQEQWAL+LXd3wRuDbksJi2L59e9YETofyEm/KQhoxQyTWoQn5PSx2\nKtpt2LAh5TqrnE5dpeNtuWJWJZe3VjJjlI7RkmlhwgEvSydo6KSi1G/n/Fwys2JUmQsxt8PnsTi4\n861hnfhlTeWsaC5PKmskIbRuoiRb9zua0q/cNtp+Bluv8ebtTJa5taUsnxFJma6xZdNGpoUDRZPO\nEfRa7Hor7bHUAdtTXeb3jvCKTpRSv4dFDWWU+j3xwhruAht+56VRjPOqQ3gtYd+OLUWzn2Nk67mU\ny1iu5cA2VX0bQEQeAt4NbHEt827gPwBU9WURiYhIPdCaxn8BWL9+fcYE7h0cYlNHF+sPdvH6/tO8\ndaQnHk5xeWsFd1/cFH/Y5IvVq1fndLDlsbBEuKg5wkXNEY51D/Cb3SdZs/cUbxzqYm9nH3s7+3h8\n81EsgbbqIPPrSmmuKKHC6Qio2iErAa8dQmK/1bPweQSfRwpO32xzrukLhaNz76EjbP/qD9j3gD32\nedUlS2n/t7/F8mb2tjlZfcvmtnLpr/+T9Xf9JcdfWMsrv3M3bZ/6MOH5bUSWLsRbOr5CBdkmk/fo\nTOKEHs5MaH43cIUz/UPg19iG1y3Yw5AMArtFZBv2M+7lxPV2d+cmv2AiabCza0K0VgWHddxjb8U7\nO1PXDPF7LC5vrYwbb5ZIqirncapCvqw9L2NettFkLlSSyZwPY9BjCeUBL1YaRtxU2c+paJ8eZt2B\n05xXPfFiIZOlMuQjONQ3rrLlpX4P75iRnTLnDWE/Ib8naQjoVW1VqGr8vC3G8yNbz6VcGlmNwF7X\n/D7sh9JYyzSm+d9hDA4pGw91xY0iAURgSO3BdQeHlP6o0jsY5czAEL0DQ/QODnFmIMqxngH2dvax\n+/gZoq4gdZ8lLJ9Rzu8sqktavckwnOpSH+9ZWMt7FtYyEB1i69Ee1h3oYu3+02zq6GLb0TNsO3pm\n7BW5OLTuEBsf2khF0Es44CHk8xD0WYR8HkJ+DyGfHfbgd4wyS8SJLbeTV93PLvs3u91r2XHIsd9b\nq4LjqjpkKDwGu7rpXLeFviPH0P5BrIAf8ViI1wMiDHZ2cWZ/B0O9fXjDpUR7++g7fAztH2Cg8zRH\nn32Zob5+xOth9mfuovXu30OswjwnArVVLPvxV1l/119w+Fer2fKX/wyAJxSk6rJllC+cTXDGNDyh\nEnRwEDwWwcYGKpcvzrPkBU+dqnYAqOohEalz2huBF13L7Xfa8kbQ56G7P4p3nOfoRD0jo5WZTYD8\nqwAACeZJREFUb6kM8vaJ3gmXlTbkh2Xj8GZNZSqDPq6YVZl3b0w44CmYvHYRGTH8QeLvhpEUxtFL\nzYSPWk9/lD97YnJhGpbA7JogixvKWDwtTPv0sqwPvjdV8XnsMToW1pdxxwUNnBmIsuVwD9uP9bCv\ns4/TfYNEh2xDWIC+6BCneqOc7hukz6nS1Dc4RHQIOrr66ejK7ijw//a+eaOW2jUUPl1bd7Pm/Z+Y\n+ApEqL/5Smb/+Ucom9uaOcGyhKckwAU/+BIH//spjv76Fbq27ebU+i0cWbmaIytHhiRWXbKU5b/4\nlzxIWtQkqw0xKocOHcqGHCOYWxMi4LVoylDe0J49eyb839aqIC2VJTnveE1G5nxhZM4N45U53wYW\nFOd+huKVOxvk0sjaDzS75puctsRlZiRZxp/GfwEoLS3lnnvuAexg+SVLlsRL6E6MHvtz7DCbj01i\nNVmirq6OtWvX5luMCdMGtJUCadYRWKeLaW8fdz9n3BzbtZlju7K+mTEp9uM7ETKpc90TkzMiFNja\nfQLWnhhz2YmS8WM8qw5m/TYlwFh+hFycW+vWrRsWilFaWhhFQ9KkQ0TqVbVDRBqAw057qmfVCNra\n2uLPJMjEM2l0RsTQT5ALL7yw6O49RubcYGTODcUoMxSH3Ll6Lolq9jusACLiAd4CrgEOAq8At6vq\nZtcyNwEfU9WbRWQF8HVVXZHOfw0Gg8FgmAwi0gI8pqrnO/NfAY6r6lecqraVqvoZp/DFj4CLsMME\nnwJma64eqAaDwWAoeHLmyVLVqIh8HFiJXdXw+6q6WUTusn/W+1T1CRG5SUS2A93AnaP9N1eyGwwG\ng2FqIyI/Bq4EqkVkD/B54MvAz0Tkw8Db2BUFUdVNIvJTYBMwANxtDCyDwWAwuMmZJ8tgMBgMBoPB\nYDAYzgUKs1RWCrI1WGShkkLfv3f0WSciPxeRctdvRa0vJNfZ9dufisiQiFS52opa51T6isgnHJ02\niMiXXe1TTl8RWSIiL4rI6yLyiohc6Pqt2PVtEpFnRGSjcyz/xGmfkvetJPp+wmmf0vetVIjIDSKy\nRUS2OuGGud5+Rp6ZIrJURN5w9Pi6q90vIg85/3lRRNy50xOVOWPXTK7kFpGAiLzs3MM2iMjnC11m\n13otEVkrIo8Wg8wisltE1jv7+pUikTkiIj9zZNgoIhcVsswiMsfZv2u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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pm.plots.traceplot(trace=trace, varnames=[\"centers\"])\n", + "pm.plots.plot_posterior(trace=trace[\"centers\"][:,0])\n", + "pm.plots.plot_posterior(trace=trace[\"centers\"][:,1])\n", + "pm.plots.autocorrplot(trace=trace, varnames=[\"centers\"]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first plotting function gives us the posterior density of each unknown in the `centers` variable as well as the `trace` of each. `trace` plot is useful for inspecting that possible \"meandering\" property that is a result of non-convergence. The density plot gives us an idea of the shape of the distribution of each unknown, but it is better to look at each of them individually." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The second plotting function(s) provides us with a histogram of the samples with a few added features. The text overlay in the center shows us the posterior mean, which is a good summary of posterior distribution. The interval marked by the horizontal black line overlay represents the *95% credible interval*, sometimes called the *highest posterior density interval* and not to be confused with a *95% confidence interval*. We won't get into the latter, but the former can be interpreted as \"there is a 95% chance the parameter of interest lies in this interval\". When communicating your results to others, it is incredibly important to state this interval. One of our purposes for studying Bayesian methods is to have a clear understanding of our uncertainty in unknowns. Combined with the posterior mean, the 95% credible interval provides a reliable interval to communicate the likely location of the unknown (provided by the mean) *and* the uncertainty (represented by the width of the interval)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The last plots, titled `center_0` and `center_1` are the generated autocorrelation plots, similar to the ones displayed above." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Useful tips for MCMC\n", + "\n", + "Bayesian inference would be the *de facto* method if it weren't for MCMC's computational difficulties. In fact, MCMC is what turns most users off practical Bayesian inference. Below I present some good heuristics to help convergence and speed up the MCMC engine:\n", + "\n", + "### Intelligent starting values\n", + "\n", + "It would be great to start the MCMC algorithm off near the posterior distribution, so that it will take little time to start sampling correctly. We can aid the algorithm by telling where we *think* the posterior distribution will be by specifying the `testval` parameter in the `Stochastic` variable creation. In many cases we can produce a reasonable guess for the parameter. For example, if we have data from a Normal distribution, and we wish to estimate the $\\mu$ parameter, then a good starting value would be the *mean* of the data. \n", + "\n", + " mu = pm.Uniform( \"mu\", 0, 100, testval = data.mean() )\n", + "\n", + "For most parameters in models, there is a frequentist estimate of it. These estimates are a good starting value for our MCMC algorithms. Of course, this is not always possible for some variables, but including as many appropriate initial values is always a good idea. Even if your guesses are wrong, the MCMC will still converge to the proper distribution, so there is little to lose.\n", + "\n", + "This is what using `MAP` tries to do, by giving good initial values to the MCMC. So why bother specifying user-defined values? Well, even giving `MAP` good values will help it find the maximum a-posterior. \n", + "\n", + "Also important, *bad initial values* are a source of major bugs in PyMC3 and can hurt convergence.\n", + "\n", + "#### Priors\n", + "\n", + "If the priors are poorly chosen, the MCMC algorithm may not converge, or atleast have difficulty converging. Consider what may happen if the prior chosen does not even contain the true parameter: the prior assigns 0 probability to the unknown, hence the posterior will assign 0 probability as well. This can cause pathological results.\n", + "\n", + "For this reason, it is best to carefully choose the priors. Often, lack of covergence or evidence of samples crowding to boundaries implies something is wrong with the chosen priors (see *Folk Theorem of Statistical Computing* below). \n", + "\n", + "#### Covariance matrices and eliminating parameters\n", + "\n", + "### The Folk Theorem of Statistical Computing\n", + "\n", + "> *If you are having computational problems, probably your model is wrong.*\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion\n", + "\n", + "PyMC3 provides a very strong backend to performing Bayesian inference, mostly because it has abstracted the inner mechanics of MCMC from the user. Despite this, some care must be applied to ensure your inference is not being biased by the iterative nature of MCMC. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "1. Flaxman, Abraham. \"Powell's Methods for Maximization in PyMC.\" Healthy Algorithms. N.p., 9 02 2012. Web. 28 Feb 2013. ." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter3_MCMC/Chapter3.ipynb b/Chapter3_MCMC/Chapter3.ipynb deleted file mode 100644 index d33dd57b..00000000 --- a/Chapter3_MCMC/Chapter3.ipynb +++ /dev/null @@ -1,1460 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Chapter 3\n", - "\n", - "\n", - "_______\n", - "\n", - "## Opening the black box of MCMC" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The previous two chapters hid the inner-mechanics of PyMC, and more generally Markov Chain Monte Carlo (MCMC), from the reader. The reason for including this chapter is three-fold. The first is that any book on Bayesian inference must discuss MCMC. I cannot fight this. Blame the statisticians. Secondly, knowing the process of MCMC gives you insight into whether your algorithm has converged. (Converged to what? We will get to that) Thirdly, we'll understand *why* we are returned thousands of samples from the posterior as a solution, which at first thought can be odd. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Bayesian landscape\n", - "\n", - "When we setup a Bayesian inference problem with $N$ unknowns, we are implicitly creating an $N$ dimensional space for the prior distributions to exist in. Associated with the space is an additional dimension, which we can describe as the *surface*, or *curve*, that sits on top of the space, that reflects the *prior probability* of a particular point. The surface on the space is defined by our prior distributions. For example, if we have two unknowns $p_1$ and $p_2$, and priors for both are $\\text{Uniform}(0,5)$, the space created is a square of length 5 and the surface is a flat plane that sits on top of the square (representing that every point is equally likely). " - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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80cDcJHheA4FAIBCYQorFYgyciSVgLQEWuF1Hun/vBq4GdtQxbVXPKzMvXvdB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\nXkxEVd29Vd5Ot/W4aZrruttt7S56i3+AbdvD2UmhSr3AQ+tcn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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%matplotlib inline\n", - "import scipy.stats as stats\n", - "from IPython.core.pylabtools import figsize\n", - "import numpy as np\n", - "figsize(12.5, 4)\n", - "\n", - "import matplotlib.pyplot as plt\n", - "from mpl_toolkits.mplot3d import Axes3D\n", - "\n", - "jet = plt.cm.jet\n", - "fig = plt.figure()\n", - "x = y = np.linspace(0, 5, 100)\n", - "X, Y = np.meshgrid(x, y)\n", - "\n", - "plt.subplot(121)\n", - "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", - "uni_y = stats.uniform.pdf(y, loc=0, scale=5)\n", - "M = np.dot(uni_y[:, None], uni_x[None, :])\n", - "im = plt.imshow(M, interpolation='none', origin='lower',\n", - " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", - "\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n", - "plt.title(\"Landscape formed by Uniform priors.\")\n", - "\n", - "ax = fig.add_subplot(122, projection='3d')\n", - "ax.plot_surface(X, Y, M, cmap=plt.cm.jet, vmax=1, vmin=-.15)\n", - "ax.view_init(azim=390)\n", - "plt.title(\"Uniform prior landscape; alternate view\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Alternatively, if the two priors are $\\text{Exp}(3)$ and $\\text{Exp}(10)$, then the space is all positive numbers on the 2-D plane, and the surface induced by the priors looks like a water fall that starts at the point (0,0) and flows over the positive numbers. \n", - "\n", - "The plots below visualize this. The more dark red the color, the more prior probability is assigned to that location. Conversely, areas with darker blue represent that our priors assign very low probability to that location. " - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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a/qRKucViaQb5fP5I9MStDFoa7Xz06x2Addls9que5+3V399/KTBfRDYrpfYE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\nAwMD5wVBcBywDWgRkR2O4xQqNjZJpHk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KpVBzOMxI1xEEQZhyk2Kx+LpSqbQpoiqxwXGc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\nF1j2n/IxtlP/ahPR9QDKmHkPjP8UQhcoSoQt+M3NzQ1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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 5)\n", - "fig = plt.figure()\n", - "plt.subplot(121)\n", - "\n", - "exp_x = stats.expon.pdf(x, scale=3)\n", - "exp_y = stats.expon.pdf(x, scale=10)\n", - "M = np.dot(exp_y[:, None], exp_x[None, :])\n", - "CS = plt.contour(X, Y, M)\n", - "im = plt.imshow(M, interpolation='none', origin='lower',\n", - " cmap=jet, extent=(0, 5, 0, 5))\n", - "#plt.xlabel(\"prior on $p_1$\")\n", - "#plt.ylabel(\"prior on $p_2$\")\n", - "plt.title(\"$Exp(3), Exp(10)$ prior landscape\")\n", - "\n", - "ax = fig.add_subplot(122, projection='3d')\n", - "ax.plot_surface(X, Y, M, cmap=jet)\n", - "ax.view_init(azim=390)\n", - "plt.title(\"$Exp(3), Exp(10)$ prior landscape; \\nalternate view\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These are simple examples in 2D space, where our brains can understand surfaces well. In practice, spaces and surfaces generated by our priors can be much higher dimensional. \n", - "\n", - "If these surfaces describe our *prior distributions* on the unknowns, what happens to our space after we incorporate our observed data $X$? The data $X$ does not change the space, but it changes the surface of the space by *pulling and stretching the fabric of the prior surface* to reflect where the true parameters likely live. More data means more pulling and stretching, and our original shape becomes mangled or insignificant compared to the newly formed shape. Less data, and our original shape is more present. Regardless, the resulting surface describes the *posterior distribution*. \n", - "\n", - "Again I must stress that it is, unfortunately, impossible to visualize this in large dimensions. For two dimensions, the data essentially *pushes up* the original surface to make *tall mountains*. The tendency of the observed data to *push up* the posterior probability in certain areas is checked by the prior probability distribution, so that lower prior probability means more resistance. Thus in the double-exponential prior case above, a mountain (or multiple mountains) that might erupt near the (0,0) corner would be much higher than mountains that erupt closer to (5,5), since there is more resistance (low prior probability) near (5,5). The peak reflects the posterior probability of where the true parameters are likely to be found. Importantly, if the prior has assigned a probability of 0, then no posterior probability will be assigned there. \n", - "\n", - "Suppose the priors mentioned above represent different parameters $\\lambda$ of two Poisson distributions. We observe a few data points and visualize the new landscape: " - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "observed (2-dimensional,sample size = 1): [[3 3]]\n" - ] - } - ], - "source": [ - "# create the observed data\n", - "\n", - "# sample size of data we observe, trying varying this (keep it less than 100 ;)\n", - "N = 1\n", - "\n", - "# the true parameters, but of course we do not see these values...\n", - "lambda_1_true = 1\n", - "lambda_2_true = 3\n", - "\n", - "#...we see the data generated, dependent on the above two values.\n", - "data = np.concatenate([\n", - " stats.poisson.rvs(lambda_1_true, size=(N, 1)),\n", - " stats.poisson.rvs(lambda_2_true, size=(N, 1))\n", - "], axis=1)\n", - "print \"observed (2-dimensional,sample size = %d):\" % N, data\n", - "\n", - "# plotting details.\n", - "x = y = np.linspace(.01, 5, 100)\n", - "likelihood_x = np.array([stats.poisson.pmf(data[:, 0], _x)\n", - " for _x in x]).prod(axis=1)\n", - "likelihood_y = np.array([stats.poisson.pmf(data[:, 1], _y)\n", - " for _y in y]).prod(axis=1)\n", - "L = np.dot(likelihood_x[:, None], likelihood_y[None, :])\n" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "(0, 5)" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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hZaQpRW1s9ibdyOHkUdgib0xDAVxUdmJi+vnmCdoskkDnOPAkg5XwMkl5yiTu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8231hr0FF9Edi4W80AuZj3SK6sQLI+88p7rlR7uPsYXKUvhY96DDkFWrjP4embklffAY332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\nLwL4RD6tzysi8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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 12)\n", - "# matplotlib heavy lifting below, beware!\n", - "plt.subplot(221)\n", - "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", - "uni_y = stats.uniform.pdf(x, loc=0, scale=5)\n", - "M = np.dot(uni_y[:, None], uni_x[None, :])\n", - "im = plt.imshow(M, interpolation='none', origin='lower',\n", - " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", - "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n", - "plt.title(\"Landscape formed by Uniform priors on $p_1, p_2$.\")\n", - "\n", - "plt.subplot(223)\n", - "plt.contour(x, y, M * L)\n", - "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", - " cmap=jet, extent=(0, 5, 0, 5))\n", - "plt.title(\"Landscape warped by %d data observation;\\n Uniform priors on $p_1, p_2$.\" % N)\n", - "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n", - "\n", - "plt.subplot(222)\n", - "exp_x = stats.expon.pdf(x, loc=0, scale=3)\n", - "exp_y = stats.expon.pdf(x, loc=0, scale=10)\n", - "M = np.dot(exp_y[:, None], exp_x[None, :])\n", - "\n", - "plt.contour(x, y, M)\n", - "im = plt.imshow(M, interpolation='none', origin='lower',\n", - " cmap=jet, extent=(0, 5, 0, 5))\n", - "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n", - "plt.title(\"Landscape formed by Exponential priors on $p_1, p_2$.\")\n", - "\n", - "plt.subplot(224)\n", - "# This is the likelihood times prior, that results in the posterior.\n", - "plt.contour(x, y, M * L)\n", - "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", - " cmap=jet, extent=(0, 5, 0, 5))\n", - "\n", - "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", - "plt.title(\"Landscape warped by %d data observation;\\n Exponential priors on \\\n", - "$p_1, p_2$.\" % N)\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The plot on the left is the deformed landscape with the $\\text{Uniform}(0,5)$ priors, and the plot on the right is the deformed landscape with the exponential priors. Notice that the posterior landscapes look different from one another, though the data observed is identical in both cases. The reason is as follows. Notice the exponential-prior landscape, bottom right figure, puts very little *posterior* weight on values in the upper right corner of the figure: this is because *the prior does not put much weight there*. On the other hand, the uniform-prior landscape is happy to put posterior weight in the upper-right corner, as the prior puts more weight there. \n", - "\n", - "Notice also the highest-point, corresponding to the darkest red, is biased towards (0,0) in the exponential case, which is the result from the exponential prior putting more prior weight in the (0,0) corner.\n", - "\n", - "The black dot represents the true parameters. Even with 1 sample point, the mountains attempts to contain the true parameter. Of course, inference with a sample size of 1 is incredibly naive, and choosing such a small sample size was only illustrative. \n", - "\n", - "It's a great exercise to try changing the sample size to other values (try 2,5,10,100?...) and observing how our \"mountain\" posterior changes. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Exploring the landscape using the MCMC\n", - "\n", - "We should explore the deformed posterior space generated by our prior surface and observed data to find the posterior mountain. However, we cannot naively search the space: any computer scientist will tell you that traversing $N$-dimensional space is exponentially difficult in $N$: the size of the space quickly blows-up as we increase $N$ (see [the curse of dimensionality](http://en.wikipedia.org/wiki/Curse_of_dimensionality)). What hope do we have to find these hidden mountains? The idea behind MCMC is to perform an intelligent search of the space. To say \"search\" implies we are looking for a particular point, which is perhaps not an accurate as we are really looking for a broad mountain. \n", - "\n", - "Recall that MCMC returns *samples* from the posterior distribution, not the distribution itself. Stretching our mountainous analogy to its limit, MCMC performs a task similar to repeatedly asking \"How likely is this pebble I found to be from the mountain I am searching for?\", and completes its task by returning thousands of accepted pebbles in hopes of reconstructing the original mountain. In MCMC and PyMC lingo, the returned sequence of \"pebbles\" are the samples, cumulatively called the *traces*. \n", - "\n", - "When I say MCMC intelligently searches, I really am saying MCMC will *hopefully* converge towards the areas of high posterior probability. MCMC does this by exploring nearby positions and moving into areas with higher probability. Again, perhaps \"converge\" is not an accurate term to describe MCMC's progression. Converging usually implies moving towards a point in space, but MCMC moves towards a *broader area* in the space and randomly walks in that area, picking up samples from that area.\n", - "\n", - "#### Why Thousands of Samples?\n", - "\n", - "At first, returning thousands of samples to the user might sound like being an inefficient way to describe the posterior distributions. I would argue that this is extremely efficient. Consider the alternative possibilities:\n", - "\n", - "1. Returning a mathematical formula for the \"mountain ranges\" would involve describing a N-dimensional surface with arbitrary peaks and valleys.\n", - "2. Returning the \"peak\" of the landscape, while mathematically possible and a sensible thing to do as the highest point corresponds to most probable estimate of the unknowns, ignores the shape of the landscape, which we have previously argued is very important in determining posterior confidence in unknowns. \n", - "\n", - "Besides computational reasons, likely the strongest reason for returning samples is that we can easily use *The Law of Large Numbers* to solve otherwise intractable problems. I postpone this discussion for the next chapter. With the thousands of samples, we can reconstruct the posterior surface by organizing them in a histogram. \n", - "\n", - "\n", - "### Algorithms to perform MCMC\n", - "\n", - "There is a large family of algorithms that perform MCMC. Most of these algorithms can be expressed at a high level as follows: (Mathematical details can be found in the appendix.)\n", - "\n", - "1. Start at current position.\n", - "2. Propose moving to a new position (investigate a pebble near you).\n", - "3. Accept/Reject the new position based on the position's adherence to the data and prior distributions (ask if the pebble likely came from the mountain).\n", - "4. 1. If you accept: Move to the new position. Return to Step 1.\n", - " 2. Else: Do not move to new position. Return to Step 1. \n", - "5. After a large number of iterations, return all accepted positions.\n", - "\n", - "This way we move in the general direction towards the regions where the posterior distributions exist, and collect samples sparingly on the journey. Once we reach the posterior distribution, we can easily collect samples as they likely all belong to the posterior distribution. \n", - "\n", - "If the current position of the MCMC algorithm is in an area of extremely low probability, which is often the case when the algorithm begins (typically at a random location in the space), the algorithm will move in positions *that are likely not from the posterior* but better than everything else nearby. Thus the first moves of the algorithm are not reflective of the posterior.\n", - "\n", - "In the above algorithm's pseudocode, notice that only the current position matters (new positions are investigated only near the current position). We can describe this property as *memorylessness*, i.e. the algorithm does not care *how* it arrived at its current position, only that it is there. \n", - "\n", - "### Other approximation solutions to the posterior\n", - "Besides MCMC, there are other procedures available for determining the posterior distributions. A Laplace approximation is an approximation of the posterior using simple functions. A more advanced method is [Variational Bayes](http://en.wikipedia.org/wiki/Variational_Bayesian_methods). All three methods, Laplace Approximations, Variational Bayes, and classical MCMC have their pros and cons. We will only focus on MCMC in this book. That being said, my friend Imri Sofar likes to classify MCMC algorithms as either \"they suck\", or \"they really suck\". He classifies the particular flavour of MCMC used by PyMC as just *sucks* ;)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Unsupervised Clustering using a Mixture Model\n", - "\n", - "\n", - "Suppose we are given the following dataset:\n" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 115.85679142 152.26153716 178.87449059 162.93500815 107.02820697\n", - " 105.19141146 118.38288501 125.3769803 102.88054011 206.71326136] ...\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "data = np.loadtxt(\"data/mixture_data.csv\", delimiter=\",\")\n", - "\n", - "plt.hist(data, bins=20, color=\"k\", histtype=\"stepfilled\", alpha=0.8)\n", - "plt.title(\"Histogram of the dataset\")\n", - "plt.ylim([0, None])\n", - "print data[:10], \"...\"\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What does the data suggest? It appears the data has a bimodal form, that is, it appears to have two peaks, one near 120 and the other near 200. Perhaps there are *two clusters* within this dataset. \n", - "\n", - "This dataset is a good example of the data-generation modeling technique from last chapter. We can propose *how* the data might have been created. I suggest the following data generation algorithm: \n", - "\n", - "1. For each data point, choose cluster 1 with probability $p$, else choose cluster 2. \n", - "2. Draw a random variate from a Normal distribution with parameters $\\mu_i$ and $\\sigma_i$ where $i$ was chosen in step 1.\n", - "3. Repeat.\n", - "\n", - "This algorithm would create a similar effect as the observed dataset, so we choose this as our model. Of course, we do not know $p$ or the parameters of the Normal distributions. Hence we must infer, or *learn*, these unknowns.\n", - "\n", - "Denote the Normal distributions $\\text{Nor}_0$ and $\\text{Nor}_1$ (having variables' index start at 0 is just Pythonic). Both currently have unknown mean and standard deviation, denoted $\\mu_i$ and $\\sigma_i, \\; i =0,1$ respectively. A specific data point can be from either $\\text{Nor}_0$ or $\\text{Nor}_1$, and we assume that the data point is assigned to $\\text{Nor}_0$ with probability $p$.\n", - "\n", - "\n", - "An appropriate way to assign data points to clusters is to use a PyMC `Categorical` stochastic variable. Its parameter is a $k$-length array of probabilities that must sum to one and its `value` attribute is a integer between 0 and $k-1$ randomly chosen according to the crafted array of probabilities. (In our case $k=2$) *A priori*, we do not know what the probability of assignment to cluster 1 is, so we create a uniform variable over 0,1 to model this. Call this `p`. Thus the probability array we enter into the `Categorical` variable is `[p, 1-p]`." - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "prior assignment, with p = 0.31:\n", - "[1 1 0 0 0 0 1 1 1 1] ...\n" - ] - } - ], - "source": [ - "import pymc as pm\n", - "\n", - "p = pm.Uniform(\"p\", 0, 1)\n", - "\n", - "assignment = pm.Categorical(\"assignment\", [p, 1 - p], size=data.shape[0])\n", - "print \"prior assignment, with p = %.2f:\" % p.value\n", - "print assignment.value[:10], \"...\"\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Looking at the above dataset, I would guess that the standard deviations of the two Normals are different. To maintain ignorance of what the standard deviations might be, we will initially model them as uniform on 0 to 100. Really we are talking about $\\tau$, the *precision* of the Normal distribution, but it is easier to think in terms of standard deviation. Our PyMC code will need to transform our standard deviation into precision by the relation:\n", - "\n", - "$$ \\tau = \\frac{1}{\\sigma^2} $$\n", - "\n", - "In PyMC, we can do this in one step by writing:\n", - "\n", - " taus = 1.0/pm.Uniform( \"stds\", 0, 100, size= 2)**2 \n", - "\n", - "Notice that we specified `size=2`: we are modeling both $\\tau$s as a single PyMC variable. Note that this does not induce a necessary relationship between the two $\\tau$s, it is simply for succinctness.\n", - "\n", - "We also need to specify priors on the centers of the clusters. The centers are really the $\\mu$ parameters in this Normal distributions. Their priors can be modeled by a Normal distribution. Looking at the data, I have an idea where the two centers might be — I would guess somewhere around 120 and 190 respectively, though I am not very confident in these eyeballed estimates. Hence I will set $\\mu_0 = 120, \\mu_1 = 190$ and $\\sigma_{0,1} = 10$ (recall we enter the $\\tau$ parameter, so enter $1/\\sigma^2 = 0.01$ in the PyMC variable.)" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Random assignments: [1 1 0 0] ...\n", - "Assigned center: [ 174.74278858 174.74278858 126.25164007 126.25164007] ...\n", - "Assigned precision: [ 0.00034557 0.00034557 0.00012237 0.00012237] ...\n" - ] - } - ], - "source": [ - "stds = pm.Uniform(\"stds\", 0, 100, size=2)\n", - "taus = 1.0 / stds ** 2\n", - "centers = pm.Normal(\"centers\", [120, 190], [0.01, 0.01], size=2)\n", - "\n", - "\"\"\"\n", - "The below deterministic functions map an assignment, in this case 0 or 1,\n", - "to a set of parameters, located in the (1,2) arrays `taus` and `centers`.\n", - "\"\"\"\n", - "\n", - "@pm.deterministic\n", - "def center_i(assignment=assignment, centers=centers):\n", - " return centers[assignment]\n", - "\n", - "@pm.deterministic\n", - "def tau_i(assignment=assignment, taus=taus):\n", - " return taus[assignment]\n", - "\n", - "print \"Random assignments: \", assignment.value[:4], \"...\"\n", - "print \"Assigned center: \", center_i.value[:4], \"...\"\n", - "print \"Assigned precision: \", tau_i.value[:4], \"...\"\n" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# and to combine it with the observations:\n", - "observations = pm.Normal(\"obs\", center_i, tau_i, value=data, observed=True)\n", - "\n", - "# below we create a model class\n", - "model = pm.Model([p, assignment, observations, taus, centers])\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "PyMC has an MCMC class, `MCMC` in the main namespace of PyMC, that implements the MCMC exploring algorithm. We initialize it by passing in a `Model` instance:\n", - "\n", - " mcmc = pm.MCMC( model )\n", - "\n", - "The method for asking the `MCMC` to explore the space is `sample( iterations )`, where `iterations` is the number of steps you wish the algorithm to perform. We try 50000 steps below:" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[****************100%******************] 50000 of 50000 complete\n" - ] - } - ], - "source": [ - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(50000)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below I plot the paths, or \"traces\", the unknown parameters (centers, precisions, and $p$) have taken thus far. The traces can be retrieved using the `trace` method in the `MCMC` object created, which accepts the assigned PyMC variable `name`. For example, `mcmc.trace(\"centers\")` will retrieve a `Trace` object that can be indexed (using `[:]` or `.gettrace()` to retrieve all traces, or fancy-indexing like `[1000:]`)." - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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L9npkcgJjE1M0NOh+RrXNEly43Tr60pWTuWmmUwrlESW5tBEDHc3a3UZOCCQy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\neX1Wr16N4OBgjBkzBgEBAfjoo4+gVCrh6emJn3/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okvP159dtXeDp14X1hDuV3lVdTreH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Sz/2RwJJvnnswBavDs+hyehnJRacUeCoaWmnu++XsKq2O9V10vtI2ytinQBAEWiRSVDe2olUi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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 9)\n", - "plt.subplot(311)\n", - "lw = 1\n", - "center_trace = mcmc.trace(\"centers\")[:]\n", - "\n", - "# for pretty colors later in the book.\n", - "colors = [\"#348ABD\", \"#A60628\"] \\\n", - "if center_trace[-1, 0] > center_trace[-1, 1] \\\n", - " else [\"#A60628\", \"#348ABD\"]\n", - "\n", - "plt.plot(center_trace[:, 0], label=\"trace of center 0\", c=colors[0], lw=lw)\n", - "plt.plot(center_trace[:, 1], label=\"trace of center 1\", c=colors[1], lw=lw)\n", - "plt.title(\"Traces of unknown parameters\")\n", - "leg = plt.legend(loc=\"upper right\")\n", - "leg.get_frame().set_alpha(0.7)\n", - "\n", - "plt.subplot(312)\n", - "std_trace = mcmc.trace(\"stds\")[:]\n", - "plt.plot(std_trace[:, 0], label=\"trace of standard deviation of cluster 0\",\n", - " c=colors[0], lw=lw)\n", - "plt.plot(std_trace[:, 1], label=\"trace of standard deviation of cluster 1\",\n", - " c=colors[1], lw=lw)\n", - "plt.legend(loc=\"upper left\")\n", - "\n", - "plt.subplot(313)\n", - "p_trace = mcmc.trace(\"p\")[:]\n", - "plt.plot(p_trace, label=\"$p$: frequency of assignment to cluster 0\",\n", - " color=\"#467821\", lw=lw)\n", - "plt.xlabel(\"Steps\")\n", - "plt.ylim(0, 1)\n", - "plt.legend()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice the following characteristics:\n", - "\n", - "1. The traces converges, not to a single point, but to a *distribution* of possible points. This is *convergence* in an MCMC algorithm.\n", - "2. Inference using the first few thousand points is a bad idea, as they are unrelated to the final distribution we are interested in. Thus is it a good idea to discard those samples before using the samples for inference. We call this period before converge the *burn-in period*.\n", - "3. The traces appear as a random \"walk\" around the space, that is, the paths exhibit correlation with previous positions. This is both good and bad. We will always have correlation between current positions and the previous positions, but too much of it means we are not exploring the space well. This will be detailed in the Diagnostics section later in this chapter.\n", - "\n", - "\n", - "To achieve further convergence, we will perform more MCMC steps. Starting the MCMC again after it has already been called does not mean starting the entire algorithm over. In the pseudo-code algorithm of MCMC above, the only position that matters is the current position (new positions are investigated near the current position), implicitly stored in PyMC variables' `value` attribute. Thus it is fine to halt an MCMC algorithm and inspect its progress, with the intention of starting it up again later. The `value` attributes are not overwritten. \n", - "\n", - "We will sample the MCMC one hundred thousand more times and visualize the progress below:" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[****************100%******************] 100000 of 100000 complete\n" - ] - } - ], - "source": [ - "mcmc.sample(100000)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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SzpURFxdH8+bNy6SnpKSQl5fHgAEDpDQhhJ50x8rKSu9amZqaVuhMR0dHk5CQ\ngLOzs5Sm0Wjo1auXtF30kVcR5ubmepKtrKwszM3NKz3m30Z23h8zfHx8HoueoLjfj0q/s66HSL+V\nCckUxCeTE3KHeu1bYlBi4lFuWBTmLR1rrU6Pi20fRmTb1i6yfWsP2ba1R3Z2drV732NjY6XfMTEx\n2NnZSdulJSwODg5s2LCBp59+utyy3Nzc+PLLL3nmmWdQKpX06dOnTB5ra2uMjY2JioqSesBjYmIk\nx9DMzIy8vDwpf2Jiot7xAwcOZODAgSiVSj799FPmzJkj6epLUtJpLUnJNimVSqZNm8aWLVsYMWIE\nhoaGTJkyBSEE+bGJ2NvYcDswCFX/dAAK4pNQ1TWmadOm1K1bl9u3b5eZtAkgtAKtUomhqa532s7O\nrkx7S9q5Mpo2bUpAQECZdGtra0xNTfH19a12WRXZAXTX1snJCT8/vwrzVzW5t127dly/fp2uXbsC\ncOPGDb0PnIcBWfMu81ChyVdSmFPx8FTK6b+ggtn1aRcCEBVMtJGRkZGReTwRQvDDDz8QFxdHeno6\nX331lSTPKI9p06bx6aefEhMTA+h6f48eLe4wcnV1JTo6Gg8PjwonXxoaGvLCCy+wYsUKcnJyiI6O\nZvPmzYwbNw6ATp064evrS0xMDFlZWaxdu1aqa4SvP3/u3Udubi7GxsaYmZmV6zwD2NjYEBUVVUaW\nUnJbpVKhUqmwtrbGwMCAEydO4O3tjValRpWSxvgRo/jd8wgXAvzRarXEJyQQGnwTOzs7end7kg/m\nziPW928KC5TcDrkl6dfV6Znk3AqXzjNmzBhWr15NamoqqamprFy5kvHjx1do55KMHTuW06dPs3//\nfgoLC0lLS+PGjRsYGBgwZcoUFi1aREqKTnoVFxenp1GvDBsbGyIjI6Xt7t27U69ePdavX09+fj4a\njYagoCAuX75cxm4V8fLLL7Np0ybi4+OJi4tj06ZNTJgwoVr1+beQnffHjKIeIE2BkphfD923clPO\n+pFzO7LqjDWkMCdXbxJq3N5jxO87UaMy1Fk5xRu1uGyB3LtWe8i2rV1k+9Yesm1rj5po3seOHYub\nmxvdunWjRYsWvPfee3r7SzJjxgyGDRuGm5sbjo6ODB06VK9XuE6dOjz33HOcPXu2zITGkmV98cUX\nmJmZ0a1bN0aMGMG4ceOkiCf9+/fnxRdfpE+fPgwaNIihQ4eiUCjIC4+hsCCfTRs24uLiQsuWLfH1\n9eWLT1eiWQUUAAAgAElEQVQAoFUXSp1QWnUho0aMBKBly5aSZrt0PSwsLPDw8ODVV1+lRYsW7N27\nl+HDh6NOzwSgc7v2rHx/EZ98vZ7Oo4Yy4d1ZpCYnoUxOY/UHSynIzGLItMm0atOaV6ZOJTExEaHR\nSvXQKFUIIZg3bx5dunShT58+9OnThy5dukja8vLsXBIHBwd2797N119/TcuWLenXrx+BgYGALqZ6\nixYtGDJkCE5OTowZM4awsLBqlTt58mRCQkJwdnZm6tSpGBgY8Ouvv3L9+nW6detG69ateffddyUZ\nTHV63qdNm8awYcPo3bs3ffr0YdiwYQ9VmEiQF2l6bFGlpJN49AzNprxwX8qL/nk/APU7t8ey071p\nzbVKFaqMLNIvXsV+9CCpXFPHJjTq97TeeaqD/YuuKJPSSDvvj+2I/iQeOU3TCc/pSWnKIz86HpMm\nNigq6OmQKZ/C3DyST5zH/gXXqjPLyMg8NjzsizR16dKF9evX07dv3wddFQl1Vg6FWTmYOuhLQTKv\nBku/6z/RBk1eAQojQ3JuhVOvjbPU012nYQNUaRlSvqL3lTo7FyNzMxQGOge0MK8AZUIy5i2aUZqS\n56oJlp3bk3k1GGMrS+kDwLRZE+o0tLyn8mqKVqNBqNSSXOdh5UEu0iT3vD+iCK0WZXJamfTSMYfV\nmWXj5KqzcihIvLfIAFlXg0k67kP0z/spzM2jMDev6oOA/JgEYncfQZmQQmGWfp3yo+LQFhbWuC7x\n+06Qdt4foLj3XqOt8gMg5fRf5EXG1fh8//V4zgkHvLg6o+wqc/eD/7ptaxvZvrWHbNvao7px3h9G\nVKkZqFLT0ap17zah1aLO1peEZt24Re6dYkmMMiW9+Pi7jjtAXlTxJNi8O1F671B1eiaF2Tlo8gvQ\nFCirXb98UbHEtMjpL3LcAbRqNaDTy2cHh+mPeN9FaLXkxxZr+wsSU/RG1nPDYyhIqNr3UMYl6cl1\nZMoiO++PKHkRsSR5nq1wf9HDIOGgFwAFcUnSvjQff5KPl33hVFcvrrzr+MfvPU783uM66UslAzgF\ncUmkeF/US8uPSdBzsmN/PfSPZDm5YVG6cnYfAZAemPmxiRTEJ1OYm0fSsXP3XH5lZF4JRqvSPdiS\nvXxJ/+sq6ows6eEmNJpq6ezuJ6k+fxO940CNjjk/2J0038tlyvG061XBEeA3bja3Pn+4l+2WkSlN\nblgUBQnJD7oaMo8hRRKTIglndlAoAPlR8eTdiSr/mBxdJ5i6hMNekiIHuOgdXfJtokrRdeLl3Aon\nNzQSrbpQL8jD/UKo1GiUKpRJqWhVKvLCo8vkKdLYa/J1HxHKhGSybtyS3oWFWdnSB0HunWg0ShV5\nUXHkhIRTmFeAtlCDKi1Ten/LVIzsvD9iZAQEke53HVHBze0UnkJBYgp54TFSWrrfdZK9LqAq+qqv\nQO4V88tB8iJ0xwkhyI/Wfe2X94VdkryIWGJKOYrawkJUabo/0mSvC1J6UR2KnO2SpJdyHGtCbinH\nX5mUitBoSDnlS/LJ8ySf9EWZlEruHd0DJzswtEYLPmnyCujaxAnQtaGkk5t1PYTYXbooAQVxieTc\nCifhz1MkHDgJQMzOP8m6Uv7wpTozm8LcfDQFyvu6ANWN9zwInPdFlflUqRnS6Ez2jVBSz/qRFxXP\ncaf+XJu1nKyrlb8EUs/9zZ112ynMzef0kxVPEKsKWTdcuzxI+0Z8t0uv57A2iNvjWaOP/3PPvszf\nL825L+eW793ao7qa9ytXrtxXyYzQavWex9rCss9mrboQrUqNMjlNr8c752YYuaGRFGbrvzfVmVkV\nnq8gPqnCfQCisJDMq8HFTrlGi1atpjAvv1S9NWQHhSK02iolM6aKmrl/qrQMcm6G6aVlXg1GnZmt\n19sOkHs7Qq9uhTl50jtfq1Lp0rJzKMzORZ2RjaaggNzQcLIDb5EfHSfZrjA7l8yrweTHVW6f/yJy\nqMhHjJybdxCaYsddlZ5FHav6FCQkk+Gvm/xRule96A8u8egZzFs5SenRP+/H/kVXjOoVxy8tvDus\np0xI0UV2Aahickfm5SAAsoPDMGvuQHZQKKrUTJSJyVj3eVIvb0Gc7o9cVWJ4sDZIOeVLnUZW0nbR\nMGPWNd3DT52RRV5ELAojI+o0aoCRuVmFZWVevUnWNd3qauYtmpEfm0ju7Uga9uxapdynqAci68Yt\nVKkZGNYzQ5OTR+PBvShITCH5uA/GDeqjztA92O91joImT7eUtKGZCSmn/yK/mrKgMz3GYubUlGe9\ntgG63pCzT7sBELfnGE3GF88LKBo9+Hvie7T/dA5mzsWxgFWpGRTEJJB5LeSe50TcL4RWS9qFAKx7\nP1l1Zpn7SnZwGBbtW+ql3Vy6DmVCCm2Xvi2lhXz8NVk3bvHU7rLxs++Fa7M+xu75QXT59pNqH1Oy\nU6IwN5+TLQfhNP0l2i//H6DrAJDWl5D5zyC0WslJtuzcnsKcXHLDorDs3B6NUoXCyBADQ0OpR72I\nem1bYGhSFwBNvr5Tfa/a8yK0SpXedn5M7X4M14SiDj/TprbSe0hoteSGRkh5VMmpescUOfvaAiVU\nIt/JvTtSoUpOxbRJ+YtY/VeRe94fMUo67gCJh07pnMAT51GnZeAXWvkSvrm3IxElehHi950g3e86\n2cFhd8vXUpibpy+hqabkI+Pv68TtOUp20G2Uiboh6dRzf5ebV1Oqx6A2KO8DoWRvSNqFAFLPXiJ+\n73HyImPR5CtJPqUv78m5HSk57uXZVplY/FAq/YAFiNtTHH6sID6J3NAIXYzd1AzpI6vIcS86XxGa\nAmWFUp/sm3ekkRFVWiZxf3iScMgbrVIlpQN42vWiMLfY1qnn/taT8Ghy8iiITyLzqq5tCQe89Ot/\nV4ZUMkRnyilfzvV6ieBFX0n5ihx+3yGvVDlSUx73UzecERCI39jZ9628x4Ha1mUXZueSERDE+QFT\npHkwqvSs4pe5Rv8FnXDYm9Sz5cdhrm2KQtEq45M54ayL3lF0nyceOg1ATmgE3p1GAbrRsaK/0fzY\nRL2/V7g/ti1vFU2ZB6N5F9ri6yCEkHqMM68Gk3MzjOwbt8o9Li8ittz0h5XKNO/3gjozm/zo6nUa\nFUl9VKm124n3OCM77w8R0T/vR5WuezHk3olGqy4k8eiZ4h7wCsi4dK1G5yn98sm5GUbG39cBnQQk\nfu9xUk751qjMR53Us37E7TlKQWyCzgGOTUSVlllGyhP9837JEVFnZOnZqUhvXx0Sj5wuNz3d9zJC\nqyXx6Bnifj+KMim1zJAkQIbfNTL8bwC6IUkArVJZbh2KPiryYxLwGzebqJ/26u1XKBT4Dn210vr+\n/fK7JB4+o5cW9dMf5ea9MWcFyuQ0sq6HSI6SKiWdlLN+nB/sXul57gva8p0grVJV7gRumXsnJzSC\nnNuRnGztysURrwOQ/tc1Us76car9MP6e8C5Q8XwaTYHug7nkCNadDT9ze9UPgE5+V/rYwuxcAtwX\nVKt+eZFxXP/fp+SERpD+11VSz/3NyVbF0ZI0+QWk+vxN0AerASiITST9r6sok9LuHh/L+UHuXHB9\nBYAz3V/Eq92wMudJ97te5rlaE2J2/skx+2fv+fhHmbyImErX9vg30KoLUSalos7KQZS4F4s6bkqj\nLKdjSKusfI2Sx52iHniZfwdZNvOQUDRBozArmzpW9Uk7749Vz65S73FBfDIKo/JDG5Z8aTzVul3t\nV/YxJ/V8AAWxZZd8LrJtdqCu5yXhz+otIlFTYn45qLedcsqXZlNeQJ2ZTcJBL0laU5idq7svKlc1\nocnLJ/6sH1dnfAhA8KLVZAfeosXsqTWqV+lJxxWhTEnnzFNj0BaosBs9iHYfvcPpbsVyoPAtv+I8\nQ3/Bi39DNxz4/kpifzvMsIQLVWd+zPin9vW060Xvczup17q5XrpPn4llQq76T5wr/U7/6yoAkd/u\nIvX0JTpuWIpl53YUxOtG5k401y2J3n3nVzQe+AwAt1ZsBqB+p7ZcnbkMTU4ezxz5jvpPtAGFgkTP\nsyQd80GdkYVxg/rSqGHCQS/yP5qFaVNbQNdrGr3jALG7jhC7q+IP69KjNH+Nfkv6fbbHOOl3XmT5\nPau9e/fG064Xzaa+gMuX1fuoKE1mgE7y6D91Ac2nv4z1s/+dUMrqzGwURkZ68s0izE1M0ShVGNat\nU/3ysnIQGi11rOpX+5js4Ns1WiOkvPcDlD+X62Glppp3mYcL2Xl/SIj9rZwFlUoMNSefPP8v1ua/\nTUUP5geJJq8ATb5OgqBKLY5IUJ374kw5E0ljfvmTmF/+LFPe/aDkSFDCAa8yUpyQZRtwnjGBvKh4\nIr/9jVbzXkNoBcZW9atcPOOfUDTfQUYfVUo64Vt+pe2SmZXmSzrmU8Z5B6o90TrnVji+Q1/lWe+f\nEXejM5Uuo2QPfMDUYkf44og3ALBwaU12oL7W+PyAKcVtSUrFpIkNWqWKtPMBhG/4uVp1qw4lHfmb\nyzbQav7rGJmbcvm1Rbq6321T0eTFIv1zdSj6W0w+7oNpE5v/lPNeRHbQbeo2saFOg/qoUjPIj4nH\n0NwMTW4elp2rvzR9URQUY0sL1JlZKBQGGDconviqVatRGBqiMNA5r0IrauS4yzwYhBC1+n541JA/\nvR5i0i9drfExVWneZe6dB2nb+P0nyLkVAVQsuXmUUKVlcvZpNyK//x2vdsPY2K4v0dv3c2fjDiK+\n3fXPCi/nAX/m6bFkB93WS8spMaHqcUaVlsnJ3Xsr3H/qiZGEb9xRJv3m8o2c61M8QnLr002kXbhM\n6MrvAYgv9VFWXRIPny6bqNUSvGQNN5dWPoG1pOOefuk6AdPe19uvKVAS++shTjQfgP+k90offt+I\n2PKrNELg/acu0lRhdi7eXUdzovkAaUQBKHc9jiKEVltmrkx1Q/Y+7NREx69VqdGq1ajvykaLPoDy\n1DrbZF4NJvNaSLFEsFAjTQKt6Dx5d6LJj4ojLzIGTX6BbsVQIcgOuk3W9RCpjPyomq358cSIwcQk\nPDwTRmuKgbExcP817wA7DuzjyTHP0XGkK5nZ9y4jKw91WmbVmf5DyD3vD5Bk74sUZuVKq40CZPgH\n6k2YkZEBXc9kfgXD9o8iRfrokgS9v1L67TDxuTLD6FfeWILLygUYNyh/OLwgPpm6do2I+/2olL/J\n2KEEfbBab52DmF8PYWxpweVXP/hPSGiuvLmEa2fPMnh8zUJ5pp7zIzc0Uk8ucmmMLmKM02vjuDp9\n6T3Vp0jPXhKtupDI73+vUTkBU+eXSbv04tvl5KwdEg56EfXjHmm7vI8SrboQ747P6d1nWqUKTYGS\nhEPeJBz0IvWM/sTdkmF+S6LJV2JoWv3e/NqmMCcPg7rGkjNYmoK4JERhIaaOTarsMZVCA5ZawE+r\nVEGRvENoyQ2LxKBuXcyaNwUgJzQSTV4eJk1sqdu4oZ7mvDC3+LcyMUUnzzEolngVyR8rC+FYHjeO\nnKxR/n/K2q0/EBkXy5pFH96X8uraNcbIwoz8wPIn3t4r6sJCVmzewP7N39PWucV9Lbsy3n77bZo0\nacLixYvvW5nnzp1j5cqVXLt2jQYNGnDlypX7Vvb9otKe9+joaAYMGICLiwtPPPEE69evByAtLQ1X\nV1fatGnDkCFDyMgoHnb//PPPad26Ne3ateP48eO1W/uHmIpWQC1JQUwChVnZxO8/IaVpcvNI8yk/\nQkt1eJw077bD+0m/zcsZrv+3eZxs+6ApHZmhg4G+o36ylSvhm3bqSTIS/jxFdlBxnOHcu05O0nEf\nPO16cbrraKK37SN6+34p/5U3l+o57gA33v2My69+AOi03Lc+30LU1r2V6qL/CTm3Ix9oJBFNbr6e\nfZXJaZLmvCTZwWF42vXiuLOu1zj7hq6Xu6RcpIiSUpX7wZXX79+L99+iaD5S6Xu3JDeXri2TFrhw\nFV5thxL4nkcZxx3Kj9Dl9/IcTjgP4NbnWyR5Tk24/Nqie14EL+3iFXLLiaSSGxZJfnRZiWHRyIE6\nPQt1RhZZ125Kq3Oqs3PIj0sk82pwhXKrzKvBaO+G2C1Pl61VKiVtuSZP1xOvyVfqonlVoDkvmqgu\ntBoKNY/XAkA1GeEwtrLE2Ko+oLjvmvfktFSUKhWtHJ2qzvwQoSnnPjQ3N2fKlCksX778AdSoelR6\n9YyNjVmzZg2BgYFcvHiRr7/+muDgYDw8PHB1deXWrVsMGjQIDw8PAIKCgti1axdBQUF4enoyc+ZM\ntI/JEGBNyb0TLa2Aqs7KIdn7ou6PTKulMDdfLwRgYfZ/d4Z6ZdRpZIWZswP2L7rS8JkuD7o6Mv8y\nIR9v5Nps/bjdRS+pi6Omc67neK7PWUH4pp3S/qCFq/Tylxe+szR31m0naOEqrv/vUyktbN22SleW\nrYqiVXXzYxPx6T2B2F/LmdNSDS64TiPyR11UH61SdU+rgioMix/zQgguDJ7GmafG4GnXi9QSHQU5\nIbrlyLX5yirbXrTKskzFZF4LIWqrTq4U+f3v5EfH6yZNV+NeOO48gLA1PwG66556+hKgu1e92g+v\n8vjoXw4S8c1vpF24jCotk8TDp0k5VfGEc3VmdoXXPGjhKjL8dNHIhBBS+M/y0OQXkHU95K5zXuwk\nZwfdJvdONHl3olHd7dTKunFLmsdTmpK95uUhSq2v0WPoINauXcuQaZPo8vwwFnzxGcq7iwFdvBJA\nz3EvsOXXX3ja7Xne//JzhBBs3vkz/SeNp9voEcxavlSSeUx7/z2279OPpDX8NXeO++je5y0G9iYq\nTvcxk5WTw9zPPuHJF0fS+2U3Nu7YJj2j1m79gXc/+1gqIyYhnhYDe0s+0R7Pw/SbNI6OI13pO3Ec\nB06W7ew8c+kim3f+zGFvL54YMZiRb0wD4OU5s1j1w7eMnTWDDsMHERUXy+9HD+M6bRIdR7rSb9I4\ndv6pv3DicZ9zDH15HM2bN+epHk9z5tJfUhsWfvUlPcaNpue4F1j947cV+m1KlYqPN67lmXGjeWbc\naD75eh0qtZo70VG4uk8CoPOooUx+73/lHu93/Spus6bTedQwnn1pDH94HpHKXbF5I8++PIanxoxi\nyZqVKFVK/ev34/e0bduWDh06sHOn7pm/detW9uzZw4YNG3B0dGTSJF0d4uPjmTp1Km3atKFr1658\n++23Uh08PDxwd3dnxowZODk58euvv5apZ7du3Rg3bhxOTg/vh0ilzrudnR1duuicpnr16tG+fXti\nY2M5ePAg7u66kG/u7u7s36/r6Tpw4AATJkzA2NiY5s2b06pVKy5dulTLTXh4KOoRyQ4OQ1vioZR4\nyJuCmASESk1GQCDxe4+hTEqtqJh/xOOmebfu/aQknzA0M32gdXncbPswEaQt/2Ud/4f+C61oeL3I\nmYj97TDpF+/fkKanXS887XoR+vk3AAS8srDKY3LDY9Cq1ORFxqFKy+TqzGUca9qHY/bPSusAxP7u\niSolvdxly4UQFX5kZF2/RfJJneTi1uffcLrL6ErrkhUYKsX197TrRcIhbzAwkOybeuYSysQUaa0H\n/UgrslzvXqjo3vUd8or0O3jJGs485Ub0tn3VKlObryT0i+9QJqdx3Km/3j5Nbh6edr2ke0lbWKi3\npkWa72UC3/Pg5kfruTTmbU510Dn7RT3i8ftPcuvzLVL+yB//wKvt0IorU0Lyos7IIic0XG935tVg\nadVMUc5KpEWUXnEUkDTuFVETXfYBrxNsX7mWM7/sJjwmmo07tkr7UtLTyMrJ4vyuvXz23gK2/vE7\nJy/4sGvd1/z1x0EsLSz4cK1u3YrnB7ny56liaUxoRDhxSYkMeKbsx82y9WvIzc/j7M49/Lb2a/Ye\nP8rvR3VzICqTCuXl5/PxxnVs/eIrrh8+wR8bv6FDq9Zl8vV7+hlmTprKcwMGc+PISQ5/V9ym/SeO\n4TF/IYFHTtLUzo5GVlb8+PlKrh8+wZcLFvPppvUEhuqkMTczUpjn8SnLPlhEZGQkBw8cpLGtLirT\n++tWYdaoIQEBlzn03U+c8/Pjt8N/llvvr3ds4+rNYI58v40j32/janAwG3/eSotmjhz7STdv5tqh\n4+xYXXbuSkxCAq8unMcrY8YRsP8wh7/bSvu7bf7yu81ExsZw9PttnP5lFwkpyazf9pPe9cvOziEo\nKIh169axYMECsrKymDZtGmPHjmX27NlERUXxyy+/oNVqmThxIp06dSIoKIj9+/ezZcsWTp0qjg7n\n6enJ6NGjiYyMZOzYsRVep4eZamveIyIiuHz5Mj169CAxMRHbuxfe1taWxERdHOq4uDieeeYZ6RgH\nBwdiYx8fnW5lCCGI3XWY+h3bknU9BGNLnS43ZuchaXhQlZFFTnBYZcXI3MVmWNmlro3qmaHJy8d2\n5AASD3sDUK+NM5ZdOxC76/C/XUWZfwkhBBHf/AbA5WlVO9P3k6SjZwlZsRl1eibpF6/Qx+e3MnnO\n9RxfcQFFzofQcuO9z0k65oN136do8FRHGvbqhvWz3Uj805srby6pWH9/t4zSH/w5tyNJ8b5I6tm/\nabP4LcydHbgwyB3TZvb089P1HJaWo+THVBxJSZOnrHCfzIPBu+NzFe674PoKwxIucGfddm6v/J66\nNta0/WgW194uf6g/ZNkG0ApCPt4IQKt5r6MwMiR40Wopz5UZH2Lu3IzW7+ui+6izcsgJDsMCKMzL\nr/AjU6NUE/PrYbQFSlRp9x69ynZEv6ozlYNCoWDqC27YNW4MwNuTp7Js/Rree/VNAAwMDJgz7XWM\njYwAI3YeOsDy2XOxbaTL/z/3V+n9shtrtB8ypHcflq5ZRVxSIk1sbNl/8jjD+va7e2yJNms0HD7t\nxZHvt2FmaoqZqSmvj5vAvhOejB/xXJVSFgMjI0LuhGHf2AZbW1saN2xYbj4hBKLUh7VCAWOHjaCV\nU3NdWRjofVz06NyFPk8+zaVrV+ncrRu/bf2W8SOeo29fnX2bNG2CYWomyWlpeJ89S3hEOHWNjbFu\nYMWrY8fz25FDTBw1GiOLenofXQe9TrD8f3NpaNkAgNnur7D4q5XMffUNqvr4P+h1nN7dn+K5gYMB\naFC/Pg3q10cIwW+H/uToD9uoX08XFWjmxKnMWbGc+W/MAMDIyIj33pmNoaEhrq6umJubExoaSvfu\n3SUbFREQEEBqairz5s0DwMnJiSlTprB3714GDtQtyvb0008zfLjuo9bExKTSej+sVMt5z8nJwc3N\njXXr1mFhYaG3T6FQVPqF+V8J7VMUhq50z1rJocOiFTVrk0ddl93gyY4oDA2p27jsg8ykqS1Cq8XI\nvLgHvn7HthjUMZaOLVpsqjZ41G37MFOZbvh019EoEx6cTCN8w88YW9VHnZ5FdtBtLDq0IickHBMH\nO717sTwujtQ5D+kXiyNHpZ71I/WsH2Grf8S8tRO5oTotcm54DJn+N7AZ2gcji2J7SC+mUs6AT+/i\nSDDJJ4pDhuZHx3Oh1KJbHQzM8bTrRdOXRlRY1xtzP6u0LTLlU9m9W9uUlLook1IrdNyLKHLcAY43\nK9tBkrBf1+OccTmQp35bS8TmYklByeXupXkkd+/JvDtRWHa5/8/Hmuiym9jYlPhtS2Jq8TOjoWUD\n6pSYWBuTEM+MDz9AUaJ8Q0NDUtLTsLFuxIBnenLQ6yQzJkzikPdJPOaV7TRIy8xEXVhIU1s7Ka2p\nrS0JKZU/q0wd7DHOzOaHH35g48aNOslKjx588skn2OQV+wtG5uaVyofsG9vobZ/+y5d1234kIjYG\nrVZQoCzgic6dMW/RjLi4OFwHD8bYsh4ACgMD7Lq48PfFv1AXqmnfXheKU2i0CAQODg5SeE5NXgGq\ntAxUqekkpqaUaq8dSanVezbHJyfTrEmTMumpGRnkKwsYNf01KU2n4y8edbGqb0lda6tiG5qakluB\nbaKjo0lISMDZ2VlK02g09OpV/LfSpJx6PGpU6byr1Wrc3NyYMmUKL7ygW2jF1taWhIQE7OzsiI+P\nx+buH03Tpk2Jjo6Wjo2JiaFp06blljtz5kwcHR0BsLS0pGPHjtJCIkXLTT8q2+fOniX55AXJufML\nvYlRPTO62jtK24De/trerv9Ea9oqDf+V813Pz6AgJqHK/KMXziHuD0/8Qm9Sp1FDOlvZlMlv0b6l\nzr5JMeXau/4TbXTbzo3o0akLhmYm+Pj4IJpb06d9SzT5Sk7tP/iv2/th247Q5kpORdGw/qO6fTku\n8sHXJ1Vnz/MDp5Lh1oe43z3pYGDOoJBj/6j83NDIYtnF3R78ou0hk18G4Nwpb5I3/0CTu47SVzad\nqy7/sn+5+2N3HXng11PefgS2T3nTJSOLsDU/EaTNxYxipzJfaMlPSsZUYUBhTq4kbSlytB/EtgDi\n7ioA8oWW8MQEbK0bAaAUQk/6ky+02NvYsur9xXRzeaLc8oYOHMSW7Vt5ulNnCpQqunTpSkkKhKCp\npSXGRkbcjo+lpVNzTBUGxCYmYtuoMflCi6mJCQUFBVL5yWm6kTNlHUMMbBsysJUTAwcOJCUlhZUr\nVzJnzhx+3/QdWenpKAwNsG3lSHbIHTQK0JT4cM8XWrQUd4zmCy0qlYq3PlrMmkUf0rvXsxgaGjLn\nw8UIBWRnZ2NjY0N4RASg2wawsLDAobkTderU4cqVK1haWurtLyJPowZLc0hNx9a6EWHxcTg0b46J\ngNjEBBpbN9KTN+ULLQai2J4KR3vyImNpYmPD1ZtBZextWt8Ck7p1ObF1BzZ3yzJpYoMiPkW6fgJQ\nGCik+pXU5BcWFqJSFY8INWzYkGbNmuHv71+mvaDzaQtLzJkovb/0tlarJTs7u8L9Pj4+XL9+ncxM\nXSjLqKgoXn+9bDS1+41CVDK2I4TA3d0da2tr1qxZI6UvWLAAa2tr3n//fTw8PMjIyMDDw4OgoCAm\nTpzIpUuXiI2NZfDgwdy+fbtM77uXlxfduj2ci1DkhkWhycsHAwPqu5TVoJVH0onzKO9hIllt4Bd6\nk0C3A+YAACAASURBVKdat8P+BVe9KDa1if2YoWQH3SbnZsWSoMaDn8XEvjFpFy6TGxZJsykvEP3z\nfuraNdazXdHqof+ErMBQMgMCcZj0vLRaqc2wvtIE4nulyLaPAoHzv3zQVagRQSU+Nh4lnjnynbSA\n0MPMo2rfR4H/gm3tP5pJ817d//Xz5gtttXrfe7/shoV5PX7yWIVJ3bq8sfh9enTpyrzX3uTilQDm\nfvYJF3YXzzf4cc8uTpw/x6qFS2hqa0dqRjoBgTdwfbYPACq1mqfdRtGxbTvaOrdkycx3pGNbDOzN\n6R27cGzSlHc/+xilRsPKee+TnpnFtPfn8uZLExk/4jl8/P343yfLOPrLLhrY2fC/JR9w7NgxkpOT\nSU1Nxc/Pj379+mFqasoXX3yBr68vBw8eJOd2JAbGRpg5NUVotGz57Av2nTzG7nWbJF9qwruzeGHw\nUF4aOQqz5g4kBYXQZdRwfvlqPU936syZSxeZuWwJM15/g6UfLycgIAA3Nze2bdtG7969SUhIICkp\niS5dujB58mSaNWvGokWLMDc3JzIykvj4eL2eatDNbVj947f4BgTw674/yA4KZfqSD+jZtRtzX32D\nmIR4+k4cx+2TZzEwKL5mlp3bkx+TQETwTYa+MhmP+R8wtE9fsnNyiU9OokOr1ny8cS1Jqaks/99c\nrBtYkdPAnIATp+j7VA/p+gWGFM8569KlC+vXr6dv3758/PHHxMTESJNStVotgwYN4sUXX+SNN96g\nTp06hISEoFQq6dq1Kx4eHkRERLBlyxYqQgiBUqnk3LlzzJs3j0uXLqFQKKhTR3+l35SUFBo1alTm\n+ICAAAYNGlQm/X5S6V/F+fPn2bFjB97e3nTt2pWuXbvi6enJwoULOXHiBG3atOHUqVMsXKgbUurQ\noQPjx4+nQ4cODB8+nE2bNj1yspm0CwFkXgkmMyCQ6J/3o86oOgbsg3DcGw/pjVkLxzLp5i0dadD9\nCWmo3W704PtzwrvXsdmUF/Qc7CZjh2NkborVUx1r7Hg3GTscG9dnaTblBSy7udyfegL1XVrTbMoL\n0gp6gBQf2XZ4Pxo+W/svIaunO1eZx7zlwzuTve3SquNlt/1wFgBWPapu6+PKxeemP+gqyMj851Eo\nFIwe7MrU+XPoN2k8zR0ceGeKu97+krziNp7BvXozdf67dBzpitvb07l6M1jaX8fYmKF9+nEhwJ/R\ng1zLnKuI5bPnYtGoIf2nvMxL/5vJ6MFDGDd8JAC9uz/FmHFjGTJpPCNeGsuwYcOkY7VaLZs3b8bF\nxYWWLVty8eJFVq3SRcqq18oJMyedYkFhaMDLs3S6766jh/P89FfL1MPY0gLbzi589M4cZi1fSpfn\nh3PQ6ySuvfpIktJu3bqxceNGFi9eTPPmzXn++eeJi9MtTrVp0ybUajU9e/akRYsWvPLKK9I8xtLM\nmfkOnZ54gr59+zL8tal0bN+eWVOmVWjnIumNib0Nji1a8KPHKr7f/SvdRo/guTdf4eYdXYff0g8W\n49TUgTGzptPpuSG4vTSemOxMKUR0ZX7k5MmTCQkJ+T975x4XZZ32/8+cGBjOZ5CDgKCogIomImqm\nZpilVuamu1qaZdlTW/4qy3affWrbp9Nu+VRbdlorXQ9lW7Z5XjINz8dEkAABBxBQzjDAMIf798cw\nN3M+wNzMgev9vJ7Xch/mvr/zaZy57uv7+V4XEhMTsWLFCvD5fGzfvh0FBQXIzMxESkoKnnnmGTZj\nbs3qDWhi35iYGDzwwAOoqanBsGHDcP/9xiVznYnFzDtXODvz3nK+CAIfMfxHjzA6VrXlO6N92qC0\n+/oNiKPCwOPzoVYo0X65BP7pI/tdBq6/hM+dBu/IMJPjjVl6F/hCIRi1Gu2FpQhIH4Xr/zoIcUSI\n2eYfthD72wVQtnWwDXKqtnwHv9EjEDwpXe88RqVC9ba+leoxS+9CzfYfEDnvVniFBUNWUY22S7/q\nNaYCNOXQar7a65DMuy5VW75DQNpIBE4YA6WsE0JfCeQ3mwachTfEf2wK/EYmoPbbQ4haOAeiAD+0\nXvoVYBi0XTJdpSbolgy0nLlktD8gI9Xsa2xloJn33LrjqP3uEOQ3m5DwyG9wKHGWUVm3KXs+xsn5\njyLzy7dMNszRJXL+TNOdNQnCBRBHh0NuUPte4CfBnJKDODBsmpNG5To4K/NuK9OXLsYbz72IqZmD\nO0bfpHi99SmtvxQDYCDwlYDvJYIk3jHeam03Wd+UBL21B16hwfCJ1XjQFe0d6CyvgldYCATeXuiq\nrmODZ0egVijBEwrYwLf1lyvgi0RsDX/Dxa0CiQ/8DPqzaN+HMMAfXsEBEPj7gi8QsMeEAf5QtrXr\njZtRqwGGAU8ggKvhspl3T6W9sARtl+3vLnYz7zjblKJmxw9ou1yCxqP9b6jUX7SBux58/f+UPD4f\nAemjAADR99yO0GmT+nUvbZaax+cbdbb0H51sdD5PIEDMA3chZKrm4YwvFGLYfbnwCtMsNvFNjDUK\n3AEAAm4+isMWz0PAOI3VRegr0Tum+6VrDzG/mc/+HTYzC8HZE+A3KglCP1/ELV8EUYBmUVBgxigE\njjO22fiNTIT/2JGQDI9ByNRMBKSPQvjcvgDBNymuX+MyRc7hLXa/5tZzmunl6EW3I+GR3wAA/FI1\nHfP8xyRj4va3IQoJhCRRM87w26ci++BmjHn9WbPXHP2XZ4w+owRhK9NPfMXJdVNffRoZ7/83Mj9/\ng90Xfd9cpP/fH3B72X/A4/NtmoUiPA+BT99idP+xKQhIG6V33H9MitFviHd0OIT+fvBNindY4K6F\nLxJBKPGBd0zfglFt4A70/b55hQbBKzTYoYG75v5CvYy174jhEPQu2A/ISDX63TIM3AHAe1gkJIlx\n8E2MhSgogA3cAcBneAy8I8MgkOj/TvP4fJcM3J3NkP011X4Im88UoPVCkcVzO6W1rA2FUSqhVvQt\nduiuMV96zVFEzr8N4shwi+fE/XYBACD/2DGjY9r3Gn3P7UbH9OgNrkKmTULknTMh8PGGJDFWr9Op\n3uleptti80VC8HTKagkk1ksx8YVCDFtsvfmIvQh8xHr2GV205SiDs/QbQEXfa7rmcVmYD6LvuV3v\nffvERcMvebjFqiPR994BnkAIcWQ44pYvQnDWOARljoHARwzfEfEIHD8a4ohQAIAkMQ5Cf18ETUyz\n631qCZuZhYjcGfAbqVlp7z96BIav+Y3F1wh8Jcje/xky/v4nJD7xW/jERBqdM/IPawFoSrmF3zYF\ns4v2wSskELl1x8Hj8RCYMQrxD91r8vq3FfwA76hwTNzyltkxmKuVTTgGrvXNrTuOqYc2W/+O6Se+\nibEY/eozmF283+jYnKvW29VH3nmrXinOjA/+B9OP7UDC6iUYtjgXgeNSMWXvpwCA4EnpelV5wm7L\n0ruW4eecPrvcYU+dd0fhHaX5rfUbmYCA9FHwH50MvlCoaXbW67/ni8Xgi4zrfYgjQuGbFMcurnQU\n/mNT4DdKk0DxCg2Cd3SE0Tk8Ph8BaSMh8BbbdE3Dhan2IvSTwHtYJHyTh/dZeII0i17NxSvi8BA2\nuWWIV1AABBJv+KW4rp3UlRiywbuWjuKraL9SDkATpJui8cgpKHvbKzcdP4+aHYNrk+GLRYiYm4OI\n3BnwiYvWOxZ51yybg16hn6+mtvT0SZAkxLL7Y5beBb9RSQjq9Z2LI0LhFRqEYYs1Hj1t1lyXuOWL\nTH55DQStL51rRAF+8I6OYL9w/EYmsOsHwudOYwPxyDtnIvZ3CxHQm8EQ+fuyDaNiltyJYffbqLuv\nD4bdn4uwWVlmz9GOxStUUz/Xf4zxrIYuup8DgZ9Eb784PAS+Ol+Ao1823e1Oy5ySAwgcPxrD7rvD\nbJbRJ1YT0Cf9/kGTx3XRZum1sE22enU1F+QT7k1A+iiM+/BlhEzN1MuUTdnzMTv7BQCB4zX/noKz\nxiFw/GjcXnHY5PVu2fUufFMSMPO8xho4fPX9EAUFYOK2txFxh2amKmX9I0YzaibH1nvP2b8egFd4\nCKIXzYHvCP01Q0GZYzDz/HeIW6Fv3fNNSWC9t/5pKUYzTD7DTVdUIwaPn7fvcphlRhwZBt9kzfcn\nj8/XS9YEpGmKWJj6TeQS9uEBmt8Kr/AQszPfgzoukVDv359A4g0ejw/vKBPuAMKhDPngHdDUYmcY\nBo1HTpk9p/HnwbfHAJpsufYfhzg8BGEz9QNAr+AAvaB3Wk6Oxev5joiHJCEWodM1Nhq+WAy+UIjg\nyRnsGgBHLDL2HhaBIAM/vKvAF3shfM5U8MVeiF12NwAgeFIaIuffpmdJ4vVOE0oSYuCXOoItXam9\nhq0ZDkDzJccXWn7YiVu+SG8dRkDaSABAYOZYiHuzQdqMvMBXgrjlizDs/nmIXjDbaPo24+9/wuyS\nvu6k2mA+++Bm5Py0Fbdd6luXYMsXvmR4DO6oPWbTA1vk/Jns3zk/bWU/n75JcRCFBCJqgbFtauGL\nT4Pv7WW0n3AMA6mGMvZvlhtjeQ/TzwJmfvkGbiv4ATG/uROpf/49giamYeKWtxC1YDZy646z2fms\n3R8ie/9nEPiIEX3fXPb1YbdNAV/shdBpkzD9521G1w+fNQWZX7yJmb98j8T/Wq55f28+j8Dxo9kg\nW8vMC7uRW3ccI55aAUCzuG9WwQ9mZ+O8h0UY/Xvgi4SY8oOm4+6IZzRdUwMnjoUoSFMqLsOfAhVH\nI0mMg098jF113h1BQIZpi6UWHp+PwHGjIR7k4N1oHDye2ZlvWzHs2eMIxOEhCMgYZf1EYsA4NnXq\nThgEqNp26+awpeqMI/GJi4b/mGQ2a2kLksRYu5+8vaONp7d4DvCf80VCkwuCXQ2tXnyxF7zEfcFj\nxB3T2ek9UYAfgm8Z/AcRv9EjIAoJgmT4MASMTYFaqQRfKIRXWDC7/kD7ABE4fjTk9X0dOAXeYr2H\ni2k/bYWsohp+yX0Z+fT/+wNu5p2weTw2P9TpLIH3G5nA/i2OCMXson0ANDaLw+MXQF7XgPDZ2Rjx\nzEqMeGalXtMZwjXQVr6YceprHM3qq7gQMjUTPQ3NSHh8qd752u+s9P/7A7tPHBGK8R//GQDgM9zY\nC5zy/COo/UbzsDnhH6+xi+AsofugHb9iEeJ7M+a6nyFT32/9QRToD55AAP/eWaXsPZ8AAI7NfhCh\n0ychMHMMqrd+3+/rp778FLqqauGXmoTCZ9+w/gIPgycUglEqAR4f4shQCH0lRl1F2XP5fM0iRhsQ\n+vlC2WHd1uQVEgRRSKDbVccjhi5DLvOuaNOshlZ1dunvbx2Y/2sgGHquAY13WeuDtpXQaZNwzITn\n3Rz+Y0caWRxiHrgLfDFlQE1pr20WNVgIvMWQ6AQ62sy9OCLUKOsiSYi1WLKRJxDoBe4AEPObO9mA\nylGEzcpGxO2a4Cnn8BazGU7NoDQ/lBP/+TfOtc2tO47cuuOYXbwfCY8v4/RershAfNmh0ybi9srD\nkAyPQdrGlxB66y3wCg/BuE0vY9rRfyJ26V12XS8ydwbmVutXe5IMj0Ha2xsAaOxz5nyxtnDL1+8C\nAG4v/7Hf1zDFHTU/G1ltcvK+QMOcCUj76wuY/O3fkfryU4hftRiTv/vArmsnrHkAo199BnG/W+jI\nIbsdfJEQ3pFh4An44AsE4CfFwn+s1qoSAu+oCJOWFZ+4YfAeFsn+HZA+Cr4jhhv999Ki9bX3vT7a\nJvuVJzFQzzvhXDw+865WKsEoVOzUfd3uvsVNsvIqcy8bNPxGj4DfyAQ0n7rI7tNaWrgmKHOM0T5H\n+9iJocWkbX9j/xYFWp6W5SLLNafsEP6T3Ldo0js2Clk6gZQoKACpf/ovVH64jd3nN3oEOq6YbzA2\nFAnOGofmU7+w29pZnNgH5iP2gfnmXmYzpixkAeNGQeKASkuh0yfpLU4dLEKyJyAke4LV85KeWoHG\nY+fQeq4QAJD29osmz5tbfRQHY2c4dIyuhjgiDPIbDeB7eUEyMgGA8XcCXyg0qpwi9PNFd+1NqLo0\nSTivEM1CSUVzGwS+PuDx+RD2rgWSJMVBJeuGvL6vFKgoNFiTpOLz0Vnh/DiAIOzF4zPvzScu4vou\nzVS9YU30pmPn2L+d1iHVxMyg7mJSe9H1ZROOhbS1nfGf/gViK5aF6PvuQESupqOhVlvdhbbhs7Mx\nbtMrdt1Xa9nI/FJT2YYvFOiVUzPFtMNbkPH+fyPt7RchGRGPKXs+tuue7oCh5113zYOhjSXjw/9x\nSmm2gLEpmHF856Dfd6CY+17QeuIBzSyAdjt22V0ImaKZbZ24/W123Y2WcR9pZsP4QqHJh5DJ3/7d\n5rEZVsrhEoG36apiPnF9ny9tNRK/UUmQJMXDOzoc/mNHwjcpFnyRyCh5ZM6XLfT31bPkafEbmQCB\nwcyxyN8P3lFhbLUWQPO9IAoKgCjAz+ElFd0FLjzvxODh8cG7qksOAOgoqXTuQGwkZsmd1k8iCBcn\n6q7brGbWR730uF59bQDI+XELwmdnAwAyt/5Vb/GrPYiCAxCSk4nIO02/Pjh7AuIfXoycn7YCAIYt\nzkXssrsx49gOvTKd2Qf+YfM9xRGhCMlxXvM5Q7xNPLRoqxSJI0KR9vYG+I0ewXbKBYCphzZj2D1z\njV5H2M/wRx9g/+YJ+Eh84ncANMkZQa9FI/y2KUavM1epQ9sLIiR7AvtwamqmInhKn31u0vZ3+jl6\n+zFecM6DV2gwmxUXh4dCMnwY/MemQOAthqh3kT1fKBjQw6IoMMD6SdDMHvHFg1PRzJUoLS3FjBkz\nEB8fj08++cTZwyEchMcH79pZOGd62i2hndoL7C3TOFC/+WD7socSpC13aLXli4QYdn8uQqZN1FRU\n6M3Ehd9uXEXJKzQI0098hZkXd2NW0T62pCAAgAdM/uZ9jPpv06Uvs779O8b8ZR27ANGQGSe/Qm7d\ncZNNtkzBEwlx26V/I2HNUusnDwI+w4dh7Bt9XW+1nnfdhX6xy+7CtMNbII7sW9+hbeymzWoaetMJ\nY8x9LwRPzgAAZH7xBvhiL8Q/dC+G9SZnEtcuYx8cDTFcjKnN2I9963lM2PwaACBibg6ydn+ICJ1/\nF1pvOHh8ZH75JlJffdqu92GtH4Q5tBl3UUgQfHtL7gaOG43AcansrFfguNFs1SBrVbd0scWX7YgC\nC/YilUoRGhoKtY0LZ53Ju+++ixkzZkAqleKRRx5h93Ppec/Pz0daWv96lVjiyJEjyMrKQmxsLBYu\nXIjq6v53jXd3PD54t7hgjkPEprqg6uCbkoDQ6ZPcoiILQQwm0Ytux+Rd77HbU/Z+auQLDhiXiuDs\nCfBNjIV3VDi8QgLZ4CD1ld8jMH1g5crsta5NPbgZgCaoyq07rlfXHAB4OguMM794A6KQoAGNTxev\nsGDcoqPXsCV34tZTuxA+Oxu5dccRMq2v/nVAWgoEEv2GYsGT0nF7+Y96CzxTX30at1cctivQIgzR\neCIj7tBYw4T+vsh4V1OBR+AtNvvg6DsiXs9yNuvKfkzL3w7vyDC9hnmGC9Rz8r4AX+yFgIyRiJg7\nDQmrlwDQWMh0s/GGpfy0C0DjH7qP3adbZlaLKXuJ74jh8EnQVCPiCfgQ+Engm5xg8n1xhh1rZ7xC\nAo06hQ8EbfNGU6hUKofdZyBUV1dj1Cj3Kt+oVCqN9jU2NuLBBx/ESy+9hPLycowfPx6rVq1ywuhc\nA48P3tHb6Uwt7+H8Vtq63EBfeTVddGtxB6Sl6AUIPnHRkCT23+uuhXzZ3EHacoclbYMyx0AcHqK3\nb+qBf2DCp38xeX7Co79xaMWkGae/0YwxfzumHtps8hzDh/CpB/6BpKc1Da1CcjKR9ORyDF+tKbMY\nccd0uxtVZep0pxX46HuLo+6ehdBpE3FbwQ+Ye+0npG/coHd84pdv4b+uHAGgWZx7e3me0fUFEm+9\nTsh8oXDQmqa5O+Y+u0ET0zH61Wfsvp44IhS3XdjNbvN4PKNKUVpily8EX+e/05yy/yD1T0/qnRMx\nNweT/6XxyWdueQtBOmVvb/nmfUTeqXkg8O39/QnISDVrYxH691UBCkgfBaGfBAKxF3giEQTeYvB4\nPIvdpu3FFl8231uMcePG4f3338f06dORkJCAhx9+GHK5nD3nwIEDmDFjBlKzJuHeNQ+jqEjTVf2f\n//wnli3rqz41adIkrFy5kt1OS0tDYWGh0T3nz9cs2k5MTER8fDzOnDmDbdu2ITc3Fy+99BKSk5Px\nxhtvoLKyEgsXLkRycjJSUlKwZs0atLX1lZ2urq7GihUrMHLkSCQnJ2P9+vXssa1bt2LKlClISkrC\n4sWLLWaZ9+3bh+zsbCQmJmLBggUoKSkBACxcuBD5+flYv3494uPjUV5ebqRtc3MznnjiCYwdOxZJ\nSUlYvny5kW6JiYnIzc1ldQNgVnOZTIYlS5agrq4O8fHxiI+PR319PRiGwcaNGzFx4kQkJydj1apV\naGlpAdA3k7F161ZkZGTgnnvuMXqP//73vzF69GgsWLAAXl5eWL9+PQoLC1FWVmZWF0/G44P3npvN\nAMD5ivLQW7PAE/Z94Qn9fRGRq6kUELVwDoA+S0zssruN6reLAvwQOm1wqswQhDsyq3Avcn78EnOl\nRwb1vpJ4jU/cOzqCtZXYQtCEMeCLvTD5m/eR8txqva65geNHA7qzgr1/T/t5m+FlwBd76fmg41f1\nZUhn/vI9Rv1J41kXh4eAL/Yymm0USLzhFRoEgY83gjIdP5VNmEbgI2Yf2LjCL3k4Zl36ge2MzBcJ\nTc8292anw+dMRerLT2FMr6UqNCcTo/70JGac2gUASFz7WySuXQqhrw+y939m5GP37fXYe4UE6WW8\nA8YkO2WWW9swicfjYffu3di1axcuXryIwsJCbN++HQBw6dIlPPXUU9i4cSPKy8vx0EMPYdmyZVAo\nFMjJycGJE5peF7W1tVAoFDh7VtOQsbKyEp2dnRg7dqzRfffu3cueI5VKccsttwAAzp8/j8TERJSU\nlGDdunVgGAbr1q3DlStXcPLkSdTU1OD1118HoMnML126FPHx8fjll19QWFjIBq179+7Fxo0bsWXL\nFpSVlSE7OxurV682qUFZWRkeffRRvP766ygrK8OcOXOwbNkyKJVK7N69G9nZ2XjzzTchlUqRlGQ8\n2/PYY49BLpfjxIkTKCkpwdq1a63qBsCs5r6+vvj6668RFRUFqVQKqVSKyMhIfPTRR9i3bx9++OEH\nXLlyBUFBQXjuuef0xnLixAmcOnUKu3btMhpncXGxnhVHIpEgMTERV65cMamLp+Pxc6K2NPtwBEYz\ndzwexOEhiLp7FtA7tRY0KR039h/ltJJDfn4+ZYg5grTlDlu09QoNgleo4+wm9jD71wN6GcXYZXej\n6dQv6Lwqxe0Vh02+JuKO6Zh77Se918T01kSPmJuD3Ov5qPxoB9qvXEXNV5qKWH4pCZhx6msI/Xwh\n9PfFsdkPQujrg4D0UZhzNQ+MUglRoD9kZdfgPSxSr1GRJfLz83F7hWPrnhManP29IPT3ReITv7V4\nDo/Hw/RjO8Dj8cATChG79C7WtiP09WE/27prRALHj0ZI9gQ0HDbuPO7VGzDrMvfTCwN9Kzi4Wr/U\nZnt7u81VUdasWYPISE2t99zcXBQUaBovfvHFF3jwwQeRmalZTP7AAw/gnXfewdmzZ5GdnQ0/Pz9c\nunQJpaWlmDVrFi5fvozS0lKcPn0aU6eabhpnzi4TFRXFBtne3t5ITExEYmIiACA0NBSPP/443npL\nM4t27tw51NfX45VXXgG/98FnyhTNAubNmzfj6aefRkqKZh3DM888g3feeQfV1dWIjdWfof/2228x\nd+5c3HqrZgblySefxEcffaQ3flPjbW9vh0wmQ15eHsrLyxEQoLETZWdn26SbJc1N3e/zzz/Hm2++\niehoTTLk+eefx7hx4/DRRx+x56xfvx4+PqZnbjo7OxEWpv995+/vD5ms/z0s3BmPD94xSAtKvEKD\n2S6sPvHD2BX2oqAAdv9AGo8QBOE8dGvWT9q5EUETx6KnsQXy+ka77CWGAU/CGk1FEq/wEDBKjUdW\n13I39eBmdtG97sND5hdv2v0eiKGNbsMivpfIYlM3LRO3vY0uaS1alX2204CMVJOVpAwD78EmIiKC\n/dvb2xt1dXUAgKqqKuzcuVOv0opSqURtbS0AICcnB/n5+aioqEBOTg4CAwNx7NgxnDlzxmzwbo6Y\nGH277I0bN/Diiy/i5MmT6OjoAMMwCArSJCBqamoQFxfHBu66VFVVYcOGDfjjH/+ot7+2ttYoeK+v\nr9fbx+PxEBMTw74/7T5T1NTUIDg4mA3cDcdgSTfAvOamqKqqwvLly/Xer1AoxI0bN9htQ/108fX1\nNVpk29bWBj+/oRlXeX7wPkgIJN7g93pRw26drHeMJxKZegknUGaYO0hb7nAnbbX/voV+vibXtvSH\nUS89bnK/o3zn7qSvu+HJ2vJ4PEiGD0NnQ4PevsFiILXIteOMjY3FunXrsG7dOpPnTZ06Ffv374dU\nKsW6desQGBiIr776CmfPnsWjjz5q8drW9v/5z3+GQCDA8ePHERgYiD179rC+9piYGFRXV0OlUkFg\nMBsfGxuL5557Dvfddx+sERUVpedFZxgGNTU1bIbbHP7+/oiJiUFzczPa2tqMAnhrulnClD6xsbF4\n7733MHnyZKNjUqnU7Ou0pKamYseOHey2TCZDZWUlUlNtqwjmabit551Rq1G9ra/RiLpHwTZh0nZO\n7Si7Nqhj8h0Rj2H3zzPaL/T1QezvFoIv9jJbd5ogCIIgCMegtW6sWLECmzdvxrlz58AwDGQyGQ4e\nPIiOjg4AfZl3uVyO6OhoZGVlIS8vD83NzcjIyDB57dDQUPD5fFRUVFgcg0wmg0Qigb+/P65fv473\n3uurCjVx4kRERkbi5ZdfRmdnJ7q7u3HqlMaitHLlSrz99tsoLi4GoMkwf/fddybvsWjRIhw6kV2p\nqQAAIABJREFUdAhHjx6FQqHA+++/D29vb70g2ZLNZ86cOXj22WfR2toKhUKB48eP26SbJcLDw9mH\nAi0PPfQQXn31VXbhbUNDA/bt22f1WlruuusuXLlyBf/+97/R3d2NN998E2lpaUhOTrb+Yg/EfYN3\npQqMTikmXW9707FzULR1QNHcZuqlnMHj8dg24qaOAeDcs0u1yLmDtOUO0pZbSF/uIG25o7+1yHk8\nHvubO378eGzcuBHr169HUlISbrnlFr0M7ogRI+Dn58f6zQMCApCYmIisrCyzmWCJRIJ169Zh3rx5\nSEpKwtmzZ/XuqeX555/HpUuXkJCQgGXLluHuu+9mzxEIBNi2bRsqKiqQkZGB9PR0NkCfP38+fv/7\n32P16tUYPnw4cnJy8OOPptesJCcnY9OmTVi/fj1SUlJw6NAhbNu2DUKdMq+m3odW202bNkEkEiEr\nKwujRo1iPejmdLM066A9NnLkSNx7773IzMxEUlIS6uvr8dhjjyE3Nxf33Xcf4uPjcccdd+D8+fMW\nx6hLaGgovvjiC7z66qsYMWIELl68iM8++8ziazwZHmOpUClH5OXlsYsg+ou6R4GanXsQt3wRAEAp\n60Ltvw4gbvkiNgM/WASOH21XFQoucfbiKU+GtOUO0pZbSF/uGAraNjQ0GC0WHAzsWbBK2AdpO3DM\n/bs4f/48Zs+ezem93Tbzbg51j4Ory5h5GvRNHo7Y3y3UnDKInnZrePqPiDMhbbmDtOUW0pc7SFvu\noOCSO0hb98btg3e1QglVl5ydcqnd/R+HXDdkqvHMgG5nNnFkGHtPZ3VxJQiCIAiCIIYWTos6Fa39\n87IZ0nj0DK7v2sdmyNXdciuv6CPq7lkm90sSY/XKamkJSO/roKpX9nHwFt9bhfyX3EHacgdpyy2k\nL3eQttzRX887YR3S1r1xWqnIlvOFCL9tyoCv0329HgCgaLP/g6ibSdcSs+ROvU6pWgR+EoCnedbR\n+uy1CH0ldt+bIAiCIAiCIOzFeXXeHbxMtrvafHMAe+CLvYz2hc6YDK+wIPQ0NBsdi112N6cdU+2F\n/JfcQdpyB2nLLaQvd5C23EG+bO4gbd2bIWfW9h0xHAAg9Pdjt7V/m0MyfJgmu26iMI8rBe4EQRAE\nQRCEZ+P04L27vgHd9Q3WT7QCo1LbdJ5A22K81yMfMnUCohfNAQCII8NNXLgvYLcW5LsC5L/kDtKW\nO0hbbiF9uYO05Q7yZXMHaeveOD14v/mf47h50PYvP0alMlnHvePXcrvuGzxlnF3nA5oGS4Z+d4Ig\nCIIgCIIYLJwavDMMw2a2be0VpVYoB3RPgY83AECozcDrwPc29ru7G+S/5A7SljtIW24hfbmDtOUO\n8mUPnNLSUsyYMQPx8fH45JNP2P2krXvjvOCdYcCoVODxBWYbIenSWVkNAFB1aUpBKttldt8y8q5Z\n8E0ZbvJY9L1zEZI9QW9fRO4MROTOsPs+BEEQBEF4JlKpFKGhoVCrbbPrOpN3330XM2bMgFQqxSOP\nPDIo98zPz0daWppDr6lQKPDggw9i/PjxCA0NxbFjxxx6fXfDavC+atUqREZGIj09nd13+vRpTJ48\nGRMmTMAtt9yCM2fOsMdee+01pKSkIDU1FQcPHjR7XUalhqz0GngC688P6h4FGn8+i+7rN9g4v37v\nT1ZfZ4hA7MU2VjJ8YBD6SsAX6RffEYeHQBweYvd9nAn5L7mDtOUO0pZbSF/uIG25w9V92ZYcAyqV\nahBHYp7q6mqMGjXKaL8ra6tUmnZYTJ06FZs2bUJkZGRfLDdEsRo5r1y5Evv379fb9/zzz+PPf/4z\nLly4gFdeeQXPP/88AKCoqAg7d+5EUVER9u/fj7Vr15p9MlW0tqGtoAT+Y5M1gbQNtplO6XWbsvS6\n6NVy1y5SnTYJAomxbYYgCIIgCPdi3LhxeP/99zF9+nQkJCTg4Ycfhlze17DxwIEDmDFjBhITE5Gb\nm4uioiIAwD//+U8sW7aMPW/SpElYuXIlu52WlobCwkKj+82fPx8AkJiYiPj4eJw5cwbbtm1Dbm4u\nXnrpJSQnJ+ONN95AZWUlFi5ciOTkZKSkpGDNmjVoa2tjr1NdXY0VK1Zg5MiRSE5Oxvr169ljW7du\nxZQpU5CUlITFixejurra7Pvft28fsrOzkZiYiAULFqCkpAQAsHDhQuTn52P9+vWIj49Hebnx2sDm\n5mY88cQTGDt2LJKSkrB8+XKrulnSXCaTYcmSJairq0N8fDzi4+NRX18PhmGwceNGTJw4EcnJyVi1\nahVaWloA9M1kbN26FRkZGbjnnnuMxikSibBmzRpMmTIFfOpqbz14nz59OoKDg/X2RUdHo7W1FQDQ\n0tKCmJgYAMDu3buxdOlSiEQiJCQkIDk5GadPnzZ7bYGvDwLSeruW2uJ5t9EXr0vQ5AzELrtbb59v\nYqzHPrWR/5I7SFvuIG25hfTlDtKWO2z1ZfN4POzevRu7du3CxYsXUVhYiO3btwMALl26hKeeegob\nN25EeXk5HnroISxbtgwKhQI5OTk4ceIEAKC2thYKhQJnz54FAFRWVqKzsxNjx441ut/evXvZc6RS\nKW655RYAwPnz55GYmIiSkhKsW7cODMNg3bp1uHLlCk6ePImamhq8/vrrADSZ+aVLlyI+Ph6//PIL\nCgsL2aB179692LhxI7Zs2YKysjJkZ2dj9erVJt97WVkZHn30Ubz++usoKyvDnDlzsGzZMiiVSuze\nvRvZ2dl48803IZVKkZSUZKTtY489BrlcjhMnTqCkpARr1661qpslzX19ffH1118jKioKUqkUUqkU\nkZGR+Oijj7Bv3z788MMPuHLlCoKCgvDcc8/pvZcTJ07g1KlT2LVrl03/3Ycy/WrS9Prrr2PatGl4\n9tlnoVar2Q//9evXMWVKX9fU2NhY1NTUmL6Ig5s0mUMcFky12AmCIAiCQ/ZHTR3wNXLrjvf7tWvW\nrEFkZKTmOrm5KCgoAAB88cUXePDBB5GZmQkAeOCBB/DOO+/g7NmzyM7Ohp+fHy5duoTS0lLMmjUL\nly9fRmlpKU6fPo2pU02/J3N2maioKDbI9vb2RmJiIhITEwEAoaGhePzxx/HWW28BAM6dO4f6+nq8\n8sorbCZZGz9t3rwZTz/9NFJSUgAAzzzzDN555x1UV1cjNjZW757ffvst5s6di1tvvRUA8OSTT+Kj\njz7SG7+58dbV1SEvLw/l5eUICNC4FLKzs23SzZLmpu73+eef480330R0dDQAjYNj3Lhx+Oijj9hz\n1q9fDx8fckXYQr+C94cffhjvvvsu7rnnHnz99ddYtWoVDh06ZPJccxnulz7fhNjoaPgVnARTVoVp\ncUGYPkOzOFTrIdRmNPKPHUNDaTFmJmsWm54pLQYA3JKSanWbJxAgPz8fHYp2xPZWkzG6vgdt6/ov\nXWE8nrSt3ecq4/Gk7YKCAjz++OMuMx5P2yZ9udv+8MMPkZ6e7jLj4WI7ODgYYWFhAPq80trMrXZb\nG3ibO96fbV1ftqXz1Wo1IiIi2G0+nw+ZTFPUoqKiAjt27GArrTAMA6VSidraWgDA5MmTkZeXh+vX\nryMnJwc+Pj748ccfcenSJUydOtXk/To6Othx6Y4xJiZG7/wbN27gueeew5kzZyCTycAwDAIDA9He\n3o6amhrExcWx49S9/rVr17Bhwwb88Y9/1AuEa2trERgYqHd+VVUV+94BoKOjA1FRUez7UyqVehYi\n3fHW1NQgKChIL07THq+qqsLOnTvx8ccfA9DEckqlEhUVFexi1IiICPZ8b29v1NXVob29HZ2dnSav\nt3z5cvZePB4PQqEQ5eXl6OnpMamfuf/eupo48vPWn23t96vWjSKVSs3OkjgSHmNDjcbKykrcfffd\n7FNVQEAA69tiGAZBQUFobW1lp4NeeOEFAJonsZdffhlZWVl618vLy0NkaR0EfhJEzZ+J6m3/xrAl\n88AX9j1LMCoV5Deb4B0VDnWPAjU79wAA/FJHoKP4qs1vcKjVZc/Pz6dpXI4gbbmDtOUW0pc7hoK2\nDQ0NbPA+mLS3t9tknRk/fjxbVQXQuAOuXbuGDz/8EOvWrUNsbCzWrVtn8rVffvkl9u/fD6lUiq+/\n/hqXL1/GV199hbNnz+Lzzz/HuHHGPWGqqqowfvx43Lx5k82ab9u2DVu3bmUtNYAmCy6Xy/HWW28h\nMDAQe/bswfr163H58mWcPn0ay5cvR1FREQQG7oDFixdj6dKluO+++6y+97/+9a8oKirCP/7xDwCa\nmCwtLQ2ffPIJpk6digULFmDJkiX43e9+p/e69vZ2yGQypKWl6WXetVjTzZTmlZWV2LRpE44dO4Y1\na9bg8uXL7PlZWVl47733MHnyZKNrSaVSTJgwQU9PS6SlpeHjjz82OzMyWJj7d3H+/HnMnj2b03v3\ny/WfnJyMI0eOAAB+/PFHjByp8a0vWLAAO3bsQE9PDyoqKlBaWmryP5SWvqc94+y8rKIaNw8ZlwKy\nJ3Afinj6j4gzIW25g7TlFtKXO0hb7hhILXJtXnLFihXYvHkzzp07B4ZhIJPJcPDgQTZ7npOTg/z8\nfMjlckRHRyMrKwt5eXlobm5GRkaGyWuHhoaCz+ejoqLC4hhkMhkkEgn8/f1x/fp1vPfee+yxiRMn\nIjIyEi+//DI6OzvR3d2NU6dOAdAUCnn77bdRXKxxEbS1teG774ybUwLAokWLcOjQIRw9ehQKhQLv\nv/8+vL299WIvUzlaf39/REVFYc6cOXj22WfR2toKhUKB48eP26SbJcLDw9Hc3Ky3OPehhx7Cq6++\nyi68bWhowL59+6xeSxe5XI7u7m6jv4ciVm0zS5cuxZEjR9DQ0IC4uDi88sor+Pjjj/HEE09ALpfD\nx8eHnVYZM2YMlixZgjFjxkAoFOKDDz4wa5sx+jAZfrZ0j/djoSqgqetOEARBEMTQgcfjsbHH+PHj\nsXHjRqxfvx5Xr16Fj48PpkyZwmZtR4wYAT8/P9ZvHhAQgMTERISFhZmNXyQSCdatW4d58+ZBqVTi\nq6++0runlueffx5r165FQkICkpKScP/992PTpk0AAIFAgG3btuHFF19ERkYGeDweFi9ejKysLMyf\nPx8ymQyrV69GVVUVAgICcNttt2HRImMnQXJyMjZt2oT169ejtrYWGRkZ2LZtG4Q6TgZLBTo2bdqE\nl156CVlZWejp6cH06dMxdepUs7rl5ORY1XzkyJG49957kZmZya6LfOyxx8AwDO677z7U1tYiPDwc\n9957L+bNm2d1jFomT56M6upqVisej4eLFy8arQMYCthkm3E0eXl5iCiphSjAD5F33orq7T9g2OJc\nvTrrHaWVaD55EXHLF0Et70HNV3stXNE0scvuHnKLVYfCFK6zIG25g7TlFtKXO4aCtq5umyHsh7Qd\nOG5nm3EIDGPKLcMi8BZrTlOrLTZCMIckKX7IBe4EQRAEQRCEZ+Male5NNGni9wbvYBh0SWvtvqT3\nsAjrJ3kgnp4BciakLXeQttxC+nIHacsdlBnmDtLWvelXqUiHYCWZ3lmpqQ/PMAxazhbYdenwOTkQ\nRw3+FB9BEARBEARBcIlrZN4BqFRqvW1tVZnu6jowKpVd1/KODvfYDqrW0K1JTjgW0pY7SFtuIX25\ng7TlDt2a5IRjIW3dGycG74zGLgPNKuODpU2QNhuX/WkrKBnsgREEQRAE0YsT6loQhMvjzH8XLpN5\nBwC5QfYdAIImpdt1jfA5pssYDRXIf8kdpC13kLbcQvpyx1DQViQSoaWlZdCDFfJlcwdpOzC6u7uN\nmmsNJk7zvOt9CZhYsMrCt8/+4h0dPoBREQRBEAShS1BQEDo7O9HQ0ADAtprcBOGpMAwDgUCA4OBg\np43BeQtWYdsXAM9aq1w+H1CrLT8ADCGGQs1hZ0Hacgdpyy2kL3cMFW0lEgkkEsmg3nOoaOsMSFv3\nxrl13nVRq6Fu6wCj1rfOWAvwYx+Yj9jfLgBf7OXoERIEQRAEQRCES+EanncegPJKdBz4CbLSa/a9\nls+3np0fQtCTNHeQttxB2nIL6csdpC13kLbcQdq6N66TeVcqNbt7y0JKEuMsvlzg4623TR48giAI\ngiAIwtNxbsq6N+BWd8sBlQo8aBYCqOU96KyosvhSrzD9hQJ8L7LNAFRzmEtIW+4gbbmF9OUO0pY7\nSFvuIG3dG6cuWNWFV1MLBPkADIOeljar5wdNSkNXVS27HX57Dhi1fc2cCIIgCIIgCMKdcFrwXtve\nA1/fHkTo7BMEBgAMA0apQo+SAXjmi+ALJD4A+uwyAh8x10N2C8jHxh2kLXeQttxC+nIHacsdpC13\nkLbujdNsMw2yHjR2KfX2CUKCwKgZKNs6UNLQibKGToiCAiCOotrtBEEQBEEQBOFUz7uAx0Ntuxyt\nvUE8T8BnF7IyYKAaMwp8kZAWo9oB+di4g7TlDtKWW0hf7iBtuYO05Q7S1r1xuuf9Yk07mNZuzQZf\nE7wb1no3CTVkIgiCIAiCIIYYTg3eGfRm2UNDwGtsQqtCjdZ6mSYDDwB+fprjFKjbDPnYuIO05Q7S\nlltIX+4gbbmDtOUO0ta9cW7mncfrDd81tph2NR++ZVfB5/PAjE0FLyJMc542dufzAVuy8gRBEARB\nEAThgbhEa1Jed69tJiEeoYtuR9ii24HE4TCXb/eJix60sbkb5GPjDtKWO0hbbiF9uYO05Q7SljtI\nW/fG6Z53BgBPJtP8zQB8sRf4PB7AUxqcBdbnHjYzCwzDsOUiCYIgCIIgCGIo4OQOqzp/C0VgGAY8\n8GC2uIyO953H42HYfXdwOjx3hHxs3EHacgdpyy2kL3eQttxB2nIHaeveODd41/XF8Hv97zxoMu86\n+MRFQxwZNpgjIwiCIAiCIAiXw6nBu56nvXfxqqmku//oEYiYOw3iiFCII0IHZ3BuCvnYuIO05Q7S\nlltIX+4gbbmDtOUO0ta9cbrnnQeAGZUCiL3Ybb4Z20z4XJrmIQiCIAiCIIYuPMYJRdTz8vJQl1cE\nv9goyCaMhxqAv1iAdrkKqeESiPh8FNR3AADmp2rsMrIeFXy9BIM9VIIgCIIgCIKwifPnz2P27Nmc\n3sMlSkUa4iU0Tr3/VN6MGx096FFRnXeCIAiCIAhiaOIy1WZ4vRu83v8zxc2OHhwqbRqMkbkt5GPj\nDtKWO0hbbiF9uYO05Q7SljtIW/fGavC+atUqREZGIj09XW//e++9h9GjRyMtLQ3r169n97/22mtI\nSUlBamoqDh48aPHaDANo60Jqw3WzZSIB9Kg0Dp+2biVKGjqtDZ0gCIIgCIIgPAqrC1ZXrlyJJ598\nEitWrGD3HT58GN9//z0uXboEkUiEmzdvAgCKioqwc+dOFBUVoaamBnPmzEFJSQn4fNPPCLpme1+x\nAGowJn3tpQaBevFNGW7KFBgZJrHlPQ4pqHYrd5C23EHacgvpyx2kLXeQttxB2ro3VjPv06dPR3Bw\nsN6+Dz/8EC+++CJEIhEAIDw8HACwe/duLF26FCKRCAkJCUhOTsbp06dNXpcHAExfxj3K3wszEoMR\n4eeld97Vxk42y369XQ4AuClT2Pr+CIIgCIIgCMJj6JfnvbS0FEePHsWUKVMwc+ZMnD17FgBw/fp1\nxMbGsufFxsaipqbGzFV40M2967pldK0zLV3K/gxxyEI+Nu4gbbmDtOUW0pc7SFvuIG25g7R1b/pV\n512pVKK5uRknT57EmTNnsGTJEpSXl5s8l2fGxL7p31sQHRcP5YV8+Pj6QzV1IhbMvQ0AcPrEMVy5\n0YnRmVlICPHBmZPH0dGjwujMLADAlfOnAADzU+cD6PsQaqeBaJu2udjW4irj8aTtgoIClxqPp22T\nvtxtFxQUuNR4aJu2bdnW4irjceftgoICtLa2AgCkUilWr14NrrGpzntlZSXuvvtu9ktq3rx5eOGF\nF3DrrbcCAJKTk3Hy5El8+umnAIAXXngBAJCbm4uXX34ZWVlZetfLy8vDjR+vwDszDfLYWCjVDCbG\n+CPKXwwAaJQpcLJKI8SU+ECclLaaHJe2BjxBEARBEARBOBuXrfO+aNEi/PjjjwCAkpIS9PT0ICws\nDAsWLMCOHTvQ09ODiooKlJaWYvLkySavYaGojEEJSYIgCIIgCIIgABuC96VLl2Lq1KkoKSlBXFwc\nNm/ejFWrVqG8vBzp6elYunQpvvzySwDAmDFjsGTJEowZMwbz5s3DBx98YNY2AwAMj28yOLc1YN9T\n3AAAOHy1GV0KlY2v8mwMp8QIx0Hacgdpyy2kL3eQttxB2nIHaeveCK2dsH37dpP7t2zZYnL/hg0b\nsGHDBptuzpgJ0+3NtncqVOjoUcFHZFxmkiAIgiAIgiA8Bed1WOUBjJkoXSjg6Z5mE82dyoGPyQPQ\nLqIgHA9pyx2kLbeQvtxB2nIHacsdpK1747TgnQceeDzTt/cX608IBPtYnSCAtKXbIeMiCIIgCIIg\nCFfFeZn33rtrLfE8Czn2MF8vs8cIfcjHxh2kLXeQttxC+nIHacsdpC13kLbujdOC92h/LzAC6xl1\n8IDYALHZwwqV2mhffXsP1NYrYBIEQRAEQRCEW+G04D1u2V1AhPU67b5eAlgoWIM2uabKDNPbrbW0\noRNna9rQIFM4ZJzuBvnYuIO05Q7SlltIX+4gbbmDtOUO0ta9cVrwLhQJIVeqIbAQmUtEAngJLA+x\nvr0HANCjYtClUOFaM3nfCYIgCIIgCM/EacG7n1iIOSkhmJEUbPL4lLhATIzxt3qdiuYu9u8uhbGF\nZqhBPjbuIG25g7TlFtKXO0hb7iBtuYO0dW9sMJ1zh6WseqiviP3bUqMnXU5IWwc8JoIgCIIgCIJw\nVXgMM/grO/Py8pCZmclu7yluwKSYAET6m64q061UI6+sye77zE+17qknCIIgCIIgCEdw/vx5zJ49\nm9N7OLdUpI3Y23GVIAiCIAiCIDwRtwjeB4JKzUCltj65wDAMlDac5+qQj407SFvuIG25hfTlDtKW\nO0hb7iBt3Ru3CN4Hknk/dq0F+0sarZ5X2tCFAzacRxAEQRAEQRDOwi2C94HQ3lsHvkOutHieTKEa\njOFwDtVu5Q7SljtIW24hfbmDtOUO0pY7SFv3xmWCd4sFZRxgej9S0WLZFuP+jhmCIAiCIAjCw3GZ\n4H0wcEJhnUGHfGzcQdpyB2nLLaQvd5C23EHacgdp6964RfDe38R7u4FVhsfjobCuQy+Ib+tW4soN\n2QBGRxAEQRAEQRCDg1ObNNmKrU2aDDklbTPaV9nSDYWawbAAMSL8vFDdKkdFcxfCdZpCuTPkY+MO\n0pY7SFtuIX25g7TlDtKWO0hb98YtMu/9Ra5Sm9xf0yaHtKVbb99NmcLovOauvn0Nsh6PKCVJEARB\nEARBuC8uEbx7CXjwEXE/lNNVrWaPCXqz+1cbOwFo6sMfv9Z3/qmqNlQ2dXE7QAdAPjbuIG25g7Tl\nFtKXO0hb7iBtuYO0dW9cIni/PSUU/mLuHTzNXebLRap6ffDFNzv19t+U9Vhs8rTv10a0dlsuQ0kQ\nBEEQBEEQjsAlgndbifTzcti1tAG5rjXG8BgAnK5qw6+9AX1Lt9KoYo2aYVwqeHeGj62grgNlDRqN\nCus60KNSQ6lm2FkMLaerWqEwY2VyB8gjyB2kLbeQvtxB2nIHaTswatvl+PR0jcljpK174xbBu3a5\nqq+XwGHX1Gbau5XGweThq8162xXNGrtMfUcPGjqNg/2hXiNe2tKNa71rCCpbutHUqUCDrMfELIYC\nsh7PaIZFEARBEK7MT1eb8dWlG84eBsEBbhG8C/gO6NJkAK/3kcBU8G5uoSsASJu7jfYV1Hc4bmAD\nxJk+tk4bAnN3fs4hjyB3kLbcQvpyB2nLHaTtwNAaBe749AK6DLrIk7bujVsE71pcocdSXUcPmjsV\nFn3wnkxFUxcKTTysqNQMDpf3zVgMTXUIgiAIwjVgdP5X1qPC3E8voL69x5lDIhyEWwXvg4nKwpPC\ncWkrqlqNM/CuANc+ttKGTlQ2d6PG4P2be5hpMVhTcPF6u833unJD5lI2G/IIcgdpyy2kL3eQttxB\n2g4M3V9l7U/01SaNndWStjt+qcNJqfnqfITzoeDdDIdKmyweN6wT32PCfuOJKHq/AeRKg2DdsJFW\n7+Fj1/S/ADoVtunU0qVAeVMXatvk/RonQRAEQQxlrumUt/7djkIAwP8cqrD6un+cqcVrhytR1eKa\nSUrCDYP32ACxQ67T1KUwyh7bQ7tcPyNc1+EaU1GD5WNjLBhjiuplOK+TYd9T3ICShk6z5xvS1Kkw\nCvpdAfIIcgdpyy2kL3eQttxB2g6MIxUtZo9Z07ZLocbDu644ekiEg3C74D0j2s9h17pY67iFpgzD\nGHVgVakZ1LYbd3MdLG7KHPtAYarD7J7iBqN9XSZmIUrtCN7JL08QBEEMVaTN3WatqK3dSr3fYoVK\njcpm128gSTgWq8H7qlWrEBkZifT0dKNjf/vb38Dn89HU1Gcxee2115CSkoLU1FQcPHjQsaMFwOPx\nMMxE9l3EQUUae2iQKXCgpFFv3+W6DpyvaUdBXd9DwoWadqNa8Y5E62OTK9U4XdXm0GsX35DpbZ+t\n7t/13dUKQ/5L7iBtuYX05Q7SljuGqrarv7mCfb9q4okrN2Q4VtmXQb9/awFeO1zJbn9XeBOPflNs\n1/V7lGpMmzYNfzxwFV/9Uu+QMRODi9XgfeXKldi/f7/R/qqqKhw6dAjDhw9n9xUVFWHnzp0oKirC\n/v37sXbtWqjVjvOCW7JqZMb4O+w+tnJN52nXVMnJHpXxeK+3y+GqhWq6FCq0mWg41aVQYU9xA1vL\nHQCaOpWo17EK2fPodN5g0WpVS7deoyvda/3a0Ik9xQ0ms/4EQRAE4YloSzu+deQaXv5PBZ7+voQ9\n9nNFC/ubqBt7/Ke0CW8flbLbt40INnntd/KluNHRg1NVbXpV4gDzxScI18Jq8D59+nQ9tmV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FeXbmDx1gKs+Vdf9ryssQsnpZp1Aw0yBVbsLMLlOs1n85FdV/DxqRr8pbdLXkuvlWbupxfQ0qXA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\nZvAJQ+h+5t7cvmtGBEEQGjxlp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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "center_trace = mcmc.trace(\"centers\", chain=1)[:]\n", - "prev_center_trace = mcmc.trace(\"centers\", chain=0)[:]\n", - "\n", - "x = np.arange(50000)\n", - "plt.plot(x, prev_center_trace[:, 0], label=\"previous trace of center 0\",\n", - " lw=lw, alpha=0.4, c=colors[1])\n", - "plt.plot(x, prev_center_trace[:, 1], label=\"previous trace of center 1\",\n", - " lw=lw, alpha=0.4, c=colors[0])\n", - "\n", - "x = np.arange(50000, 150000)\n", - "plt.plot(x, center_trace[:, 0], label=\"new trace of center 0\", lw=lw, c=\"#348ABD\")\n", - "plt.plot(x, center_trace[:, 1], label=\"new trace of center 1\", lw=lw, c=\"#A60628\")\n", - "\n", - "plt.title(\"Traces of unknown center parameters\")\n", - "leg = plt.legend(loc=\"upper right\")\n", - "leg.get_frame().set_alpha(0.8)\n", - "plt.xlabel(\"Steps\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The `trace` method in the `MCMC` instance has a keyword argument `chain`, that indexes which call to `sample` you would like to be returned. (Often we need to call `sample` multiple times, and the ability to retrieve past samples is a useful procedure). The default for `chain` is -1, which will return the samples from the lastest call to `sample`.\n", - "\n", - "#### Cluster Investigation\n", - "\n", - "We have not forgotten our main challenge: identify the clusters. We have determined posterior distributions for our unknowns. We plot the posterior distributions of the center and standard deviation variables below:" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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cRzscuyCgLPMy7uVc1UxA7STl3AMcvy5JOXZ18OCAac1vf/4n0Mo86L2iXobP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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(11.0, 4)\n", - "std_trace = mcmc.trace(\"stds\")[:]\n", - "\n", - "_i = [1, 2, 3, 4]\n", - "for i in range(2):\n", - " plt.subplot(2, 2, _i[2 * i])\n", - " plt.title(\"Posterior of center of cluster %d\" % i)\n", - " plt.hist(center_trace[:, i], color=colors[i], bins=30,\n", - " histtype=\"stepfilled\")\n", - "\n", - " plt.subplot(2, 2, _i[2 * i + 1])\n", - " plt.title(\"Posterior of standard deviation of cluster %d\" % i)\n", - " plt.hist(std_trace[:, i], color=colors[i], bins=30,\n", - " histtype=\"stepfilled\")\n", - " # plt.autoscale(tight=True)\n", - "\n", - "plt.tight_layout()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The MCMC algorithm has proposed that the most likely centers of the two clusters are near 120 and 200 respectively. Similar inference can be applied to the standard deviation. \n", - "\n", - "We are also given the posterior distributions for the labels of the data point, which is present in `mcmc.trace(\"assignment\")`. Below is a visualization of this. The y-axis represents a subsample of the posterior labels for each data point. The x-axis are the sorted values of the data points. A red square is an assignment to cluster 1, and a blue square is an assignment to cluster 0. " - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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+sZtpGUudn6W0u43c0UEGquvpr64nrE1EFbvSM2m58z4cjScIGE23neN9M1BG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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib as mpl\n", - "figsize(12.5, 4.5)\n", - "plt.cmap = mpl.colors.ListedColormap(colors)\n", - "plt.imshow(mcmc.trace(\"assignment\")[::400, np.argsort(data)],\n", - " cmap=plt.cmap, aspect=.4, alpha=.9)\n", - "plt.xticks(np.arange(0, data.shape[0], 40),\n", - " [\"%.2f\" % s for s in np.sort(data)[::40]])\n", - "plt.ylabel(\"posterior sample\")\n", - "plt.xlabel(\"value of $i$th data point\")\n", - "plt.title(\"Posterior labels of data points\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Looking at the above plot, it appears that the most uncertainty is between 150 and 170. The above plot slightly misrepresents things, as the x-axis is not a true scale (it displays the value of the $i$th sorted data point.) A more clear diagram is below, where we have estimated the *frequency* of each data point belonging to the labels 0 and 1. " - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 60, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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qiipceHExyv+6AJ+pTyD3hwOovZxuWK/Kyoe+QQ3bsADwJWJcWfUNMr7YgcJ9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\nO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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "cmap = mpl.colors.LinearSegmentedColormap.from_list(\"BMH\", colors)\n", - "assign_trace = mcmc.trace(\"assignment\")[:]\n", - "plt.scatter(data, 1 - assign_trace.mean(axis=0), cmap=cmap,\n", - " c=assign_trace.mean(axis=0), s=50)\n", - "plt.ylim(-0.05, 1.05)\n", - "plt.xlim(35, 300)\n", - "plt.title(\"Probability of data point belonging to cluster 0\")\n", - "plt.ylabel(\"probability\")\n", - "plt.xlabel(\"value of data point\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Even though we modeled the clusters using Normal distributions, we didn't get just a single Normal distribution that *best* fits the data (whatever our definition of best is), but a distribution of values for the Normal's parameters. How can we choose just a single pair of values for the mean and variance and determine a *sorta-best-fit* gaussian? \n", - "\n", - "One quick and dirty way (which has nice theoretical properties we will see in Chapter 5), is to use the *mean* of the posterior distributions. Below we overlay the Normal density functions, using the mean of the posterior distributions as the chosen parameters, with our observed data:" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 61, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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Eh4d/cDmUD4OOUYo0dBvJT4y/vz+mT5/e3GI0CefOncPEiRM/uByBQPCfOqAi\nLy8PAoEAn/EGUJSPyM6dO7F8+fLmFoNCoVAoXzDUgP8IhIWFoW/fvhAIBLCwsICbmxuuXbsGAE2y\nu0ROTg60tLRQWVn5wWVJk5SUhD59+kBfXx99+/ZFcnJynel//vlnzJ49+4PrzcnJgUAg+OByPgWx\nsbFo3779B5Whr6+PnJycZtlphNIwtLS0kJ2d/VHKnjRpEg4fPoxnz559lPLfFzqz9/VB+/TrgvYn\nRRpqwDcxW7duxZIlSzBv3jykpaUhKSkJnp6eOH36NAA06azr+5b19u3bGnHl5eX45ptvMGbMGGRl\nZWHs2LH45ptvUFFRIbOMxMREvH79Gp06dXovGf6ryNJ9Y/ivbp3a1C+rDaEpx5c0fD4fTk5OOHjw\n4HuVT6FQKBQKNeCbkKKiIqxZswZr167F4MGDoaSkBDk5OfTv3x++vr410suaze3QoQMuXboEAEhI\nSEDfvn0hFAphZmaGpUuXAgAGDx4MABCJRBAIBIiPjwcABAcHw8HBAWKxGKNGjUJeXh5TrpaWFv78\n80907twZdnZ2MmWRSCSYPn06FBQU4OXlBUIII0t1zp49i+7duzNhWV8FhgwZgn379gEAMjMz4erq\nCkNDQ5iYmGDq1Kks2apmO729vTF//nyMHTsWAoEAzs7OrJnQmJgY2NnZwdDQEPPnz4erqytTR3X8\n/f3h7u6OqVOnQiAQoE+fPkhJSWGup6WlYciQIRCJROjWrRuioqKYa9HR0ejatSsEAgEsLS2xdetW\nlJSUwM3NDQUFBRAIBBAIBHj8+DEIIdiwYQM6deoEY2NjeHh4MDuJVOklODgY1tbWGD58OHJzc1m6\nevToEcaPHw8jIyN07twZe/furdGG6dOnQygUIiQkpEY7O3TogM2bN6NHjx4QCAT44Ycf8OTJE4we\nPRpCoRDDhw/Hq1evmPRxcXFwcXGBSCRCz549cfnyZeba/v374eDgAIFAAFtbWwQFBTHXYmNjGV20\na9cOFhYWOHDggEzdV/X/ihUr4OTkBKFQiAkTJrB2WJk8eTLMzc1haGgIV1dX3L17l7nm7e2NefPm\nwc3NDQYGBoiNjcWZM2fQq1cvCIVCWFlZYc2aNUz6Kj0fOHAAVlZWMDIyQmBgIBITE9GjRw+IRCL4\n+Piw5KttvFSNr549e0IgEDC+v6dPn0bPnj0hEokwYMAA3Llzh9UHmzZtYvpAIpFg48aNsLS0hEAg\ngL29PWtQq097AAAgAElEQVQs9ejRA9HR0bXqrjmIjY1tbhEoTQzt068L2p8Uab66Raz9d/3dpOWd\n8ezY4LQ3btxAaWkpXF1d37s+abeKRYsWYcaMGRg9ejRKSkoYgyEyMhI2NjbIzs4Gl8tl4jZs2ICQ\nkBAYGRnh999/h6enJ8sojYyMxLlz56CoqFij3rt378LS0pIV1759e9y9e1fmSWGpqan1zr5zOBym\nPatXr0a/fv1w4sQJlJeX4++/a++nY8eO4fDhw7C2tsZ3332HVatWYdeuXSgsLMSUKVPwxx9/YODA\ngdi5cyf27t2LsWPH1lpWVFQUdu3ahR07dmDbtm2YMGEC4uPjUVlZifHjx2PixIk4duwYrl69im++\n+Qbnz5+HkZERZs6cicDAQDg4OKCoqAjZ2dlQVlbG4cOHMW3aNJZ7UUBAAE6dOoUTJ06gVatW8PHx\nwfz587Fz504mzdWrV3H9+nVwuVw8fvyYJaOnpycsLS0RFBSE9PR0jBgxAiKRCI6OjkwbgoKCEBAQ\nIHMXCA6HgxMnTiA8PBwVFRXo3bs3kpKSsGXLFpiYmGDMmDHYvn07FixYgPz8fIwbNw4BAQFwcnLC\nhQsX4O7ujhs3bqBly5bQ1tbGoUOHIBQKceXKFbi5ucHW1hbW1tYAgKdPn+L169e4c+cOYmJiMGXK\nFLi6ukJdXV2m/g8dOoQjR45AIBBgxowZWLhwIQICAgAA/fv3x9atW8Hj8eDr64tp06bh4sWLTN4j\nR44gNDQUdnZ2KCsrQ3x8PAICAmBubo47d+5gxIgRsLKywqBBg5g8iYmJSEhIwOXLlzFu3Dg4Ozvj\n+PHjKC8vR+/evTFs2DB069atzvFy8uRJaGlp4a+//oKhoSEA4Pbt25g5cyZCQkLQsWNHHDp0COPH\nj0dcXBwUFBQAAEePHkVoaCi0tLSQmZmJXbt2ISYmBm3atEFeXh5rZt7ExKReFzUKhUKhUGqDzsA3\nIS9evICWlhZjVH8oPB4P9+/fR2FhIZSVldG5c2cAsj/tBwYGYvbs2TAxMQGXy8WcOXOQnJzMmoWf\nM2cOWrRoAT6fXyN/cXFxDSNMTU0Nb968kSnbq1evoKqq2qi25OTkID8/HzweD/b29rWmdXV1RceO\nHSEnJ4dRo0YhKSkJwLtZcXNzcwwePBhcLhfTpk2DtrZ2nfXa2NhgyJAhkJOTg7e3N8rKyhAXF4f4\n+HiUlJRg9uzZkJeXh6OjI1xcXJhDTxQUFHD37l0UFRVBXV2dMWBl6T4oKAhLliyBjo4OFBQUsGDB\nAkRERLC+Rvj4+EBJSamG7vPy8nDjxg34+vqCx+Ohffv2mDhxIsu9ws7ODgMHDgQAmS9fAODl5YVW\nrVpBR0cHDg4O6NKlC9q3bw8+n4/BgwczOjx8+DCcnZ3h5OQEAOjduzdsbGxw5swZAICzszOEQiEA\noFu3bujTpw+uXr3K1FPVPjk5OTg7O0NFRQUZGRkyZeJwOBg7dizMzMygrKyMxYsXIzw8nNHh+PHj\noaKiAgUFBfj4+CA5ORmvX79m8g8ePJj5WsTn89G9e3eYm5sDACwsLDB8+HDW1wMA+PHHH8Hj8dCn\nTx+oqqpi5MiR0NLSYvRSpYeGjBdp9uzZA3d3d9ja2jLt4vP5zNcvDocDLy8v6Orqgs/nQ05ODuXl\n5bh79y4qKiqgr6/PvAwAgKqqKoqKimTW1VxQ/9qvD9qnXxe0PynSUAO+CdHU1ERhYWGT+etu2rQJ\n9+/fh4ODA5ycnBgjSxa5ublYvHgxRCIRRCIRjIyMALxzz6hCT0+v1vyqqqos4wl45xKkpqYmM72G\nhkaN9HXh5+cHQgicnZ3RrVs37N+/v9a0rVu3Zv5WUlJCcXExgHenClY//bO+00Clr3M4HOjq6uLR\no0coKCiooQ8DAwNGX3v27MHZs2eZF4C4uLha68jNzcXEiRMZ3Xft2hXy8vJ48uQJk6Y23RcUFEBT\nUxMqKipMnL6+PqvfpNswevRoxn3nyJEjTHx1nUmH+Xw+8yKWm5uL48ePM7KKRCLcuHGDkTU6OhrO\nzs4wMjKCSCRCdHQ0nj9/zpSlqanJekGV7h9ZSLdbX18fFRUVKCwshEQiwfLly9GpUycIhULY2NgA\nAKuu6n0bHx+PoUOHwtTUFIaGhtizZw9evHjBSiP9QqeoqMgKS8vakPEiTW5uLv744w+W3vLz82sd\nX2KxGKtXr8aaNWvQrl07eHp6oqCggLn+5s2bWr9aUCgUCoVSH1+dC01jXF6aGjs7O/D5fJw4cQJD\nhw6VmUbaRUZZWRn//PMPE5ZIJCgsLGTCYrGYccOIiIjA5MmTcf/+fZm7l+jr62P+/PkYOXJkrfLV\nteuJmZkZtm7dyopLSUnBt99+KzO9paUl7t+/z2oL8O4o+KqZeWlXEW1tbWzYsAEAcO3aNYwYMQLd\nu3dnzUrWR9u2bVkuQYQQ5Ofn15nn4cOHzN+VlZXIz8+Hjo4Oc40QwuglNzcXJiYmAICOHTsiODgY\nEokEO3bsgIeHB5KSkmrV/ebNm2WuLajaHrM23bdt2xYvXrzAmzdvGL3l5eXVePGo4vDhw3W2t4ra\nFmDq6+vDzc2N6QtpysrKMHnyZAQEBGDQoEGQk5PDxIkTP2jhtfSMdl5eHhQUFKClpYXQ0FCcOnUK\n4eHhMDAwwKtXryAWi+usy8vLC15eXggLCwOPx8PixYtZBn9jaMh4qZ5+7ty5mDt3bq1pqvfxyJEj\nMXLkSLx+/Rpz587F8uXLsW3bNgBAeno6rKys3kv2jwXdY/rrg/bp1wXtT4o0dAa+CVFXV8fChQux\nYMECREZGoqSkBBUVFYiOjmaOn5Y2UIyNjVFWVobo6GhUVFRg3bp1zOl6ABAaGspsNaeurg4OhwMu\nl8u46WRlZTFpp0yZgvXr1zMLAYuKihp18EaPHj0gJyeH7du3o6ysDNu3bweXy0XPnj1lpnd2dsaV\nK1eYcJX7RmhoKCQSCYKDg1mLT8PDwxljukWLFkxbGoOzszPu3LmDyMhIvH37Frt27WLNcsvi1q1b\nOHHiBN6+fYtt27aBz+ejS5cusLW1hZKSEjZt2oSKigrExsbi9OnTGDFiBCoqKnD48GEUFRVBTk4O\nqqqqkJOTA/BupvvFixcs94fJkydj1apVjLH67NkznDp1qkFt0tfXh52dHVauXImysjKkpKRg//79\ncHNza5RuGsro0aNx+vRpxMTEQCKRoLS0FLGxscjPz0d5eTnKy8uZ+ys6Ohrnz59/77oIIQgNDUVa\nWhpKSkrwyy+/YNiwYeBwOCguLgafz4eGhgaKi4uxcuXKessrLi6GhoYGeDweEhIScOTIkUZvxVk1\n/uobL9ra2qzxNWnSJAQGBiIhIQGEEBQXF+PMmTO1upjdu3cPly5dQllZGfh8Pvh8Put+v3z5ssy1\nJRQKhUKhNARqwDcx3t7eWLVqFX777Te0a9cO1tbW2L17N7OzhfTCTnV1daxduxazZs1C+/btoaKi\nwvoMHxMTg+7du0MgEGDJkiXYtWsX+Hw+lJWVMXfuXAwcOBAikQgJCQkYPHgwZs2aBU9PTwiFQnTv\n3h0xMTFMWfUZOgoKCggODsahQ4cgFotx6NAhBAcHQ15e9kcaa2trqKurIyEhgYnbsGEDNm/eDGNj\nY6SlpbH83G/evIn+/ftDIBBgwoQJ+OWXX5i936vLVltYS0sLgYGB8PPzg7GxMdLT02FjYyPTp78q\n38CBA3Hs2DGIxWKEhYVh7969kJOTA4/Hw4EDB3D27FmYmJhgwYIFCAgIgLGxMYB3L082NjYQCoXY\ns2cPtm/fDgAwNTXFiBEjYGtrC7FYjMePH2P69OkYMGAARo4cCYFAABcXFyQmJtape+m4nTt3Iicn\nBxYWFpg0aRIWLlzIvDhJ3y+NQTqPdBl6enoIDg7G77//DlNTU1hbW2Pr1q0ghEBNTQ3+/v7w8PCA\nWCzG0aNHGd/7utpSlwxjxoyBt7c3zM3NUVFRAX9/fwDAmDFjYGBgAEtLS3Tv3h1dunSp9z5Yu3Yt\nc9+sW7cOw4cPb7RsVWnqGy8+Pj7w9vaGSCTC8ePHYWNjgw0bNsDHxwdisRhdunTBwYMHa62zvLwc\nK1asgImJCczNzfH8+XMsW7YMwLtTLc+ePYtx48bVK++nhM7sfX3QPv26oP1JkYZDPuPjIM+dOwdb\nW9sa8fn5+fX6PlM+PufPn8fu3btr3cbxY1NZWQkrKyvs2LGDtaVlFWvWrEFWVhaz6wnl0zJ06FC4\nublhwoQJzS3KZ8XOnTuRn58vc2tZgD7fKA3j1q1b6NOnD6ytrXHhwoWPWldAQAAWL14MLy8v5iWc\nQqF8GImJiR/0JZbOwFPemz59+nxy4z0mJgavXr1CWVkZ1q9fDwDM7jzV+YzfTf8z0D6oybffflur\n8d6c0D2mv3wIISgvfInirDyUPMjHxeizzS0SpQmhY5QizVe3iJXydRMXFwcvLy+Ul5fDzMwM+/bt\nq9OF5n3cTyhNB9U/hfJxUa8gyNy8D88uXEfR7TS8ff3vrlB3KotRqSOERuf2aO3cHW0G9YKCesO3\n/6VQKJ8v1ICnfFH4+PjUOFGzrrSU5iMiIqK5RaA0Aupf+2VRnpaNefJ6sL1fgfSft8lMY8FVQdnj\nZ3h88gIen7yA1EW/QW+8K8Q/TIRi29Yy81A+X+gYpUhDXWgoFAqFQvlCKC98idvfL0fhzDXoxFVD\n9W9cXEU+eK1bgqelAY68HOua5J9S5PwZhr+6jkHm5n0gEsmnE5xCoTQpdAaeQqFQKHSP6S+AwsuJ\nuO3th7KCZ6x4tfamaNnVBmrmRlDQ0mBc164n34K1RhsU3bqLwsuJKM17d5iY5J9SpP+8DU/PXYH1\n5mVQMtD55G2hNB46RinSUAOeQqFQKJTPGEII7v+2G/d+2w1ILQy/UfkaiW342LHAU3ZGDhdK+m2h\npN8W2oN6oSgpHfmHIvFP7rsThF9cu4XLfSehQ8AKtO7X9VM0hUKhNBHUhYZCoVAodGbvM6Xy7Vsk\nz1mNe+v+ZIx3eTUVyH8zABvePsQzhdrz2lv+e9ovh8NBC+t2MFsxE23/5wT8/8Fib18XI3HSAjw8\nFPlR20H5cOgYpUhDDXgKhUKhUD5DKsvKcWvaMjw8eJKJUzU3gtmq2ZAzFb5XmRw5OeiO6I92P80A\nr5UmAIBIJEiatQqZW4KbRG4KhfLxoQb8J8bf3x/Tp09vbjGahHPnzmHixIkfXI5AIEBOTk4TSPRl\nkJeXB4FAQPdI/4+yc+dOLF++vLnFqAHdY/rzovLtW/ztuQSPT15g4rQcO8NkgSd4mi0aVMb1lKRa\nr6kYC2G69DuW/3v6qj+QvSv0vWWmfFzoGKVIQw34j0BYWBj69u0LgUAACwsLuLm54dq1awCaZl/s\nnJwcaGlpobKy8oPLkmb27Nmwt7dHq1atEBISUm/6n3/+GbNnz/7genNyciAQCD64nE9BbGws2rdv\n/0Fl6OvrIycnh+6R/hmjpaWF7Ozsj1L2pEmTcPjwYTx79qz+xJT/JIQQpMz/FU+jLzNx2gMcIfAc\nDY6cXB05GwdPswVMl0yHqrmYibv70wbkHz3TZHVQKJSPAzXgm5itW7diyZIlmDdvHtLS0pCUlARP\nT0+cPn0aQNOeTPm+Zb19+1ZmvJWVFdauXYsOHTrUa1wmJibi9evX6NSp03vJ8F+lNt03FMl/dNu3\npn5ZbQhNPb6q4PP5cHJywsGDB9+r/I8F9a/9fLi39k88DDnBhNsM7g29ca6NfumX9oGvDTllJRjP\n9YCKyb8uOUkzV+Lp+WuNqovy8aFjlCINNeCbkKKiIqxZswZr167F4MGDoaSkBDk5OfTv31/m0emy\nZnM7dOiAS5cuAQASEhLQt29fCIVCmJmZYenSpQCAwYMHAwBEIhEEAgHi4+MBAMHBwXBwcIBYLMao\nUaOQl5fHlKulpYU///wTnTt3hp2dnUz5p06dip49e9Z6sqk0Z8+eRffu3ZmwrK8CQ4YMwb59+wAA\nmZmZcHV1haGhIUxMTDB16lSWbFWznd7e3pg/fz7Gjh0LgUAAZ2dn1kxoTEwM7OzsYGhoiPnz58PV\n1ZWpozr+/v5wd3fH1KlTIRAI0KdPH6SkpDDX09LSMGTIEIhEInTr1g1RUVHMtejoaHTt2hUCgQCW\nlpbYunUrSkpK4ObmhoKCAggEAggEAjx+/BiEEGzYsAGdOnWCsbExPDw88PLlS5ZegoODYW1tjeHD\nhyM3N5elq0ePHmH8+PEwMjJC586dsXfv3hptmD59OoRCocwvIx06dMDmzZvRo0cPCAQC/PDDD3jy\n5AlGjx4NoVCI4cOH49WrV0z6uLg4uLi4QCQSoWfPnrh8+d9Zvv3798PBwQECgQC2trYICgpirsXG\nxjK6aNeuHSwsLHDgwAGZuq/q/xUrVsDJyQlCoRATJkxg9AIAkydPhrm5OQwNDeHq6oq7d+8y17y9\nvTFv3jy4ubnBwMAAsbGxOHPmDHr16gWhUAgrKyusWbOGSV+l5wMHDsDKygpGRkYIDAxEYmIievTo\nAZFIVONgr9rGS9X46tmzJwQCAcLDwwEAp0+fRs+ePSESiTBgwADcuXOH1QebNm1i+kAikWDjxo2w\ntLSEQCCAvb09M66Bdz/E0dHRteqO8t8lPywK99fvZsIte3SCrtvAj/rFjsvnwWjOFCjqtQEAkLcS\n3Jq2DMVZefXkpFAozcVXZ8BHte3WpP8aw40bN1BaWgpXV9f3ll/6Ib1o0SLMmDEDDx48QGJiIoYN\nGwYAiIx8t1tAdnY2cnJy0LlzZ0RGRmLDhg3Yt28f7t27h65du8LTk721WGRkJM6dO4erV6++t3xV\npKamwtjYuN62VLVn9erV6NevH7Kzs5GSkgIvL69a8x07dgw+Pj7IysqCWCzGqlWrAACFhYWYMmUK\nfH19kZmZCWNjY8TFxdX5wxYVFYX//e9/yMrKwsiRIzFhwgRIJBJUVFRg/Pjx6NevHzIyMrBmzRp4\neXnh/v37AICZM2fi999/R05ODq5evQpHR0coKyvj8OHDaNu2LXJycpCTk4M2bdpg+/btOHXqFE6c\nOIHU1FRoaGhg/vz5LDmuXr2K69evIywsrMbMrqenJ/T19ZGamoqgoCCsWrUKf/31F6sNw4YNw4MH\nDzBq1CiZej5x4gTCw8Nx/fp1nDlzBm5ubvD19UV6ejoIIdi+fTsAID8/H+PGjcP8+fORlZWFFStW\nwN3dHc+fPwcAaGtr49ChQ8jJycGWLVvw008/4fbt20xdT58+xevXr3Hnzh1s3LgRCxYsQFFRUa36\nP3ToELZs2YLU1FTIyclh4cKFzLX+/fsjPj4eGRkZsLa2xrRp01h5jxw5gh9//BG5ubmwt7eHiooK\nAgIC8ODBAxw6dAiBgYHMWKgiMTERCQkJ2LVrFxYtWoTff/8dx48fx5UrVxAeHo4rV64AQJ3j5eTJ\ndwsG//rrL+Tk5OB///sfbt++jZkzZ2LDhg3IzMzE5MmTMX78eFRUVDB1Hz16FKGhocjKykJmZiZ2\n7dqFmJgY5OTk4MiRIyw3MRMTEyQnJ9eqt+aA+tc2P69T7yN5/r8vpurW7SD0GPXexntdPvDVkVdV\nhvF8Tyi01AAAvC16g789FkFSUvpedVOaHjpGKdJ8dQZ8c/LixQtoaWmBy20atfJ4PNy/fx+FhYVQ\nVlZG586dAcj+tB8YGIjZs2fDxMQEXC4Xc+bMQXJyMmsWfs6cOWjRokWDZtjr49WrV1BVVW1UW3Jy\ncpCfnw8ejwd7e/ta07q6uqJjx46Qk5PDqFGjkJT07kcoOjoa5ubmGDx4MLhcLqZNmwZtbe0667Wx\nscGQIUMgJycHb29vlJWVIS4uDvHx8SgpKcHs2bMhLy8PR0dHuLi4ICwsDACgoKCAu3fvoqioCOrq\n6rC2tgYgW/dBQUFYsmQJdHR0oKCggAULFiAiIoL1NcLHxwdKSko1dJ+Xl4cbN27A19cXPB4P7du3\nx8SJE1nuFXZ2dhg4cCAAQFFRUWY7vby80KpVK+jo6MDBwQFdunRB+/btwefzMXjwYEaHhw8fhrOz\nM5ycnAAAvXv3ho2NDc6ceefz6uzsDKHw3af0bt26oU+fPqwXvqr2ycnJwdnZGSoqKsjIyJApE4fD\nwdixY2FmZgZlZWUsXrwY4eHhjA7Hjx8PFRUVKCgowMfHB8nJyXj9+jWTf/DgwczXIj6fj+7du8Pc\n3BwAYGFhgeHDh7O+HgDAjz/+CB6Phz59+kBVVRUjR46ElpYWo5cqPTRkvEizZ88euLu7w9bWlmkX\nn89nvn5xOBx4eXlBV1cXfD4fcnJyKC8vx927d1FRUQF9fX0YGhoy5amqqtb54kP57/H2TTH+9lyC\nyn/KAAB8HW2IvL+pcZrqx4TXsgXEMycydb5JvY/k+f6svecpFMrnATXgmxBNTU0UFhY2mb/upk2b\ncP/+fTg4OMDJyYkxsmSRm5uLxYsXQyQSQSQSwcjICMA794wq9PT0mkQuANDQ0GAZW/Xh5+cHQgic\nnZ3RrVs37N+/v9a0rVu3Zv5WUlJCcXExAKCgoAC6urqstNXD1ZG+zuFwoKuri0ePHqGgoKCGPgwM\nDBh97dmzB2fPnmVeAOLi4mqtIzc3FxMnTmR037VrV8jLy+PJkydMmtp0X1BQAE1NTaioqDBx+vr6\nrH6TbsPo0aMZ950jR44w8dV1Jh3m8/l48+YNI+vx48cZWUUiEW7cuMHIGh0dDWdnZxgZGUEkEiE6\nOpqZnQfe3ePSL6jS/SML6Xbr6+ujoqIChYWFkEgkWL58OTp16gShUAgbGxsAYNVVvW/j4+MxdOhQ\nmJqawtDQEHv27MGLFy9YaaRf6BQVFVlhaVkbMl6kyc3NxR9//MHSW35+fq3jSywWY/Xq1VizZg3a\ntWsHT09PFBQUMNffvHkDdXX1WvXWHFD/2uaDEILkuf4ouf9uNy4uTwHiHyZATkn2C3tDaYgPfHVU\nxAYwmPQ/JvzoyBmoJt77IDkoTQMdoxRp6j2JNSoqCrNnz4ZEIoGnp2cNP1LgnbvBqVOnoKysjKCg\nIHTs2BEA4OHhgZMnT0JbW5uZ+QLe/UiPGTMGDx48gKGhIUJDQ6GhodEkDRpQcKVJynkf7OzswOfz\nceLECQwdOlRmGulPocrKyvjnn3+YsEQiQWFhIRMWi8XYuXMnACAiIgKTJ0/G/fv3ZX5O1dfXx/z5\n8zFy5Mha5WtKH0pLS0vG3QR41xYAKCkpYWbmHz9+zFzX1tbGhg0bAADXrl3DiBEj0L17d9asZH20\nbduW5adOCEF+fn6deR4+fMj8XVlZifz8fOjo6DDXCCGMXnJzc2FiYgIA6NixI4KDgyGRSLBjxw54\neHggKSmpVt1v3rxZ5tqCqu0xa9N927Zt8eLFC7x584bRW15eXo0XjyoOHz5cZ3urqG0Bpr6+Ptzc\n3Ji+kKasrAyTJ09GQEAABg0aBDk5OUycOPGDFl5Lz2jn5eVBQUEBWlpaCA0NxalTpxAeHg4DAwO8\nevUKYrG4zrq8vLzg5eWFsLAw8Hg8LF68mGXwN4aGjJfq6efOnYu5c+fWmqZ6H48cORIjR47E69ev\nMXfuXCxfvhzbtm0DAKSnp8PKqvHGFeXr5NGR0yiIOMeEBR6joKTfttnkadXbHsX3c1F48QYAoOXp\nOGijjhOjKBTKJ6fOGXiJRILvv/8eUVFRuHPnDkJCQpCamspKExkZiXv37iEjIwM7duzAjBkzmGtT\npkxhGVxV+Pv7w9nZGenp6ejXrx/8/f2bqDnNi7q6OhYuXIgFCxYgMjISJSUlqKioQHR0NPz8/ACw\nDStjY2OUlZUhOjoaFRUVWLduHcrKypjroaGhzFZz6urq4HA44HK5jJtOVlYWk3bKlClYv349sxCw\nqKiIWXzXUCoqKlBaWorKykqUl5ejtLS0VoPK2dmZ8ScGwLhvhIaGQiKRIDg4mLX4NDw8nDGmW7Ro\nwbSlMTg7O+POnTuIjIzE27dvsWvXLtYstyxu3bqFEydO4O3bt9i2bRv4fD66dOkCW1tbKCkpYdOm\nTaioqEBsbCxOnz6NESNGoKKiAocPH0ZRURHk5OSgqqoKuf/fuq1169Z48eIFy/1h8uTJWLVqFWOs\nPnv2DKdOnWpQm/T19WFnZ4eVK1eirKwMKSkp2L9/P9zc3Bqlm4YyevRonD59GjExMZBIJCgtLUVs\nbCzy8/NRXl6O8vJy5v6Kjo7G+fPn37suQghCQ0ORlpaGkpIS/PLLLxg2bBg4HA6Ki4vB5/OhoaGB\n4uJirFy5st7yiouLoaGhAR6Ph4SEBBw5cqTRL6VV93N940VbW5s1viZNmoTAwEAkJCSAEILi4mKc\nOXOG+bJRnXv37uHSpUsoKysDn88Hn89n3e+XL19Gv379GiX7x4b61zYPpY+e4s7i9UxYq7cdWnbr\n2CRlN8YHvjoGE4eBr/PuCxa3/C2my+sAldSVpjmhY5QiTZ0W1I0bN2BsbAxDQ0MoKChg7NixOH78\nOCtNREQE3N3dAQD29vZ4+fIl86nY0dERmpqaNcqVzuPu7t5oQ/NzxtvbG6tWrcJvv/2Gdu3awdra\nGrt372Z2tpBe2Kmuro61a9di1qxZaN++PVRUVFif4WNiYtC9e3cIBAIsWbIEu3btAp/Ph7KyMubO\nnYuBAwdCJBIhISEBgwcPxqxZs+Dp6QmhUIju3bsjJiaGKashhs6IESOgp6eH+Ph4zJkzB3p6erUu\neLW2toa6ujoSEhKYuA0bNmDz5s0wNjZGWloay8/95s2b6N+/PwQCASZMmIBffvmFWdRXXbbawlpa\nWggMDISfnx+MjY2Rnp4OGxubWn36ORwOBg4ciGPHjkEsFiMsLAx79+6FnJwceDweDhw4gLNnz8LE\nxAQLFixAQEAAszA3NDQUNjY2EAqF2LNnD7MI1NTUFCNGjICtrS3EYjEeP36M6dOnY8CAARg5ciQE\nApVDIoUAACAASURBVAFcXFyQmJhYp+6l43bu3ImcnBxYWFhg0qRJWLhwIXr27Mmke58vJ9J5pMvQ\n09NDcHAwfv/9d5iamsLa2hpbt24FIQRqamrw9/eHh4cHxGIxjh49yvje19WWumQYM2YMvL29YW5u\njoqKCuZlfcyYMTAwMIClpSW6d++OLl261HsfrF27lrlv1q1bh+HDhzdatqo09Y0XHx8feHt7QyQS\n4fjx47CxscGGDRvg4+MDsViMLl264ODBg7XWWV5ejhUrVsDExATm5uZ4/vw5li1bBgAoLS3F2bNn\nMW7cuHrlpXzdvHOd+QVvi969CPJat4T++CHNLNU7uDwFGE4bA/z/i6cZVxkGKXRXGgrlc4FD6vhm\nHRYWhtOnTzNuHMHBwbh+/To2b97MpBkyZAgWLVqEbt3e7dji5OSENWvWMPuDZ2dnY8iQISwXGk1N\nTcZ3lRCCli1b1vBlBd6d9Glra1sjPj8/v17fZ8rH5/z589i9e3et2zh+bCorK2FlZYUdO3awtrSs\nYs2aNcjKykJAQEAzSEcZOnQo3NzcMGHChOYW5bNi586dyM/Pl7m1LECfb/8lcvdHIGXe/3+B5nBg\nsmga1MzEdWf6f1Ky7mPkojmwMBTjqH9Nl7im4tGxaDw69m7L00ouB71iD0JFbPDR6qNQ/iskJiZ+\n0JfYOmfgGzrbVv0doLGzdPREyi+TPn36fHLjPSYmBq9evUJZWRnWr3/32blqd57qNOWhWZT3g/ZB\nTb799ttajXfKf4eyp8+RvnIrE9bu36PBxvunpO2QvvhH8936HG4lwR2ftXRcUyifAXUuYtXT00Nu\nbi4Tzs3Nhb6+fp1p8vLy6t3tpE2bNigoKEDbtm3x6NGjOrcC/O677xhXixYtWsDKygpi8ef3kKN8\nGuLi4uDl5YXy8nKYmZlh3759dbrQ0JfD5oXq//2p8net2nniY4e3bdsGKyurT1bffz186PtFePa8\nABZcFfC0WyKvvT4epiQxO8dU+a/XFk7OZO8MIyt9anYmJg8e1qDy6go/7GKM0lOXweUAFn/F49HR\nM8hso/JZ6fO/EE5KSmLWGX4O8tBw4/uv6lDFnJycGmf1NJY6XWjevn2Ldu3a4dy5c9DV1YWdnR1C\nQkKYvZiBd4tYt2zZgsjISFy7dg2zZ8/GtWv/HsEsy4VmwYIF0NLSgo+PD/z9/fHy5UuZC1mpCw2F\nQvmv0VzPt9jYWLpN3Sfi+bWbuPG/75iw0TwPtOhg1qgyGuJCc13qheBD2BsZgZz9ERgk1xIAwGul\nCcfYEChofF5boX7t0DH6dfFRXWjk5eWxZcsWuLi4wMLCAmPGjIG5uTn+j707D4+yOhs//p0tO9n3\nhACBsEkIhCWAbIqsWhSpgvZVVOyLW3m1tmpf9fe6VbS11iqVgguKFcQVYgWUxYJRAyioyJYECNlD\nyL5nMjO/P4ZMJgWyMTPPLPfnuriunMnzzHMPJydz58x9zrN69WrLor558+aRmJjIoEGDWLZsGa++\n+qrl/JtuuolJkyaRlZVF3759Wbt2LQCPPPII27dvZ/DgwezatavD3RmFEEI4niQGjmHUt3LkkRcs\n7eBxyT1O3rvLFsl7mw8NZ2nyNn9o33K2kuzn1tjsuUX3yBgV1rrcB37u3Lnn7UTxn7c8X7ly5QXP\n3bBhwwUfDw0NZceOHd2NUQghhHAL+W9/Qt2xkwCovb2cZteZrjRh5EhSBKk/m29elv/OZhJuX0jA\nkAEKRyaEZ5I7sQohhJA9ph1AX11LzotvWtrR112FV5htbmJ4IZeyD/yFlEb402e4eatdk8HAsSde\n6eIMYUsyRoU1SeCFEEIIBzjx0tvoK8yL2LwiQomcef72t05NpSLu5mvg3OL0s19mUrYrs4uThBD2\nIAm8EEIIqa+1s4bThZx+4wNLO+7Guai9dHa9pi1r4Nv4JcQSNnWcpX38iVcwtrba/DrifDJGhTW3\nSOAXLVpEaGioXf8tWrSoW7GkpKSwe/fuC37v22+/7XB3Uk917733kpiYyMyZM7s8Ni8vj7CwMIxG\nowMiE0II+8j64z8wtegB8B/Uj+DxIxWOqPdiF85G7eMFQF3WKYre36ZwREJ4HrdI4Ldv3+401+hs\n7/GJEyeyd+/eLp/jueee46677upRfK7i22+/Zffu3Rw5csTm/ZaRkcGIESNs+pxCeAqpr7WfmkPH\nKUnfaWnH3XSNQ+6RYOsa+Da64D5EXX2FpZ3zlzcwNrfY5VqinYxRYa3LXWhcSUVFhV2eNzQ01C7P\nq4TW1la0WuW6PT8/n4SEBHx8fBSLQQghHCn7+dcsXweNGUFAUj8Fo7GNyNmTKfsig9baepoKS8l7\nZxP977xR6bCE8BhuMQPvbH766SemTJlC//79Wbp0Kc3NzcD5M8R/+9vfuOyyy0hISCAtLY09e/aw\nY8cOXnrpJT755BMSEhKYNm0aAMXFxdx8880MHDiQsWPHsm7dOsvzNDY2cs8995CYmMiECRN4+eWX\nO1wnJSWFl19+mcmTJ5OQkIDBYOCll15izJgxJCQkMHHiRD777DPL8evXr2fOnDk8+uijDBgwgDFj\nxrB3717effddkpOTGTJkCO+9995FX//FYn3nnXe4//772b9/PwkJCTz//PPnnWs0Gnn88cdJSkoi\nNTWVL774osP33333XSZMmEBCQgKpqam89dZbANTX13PjjTdSUlJCQkICCQkJlJaW8v333zNr1iwG\nDBjA8OHDefjhh9Hr9d3tSiE8htTX2kfld4co2/GNuaFSEbtwlsOubY8a+DYaH2+i57ffhObkS2/T\nWt9gt+sJGaOiI7eagXcGJpOJzZs38+GHH+Lt7c2cOXPYsGEDt912W4fjsrOzef3119m1axdRUVEU\nFBTQ2tpK//79eeCBB8jNzWXVqlWW4++8804uu+wy3nrrLbKysrj++usZMGAAU6ZM4U9/+hMFBQX8\n8MMP1NXVceONN5738ezHH3/M+++/T1hYGBqNhgEDBrBlyxaioqL45JNPuOuuu/j++++JjIwEzHcI\nW7JkCSdPnuTZZ5/ljjvu4JprruHAgQNkZGSwZMkS5s+fj5+f33n/BxeL9ZZbbkGr1fLOO++wZcuW\nC/7/vf3223zxxRfs3r0bPz8/br311g6vJTIyko0bN9KvXz+++eYbbrzxRlJTUxk5ciQffPABy5Yt\n4+eff7YcX1JSwooVKxg9ejSFhYXccMMNvPHGG25boiSEcC7ZK1Zbvg6ZOArf+GgFo7Gt8CsnULp1\nD/qKKlrOVnL6tfcZeP9tSoclhEeQGXgbU6lULFu2jKioKIKDg5kzZw6HDp1fh6jRaGhpaeHYsWPo\n9Xri4+Pp378/YP4jwGQyWY4tKChg3759/N///R9eXl6MGDGCW265xTILvnnzZh544AECAwOJjY1l\n2bJlHc5XqVT893//N7GxsXh7ewNw7bXXEhUVBcCCBQtITEzk+++/t5zTr18/brrpJlQqFQsWLKCk\npITf//736HQ6rrjiCry8vDh16tR5r6urWK3jupBNmzZx9913ExsbS3BwMA888ECHc2bOnEm/fuaP\nnydNmsQVV1zBt99+e9HnTklJYcyYMajVavr27cuSJUv45ptvOo1BCE8k9bW2V57xHRVfHzA31Gpi\nFnS9cN+W7FUD30at03Z4Tbn/2EBrbb1dr+nJZIwKazIDbwdts9gAPj4+lJSUnHdMYmIizz77LM8/\n/zzHjh3jyiuv5JlnniE6+vzZmZKSEkJCQvD397c8Fh8fzw8//GD5flxcnOV7sbGx5z2H9fcB3nvv\nPVatWkVeXh5gLkGxXkMQERHR4TUAhIeHd3isrq6u27EePHjwvGMv5D9fS3x8fIfvb9++nT/96U+c\nPHkSo9FIY2Mjw4cPv+jz5eTk8Nhjj/Hjjz/S0NCAwWBg1KhR3YpFCCF6qrW1leJi891KT634h+Vx\n3/EjKFcboeyMTa5TVmmfNV89FTY5ldJ/7aK5tBx9VS15b31M4m9uUTosIdyeJPAKWrhwIQsXLqS2\ntpbf/va3PPnkk6xateq88pfo6GgqKyupq6sjICAAMM90x8TEABAVFUVhYSGDBw8GoLCw8LxrWT9n\nfn4+DzzwAJs2bWL8+PGoVCqmTZvW5ex4d1ws1gv9UXGx863jLygosHzd3NzMbbfdxj/+8Q/mzZuH\nRqPhlltuscR9oV0dfve735GSksIbb7yBv78/q1at4tNPP72UlyiEW5L6Wtv4xS9+wd69e0lS+fKk\nzvxpYavJxK/3fMLZPe87NBZ71sC3UWk0RF1zBXlvfAiYZ+H7Lb0BjZ9sVGBrMkaFNbdK4F1pt5ic\nnByKiopIS0vD29sbb29vSyIaFRXF7t27MZlMqFQq4uPjGT9+PE8//TRPPfUUOTk5vPvuu6xZswaA\n6667jpdeeonU1FTq6+t5/fXXO92irL6+HpVKZdlf/b333uPo0aM2eV1dxdqV6667jtWrVzNr1iz8\n/Pz429/+ZvleS0sLLS0thIWFoVar2b59O19++SXDhg0DzJ8aVFZWUlNTQ2BgIIDlDwk/Pz+ysrJY\nu3Zth08ShBDCltrW4Cz2i4Vz6+UPejXjFRRM96Yxuk+lUrFg+lU2ftaeC708leJPdphr4curyF+f\nLjvSCGFnbpHAz5w50+57wXfnpkMX8p/7wrd93dLSwlNPPUVWVhY6nY60tDT++te/Aub69Pfff5+B\nAwfSv39/du3axWuvvcaDDz7I8OHDCQ4O5pFHHmHq1KkA/P73v+fBBx9k1KhRREdH88tf/pL169df\nNKahQ4dy7733Mnv2bNRqNYsWLWLChAkXjdk67u7oLNbO9skHuPXWW8nJyWHq1KkEBgZy7733Wur+\n+vTpw3PPPccdd9xBc3Mzc+bMYe7cuZZzBw8ezPXXX09qaipGo5Fvv/2Wp59+mvvvv59XXnmF5ORk\nFixYIHWEQlxARkaGzPDZSD+VN8P05+6yqlKx5JnHWBYT2flJdrD38CGHzMKrtVqir5lO/rpNAJz6\n+7sk3HIdam8vu1/bk8gYFdZUJlvUTdjJzp07SU1NPe/xoqKibpdkeKI333yTTZs2kZ6ernQoQoge\nUur3myQHttG3b1/ubA4iTW3+FDB4/EgS7/svRWKxVQK/bks6z657nVvm/IJHb/v1BY8xtuj5+cHn\naK2uBeCyPz9E31uuu+Rri3YyRt3LgQMHmDFjRtcHXoTsQuMGSktLyczMxGg0kp2dzauvvsrVV1+t\ndFhCCBciiYFtRJu0jFP1aW//4krFYnHE7HsbtZeOqHlTLe2TL7+DUd/qsOt7AhmjwppblNB4Or1e\nz4MPPkheXh6BgYEsXLiQpUuXKh2WEEI4jdraWoxGo92vM8fQB/W5MsHAlKH49XOfT4tbWvXU1J+/\n+1gb7/HJqNN3YaxvpDG/mJPrNxNxXc9r9H18fCxbHgshLkwSeDcQHx/P119/rXQYQggX5s4fz7/w\nwgs8++yzdr9OODr+qkuEc8t8rO9UqgRb18Bv3LGNjTu2dXrMdeowbtSatyH+90PP8tADFy656UxA\nQAA7d+4kKSmpV3G6K3ceo6LnJIEXQgjh1vbu3QuAn58fWq393vau1QeiMZiz94BhAwlI6me3aznS\n+MuSiYuIpKa+65s0fWNqZr7BiA9q4lXeTPSP4LCmudvXamhooK6ujiNHjkgCL0QnJIEXQgjhETN7\na9eu7fWOYl3RV9fy79QFGOobAIi+erpdrtMTtpp9H9pvADtfeb3bxxe8m86Zz827fT0xYTbjPni5\n2+cuWbJE7tVxEZ4wRkX3ueQiVo1GQ0NDg9JhCCGETTU0NKDRaJQOQ/RCwbufWpJ3n7go+iQPVjgi\n5UTMmgzn1gGUf/UdNT9nKRyREO7HJWfgIyMjOXPmDFVVVUqHInqgurqaoKAgpcMQNiL9aXsajYbI\nSMfvFw5SX3spjPpWTr/efpfVyDlTe3TvDHtx1D7w/8k7IpTgcclU7fsJgNzVGxn5yuMOj8PdyBgV\n1lwygVepVERFRSkdhuihkydPWu6aKlyf9KcQZiX/2kVT0RkAtIEBhE4cpXBEyouaO9WSwBdv2s7g\nR+/CJzpC4aiEcB8uWUIjXJPMHLgX6U/3Iv3ZOyaTidx/vGdpR1w1EbWXTsGI2ikx+97Gf2AC/kn9\nATDpWzn9xoeKxeIuZIwKa5LACyGEEL1UufdHan48BoBKpyX8yokKR+Q8oua239gpf90mWutl7ZoQ\ntiIJvHCYjIwMpUMQNiT96V6kP3snd3X77Hvo5anoAgMUjKajvYcPKXr9oNTheEeGAdBaXUvhhs8U\njcfVyRgV1iSBF0IIIXqhIbeAM9u+srQjZ09RMBrno1KriZzT/n9y+s0PMTngbrhCeAJJ4IXDSP2e\ne5H+dC/Snz13eu1HYDIBEDhyCL5xzrW5gpI18G1Cp4xF4+cDQMPJfM7u3qdwRK5LxqiwJgm8EEII\n0UOt9Y0dSkIiZklydSEaby/Cpoy1tPNkMasQNiEJvHAYqd9zL9Kf7kX6s2eKP/6c1po6ALyjwggc\nkaRwROdTuga+TfiM9oW9ZTu/pSG3QMFoXJeMUWFNEnghhBCiB0wmE6ff/MjSjpgxCZVa3k4vxic6\ngsCRQ8wNk4m8tz5RNiAh3ID8xhEOI/V77kX6071If3Zf5d4fqTt6AgC1l45QqxIRZ+IMNfBtImZO\nsnxdsOFftNY3KhiNa5IxKqxJAi+EEEL0QJ7V7Hvo5alo/X0VjMY1BCYP6bClZPEnXygckRCuTRJ4\n4TBSv+depD/di/Rn9zQVl1G65d+WdsRVky5+sMKcpQYezFtKhl/VXguf9+ZHmM7t4CO6R8aosNZl\nAr9t2zaGDh1KUlISzz///AWPWb58OUlJSaSkpHDw4MEuz923bx/jx49n9OjRjBs3jv3799vgpQgh\nhBD2lf/OZkytBgAChibi2zdG4YhcR9iUsai9dADUHsmhMvMHhSMSwnV1msAbDAbuu+8+tm3bxpEj\nR9iwYQNHjx7tcMyWLVvIyckhOzubNWvWcPfdd3d57kMPPcTTTz/NwYMHeeqpp3jooYfs9PKEM5H6\nPfci/elepD+7ZmzRk//OJkvbmWffwblq4AG0/n6EXp5qaeet/VjBaFyPjFFhrdMEft++fQwaNIj+\n/fuj0+lYvHgxmzdv7nBMeno6S5YsASAtLY2qqipKSko6PTcmJobq6moAqqqqiIuLs8drE0IIIWym\ndOseWsoqANCFBBKcepnCEbme8Bntf/SUbt1N87n/TyFEz3SawBcWFtK3b19LOz4+nsLCwm4dU1RU\ndNFzn3vuOR588EESEhL4/e9/z4oVK2zyYoRzk/o99yL96V6kP7tWsD7d8nXYtPGotBoFo+maM9XA\nt/FLiMF/UD8ATPpWCt/7rIszRBsZo8KatrNvqlSqbj1JTxeiLF26lJdffpkFCxbwwQcfcMcdd7B9\n+/YLHnvPPfeQkJAAQFBQEMnJyZaPkdp+mKXtGu1Dhw45VTzSlv6Utuf0J8Dhw4eZOXNmr87f8dEm\nfvry3wxX+4NKxanoAPIPH7KUqbQly87UPpp70qniaWuHX5HG/qwjAPj+czMD7v0VX3/zDdaOHTtG\nWFiY0/z8OEP70KFDThWPtHvef23VJ3l5edx5551cCpWpk+w7MzOTJ554gm3btgGwYsUK1Go1Dz/8\nsOWYu+66i+nTp7N48WIAhg4dyu7duzl16tRFzw0MDKSmpgYwJ//BwcGWF2Vt586dpKamnve4EEII\n0V033HADO3fuZOPGjZYEvqeynlvNyZfeBiBw5BAG/W6pLUP0KMYWPYeWP4OhwbwX/Nj3/kr49DQA\nlixZwqeffsratWu59tprlQxTCLs6cOAAM2bM6PX5nZbQjB07luzsbHJzc2lpaWHjxo3Mnz+/wzHz\n589n3bp1gDnhDw4OJioqqtNzBw0axO7duwHYtWsXgwcP7vULEEIIIezJ2Nqx1KMt2RS9o/bSETp5\njKWd/87mTo4WQlxIpwm8Vqtl5cqVzJ49m+HDh7No0SKGDRvG6tWrWb16NQDz5s0jMTGRQYMGsWzZ\nMl599dVOzwVYs2YNDz30EKNGjeKxxx5jzZo1dn6Zwhm0faQk3IP0p3uR/ry4s7syaS45C4A2KICg\nUcMUjqh7nLEGvk34Fe1/BJ3Z9hVNJWUKRuMaZIwKa9quDpg7dy5z587t8NiyZcs6tFeuXNntc8E8\ns793796exCmEEEIoouBdq8Wrk8c6/eJVV+AbF0XAkAHUHT+FyWCgcMO/GPjA7UqHJYTLkDuxCoex\nXkwmXJ/0p3uR/rywppIyynZ8a2mHTRunYDQ942z7wP+n8CsmWL7O/2c6JoNBwWicn4xRYU0SeCGE\nEOIiCt/7zJJYBgxLxCc6QuGI3EfwuGS0ffwBaCospWxXpsIRCeE6JIEXDiP1e+5F+tO9SH+ez2Q0\nUrD+X5Z2+DTXWrzqzDXwAGqdVhaz9oCMUWFNEnghhBDiAsozvqcxrwgAjb8vwWNHKByR+7FezFq2\n4xv8GvUKRiOE65AEXjiM1O+5F+lP9yL9eb6Cf7YvXg29PBW1l07BaHrO2WvgAXyiI+gzfJC5YTSS\nWFijbEBOTMaosCYJvBBCCPEfWsqrKN2629IOnzZewWjcW/iV7YtZBxbU0L17wAvh2SSBFw4j9Xvu\nRfrTvUh/dlT4wVZM+lYA/AYm4Ns3RuGIes7Za+DbBKdehjYwAAC/5lZSVP4KR+ScZIwKa5LACyGE\nEFZMJlOHvd/Dp8vsuz2ptJoOi1mna4IVjEYI1yAJvHAYqd9zL9Kf7kX6s13V/kPUZ58GQO3jRUha\nisIR9Y4r1MC3CZ/avr9+qioAqusUjMY5yRgV1iSBF0IIIazkWy1eDZkwCo2Pt4LReAaf2Ej8B/cH\nQKtSock8rGxAQjg5SeCFw0j9nnuR/nQv0p9m+upaSj7daWmHT3etvd+tuUoNfBvrhcLqjB8xmUwK\nRuN8ZIwKa5LACyGEEOcUf7IdY2MzAL4JMfgNiFc4Is8RPH4kLWrzHjTqM5VUZv6gcERCOC9J4IXD\nSP2ee5H+dC/Sn2bWi1fDpo1HpXLdTQ1dqQYeQOPtxckQL0vb+i64Qsao6EgSeCGEEAKo/uk4NYey\nAFDptIROGq1wRJ4nO6x9vUHJv3ahr65VMBohnJck8MJhpH7PvUh/uhfpz453Xg0ZNxKtv5+C0Vw6\nV6uBByj31ZBrbALA2NhM8SfbFY7IecgYFdYkgRdCCOHxWusbKfr4c0s7TPZ+V4ZKxb+NVZZmwfpP\nFQxGCOelVToA4Tmkfs+9SH+6F0/vz5JPd2GoawDAOzqcgCEDFI7o0rlaDXybr401/JcqGq0Jan46\nzkOLbqU62Ncu10pNTWXZsmV2eW5b8/QxKjqSBF4IIYTH63DnVRdfvOrKQgMDqcfI3tZqLtcEAdC6\naz8fGErtcr0PPviARYsWERwsd38VrkUSeOEwGRkZMoPgRqQ/3Ysn92ftsZNU7TfXi6s0GkKnjFU4\nItvYe/iQy83CP3jzEsYPT0aTXwqf7QNgZkAUE55+HLxsm7L87ne/o66uDr1eb9PntRdPHqPifJLA\nCyGE8GgFG9rrrINSh6MLDFAwGs/Wx8+feZOmYDIaObL/BM1nylE1tjDZJ5TYX86x6bUee+wx6urq\nbPqcQjiKLGIVDiMzB+5F+tO9eGp/GptbKPpgm6VtfTdQV+dqs+/WVGo1YdPGWdr578piVk8do+LC\nJIEXQgjhsUq37kZfUQ2AV3gIfUYkKRyRaBM6eQyozWlK5bcHqT+Zr3BEQjgPSeCFw8getu5F+tO9\neGp/FljN7IZNHYdK7T5vi664D7w1r5AgglKGWNoFGzz7zqyeOkbFhbnPbyohhBCiBxpyCyj/6jtz\nQ6UibKp7LF51J2FWJU1FG7dg1LcqGI0QzkMSeOEwUr/nXqQ/3Ysn9qf1jG7gyCF4hbrXVoKuXAPf\nJihlKLrgPgA0nymnbOc3CkekHE8co+LiJIEXQgjhcYytrRS+t8XSDp+epmA04mL+c1vPAlnMKgQg\nCbxwIKnfcy/Sn+7F0/qzbMc3NJeeBUAb1IeglKEKR2R7rl4D3yZsavtuNGU7v6WpuEzBaJTjaWNU\ndE4SeCGEEB6n4+LVsai0GgWjEZ3xiQonYFiiuWE0UrjxM2UDEsIJSAIvHEbq99yL9Kd78aT+bCo6\nQ9nOby3t8Knus/e7NXeogW9jvT9/wfp/YTIaFYxGGZ40RkXXJIEXQgjhUQre+wzOJYB9hg/COypM\n4YhEV4LHJqPx8wWgMa+Iiq8PKByREMqSBF44jNTvuRfpT/fiKf1pMhopWG9VPjPdPWffwX1q4AHU\nXjpCJ422tPP/uVnBaJThKWNUdI8k8EIIITxG+Z79NBWUAKDx9yM49TKFIxLdFWa1U1Dp1j20lFcp\nGI0QypIEXjiM1O+5F+lP9+Ip/Zn/z3TL12GTU1F76RSMxr7cqQYewC8hBr/EvgCYWvQUfbhN4Ygc\ny1PGqOieLhP4bdu2MXToUJKSknj++ecveMzy5ctJSkoiJSWFgwcPduvcV155hWHDhjFixAgefvjh\nS3wZQgghROdM1XWc+fwrS9v6Lp/CNXRYzPrup5hMJgWjEUI5nSbwBoOB++67j23btnHkyBE2bNjA\n0aNHOxyzZcsWcnJyyM7OZs2aNdx9991dnvvll1+Snp7OTz/9xM8//8zvfvc7O7084Uykfs+9SH+6\nF0/oT1PGj5j0rQD4D+qHb3y0whHZlzvVwLcJmZCC2tsLgLqsU1R997PCETmOJ4xR0X2dJvD79u1j\n0KBB9O/fH51Ox+LFi9m8uePCkfT0dJYsWQJAWloaVVVVlJSUdHruqlWr+MMf/oBOZ/7oMiIiwh6v\nTQghhLAw7W7fuSTcjRevujONrw8hE1Is7QIPXMwqBHSRwBcWFtK3b19LOz4+nsLCwm4dU1RU3rZO\nBgAAIABJREFUdNFzs7Oz2bNnDxMmTGD69Ol89913NnkxwrlJ/Z57kf50L+7en0NUvlBsvvOq2seb\n4LSULs5wfe5WA98m3Goxa0n6LvQ1dQpG4zjuPkZFz2g7+6ZKperWk/S0Bq21tZXKykoyMzPZv38/\nN954IydPnrzgsffccw8JCQkABAUFkZycbPkhbvs4SdrSlra0pS3tztpDVL4cMdYzXO1P6MRRfJdz\nHGhPctvKTaTt/G2/xL7khHnTUlbB8EYo/mQ7eQPNn+T35OejpaWFNkr/fErb/duHDh2iuroagLy8\nPO68804uhcrUSfadmZnJE088wbZt5pXeK1asQK1Wd1h0etdddzF9+nQWL14MwNChQ9m9ezenTp26\n6Llz587lkUceYdq0aQAMGjSIvXv3EhbW8WYaO3fuJDU19ZJeoHAeGRkZlh9m4fqkP92LO/fnrxYs\nZNE3hXipzB86D31yOX4D4hWOyv72Hj7ktrPwZ77IoODcjkKBI4cy6Ys3e/wcgwcP5uzZsxw/ftwl\nSnndeYx6ogMHDjBjxoxen99pCc3YsWPJzs4mNzeXlpYWNm7cyPz58zscM3/+fNatWweYE/7g4GCi\noqI6Pfe6665j165dAGRlZdHS0nJe8i6EEELYwsAzDZbk3bdfrEck7+4udFIqKp0WgJqfjlFz6LjC\nEQnhWNpOv6nVsnLlSmbPno3BYGDp0qUMGzaM1atXA7Bs2TLmzZvHli1bGDRoEP7+/qxdu7bTcwHu\nuOMO7rjjDpKTk/Hy8rL8ASDcm8wcuBfpT/firv1pMpkYWlxvaYd70NaR7jr7DqAN8CN47Agqv/0B\nMG8pOfy5IQpHZV/uOkZF73RaQqM0KaERQghxKaoOHCZz3q8BMGk1jFr5/9D4+SoclbCF2qMnyF5h\nnlDUBgZwxQ/paPx8un2+q5XQCPdi1xIaIWypbVGHcA/Sn+7FXfsz/532bQZbhyR4VPLujvvAWwsY\nmoh3lLn8trWmjpJPdykckX256xgVvSMJvBBCCLekr6mjZNOO9nZyooLRCFtTqVQd7qZbsP5TBaMR\nwrEkgRcOI/V77kX60724Y38Wf/wFhsYmAPKMTRijPWuzBHeugW8TNnksaMypTOXeH6nLylU2IDty\nxzEqek8SeCGEEG7HZDJ1KJ/ZZayCbt7bRLgOXXAfgkYNt7RlFl54ik53oRHClmQPW/fi6f1ZWVnJ\nnj17MBgMDrneqFGjSEy0XwmIu/VnzQ9HqT2cDUCrCjKMNfxS4ZgczZ33gbcWPn081d//DEDh+1sZ\n/IdlqL29FI7K9txtjIpLIwm8EEL0wgMPPEB6errDrhceHs7x48e7fYdsT5f/z/bZ95xADQ1lRgWj\nEfYUmDwYXWgw+ooq9BVVnPk8g+j5VyodlhB2JQm8cBiZOXAvnt6fZWVlgPn/ITw83K7X2rRpE2fP\nnrXrNdypP1tr6yn+pH3x6pFgLZQpGJBCPGH2HUClVhM2daxlwXL+u5vdMoF3pzEqLp0k8EIIcQke\neeQRJk2aZNdrbNq0ya7P726KPtmOoaERAJ+4KEp9axSOSNhb+NRxlGzeCSYT5bv303C6CL9+sUqH\nJYTdyCJW4TCyh617kf50L+7UnwVW5TPhV6R57OJVd98H3ppXeAiByYMt7cL3/qVgNPbhTmNUXDpJ\n4IUQQriN6h+PUfPTcQBUOi2hk+Ru3p6iw57wG/6FsbVVwWiEsC9J4IXDSP2ee5H+dC/u0p/Wi1dD\nxo9EG+CnYDTK8pQa+DbBo4ejDQwAoLnkLGXbv1Y4IttylzEqbEMSeCGEEG6hta6e4o+3W9rh09MU\njEY4mkqrIWzaOEs77+1PFIxGCPuSBF44jNTvuRfpT/fiDv1ZvGkHhvoGAHxiI/Ef3F/ZgBTmSTXw\nbcKnt695KP/3PupPFSgcke24wxgVtiMJvBBCCLdgfefV8Olpsme+B/KOCCVw5BBLO3+d7OAk3JMk\n8MJhpH7PvbhSf7YaTdQ0tVJa20JuZSPHztSTdbaB05WNFNc2U9mgx2A0KR2molypPy+k+uARan48\nBpxbvDp5jMIRKc/TauDbRMyYaPm6cONnGJqaFYzGdlx9jArbkn3ghRBuo7a5leNlDWSVNVBY00xJ\nbQsltc2UN+jpKj9XqyDcX0ekvxcRAV70D/EhKdyPweF+BPrIr0pnl/fWx5avPX3xqqcLHDkEr/AQ\nWs5Woq+opuTTXcTdMFfpsISwKXlXEg6TkZEhMwhupCf9mZ+fT0lJic1jaGiFnFoVWbUq8upVlLf0\nvmTCaIIzdXrO1OmhtL7D96ICvEiJCWBMfCBj4vq4ZULvyuOzpaKa4s3td16NuMq+N9ZyFXsPH/LI\nWXiVWk34FWkUfbANgPy3P3GLBN6Vx6iwPfd7FxJCOJWsrCwmTpyIyWSbEhVdUARho64kaPhEAvoN\nR6XWdHmOCvDRqvHSqvDSqNFp1JhMJvRGE60GE80GI41640XPL61r4YvsCr7IrkAFDI7ww5A0Gd2R\nHJu8JnFpCt/7DGNTCwB+/ePwS+yrcERCaWHTxlP88XZMBgNV3/1MzeFsAi9LUjosIWxGEnjhMDJz\n4F56MvtuMpno06cPgwcP7vqEC9F6Q/wI6J8KkQNRqS68fMdkaKWhKIf4IB8uHz+WED8tIT46gny1\naNWdz87rDUZqmgxUN7VS0ainuKaZotoWSmubMVj97WECjpc1wIg5jBw+i7W5JqpCzzI9MQQ/r67/\nmHBWrjo+TUYjeW+3l8+Ez5gki1fP8cTZ9za6wACCx42gMvNHwDwLf9mfHlI4qkvjqmNU2Ick8EII\nhxg7diwfffRRj84pqmlm8+EyPs8qp+ECM+QqIC7Im6RwPwaG+rJz/at88NorjL3nt4zre2WPrqXT\nqAnzVxPmryMRX8vjBqOJoppmcsobOVHeQEF1M235vEqt5nQDvJSRz5q9hcwaHMa1w8OJC/Lp0bVF\n7539ci+Np4sA0Pj7EjohReGIhLMIv3KiJYEv+vBzhjx+L9o+/gpHJYRtSAIvHEbq99yLPfvz55I6\nPjh0hszT1fxn4Y0KSAz1ZWRMAEnhfvhbzXqrTRcvg+ktjVpF32Af+gb7cMXAEBr1Bo6XNfDhjq9R\nRw20lPA06I1sOlzGpsNljO8byOKUKEZEB9g8Hntx1fFpvXg1bMpY1N5eCkbjXDy1Br5NwJAB+MRF\n0VRYiqGhkcIPttHvjoVKh9VrrjpGhX1IAi+EcBqHS+pYd6CYg0V1530v3F/H6Ng+jIwOUHQRqa9O\nw6jYPqz/95scz85hyXNvUagK4Wy93nLMvvwa9uXXMCo2gP8aHcPIGNdJ5F1Jw+kiynZ8Y2mHW20f\nKIRKpSL8ygkUnLs/QP7bH5Nw+/VSYiXcgiTwwmFk5sC92LI/j5fV8/b3xXxXUHve9waF+TIxIYiB\nYb5O98bbWlfJYJ9GFqQmc7Kikcy8GrLPNlg+NfihqI4firJJiQlg6bhYhkY678f3bf1ZWVnJmTNn\nHHJNf39/4uPje31+/jub4Nzi6MDkwfhEhdsqNLfgybPvbcIuT6Vo4xaMLXrqjp+iMvMHQieOVjqs\nXpH3UGFNEnghhGLO1rfw5v4iduRUdnhcrYKRMQFM7hdMRIDzl0SoVCoGhvkxMMyP8no9X+VW8mNx\nnWXv+R+L61iensWVA0O4Y1wskU76moqKihgzZgzNzY678c2qVatYtGhRj88zNDVTsP5TSztcto4U\nF6Dx8yX08lTOfrkXgNNvfOiyCbwQ1iSBFw4j9Xvu5VL6s6nVyIc/lbLxpzM0t7bXraswJ+7TBoQQ\n5q+zUaSOFeav47rLIpk6IIQ9p6r4sbjWksjvOlFJRm4VC5MjWZwSha/OeXatycjIQKvV0tzcjI+P\nD3372ncrxoqKCsrLy8nKyurV+SXpu9BXVAPgFR5CUMpQW4bnFjy9Br5NxMzLLQn8ma17aCwowTc+\nWuGoek7eQ4U1SeCFEA61P7+Gl7/Op7SupcPjQyP8uCoplAh/55yd7qlQPx3XXRbBlP7BbM8p5+iZ\nBgBaDCY2/FDKrpxKfnN5POP7Bikc6flSUlLYunWrXa/x4osv8swzz/T6fOvFq+FXTEClvvDWokL4\nxkfTZ/ggao/kYDIYyFv7EUMev1fpsIS4JPIbTziMzBy4l572p9HLnxVf5vLo5yc6JO9RAV4sGRPD\nTaOi3SZ5txbmr2NxSjS3j4khpk/76yuta+Gxz0/yzM5TlFstgFWKK43P6h+OUn3gMAAqrYawaeMU\njsg5yex7u4hZl1u+Lng3HUNDk4LR9I4rjVFhf5LACyHsymSCsDGzqJ9yF1+eaK9199WquWZYOHdN\niCMx1LeTZ3AP/UN9+e+0OOYPD8dX1/6rd8+pKpZ+eIQvssptdrdad3f69fctX4eMT0EXKLv8iM4F\njRqGV0QoAPqqWoo+2qZwREJcGimhEQ4j9XvORa/Xc/bs2V6fv2/fPsaPH9/pMTXNRt4v9GLAooc7\nPD4yOoDZQ8IIsNOdSxvq6yg/U2qX526j17d0fdB/UKtUjIkLZGiEP19klfNDsXm7zAa9kRf25JGR\nW8X9kxMI9XN8/X9bDbyj1dXVUVxc3O3j9WcqKN6009LWTEymtKK803Oa9cp/wqEEqYFvp1KriZg5\nicL1/wLg9OsfcN5NJpycvIcKa5LAC+GBjEYjU6dO5fjx43a7RtCwCfT/5YPo+oRaHgvx1XLNsHAG\nhfnZ7boAH729ho/eXmPXa1wKfy8NC0ZEMiq2D+lHyqhobAUgM6+GX390lN9M6sv0gSEKR+kYr732\nGq+99lq3j79BE84CjXm7yGPGBm5e8Qd7hSbcTPjUcRR/9AXG5hbqjp9isJ+O3k9hCKEsSeCFw8jM\ngfNoamqyJO/R0bbdjUGl8yZo2q8IGDmjw+PRrWUsnTgOL439KvfGTb6Sr774jKaGBrtdw1pkTByJ\nQy/r9fkDQn25e2I8O7Ir2JtfA0Bts4Fnv8zlu4Ia7p0U77CdaiZPnkxmZqZDrgUwY8YMNm7cSG3t\n+Xv/X4zOBDOrAi0zp9/46onQhnZ+0jlRIaEkD0rqTaguS2bfO9L4+RI2Zazl5l/TWnz4potznIm8\nhwprksAL4cF8fX05cuSIzZ7vRHkDT+/MpaimfR/xAC8N110WQVJ4os2uczHDUlJ5bfOXdr+OLXlp\n1MwbGs7QSH82HS6jusk8G/9FdgVHztTz6JX9lQ3QTlJSUti7d2+PzilY/yk//3YFYN468pU/r0Cl\ncZ6tOIXzi5g5yZLAX9bqRSSuuV2tELKIVThMRkaG0iEIG7LuT5PJxGfHzrI8PatD8j480p97J8aT\nFG7fkhl3kBjqyz0T4xkZ074gs6C6meXpWURMvNbu13f28Wkymchds9HSjrhqkiTvXdh7+JDSITgd\nn5hIAkcOAUCNilka1ylVc/YxKhyrywR+27ZtDB06lKSkJJ5//vkLHrN8+XKSkpJISUnh4MGD3T73\nL3/5C2q1moqKikt4CUIIJTXqDTz379P8LSMfvcFc2+ClUbHgsghuHBmJn50WqrojH62ahSMiWXBZ\nBF4aFQB6g4l+C5Yz8NYnqWtuVThC5VRkfE/dsZMAqL29ZOtI0WsRs9pLUaargzDUO6bkTghb6jSB\nNxgM3HfffWzbto0jR46wYcMGjh492uGYLVu2kJOTQ3Z2NmvWrOHuu+/u1rn5+fls376dfv362eFl\nCWck9XvuZfLkyZyqaOS+Tcc7bA8ZFeDFsrQ4RsX2QaVSKRih6xoV24dlaXFEB7TvGx8yYjL3bc7i\nVEWjXa7p7OPTevY9bMpYtP7yqU5XpAb+wgJHJOEdbV4I7afSUL5pl8IRdY+zj1HhWJ0m8Pv27WPQ\noEH0798fnU7H4sWL2bx5c4dj0tPTWbJkCQBpaWlUVVVRUlLS5bm//e1v+dOf/mSHlySEcIQvT1Sw\nfPNx8qvbS2ZS4/rw6/GxhLvhDZkcLdzfizvHxzK+b6DlseLaFpanZ3X4g8kT1J/Is9QtA0TMvLyT\no4XonEqtJtJqFr70nXSMrZ776ZZwTZ0m8IWFhfTt29fSjo+Pp7CwsFvHFBUVXfTczZs3Ex8fz8iR\nI23yIoRrkPo992Awmnh9XyF/eH0zzedKZnRqc8nMtcMj0NlxlxlPo9OouXpoOCfeeRJDs3nmvbnV\nyIovc1mdWYDBaLuNrJ15fJ76xwbzHcGAwJSh+MREKByRa5Aa+IsLnTKWeowAtBSWUvrZboUj6poz\nj1HheJ3uQtPdj797cvfAxsZGnn32WbZv396t8++55x4SEhIACAoKIjk52fIxUtsPs7Rdo33o0CGn\nisfT22AudWvTnfPrWwz8uzmO7wtraSjKASAxeRyLUqIoOXaAn4pg5NgJAPz0nXlLQmlfervy0B7q\nCo4z6pb/xRQ/AoC1m7fzVYYvr9y7kBBfnU3Gp8ZqUajSP59t7XGDh1H0/laOGOsBuPbqaUB7ctpW\nJiLt89tHc086VTzO1P4u5zjvU8HtmEtpNj/3EpeFejFlyhTAeX7+rduHDh1yqnik3fP+q66uBiAv\nL48777yTS6EydZI9Z2Zm8sQTT7Btm/mWwytWrECtVvPww+13VbzrrruYPn06ixcvBmDo0KHs3r2b\nU6dOXfDcq6++mhkzZuDnZ65fLCgoIC4ujn379hEZGdnh+jt37iQ1NfWSXqAQ4nwNDQ3Ex8fj6+t7\n3qdqF3OqopEnd5ykqKb9DqSDw/1YOCISH53MutvT1aMHAPDhvhw+OVzG8bL2RXdRAV48NSuRAaG+\nl3ydzMxM5s2bR1paGlu3br3k57OFrBX/4OTf1gHgl9iXIf93n6ytEDYx+9dLeLIpAi+V+ffXuI9W\nEna55BzCMQ4cOMCMGTO6PvAiOn3XHTt2LNnZ2eTm5tLS0sLGjRuZP39+h2Pmz5/PunXmX66ZmZkE\nBwcTFRV10XNHjBhBaWkpp06d4tSpU8THx3PgwIHzknchhPP49nQ1/5Oe1SF5nzogmJtGRUny7kA+\nWjWLU6K4cmAIbSlsaV0L93+aRWZetaKx2UNrfQN5b31iaUfNmybJu7CZWpWRr4zt4yb31XcVjEaI\nnun0nVer1bJy5Upmz57N8OHDWbRoEcOGDWP16tWsXr0agHnz5pGYmMigQYNYtmwZr776aqfn/if5\nZew5pH7P9ZhMJj48dIYntp+kqdVcL+qlUbFoZCQRVVmoZfw6nFqlYlpiCDePisb73FaTjXoj//fF\nST48dKZHJY3WnHF8Frz7Ka3V5ju1ekeGETx2hMIRuRapge/aZ4YK2v4aLtv5LbXntip1Rs44RoVy\nurwT69y5c5k7d26Hx5YtW9ahvXLlym6f+59OnnTewSKEJ2s1mvj7N/l8dqzc8liIr5abUqKJ6uPF\nT/kKBicYHOHH0vFxrD9YQlVTKyZgzd5C8iqb+M3l8S6/mNiobyV39XuWduS8qajUrv2ahPMpQY9v\n8mAaf8oCIHfVepL/9pjCUQnRNfltKBxG9rB1HXXNrTz2+YkOyXvfIG9+PT6OqD7mLSLbFlsK5UQF\nePHrtDgSgr0tj23LKucPW09Q09SzbfGcbXyWpO+kqbAUAG0ff8Imj1U4Itcj+8B3T+CM9t9lRR9/\nQVNxmYLRXJyzjVGhLEnghRAdFNc2c/+n2RworLU8lhwdwJIxMfjLXVWdToCXhiVjYkmJCbA89lNJ\nHcvTj1NQ3aRgZL1nMpk49ep6Szti5uWovXQKRiTcmU9iPP5J5ptKmvSt5P5jg8IRCdE1SeCFw0j9\nnvM7UlrP8s1Z5FW1J37TE0NYOOL8/d3btjkUytOe24f/qkGhlseKalq4Pz2Lw6V13XoOZxqfZTu+\nofZwNgBqLx0RMyYqHJFrkhr47ou6errl6/x1m2gpr1IumItwpjEqlCcJvBACgIzcKh7akk31udIL\njQoWjojgioEhstjcBahUKqYMCGZxShQ6tbm/apoNPLwlh4xTzpeMXIzJZOLEX9+ytMOvSEPbx1+5\ngIRHCBo1DN++MQAYGpvIfW2jwhEJ0TlJ4IXDSP2e80o/UsbTO07Rcu7Oqn46NbeNjWVkTJ+LniM1\n8M5pWKQ/t42Nwf/c9p4tBhNP7zzFJz+f6fQ8Zxmf5Xv2U33gMAAqrYbIedMUjsh1SQ1896nUaqLn\nX2lp573xIfrq2k7OcDxnGaPCOXS5C40Qwr29ub+I934stbRDfbXckhpDqJ/UHDubm65I7fanIbrg\nKOIWPYpXWCwmYFVmIc+9spryneuAC281qdfrbRdsL1nPvodNHY9XSJBywQiPEjwuGe+YCJqLy2it\nrSfvzQ8Z+MDtSoclxAXJDLxwGKnfcy4qtYa4BQ90SN7jAr25c3xct5J3qYF3nKHJowGora6ipqqy\nW//Kc49x5JV7qcs9bHmeoHHXEDzvPipr6qioqDjvX22tecZx7Fhldnyp+PYglZk/mBsaNVHXTFck\nDnchNfA9o1Krif5F+yx87pqNtNY3dHKGY8l7qLAmM/BCeKBGvZFBt/+RoCHjLI8NDvfjhpGReLn4\n/uHu6M9vfUhtde/q2PVGE1tPNpBTZZ5dDx05lQnTr+LBCREEerfvKrR3717S0tJQq9WEhITYJO6e\n6jD7PnkM3uHKxCE8V+iEURR/sp2Wsgr0lTXkv72JAffcrHRYQpxHEnjhMFK/5xwqGvQ8uiOvQ/Ke\nGteHa4aGo1F3f7Gq1MA7jlqtJigktOsDL+JXoaF8nlVOZl4NAFkVLTyVcZZn5wwkJtC8h/y8efNs\nEmtvVX3/M+V79psbKhVR11yhaDzuQGrge06l1RB9zXTy1n4MwKlV60m4fSEaX+8uzrQ/eQ8V1mSq\nTQgPUlDdxP2fZnGystny2PTEEOYP61nyLlyLWqVi7pBwZg8ObbtrPIU1zfxPehZZZ52jRODEi2st\nX4dOHI1PVLiC0QhPFjp5LLpzay9ayirIf2eTwhEJcT5J4IXDSP2eso6eqeeBT7MpqW0BwGQ0ULD5\n5V5vEyk18K5nUr9gbhgZifbcH2tVTa387l/Z7M+vUXR8Vn3/M2U7vzU3VKoOu4GI3pMa+N5R67Qd\n9oU/+fI6p6iFl/dQYU0SeCE8QGZeNQ991r7Hu1YNOW//Pyq//1zhyISjXRYVwK2p0fhozb/+m1qN\nPP7FCfbn1ygWU/Zzayxfh6SNxCc2UrFYhADz/Qd0ocEAtJytJO/NDxWOSIiOJIEXDiP1e8rYcuws\nT2w/SbPVHu83J4dRffTSZtClBt519QvxZem4WIJ8zItYjSbYWh/DuwdLMJkuvMWkvZRnfEf5V9+Z\nG2o1MQtmOfT67kxq4HtPrdMSc90MS/vU399VfF94eQ8V1iSBF8JNmUwm1n1fzEsZ+RjP5WQhvlqW\njoslro+XssEJxUUGeHHnuDiiAtp/Ft7+vpi/fZ2PweiYJN5kMpG1YrWlHTZlDD4xEQ65thBdCZs8\nFu/IMAD0VbXkrpa7swrnIQm8cBip33Mcg9HEX7/K558HSyyPxfTx4s5xsYT72yZ5lxp41xfoo+WO\nsbEkhvpSc8K8//qWY+U8ueMkTa1Gu1+/bPs3VH/fftfVmGuvsvs1PYnUwF8alVZD9IKZlnbu6vdo\nKe/ddq62IO+hwpok8EK4mUa9gSe2n2RbVrnlsUFhvtw+NpYAb9k5VnTko1Pzq9HRDAz1tTyWmVfD\nQ59lU9VovzuzmoxGsp9vr30Pv3ICXrLvu3AyoRNH4RMXBYChvoFTf39X4YiEMJMEXjiM1O/ZX1Wj\nnoe25LDXakFiSkwAN4+Kxltr2+EuNfDuQ6tWcc8Nc7i8f5DlsWNlDTzwaTbFNc2dnNl7Jem7qD2c\nDYDaS9fhDpjCNqQG/tKp1Gpirm9fl3F67Yc0lZQpEou8hwprMh0nhJsoqmnmf7edoMgq4ZoyIJgZ\nvdwmUngWtUrFrKQwAr21bD1u/vSmba/4Z+YMZHC4n82uZdS3kv3n1y3tiFmT0QX1sdnzC9ETt//x\ncbSaTtIhEyzVaYnRqzA2NvO3aQvYFqvr0TVUKhW33nort91226UFK8Q5ksALh8nIyJAZBDvJKmvg\nsc9PUHVum0gVMG9oGOP7BnV+4iX46btMmYV3I239OSEhiEBvDR/9XEar0WTZK/7xGQMY1zfQJtfK\nf/sTGk7kAaDx8yFq3jSbPK/oaO/hQzIL34mEqBgqaqrJyjvd5bFrVX78ry4BgOQqA+vPniDf1LNP\np+rr6y8pgZf3UGFNEnghXNz+/Bqe3nnKsuhQq1bxy+RIhkX6KxyZcFXDowLw99Ky4YcSGluNlr3i\nH5iSwOzBYZf03PqqGnL+8oalHT1/BtoA283uC9Fdbz3+NDkF+d0+Xv/PrZhy8lGrVPw1bR6hz/6m\nW+fl5eVx2223OXyLVuHeJIEXDiMzB7b3RVY5L36VZ9km0ler5ubR0SQE+9j92jL77l7+sz/7hfiw\ndFws7xwsobqpFaMJ/rInj7J6Pb8aFdXrsqwTL72NvtK8RsMrIpSImZdfcuziwmT2vXM+Xt6MSBzU\n7eMb77iBo4/+FUwmWg4cJa6yiYgruv496O9vm8kUeQ8V1mQRqxAuyGQysf5gCS/saU/eg3zMe7w7\nInkXniEiwLz1aLTVXvFt9xbozV7xDbkFnH7jA0s7btE81DqZRxKuwTc+mrBp4yzt40+uxGQwKBiR\n8GSSwAuHkT1sbcNgNPHK1wW89X2x5bHoc4lWRIDjbtAk+8C7l4v1Z6CPltvHmfeKb7P1eDlPbD9J\no75nycvxZ1Zh0pvXafgn9SN4nMwQ25PsA297sdfPRu1t/j1bd+wkBe995rBry3uosCZTH0I4kfT0\ndNauXYvReOGb6Jg0OlpSF2KMHmp5zFh6grxP1rNibfcXVBll1kj0gI/WvFf85iNl/FRcB8De/Boe\n3pLDU7MSCfbtekeOyn0/UfqvLy3t+Juukd2RhMvRBfch6urpFH/8BQA5z79GzLUz0AZ9vFJSAAAg\nAElEQVTImiPhWJLAC4eR+r2uvfzyyxw4cOCC39P4BZJ02zMEWCXv5Qd3kPv+nzEZWnt1vfComF6d\nB1ID72666k+tWsX1l0UQ6K0lI9d8N8pjZQ3c/2k2z84ZSGyg90XPNRkMHH38JUs7ZEIK/oP62SZw\ncVFSA28fkXOncvbLTPSVNTSfKSfnhTcZ+kT3FrReCnkPFdYkgRfCibTNvL/wwgsMGtS+uKqiRcV7\nhX5U6Nur3pK86lgwbQSq6W/3+nqJQ4b3PljhcVQqFTOTQgn00bDlmHmv+KKaZu5Pz+KZ2QMZHHHh\n3WTy39lMzY/HzM+h0xJ7w1yHxSyErWm8vYhbNI/cf7wHwOnX3idu0Tz6DBuocGTCk0gCLxxG9rDt\nvtGjRzN69GgAfi6p4+XtJ6k5V2+sAuYMCWNCQqKCEco+8O6mJ/2Z1jeIQG8tHx46075X/GfZPDaj\n/3n3HmguqyBrxWpLO/oXV+AdEWrT2MWFyT7w9hMycTRnv9xL3fFTmAwGjvzhL4z/5O92LQuT91Bh\nTRaxCuHEduVU8PCWHGqazcm7Vq3ihpGRTEiw3w2ahOiOYZH+LBkTg6/W/DbS1Grk/31xkm3n7uLa\n5vjTr9JaXQuAd2QYUfOmOzpUIWxOpVLRd8kCUJt//iszf7DUxQvhCJLAC4eRmYPuM5ngnwdLeO7f\np9Gf267P30vD7WNjuCwqQOHozGT23b30pj8Tgn1YOj6WYB/zh7lGE7z4VR7/PFCMyWSi4tuDFL2/\nxXJ8/K3Xofbq2S3oRe/J7Lt9+cZHEzm7/X3t+JMr0dfU2e168h4qrEkCL4STUWl0vJ9r3m+7TYS/\njl+PjyU+SPZ4F84lwt+LO8fHEt3Haq/4AyX8ZddJDj/yguWx4HHJBI0cokSIQthNzHVXoQsJBDi3\noPWNLs4QwjYkgRcOI3vYdoOXL4PvfI4DFe0PJYb6snRcLCHd2KrPkWQfePdyKf3Zx1vL7WNjGWi1\nV3zFuo+oP34KALW3F/G/+sUlxyh6RvaBtz+Nrw9xN11jaZ9+/QOqDx6xy7XkPVRYkwReCCdRWN2M\nZtZy+gwcZXksNa4P/zU6Gl+dRsHIhOiaj1bNzaOjGR0bQPDZUibtbL/Bje/8mXiFBisYnRD2E5KW\nQp/h53YNMxo5dP8fMTa3KBuUcHvdSuC3bdvG0KFDSUpK4vnnn7/gMcuXLycpKYmUlBQOHjzY5bm/\n//3vGTZsGCkpKVx//fVUV1df4ksRzk7q9y7u+4IalqcfRxUYaXlsZlIo84eFo1E7581upAbevdii\nP7VqFfOHhLJo60a0rXoAzkTH8ZfkWRxslD9CHU1q4B1DpVKRcMdCy/qOuuOnOPFS77f3vRh5DxXW\nukzgDQYD9913H9u2bePIkSNs2LCBo0ePdjhmy5Yt5OTkkJ2dzZo1a7j77ru7PHfWrFkcPnyYH3/8\nkcGDB7NixQo7vDwhnJvJZOKjQ2d49PMT1J7bacaob2ZKSCOT+wfLnSqFy9F/8Cn+x48DYFCr+Xzh\nLTSotbxY5s2WGi0mk8IBCmEH3pFhxN7Yfn+Dk6+so+bnLAUjEu6uywR+3759DBo0iP79+6PT6Vi8\neDGbN2/ucEx6ejpLliwBIC0tjaqqKkpKSjo9d+bMmajPbb+UlpZGQUGBrV+bcDJSv9dRS6uRF/bk\nsXpvIec2msFYX8WxVQ/Qz9egbHDdIDXw7sUW/WnIK6RpVfvMo+HKqbTExAJgQsX6Km9eq/CiRZJ4\nh5AaeMeKuGoS/kn9ATC1GsylNPre3SX7QuQ9VFjrMoEvLCykb9++lnZ8fDyFhYXdOqaoqKjLcwHe\nfPNN5s2b16sXIIQrKm/Q87vPstme3b5aNT7Im9pPX6Sh4LiCkQnROyajkcZn/grNzQCoYqIIumoy\nd3hXEK9qrwfeU6/jmVIfylvl0yXhXlRqNf3uvAGVzrytau3P2Zxa+Y7CUQl31WUC392P8E29/Fz0\nj3/8I15eXtx88829Ol+4DqnfMzt2pp77Nh3nWFmD5bHRsQHcPjYWU2ONgpH1jNTAu5dL7c+WjZsx\n/HjY3FCr8F58LSqtBn+Vif/yqiJZ3Wg59mSLhsdLfDnSJPso2JPUwDueT0wEsQtnW9o5L66l6dgp\nmzy3vIcKa9quDoiLiyM/P9/Szs/PJz4+vtNjCgoKiI+PR6/Xd3ruW2+9xZYtW9i5c+dFr3/PPfeQ\nkJAAQFBQEMnJyZYf4raPk6QtbVdof/XVV+zNr+HL5jj0BhM1J35ArYIb5s4grW8gh77fS0N9+01A\n2koa2hIraUvbWduG4zkcePllMBoYrvZHe+UUDjdUQnYlyUnD0aogMXcvLUYvsvpPxISKguwf+d9s\nE8vGDGdOn1b2HTGXe7QlnW3lH9KWtqu1I+dM4at/76apqJThen/OPLkKHSoaGtonbZR+P5K249uH\nDh2ybNiSl5fHnXfeyaVQmbqYOm9tbWXIkCHs3LmT2NhYxo8fz4YNGxg2bJjlmC1btrBy5Uq2bNlC\nZmYm999/P5mZmZ2eu23bNh588EF2795NeHj4Ba+9c+dOUlNTL+kFCueRkZHhsTMITa1GXs7IY0dO\npeUxX62aG0dGkRjWvnf2/9w8n5yjh3jpn5tJumykEqF220/fZcosvBvpbX+a6huoW7IcY765PFId\nH4P3fUtRaS+868xpo46PW4Kot/oAeJJfK0tDm/GWCXmb2nv4kMzCK6S5tJyjj7+EsclcUrbbUM3O\nAf7s27ev18/pye+h7ujAgQPMmDGj1+d3OQOv1WpZuXIls2fPxmAwsHTpUoYNG8bq1asBWLZsGfPm\nzWPLli0MGjQIf39/1q5d2+m5AL/5zW9oaWlh5syZAEycOJFXX3211y9ECGdVUN3EUztOkVvZZHks\nKsCLxSlRhPo5182ZhOipxhdetSTveHvh9auFF03eAfqp9Sz1ruCjliAKTeaf/28atBToVSwPbyZa\nJytchevzjgoj4bYF5P7jPQCmaYI4U+/8mxMI19HlDLySZAZeuLo9pyp5cU8eDXqj5bHRsQFcPTQc\nneb86UZXmoEXomXrLhqf+LOl7XXTdWjHpHTr3FYTfN7ah4OG9k+gfFQmloY2M9FfEh3hHnJXb6Ti\n6+8BaFKZmJX5IX794hSOSjgDu8/AC+HpiouLeeONNzrUL3bFiIqCsJGcCRps9WArwYX7OfPjSdZu\nvfB5ZSVFlxitEI5hyCuk8U8rLW3NmJHdTt4BtCq4WldLjErP5619MKCiyaTi7+U+HGnWc0twC15S\nUiNcXN9br6XqWA7G8mp8TCp++O/HSdu8Co2Pt9KhCRcnCbxwGFet33vjjTd48cUXu328d2gMA25+\nlACr5L2pvIgT656gsfhEt57Dv09gj+N0NKmBdy896U9TfQMNDz0FDeadZVThoXgt6N1WwKnaJqLV\nrXysD6LKZC69+bJOR3azht+ENxEnJTW9JjXwytP4+uC3eA5VK99Dq1JR8+Mxjjz8Z0a89GiPb9Tn\nqu+hwj4kgReiC20z73PnzuXyyy+/6HEmIF8dzk+aRFpV7TXAgU1ljDCcYMLNN3XrejHxCcQm9L+U\nkIWwG5PRSMOTL2D8/+3de3hU1d3o8e++zEwmkyshCSFBAiHcbxEEFLUioq19i1qspRe1BVsP1lpP\nPdVq37a+VlvsaftUq+ecvr5afR9rq31aby1Q2loVtQhCUAQaboGQkAvkPpfMZe91/pgwScwFKElm\nJvl9nmeePbP23jMrrKzsH2t+e63KqmiBaeD64iq0cxhRHK9HuMXZxIZwOnvtFACqwzrfq3Nzc3aI\nSzwRZFFikazMCfk8azXwJTMfgJrnN5AxdzoT114f55qJZCYBvBg2yT5ysHTpUm677bY+9/lCFo++\nfYydh7pmmTE0WD5lDBdNnISmLR6uag4bGX0fWc60PYNP/YbIG/+IvXZe/yn0ovHn/PkpmuI6RxvF\nVojNkXQiaASVxn82ufiww+BLY4KkSkrNWZHR98Sx2W5mjmsMC4LRG7f/+f1HSJ9ZwpgLy874PZL9\nGioGl/w5FOIc7a33se7Ff/L3bsF7TqqDWxYVsrQ466y/JhUiUYXfeIfgE8/GXpuXLMZceOZ576ej\nadGUmjXOJnK0riXo3/Gb3FvrZo8s/CSS2MueDlInRdfCURGLXbd8h0BNfZxrJZKV/DUUw+bUwgYj\nRShi81/bavjmH/dT1961VHzZ+HRuXVzI+IyRfZPSqYV8xMhwuva0Dlbiv/8nsdd66SQc/3blkNQl\nT7dY62xirtG1emujpfOjBjfPNjsJ2QOcLGJOLS4kEkNEg8l33ISZkQZAqLGFnTfdTaTdd0bnj7Rr\nqDg3EsAL8S/Yf8LP116q4IUPGrA777FLMXU+MyePa2fl4jKla4mRw66tx3fnd7tuWh2TheuL16P1\nMRXqYHFqsNLRzipHK266IvZN7Q7+vc5NZUj6mEg+zpwsJt3+RejsO+17DlC+5l7sUDjONRPJRv4C\nimEzEvL3wpbN0+8d545XKjja0rUw0+QxbtYtKWL2uLQ41m54SQ78yNJfe9otrfi+8e+oE43RghQX\nri+vRvOkDku9ZhhBvupqYooejJUdj+h8vy6F51schGSSmn5JDnxiSp8+mYlfXhV73bjlPXbf+RDK\nHvirpZFwDRWDR25iFeIMNWlp3P5SBZXdVlR1GhorSnO4oChdct3FiKMCHfi/+X3so9XRAsPA9aXV\n6AX5w1qPdM3ms45Wyq0U/hJJI4yOjcarbU62+01uGRNkeork1YjkkXPpBYSa26j9/Z8BqP3DZlz5\nY5n+/dvjXDORLGQEXgybZM3fi2gm5117B2+as3sE78XZKaxbUsSiCRmjMniXHPiR5aPtqSIR/Pf9\nEGtPRbRAA+fnP40xpXj4K0fXDa5fcTYzQeu656QuovNgg5unmpz4JYbvQXLgE9u4lZcz9vKub76O\n/N/nqHz81/0en6zXUDE0ZAReiH4opdhS2cKeCR8nb1LXcu8OXWN56RgWT8hAH4WBuxj5VDiM/zs/\nIvLO9liZ49pPYM6bGcdaRY3RLW5ytrDTSuG1SBrBznGo17wOygMGX8gKsTjVknnjRcLTNI0JN11L\nuLWd1h17AKj4weOgaUy67fNxrp1IdDICL4ZNMuXv1bQG+d7mwzz42hHCZlfwXjrWzdcuKuLC8zJH\nffAuOfAjy6n2VKEQ/nsf6jHXu7n8EhxLF8Wrar1oGiwwO7jV1cTUbrnxzZbOY40p/KghhZrw6O6f\nIDnwyUDTdSat+zxp0ybFyioeeKzPkfhkuoaKoScBvBDd+EIWT7xbw1d+v493j7XFykNtJylu+ZAv\nzB9HttsRxxoKMXRUMIT/ngeJbHk3VmZedhGOjy+LY636l6HZfMbRyqcdrXiwYuV7gwb31br5dbOk\n1YjEpzsdlNy1pmcQ/4PHB0ynEUICeDFsEjl/z1aKTRWNfPmFvfxudwORzrkhNcBzcj97frKGrOCJ\nUZnr3h/JgR9Z3n/7Tfx3P9Ajbca8/GIcn7wioX/vNQ1mGkHWuZpYZPjRiPZdC42N7Q6+ddzNG14z\nNt3raCI58MnDSHFR8r/W9griD/7kSZSK/vIm8jVUDD8J4MWoV368na+/XMHPtlTR0tG1+uOETBdf\nWVRIVs12rI4zW2hDiGRkNzbR8bP/R2TrjliZecUlOD5xeUIH792laIorHV6+4mzivG43ubbaOk80\nubivzs2ugIEahYG8SA6GyxkN4qdPjpUd/MmT7LlrPXY4MsCZYjSSm1jFsEm0/L2KEz6e2l5L+fH2\nHuUZLoMrS3OYPc6TNMFLPEgO/MhgVVbh+5/fZXptc6zMceXHcFx5WfwqdQ7ydIsbnS3stV38NZxG\nOwYA1WGdn5xIYYbL4nNZISa7Rn5ujeTAJx/D5aTkrjUcfuQZ2j88AED1c6/SUXeSJU/8IM61E4lE\nRuDFqFPV3MEDfz3M11/e3yN4N3WNyyZn8fWlE5hTkCbBuxjxIjs+wPuVu1C1DdECTcPx6U8mbfB+\niqbBLCPIOlcjHzO9OLut5LovaPC9ejePnnBxLCR9XCQew+VkyjfXMGbpgljZydf+wbbrvkZH3Yk4\n1kwkEgngxbCJd/7ekeYA6/9+hK/+YR9vHWmNlesanF+Yzh1LJ7CsZAzOIVwefiSRHPjkpZQi+NuX\n8H39Pmj3ArBXD+L68mocFy2Mc+0Gj1ODS0w/t7kaWWD40enKn9kWMLm3LpVHTrioGqGBvOTAJy/N\nNJj41RsYt3J5rGzrrp28c8WXaHx7ZxxrJhKFpNCIQbVr1y727NnT574DBw5w9OjRQfssh8PBihUr\nyM7OHvC4/Sf8/GZXHW8fbe21b1a+h8tLshnrcQ5avYRIZMrrw//Qz4m81u0/1OlpOFcsw5g5NX4V\nG0JpmuITDi+LjAB/j3j4p50S27c9YLI9YLLQHeHazDDFzpGfWiOSg6ZpjL/+Kpw5mVQ9/SIAoZPN\nvHfDN5h63/+g+LbPyzfFo5gE8GLQ+P1+rr76ajo6Ok5/8CC56aab+PnPf96rXCnF+7Venn+/nh01\n7b32T8lxs3zKGMZnuIajmiOS5MAnH+tgJf57H8KuqomV6UXjcd70GeaOyYpjzYZHjm5xvbONWtvP\nloiH/XZX/38vYPJewGSmy+KTGWHmpiT/YlCSAz8yjF22BFf+WMz/8xyRNi/Ksqj4weO07PiQWT+9\nF2d2RryrKOJAAngxaAKBAB0dHTidTlatWjWkn3Xs2DHeeustmpqaepQHIzavHWrm5T0NHG7q/R+J\nabmpXDopi6LMlF77hBipVMQi9Nzv6XjiWQiFY+XmRQtxrLwKzRxdl4ICPcINzlbqbJMtEQ8V3QL5\nvUGDvScMCh02n0gPc5EngjPJA3mR/NJnTmH6A9+g8rFn8R2MfpNdv+ENWnbuYfZP7yV3+YVxrqEY\nbqPrr7YYFmlpaTz++OO9yt96661Bm4nm1Vdf7ZFTf8IX4tW9J9nwz5O0Ba0ex2rA7HEeLinOJj9d\nUmUGywfvbZVR+CRgHTlG4IGfYu2p6Cp0OnBe/ynM87tGaHcf2Muc0plxqGH8jNMjfKYzkH8nkso+\n24UiGq3XhHX+q8nFCy1OLk0Lc3lahDwzueagfHfPbhmFH0HKa6u44L5bqfnNnzjxl7cBCNadZMcX\n7qLoC59i+v13YKZ74lxLMVwkgBdJS9MNOnJK+O6fD7G9uq3XQi0OXWP++HQuPC+THI+snipGFxUK\nEXzuRYJP/rrHqLteVIDzc9eh5+fGsXaJZZwe4dPONlpsnW1WKrusFEKdczy02Rp/bHPyxzYnc1Ii\nXJ4WocxtYcqovIgD3TSZcOM1pM+cQtWvfk+kLXoTevWvX+Xk69uY/sA3yL/6Y5IbPwpIAC+GzWCN\nvle1dPB2eyZzv/M8LenZvHusrcf+rBSTRRMyOL8wHbfDGJTPFL3J6HtiUkoReXMrHY8+gV1d27XD\n0HGs+BjmsqVoRu9+MdpG3/uSpdtcqXu51PRRbrnZFnHH5pEH2N1hsrvDJMuwuSg1wlKPxcQEvulV\nRt9Hlu7tmbVgFmlTi6l6+g+0bI/ONtRRU8+utfeRc+kFzPjBnT1WdRUjjwTwIik0eEO8friZ1w81\nc7AxAKTjSO95TDZ+ztNayAt64RDsPDQ4n3286sjgvJEQQ8w6UEnHo08Q2Vbeo1wrLMC1+hr0gvw4\n1Sy5pGiKC00/iw0/B20nOyw3h2wndKbXtFg6G9qdbGiHCQ6bpZ4IF6ZGyEmyFBsxvHwdATZve2dw\n33TRZJzZLtLe/AC9I7oCceOb23l7+U2c9+VVTL7jJly5Ywb3M0VCkABeDJuzzYFv8IZ452grrx9q\nZm+Dr89jQi0nOLnjzzRu30SwqbbPYwaLOcpu9DsdyYFPHNbBSjqefK7n1JAA7hQcVy3DvHAh2mnW\nNxiNOfCno2sw1Qgx1QjRYuuUW27et1LwdhuVPxbW+W2Lk+dbHJS6bBa6IyxMtRIiX15y4BODw4he\nO040N3HHz9YPyWd40LneyGWFnoWuaaiIxdEnXqD62Vc4b80qJt32BZw5I3+mqdFEIhKRMJRSHGwM\n8I+jrWytau0cae/N1DVKsp3U/eOP+A7vYiKKifPnAnOHrG5p6RksveLqIXt/If4VkX37Cf7373oH\n7pqGuWQBjo8vQ/OkxqdyI0yWbrNM93Gp6aPSdrLbSqHCdhHpHJVXaOwPGuwPGjzXAhMdFgtTLc53\nW5znsJN+SkrxryvKy2fddTdwsLrqnN6nqa2VMRmZ/e4/DjxxvIFL6iPM1KP93gp0UPn4r6l6+kXO\n+9J1nLfmetyF8k3cSKAppeI/TNCPv/3tb5x//vnxroY4Q42NjZSWljJmzBgOHjx4Ruc0B8LsOu6l\nvKad92raOOkL93mcrsHkMW7mjEtjeq6HFIeslipGJxUOE37tbUK/ewVr975e+41Z03BctQx9vFyk\nh1pQaVTYLnZbKRyxHbEZbD4qU7eZ67aYm2IxO8UiXW7NEUPkd69t5rv/+Rhfn3sxl/sdBKp6fjOt\nGQb5/3YZxV/9LFkLZseplgJg586dLF++/PQH9kNG4MWw8ocsPqz3srOmnV3H2/ucq/0UQ4PibDfT\n8zzMyvfgccpVT4xe1uGjhDe+RmjDX1Enm3rtN2ZNw7HiY+hFBXGo3ejk0hRzjQ7mGh34lMZ+y0WF\n7aLSdmJ1C+ZbbZ0tPp0tPgcaimKnzQyXzTSXxVSXBPRi8NXmuJn+7a/RsmMPtX/YTEdNPQDKsqh7\n+W/Uvfw3MuZMZfwNn6Dg2hWSJ5+EJIAXQ0YpxfG2IHsbfOyr9/PGli348mb0mu6xO7epUzo2lWm5\nqUzJSZWR9gQmOfBDz65rIPz6O4Q3vob1zwO9DzB0jHmzcXxsCXrhuQXukgN/bjyaoszsoIwOgkrj\noO2kwooG8wG6/o4pNCpDBpUhgw3t0eltixzRYH6ay2KKyybXUIOSciM58CPL2banputkXzCHrAWz\naC3fS8Pmt/DuOxzb37Z7P22791PxH48x9vILKbjuCnKXX4QjI20oqi8GmQTwYlDYSlHvi5A1+2Ky\nJ8/mu38+xL4GX49FldragmR8ZOppXYOizBQmj3EzeYybokwXhi7JomJ0UraNfeAw4S3vEn7zH9gV\nfU+lpGWkYS5ZiLlkAZpcbBOOS1PMMoLMMoLYCmqVySHbyWHLRY0ye6XaVId1qsM6f/NGA3qPrpjk\ntJnktJjktJnstMkZpKBejD6arpO1YDZZC2bjrzrOiT+/RdPWXahwBIiu1Hxi81uc2PwWmsMk5+IF\n5H38UnIvX4J7Qv8DA5FIhO3btxMKhYbl51i0aBFut3tYPisZSA68OCtKKZoCEapbOjjWGqSyKcDh\npgCVTQH84dPPh6wBeWnOWMA+MTsFlymj7GJ0UraNXVVDZOcHWO+9T2TH+6iWtr4PNgyMWdMwFszF\nmD6lz7ncReILKI1q20GV7aDKdlKrTOx+cue78+iKQodNocOmKLZVZOoS2Isup3Lgr1+2ggdv/Xq/\nx0V8AVq2fUDjWzvwHTjS73GpxYXkXHoBORcvJOuCOaQUdI3CPfjgg/zsZz8bzOoPqLy8nIkTJw7b\n5w01yYEXg86yFY3+MA3eEHXtIeq8IapbOqhuDVLd2nFGgfopblOnKNNFUVYKEzJdFGakSFqMGJWU\nUqgTjVj7DmDtrcDau5/I3v3g7XuKVAAMHb1kEubcGRhzZ6KlyuhTsnNrilIjRKkRAnyEFNR0BvPV\nykGtbdJB7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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "norm = stats.norm\n", - "x = np.linspace(20, 300, 500)\n", - "posterior_center_means = center_trace.mean(axis=0)\n", - "posterior_std_means = std_trace.mean(axis=0)\n", - "posterior_p_mean = mcmc.trace(\"p\")[:].mean()\n", - "\n", - "plt.hist(data, bins=20, histtype=\"step\", normed=True, color=\"k\",\n", - " lw=2, label=\"histogram of data\")\n", - "y = posterior_p_mean * norm.pdf(x, loc=posterior_center_means[0],\n", - " scale=posterior_std_means[0])\n", - "plt.plot(x, y, label=\"Cluster 0 (using posterior-mean parameters)\", lw=3)\n", - "plt.fill_between(x, y, color=colors[1], alpha=0.3)\n", - "\n", - "y = (1 - posterior_p_mean) * norm.pdf(x, loc=posterior_center_means[1],\n", - " scale=posterior_std_means[1])\n", - "plt.plot(x, y, label=\"Cluster 1 (using posterior-mean parameters)\", lw=3)\n", - "plt.fill_between(x, y, color=colors[0], alpha=0.3)\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.title(\"Visualizing Clusters using posterior-mean parameters\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Important: Don't mix posterior samples\n", - "\n", - "In the above example, a possible (though less likely) scenario is that cluster 0 has a very large standard deviation, and cluster 1 has a small standard deviation. This would still satisfy the evidence, albeit less so than our original inference. Alternatively, it would be incredibly unlikely for *both* distributions to have a small standard deviation, as the data does not support this hypothesis at all. Thus the two standard deviations are *dependent* on each other: if one is small, the other must be large. In fact, *all* the unknowns are related in a similar manner. For example, if a standard deviation is large, the mean has a wider possible space of realizations. Conversely, a small standard deviation restricts the mean to a small area. \n", - "\n", - "During MCMC, we are returned vectors representing samples from the unknown posteriors. Elements of different vectors cannot be used together, as this would break the above logic: perhaps a sample has returned that cluster 1 has a small standard deviation, hence all the other variables in that sample would incorporate that and be adjusted accordingly. It is easy to avoid this problem though, just make sure you are indexing traces correctly. \n", - "\n", - "Another small example to illustrate the point. Suppose two variables, $x$ and $y$, are related by $x+y=10$. We model $x$ as a Normal random variable with mean 4 and explore 500 samples. " - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " \r", - "[****************100%******************] 500 of 500 complete" - ] - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 62, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n" - ] - }, - { - "data": { - "image/png": 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AIBAIBDWMkIsIBAKBQCAQCAQqCLmIQCAQCAQCgUBwCSGMbEGdIrRwAn8RdUUQ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TRBggfJbqN97sTfXwUATY08EC/DSBZkC0ZDnFxAq92wwTxx5hgsWBJDkCTYFSvP9rfeB6JROCaN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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import pymc as pm\n", - "\n", - "x = pm.Normal(\"x\", 4, 10)\n", - "y = pm.Lambda(\"y\", lambda x=x: 10 - x, trace=True)\n", - "\n", - "ex_mcmc = pm.MCMC(pm.Model([x, y]))\n", - "ex_mcmc.sample(500)\n", - "\n", - "plt.plot(ex_mcmc.trace(\"x\")[:])\n", - "plt.plot(ex_mcmc.trace(\"y\")[:])\n", - "plt.title(\"Displaying (extreme) case of dependence between unknowns\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As you can see, the two variables are not unrelated, and it would be wrong to add the $i$th sample of $x$ to the $j$th sample of $y$, unless $i = j$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Returning to Clustering: Prediction\n", - "The above clustering can be generalized to $k$ clusters. Choosing $k=2$ allowed us to visualize the MCMC better, and examine some very interesting plots. \n", - "\n", - "What about prediction? Suppose we observe a new data point, say $x = 175$, and we wish to label it to a cluster. It is foolish to simply assign it to the *closer* cluster center, as this ignores the standard deviation of the clusters, and we have seen from the plots above that this consideration is very important. More formally: we are interested in the *probability* (as we cannot be certain about labels) of assigning $x=175$ to cluster 1. Denote the assignment of $x$ as $L_x$, which is equal to 0 or 1, and we are interested in $P(L_x = 1 \\;|\\; x = 175 )$. \n", - "\n", - "A naive method to compute this is to re-run the above MCMC with the additional data point appended. The disadvantage with this method is that it will be slow to infer for each novel data point. Alternatively, we can try a *less precise*, but much quicker method. \n", - "\n", - "We will use Bayes Theorem for this. If you recall, Bayes Theorem looks like:\n", - "\n", - "$$ P( A | X ) = \\frac{ P( X | A )P(A) }{P(X) }$$\n", - "\n", - "In our case, $A$ represents $L_x = 1$ and $X$ is the evidence we have: we observe that $x = 175$. For a particular sample set of parameters for our posterior distribution, $( \\mu_0, \\sigma_0, \\mu_1, \\sigma_1, p)$, we are interested in asking \"Is the probability that $x$ is in cluster 1 *greater* than the probability it is in cluster 0?\", where the probability is dependent on the chosen parameters.\n", - "\n", - "\\begin{align}\n", - "& P(L_x = 1| x = 175 ) \\gt P(L_x = 0| x = 175 ) \\\\\\\\[5pt]\n", - "& \\frac{ P( x=175 | L_x = 1 )P( L_x = 1 ) }{P(x = 175) } \\gt \\frac{ P( x=175 | L_x = 0 )P( L_x = 0 )}{P(x = 175) }\n", - "\\end{align}\n", - "\n", - "As the denominators are equal, they can be ignored (and good riddance, because computing the quantity $P(x = 175)$ can be difficult). \n", - "\n", - "$$ P( x=175 | L_x = 1 )P( L_x = 1 ) \\gt P( x=175 | L_x = 0 )P( L_x = 0 ) $$\n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Probability of belonging to cluster 1: 0.025\n" - ] - } - ], - "source": [ - "norm_pdf = stats.norm.pdf\n", - "p_trace = mcmc.trace(\"p\")[:]\n", - "x = 175\n", - "\n", - "v = p_trace * norm_pdf(x, loc=center_trace[:, 0], scale=std_trace[:, 0]) > \\\n", - " (1 - p_trace) * norm_pdf(x, loc=center_trace[:, 1], scale=std_trace[:, 1])\n", - "\n", - "print \"Probability of belonging to cluster 1:\", v.mean()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Giving us a probability instead of a label is a very useful thing. Instead of the naive \n", - "\n", - " L = 1 if prob > 0.5 else 0\n", - "\n", - "we can optimize our guesses using a *loss function*, which the entire fifth chapter is devoted to. \n", - "\n", - "\n", - "### Using `MAP` to improve convergence\n", - "\n", - "If you ran the above example yourself, you may have noticed that our results were not consistent: perhaps your cluster division was more scattered, or perhaps less scattered. The problem is that our traces are a function of the *starting values* of the MCMC algorithm. \n", - "\n", - "It can be mathematically shown that letting the MCMC run long enough, by performing many steps, the algorithm *should forget its initial position*. In fact, this is what it means to say the MCMC converged (in practice though we can never achieve total convergence). Hence if we observe different posterior analysis, it is likely because our MCMC has not fully converged yet, and we should not use samples from it yet (we should use a larger burn-in period ).\n", - "\n", - "In fact, poor starting values can prevent any convergence, or significantly slow it down. Ideally, we would like to have the chain start at the *peak* of our landscape, as this is exactly where the posterior distributions exist. Hence, if we started at the \"peak\", we could avoid a lengthy burn-in period and incorrect inference. Generally, we call this \"peak\" the *maximum a posterior* or, more simply, the *MAP*.\n", - "\n", - "Of course, we do not know where the MAP is. PyMC provides an object that will approximate, if not find, the MAP location. In the PyMC main namespace is the `MAP` object that accepts a PyMC `Model` instance. Calling `.fit()` from the `MAP` instance sets the variables in the model to their MAP values.\n", - "\n", - " map_ = pm.MAP( model )\n", - " map_.fit()\n", - "\n", - "The `MAP.fit()` methods has the flexibility of allowing the user to choose which optimization algorithm to use (after all, this is a optimization problem: we are looking for the values that maximize our landscape), as not all optimization algorithms are created equal. The default optimization algorithm in the call to `fit` is scipy's `fmin` algorithm (which attempts to minimize the *negative of the landscape*). An alternative algorithm that is available is Powell's Method, a favourite of PyMC blogger [Abraham Flaxman](http://healthyalgorithms.com/) [1], by calling `fit(method='fmin_powell')`. From my experience, I use the default, but if my convergence is slow or not guaranteed, I experiment with Powell's method. \n", - "\n", - "The MAP can also be used as a solution to the inference problem, as mathematically it is the *most likely* value for the unknowns. But as mentioned earlier in this chapter, this location ignores the uncertainty and doesn't return a distribution.\n", - "\n", - "Most often it is a good idea, and rarely a bad idea, to prepend your call to `mcmc` with a call to `MAP(model).fit()`. The intermediate call to `fit` is hardly computationally intensive, and will save you time later due to a shorter burn-in period. \n", - "\n", - "#### Speaking of the burn-in period\n", - "\n", - "It is still a good idea to provide a burn-in period, even if we are using `MAP` prior to calling `MCMC.sample`, just to be safe. We can have PyMC automatically discard the first $n$ samples by specifying the `burn` parameter in the call to `sample`. As one does not know when the chain has fully converged, I like to assign the first *half* of my samples to be discarded, sometimes up to 90% of my samples for longer runs. To continue the clustering example from above, my new code would look something like:\n", - "\n", - " model = pm.Model( [p, assignment, taus, centers ] )\n", - "\n", - " map_ = pm.MAP( model )\n", - " map_.fit() #stores the fitted variables' values in foo.value\n", - "\n", - " mcmc = pm.MCMC( model )\n", - " mcmc.sample( 100000, 50000 )\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Diagnosing Convergence\n", - "\n", - "### Autocorrelation\n", - "\n", - "Autocorrelation is a measure of how related a series of numbers is with itself. A measurement of 1.0 is perfect positive autocorrelation, 0 no autocorrelation, and -1 is perfect negative correlation. If you are familiar with standard *correlation*, then autocorrelation is just how correlated a series, $x_\\tau$, at time $t$ is with the series at time $t-k$:\n", - "\n", - "$$R(k) = Corr( x_t, x_{t-k} ) $$\n", - "\n", - "For example, consider the two series:\n", - "\n", - "$$x_t \\sim \\text{Normal}(0,1), \\;\\; x_0 = 0$$\n", - "$$y_t \\sim \\text{Normal}(y_{t-1}, 1 ), \\;\\; y_0 = 0$$\n", - "\n", - "which have example paths like:" - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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9YwFNdh1vRG/Bf3/Qwl1VyFLI8MSn5iM7UY7NCzLQpjKgQamDnQWOdajHlaNE\nXyYcEE5I5f8+CCGETB9lwgnxwZ8axfp+LRewFqbEIm8aZQv8BXuaBvV49bxS8PgFXja6vt+9Oufm\nBen45rpiLgAHgLgYCa4pdgeuR1pH/BrDM8e70THqyFDHShkkxzomKZqsdlwZEq9XdPuIEa4wvzAl\nTtD+L14mxZaF6dz2+5fFKUmpahnBmMlRY54SF8MF4C7r56Zytw+3jAiCzkhasl7M2lr+KqH9FIST\nIKKacBKNKAgnZBrOCLqiTC9bm88L9FQGK8zjstH8wJt/e1me94WBNsxL424faRudtCSl6ooK+3k1\n2LuvK8KaIvfPdIH3ntPFn5Q5Nz3O4/FtCzO42+d6x0QpSanpcf+tPrc6D0Wpwvet5AXhdX1aru97\nSlwM4qKsR7gLZcIJISR4ovOThRA/+FOjeKaH3x888FIUAEiMjZlwkR9X4G2zs7ionHx1zjWFyVx3\ni16NacKJdd1qI56qdteBbyxNw7aF6ajg7VvMunB+EM6f/OcyJy0OafGO38WYySZ4fiDMVjvq+9xf\nIq4q8PxbZSnkWJLj2dkm0parF7O2lp8JV45REE6Ch2rCSTSiIJyQCbAsi0MtKrzXOATbuHYaA1oz\nOkYcpRsyKSMIWAOVnywM+K4rSYGrDLt12IAxkxUtKgP0zjaEmQqZz/Z58hgJri1J4bZ9laSYrXb8\ntKqdq5UuSI7Fw9cXgWEYQYB/QakVbZJkyyRBOMMwggz/ud7pZeEbBnRc2VBBcixyfZQN8UtSXHIi\nqD2h2FLjYyCTOg5ArdkWtJaRhBASjaYdhI+OjuLuu+9GWVkZysvLcfLkSTHGRUjIVVdX45MuDR4/\n1IHfVnd5LKV+lpcFX5qTyC3yMh38mvK4GAm+dl0R5mc4Fk1hATQodYKykIrcxAkXUBGUpLSOYkBr\nhskZbNtZFkarHX862cO1C5RJGfz3pjlIkDt+lqKUWC47P2aycV86poNlWbTxOqPM9RKEA8DyPHe2\nuo43+TUQNbyyoYkmz1Z6CcIjbaEeMWtrJQxD2XAyI6gmnESjaXdHefjhh3HzzTfj9ddfh9VqhU4n\nfiszQkKF3wLwSOso7lqazW3z68HXTLMUxaU8R4GPWhwZ6/tX5iJDIcOyvEQ0OSdF1vdpBQv5TJZ9\nv6ogCYlyKbRmG5RaM+5/uQEAECNhYPXSKPvLawtQmuFeKZFhGFTkKlDd7ljF8kK/1mfQ7K9BnYXL\nqCbKpciwwNxaAAAgAElEQVRSeG//tyJfWApjs7OQBtidhf+FaZWXUhSXLIUc5dkKXBxwn8cirRxF\nbNmJcq5Lj1Jr9qvLDiGEkMlNKxOuVqtx9OhR7Ny5EwAQExODlJSUSV5FSGSorKwULCjTOKjDmMnR\nFtBmZwUB+uqi6bfQA4BtizLwpbUF+Pr1RbhnmSPg5wfa5/u1gkmZFbkTr84pk0qwzkt211sAvm5u\nqqBftvs9+MGw+731ZltA5SmtgkmZ8T4z+QXJschIcAToOrPNY0Eif40aLFw9vIQRZti92TBP+PuK\ntHIUsWtrBZlwmpxJgoRqwkk0mlYQ3tbWhqysLDz00ENYtWoVvvCFL0CvF6+NGSGh5CibcAd+dtbR\nrxtwBOSubG5mgkzQ53o65FIJ/qMiG7eWZXLBKX+y4OVBPTS8NnvFfrzv567Kw8bSNMxLj0NGgkzQ\n61suZZAUK8XaomQ8sq7Ya0AsqAvv14FlWbxSp8Q9L9Zj52sXoXb2K/eXcFKm7/EzDIPl/LrwAEtS\nann15GXZCijkE5cNjS9JibRyFLHxg/CpdEjRm20w2zxXeiWEEOIwrSDcarWipqYGu3fvRk1NDRQK\nBZ544gmxxkZISL1fdYQLeF3OdDkCQf4qmasLkyesy56u5LgYzE3zDFaX5ij8et+0BBm+t3EO/vTp\nMuzZsRTvPrQc73xuOfZ/fgXeeWgF3vjsMvxka6nP4HReejzXZWVIb8EThzvwl9O9sNhZ9GrMeLN+\nYEo/T+uwMBM+keX5vLrwACdn8lsTeuuKMl6WQo7KOY4rerlJco9WhuFO7NpafptCfzPhR9tGcdc/\nzuPzr12iyZzEL1QTTqLRtGrCCwsLUVhYiDVr1gAA7r77bq9B+O7du1FcXAwASElJQUVFBXfpyfWP\nR9u0HW7bfWMmaFrOAQCSS1cAAD44dARrmDk4o3KUimhaziE2ORdAcVDHsyyvBG0jRsF4KvISZ+z3\nUZ6TizPdY9C0nMNbLe7fh6blHP7ZKcFnVtyPeJnUr/2dOtEO5C4BAIw2n0P1UJzP55vbz0PT0o7k\n0hW4oNTiyMdHIZUwfo//6NGj+PBQO1CwFACAngZU61smff2jG67F1oVajF45h5PHj4XF8ejvdn19\nvaj761UZADjKlM6fPonq2J4Jn2+3s3i2Nw0sgOa6T/BXSQe+du/NYfP7oW3apm3ans6263ZnZycA\nYNeuXQgUw062gsck1q9fj+effx4LFy7ED3/4QxgMBvziF7/gHq+qqsKqVaum8xaEhMRr55V47pNe\nj/t/dcsCPPpuM1g4aoxfu78CSbExQR3Lx60j+OlH7YL7fn/nIizMTPD+ApHtOdePv53pE9wnYRwl\nOgDw1WsLcceSrEn3Y7LacccLdbCzAANg74PLJuwqw7IsPvtKAwa0FgDAU7cvRFn2xHXwfJ0jRux6\n4xIAQCGX4vX7KwKe3BmtBnVm3LfHMaE3JS4Gr91fMeHzxx+rn1+Tj/9cnhPMIRJCSMjU1NRg06ZN\nAb122i0Kn376adx3331Yvnw5zp8/j+9///vT3SUhYYFfuyzlxW3PfdLDLbm+OEsR9AAc8FyQJ0Em\nQek0u5RMxfguLJ9yTiB1efPCANdHfURvwT/O9uFo26jHfjpGjVzgnp8cO2lbR0dduLuE5Fzv1OrC\nz/JKUVbkJVIAHoD0eBl3/KuNVhgsE5eXvHFBWJ40qKPJnIQQ4s20g/Dly5fj9OnTqKurw5tvvknd\nUciscfL4ce72xvnp3O3Lg+7Jx9NdJdNf6QkyFKa4e4iX5yhmNKAsz1Ggck4K4mIkeGBVLr5RWYRt\nizKQFOsIovvGzDjRoUaP2oiv72vCi7X9+GlVm8dKl20q/+vBXfiTM+v6plYXzu9gc1WhOB1swh3/\nkqkYpBJGMDl10HlVwpuLSh0uDQgn50/0fEJcxD5uCYkEwU/hERKGbHYWHSNGFKbGQi71/C5qtbNQ\nas1QONuC31ORjYPNKo/nrZ7BwK4iN5Hr1yzG6pxTIWEY/M9N8wS9uuNlUty6OBN76pQAgBfO9kFt\ntGLU2S2FBXC+T9hXvNXPzih8/Ex4g1IHi80OmZe/2Xg6sw01vMy5P5MyiXfZiXL0ORfq6deaUOxl\nojDguCIyHmXCCSHEO1q2nkSl31Z34sv/bsSX32zEsN4zU9etNkIxbzkAIDtRhrnp8R7tAJNipVgw\nQzXZAPCfy3NQkhqHsuwEr/28Z8L47PvtS7Igc97XMWrkAnCX1nGZ8Kl0RnHJSZJzC+aYrHau5/dk\nTnSoYXEuVV+aEY+8ZO9L1c82rklEYuIvWDTgI7PdP2ZCdbtnCdKgjjLhZHLBOG4JCXcUhJOo06cx\n4YMmR1a7W23Cf+1vgdYkDB4FZRNpjmBxfOnJVQVJM1oSkp8ci+fuLsNTty+akTp0f2QkyHDj/DTB\nffxfibDPOovmIXepwvwM/7/A8Cdj+rtoz5HWEe72+AV4yNRkC5auN3l9zt6GQa7ef3leInccqI1W\nmK3UL5wQQsajIJxEnf2XhwXbrSoD/vdAG0y8QKFV5W4H6MrYji89mclSlHD2HxXZ3MS99IQYPL5t\nPvdY24iRW1WzT2OG3uL4HSfHSpGd6H25em9KeUulXxmefEGwMZNVsFT9hrlpEzx7dglGbe1kq2aO\nGiyC/6t7lmVzq50ClA0nk6OacBKNKAgnUcVmZ/FB87DH/fX9Wjx+qJ3r8NHuZQJhRW4iYp3RJgPg\nqgIKwgFgTlo8frK1FPevzMXTdyzCyoIkpMU7MvUmqx19GkfQxg+e52cmTGmBI34nGH8y4Sc61LA6\n/5YLMxOiphQlWISrZnoG1M+e6uG+YBWnxmF1YTKyFLzJnFQXHvZGDBaMjbsiSAgJLgrCSVQ51aWG\nSu/4oEmPj8FDq/O4x453qPFibT8AR3bctSCNawJhbIwEX7m2EDmJcnxudR4yFP5ncme71YXJeOCq\nPC7w4td7u0pS+KUoU62ln897fpvKwH1Z8uUwrxRlfZSVogSjtpa/ama/VliOUtOjwcEr7t/3F9fm\nQ8IwyErkZ8IpCA9ndb1j2P7SBex46QJ61MaQjIFqwkk0oiCcRJX3G91Z8C0LM7B9RS7ursjm7nv5\nXD/O92m5y+cyCYPCFPeEzJsXZ+Kfn1mC7StyZ27QEWiel44owiB8aj3OU+JikOn80mO2seiaIFDQ\nGK2ojdJSlGDJVMi5Gm+V3gqzzZH1Nlnt+N2xLu55G+al4uoiR5taQSac2hSGtfcuD8POAiYbi0Ot\nnpNrCSHBQUE4iRoDWjNOd7sXb9m2KAMAsOvqfCzJcUz8s7HAT6raADiWZC9Oi6MFXgIwl9d+sE1l\nAMuygq4mC6YwKdOFX5JyZch3Scqx9lE4m6JgcVaCIIsbDYJRWxsjYbgvQQAw6KwLf6m2H73OcqNE\nuRRfuaaQe06WgjLhkYK/9kFviDLhVBNOohEF4WTWsrMsOkeNGHG2IPygaZjr3rAyPxH5zjphCcPg\nm+uKuVZ7al6bPX/b6BEhfia8bcSAfq0ZYybHSotJsVJByzt/8UtSxrc+5DvCW6lzwzzKgosle9zk\nzNZhA149r+Tu+/zV+UjnTcbM4j1/iCZmhi2N0YpejbvEyLUWASEk+MKjzxkhQfCH4914+9IQAEd7\nP/6ko08tEvbZLk6Nw46VuXjhbB93X3LpCszzsSgJmVhRahwkDGBngV6NGfW8lS7nZ8RPaVKmiz8d\nUkYNFsHS9uvmRlc9OBC82trcRDkuQAcAqO/X4cOmYe6Kw9IcBT7lvLLkQpnwyNA0JPxf6labwLJs\nQP+j00E14SQaUSaczEpdo0a84wzAAaBXY+IyscmxUlw3J8XjNfcuy8accUH3HMqEB0QulaCIt7jR\nAd5qo1PpD843P0PYIYVlPSdnHm4d5a52LMlRCLK3ZHr4v8t/1fZz8yZiYyT4RmUxJOOCNmF3FMqE\nhyt+KQoAaM02aJznSkJIcM3aIPxkpxrf2NeEfRcHQz0UEgKv1w/AV/+MW8syvS5VL5NK8Mi6YrhC\nCU3LOUEdMpkafklKHS8THugqozmJciTKpQCAMZPNa2D3QZN74u2NpdFZihKs2tqcJM82jzIJgx/e\nNNfrMvap8TGIcZZ4jZlsMFgosAtHTYOeV5W6Q1AXTjXhJBrN2nKU3x/vwoDWgqYhPTaWpoXNCoMk\n+Eb0Fhy84s68Pr6tFPEyKS4O6BAXI/G4bM63OFuBL19TgD3nlFg9Lw1pCdSGMFBz0+NwqMXz/ql2\nRnFhGAalGfFcQH9lWC/Izl4Z0nM9xOVSBhujNAgPlpxxiytJGOD7N87BVT4WrZIwjsmc/WOOUpRB\nnQXFqdKgj5P4j2VZXB7UedzfozZhSU5iCEZESHSZlZGpxmjlFpSw2ln0jZkpCI8iey8OwuIsVl2U\nlYBVBUlgGAblOYpJXulw19Js3LU0G0BFEEc5+83zchUhQSaZ1sI5giB8yIDrStw13/wseOWcVCRG\n6f98sGpr+a06AeDb60tw/ZyJa+6zFHJ3EK41oziV5liEkyG9BSqD5wI9oZicSTXhJBrNynKU8SeQ\ngTGaFBQtDBaboBb8nmXZMz7BiDh46yyzIDPBo3Z4KviTM1t4HVLMVjs+anEvGLN1gqsdJDDZiXJ8\ndlUu5qbF4bEbSnDTgvRJXyOcnEl14eHm8oD3Cc7UIYWQmTErg/DxC3kM0Mz8qLH/8jA3ATM/WY7r\nSwLvjkE1itOTmSBDUqyw/IA/uTIQ/EmdLbwOKcc71NzfPSdRjuV50XspPZjH7WdX5eHP/1GGG+dP\nHoADwiB8iM7DYYdfirIs1/0/E4pVM+l8S6KRKEG4zWbDypUrcdttt4mxO7+NGix4++IgOkeFJ4yu\ncdsDWjr5RwOd2YY3Lgxw23dX5NBCOyHEMAzmpgmD7kAnZboUpcZBJnX8TQe0FmicPd35pShbF6ZP\nK9tOxMPvFU6Z8PBzmdee8Mb57jkUPRoT7F66DxFCxCVKEP7UU0+hvLx8Ri/7syyLHx5ow9PHu/Ht\nd5phtNq5x7pGx5WjUBA+q5ltdrx5YQCfe/UiNxcgJS4Gm/24XD4RqlGcvvElKdMNwmMkjKCNZIvK\ngAGtGTXOZeoZAFsWRncpSjgdt8I2hXQeDid2lhV0RlldmIyUOMc8CrONnfEFlsLpuCVkpkw7CO/u\n7sZ7772HXbt2ee3bGyznerW4OOC4lDZqtApOJh7lKFrKwMxWLcN6fP61S/jTyR7BSpf3rcxFbMys\nrLaKKPN4y9fHyyQoSAl8UqYLvyTlzye78b33r3DtKFcVJFFv8DAiqAmn83BY6VaboLc4kldp8THI\nUshQwJs03UN14YQE3bSjlG9+85v45S9/CYlkZgOe1+qVgu0mZ22b1c6iTyM8eSgpEz4rsSyLn33U\nLvj75iTK8Z0NJbijPHOCV/qHahSnb3G2uyNNebZClDIR/uTMVpURXbxgYWuUZ8GB8DpuheUodB4O\nJ/x68IWZCWAYBoW8L8kz3Ss8nI5bQmbKtHp4vfPOO8jOzsbKlStx+PBhkYY0udZhA850jwnucy29\n26sxcUspu6iNVpisdsqMzjJXhg3cLP5YKYOda/Jxi4+FeEhozE2Px1euKcAFpQ4PrMoVZZ9ripIh\nkzJcG0qXsuwEryuhktBJjpVCLmVgtrHQW+zQmW1QyKlXeDjgr5S5yPllmX+lqltDmXBCgm1aQfjx\n48exb98+vPfeezAajdBoNHjggQfwj3/8Q/C83bt3o7i4GACQkpKCiooKrv7L9e13Ktt7zvUDcaUA\nHKsaAkBT8tUAgPcOHoampQ/JpSsEjw/qylCYEhfQ+9F2eG4faR3h/r6f3roRdy3NFnX/lZWVYfXz\nRup2FoAfbBJ3/7+7fRUuKnXovHAGibExuOmGdchPjsWxY8dC/vOGw7ZLqMdz7NgxoLsdyFsCwHF+\nzkuODfnvh7YrcXlQz50/F211fJ6ONJ/jPj971KYZHQ+db2k7HLcvKLWoMhSgPEeBG2K7IXNWfVRX\nV6OzsxMAsGvXLgSKYUUq5D5y5Ah+9atf4e233xbcX1VVhVWrVonxFgAckywffKWBy3YzAFcP+sZn\nK/Bu4xD+errP43WPbyv1ubIbiTwsy+KBVy5ypSg/3jIP1xRTFpSQcPPou83cAks/21qKNUV0Hg41\nq53FHX+vg8Xu+PR8/f4KJMfFoE1lwJfebAQA5CfH4u/3lodymISE3CNvN+GC0lG69f+uK8Tt5Vke\nz6mpqcGmTZsC2r+o1+1nojvK3oZBLgCvyE3EfN4S2E2DekFnFH53ugFqjzWrXB7UcwG4Qi7FVQVJ\nor/H+KwiIZEg3I5bqgsPP4NaMxeAZyTIkOzsipLPm5jZP2aCxWb3+vpgCLfjlhAAGNa7Y8c955Qw\nW8X9nxAtCN+wYQP27dsn1u680plteK9RuBriokz3xK+mIb2gR/jiLPdjgzQ5c1b5uG2Uu319SQpk\nVAdOSFiiVTPDz/jJ7C6xMRLu72VngX5abZpEOX7XtWG9Be/yYlAxRFTkcrRtlGupVJwah6uLkrEg\ny92urGlQL+iUsIqXHaUOKbOHnWVxpNW9RPmGeWkTPDtwrrowQiJJuB23gl7hdB4OC/y1M3KShC09\nhR1SZm5yZrgdt4SYbXYu5nR5pU4pWJdmuiIqCK/rc3dE2bLAsSreQl45Sm3vGHRmx9LVCTIJynjt\n0WjBntmjcUDPZdSSYqVYGYRSFEKIOLIT+ZlwOg+HA35Sanxf/YIUd2//UCxfT0i44GfBXVQGK965\nJF42PGKCcJZlUder5bZX5DsCrzlp8ZA7l7Hmf2MpSo0TXGajIHz2ONLmzoJXzklFTJCWpqcaRRKJ\nwu24zUtyZ1YvDui5RAkJnQEf5SjAuEz4DLYpDLfjlhCNlyAccGTDDRZxzmMRE4T3aswYchbIJ8gk\n3IIdUgkjWEHPpSglFlmJwlpE+wyu6EmCw86yONrqrgdfPzc1hKMhhEymMCUWJWmO7KrJaheUkpHQ\nEGbCZYLH+EE4rZpJotmowR2El2cruPkSaqMVb18UJxseMUE4vxSlIjcRUl72c2GWlyA8NQ7xMimS\nYh0LQ1jtLEYM3r/VkMhR16vlvoylxMVwV0SCgWoUSSQKt+OWYRhs461kuv/yMHfbYrPjxwdbce+L\n9RScz6CJMuEFye5yFKoJJ9GMX46SqZBhx0r3gnOvnldCL8JVvZhp72GGuPrMAsDyvETBYwszvWXC\nHSeSnEQ5xkwGAI4TT0aCzOO5JDKwLIsXa/u57fVzUwVfxggh4emmBen4y+leWO0sGgf1aB8xYE5a\nPN64MIDqdjUA4JdHOjAnLQ4lafGT7M3hQPMwTndpECOVIE4qQZxMgutLUrAkN3HyF0cxO8tiUOvu\nUjO+JpyfGR8xWGCzs3SeJVGJH4SnxMVgy4J0vHxOCQC4b2Uu5CKswh4RmXCWZQWZ8GXjsp/egvDC\nVMcltSyqC581anvHUN/v+DImZYC7l2UH9f0iqUbRZjCh/blX0PPq+xBp/S0SocLxuE2Ji8F1Je7F\ntPZfHsaA1ox/1Sq5+8w2Fk8c7oDZj97ULcN6/PJIJw63juJgswrvNA7h9foBfOf9KxiiyZ8TGtFb\nuR7hybFSxMukgsdlUglSnX3D7awjEJ8J4Xjckug2PgiXSSX4+bZS/PWeMmxblCHKfLSICMJ7NCao\n9I5fhkIuRWm6MFNSmBqLeJn7R5Ew7kUHaHLm7MCyLP5+xr0S6rZFGYIJX9Gu65970fiDp1D/9Z9A\nVX021MMhxMO2Re6SlIPNKvz+eBdM41p9tQwb8I+znisej1fbM+b1fouNRX2/bnoDneUm6oziksHr\n7T5Evd1JlBofhAOOUmcx1yWJiCCcX4pSkavwuDQmYRgs4E3OzE2Khdz5S8rmnUwoCI9cn3Rp0Dio\nBwDIJAy2r8id5BXTF0k1iurai+7bdY0hHAkJtXA9blfmJ3GlDhqTDSc7Ndxjmxekc7dfOz+Aul7v\nQbaL61wAAFsXpuOa4mRuu1VlEGvIs5KvhXr4Mnllm/wVA4MpXI9bEr3URnfNtysIF1tkBOG8E/Ky\nPO8T8fiTM4t4s7uzBZlwx8lk38VBbH/pAp471UOX7iMAy7J4gZcdu3lxps8MTrQyD7kntZmHRyd4\nJiGhIZUw2LIgw+P+zQvS8a31xbjK2e+fBfDkkY4JW4BdGnBnu+8oz8KNpe4gvnU4coPwmfg84iej\nspO8n0fTQxCEExJuBJnw+CgNwlmWxfkJJmW6rC1yZ0L4i7fwgzWl1oxutRHPnOjGsN6C1+oH8OaF\nwSCMmojpWIcaV5wfrLFSBp9ZkTMj7xtJNYqmQRV326KiIDyahfNxu3VhBvjXMRVyKXatyYeEYfDt\n9SVcN6tBnQWfdGm87mNYb+EW64qVMpibHo95vBLFtgjNhL96Xom7/nEez57qCer7+JUJ511BHp6h\ncpRwPm5JeGPt4q1gyScIwmOjNAjvUpugcrYWTJRLBSdbvuX5SfjR5nl4ZF0xbivL5O7nB+GDOjP+\ndqYPdl6y4blPerjJfiT82OzCWvDbyrOow40XlAknkSAnSY6rCt1JkodW5yHN+f+coZAJzt38MkS+\nRl4WfEFWAqQSBgUpsdyibUN6i89FNsKV1c7iH2f7oLfY8Xr9QFBLJwf8qQnnnWOHKBNOwhTLsqj9\n/PdRtWgrev/9oej7j9pMeOeIEVVXVKjtHcPHbe6AYnx/8PGuLUnBtkUZgqL51PgYyJwn5zGTDUfb\nhAGKnQV+9lEbVHSiCUvvNg6hc9SxdHK8TIJ7g9wRhS9SahRZmw1mlZrb5t8m0Sfcj9tH1hVjY2ka\nHrwqD7cszhQ8tpzX+eq8H0H44iwFAEepyxxea8NIqwvvGDHAbHNnh2p8TDwVw5Qz4VFcEz505BNU\n33A/Gn/4dKiHQniuDOnRP2bC6JkLUL57GNYxHdr/uEfU97DZWYyZPCdmii3s+oT3qI34yr8buRZK\nfMvzp97/VcIwyFLI0Ttu+d2V+YloGTZAY7JBpbfi5x+14xc3zxetH6pROQSJVAp5Zpoo+wsWvdmG\n2BhJWPaBHTNZBbXgO1bkIjWesuDjmVVqgHc5jspRSDjLVMjxvY1zvD5Wlq2ATMLAYmfROWqESm8R\n1CcDwkmZi7Pdc4HmpsehacjxWKvKENSFvMTWNCT80lDToxF0kxELy7ITLtTjws+Ez1Q5SjhqfvzP\n0Da2QtvYisL7b0fi/JJQDynq7bs4iN8f7wYA3HnpBOY57zcph32/KABas42rmlDIpaK0I/Qm7DLh\nJzs1XgNwwHc9+GTGL8srYYCvX1+ExzbO4eoTz/drsb9JnD/iyOl6HFl1Fw6tuB2ahmZR9hkMxztG\ncc+L9bjnxXo8/0kPBsOsv+6Ltf0YMzkmZ+UmyXHXkqwZff9IqVHkl6IAVI4S7SLluPUmLkaCRbzA\nenw23GZncZkXhJdlK7jb/FLFSJuc2TykF2zX9mphD8IkzTGTDQaL4wt7XIyEq8EfLyMEEzPD8bjV\ntXRytw2dk7fOJMHHr2YwNjRxt03Do6JObFYbgp8FB8IwCO8YMXK3c5PkyFTIEBsjwa2LM33Wg09m\n/Lf9mxdloiAlDqsLk/Gfy92T/Hxd/pyqvjc/BGuzgbXa0Pv6B6LsMxjevTQMi52F1mzDq+cH8MDL\nDXj8UHtY1FN2jRqxr8E9afYLVxeIsjrVbDQ+CLeO6WA3R2/2ikS2FXm+S1I6RowwOnuLZyTIkKVw\nn9sFQXiElaNcGReEq43WoEwwHZ8FZxjv2b3kuBgu86c127jfeTSxqMdgHXOXPpkGxM20ksD0qN1V\nDdm97i9JsFph0+m9vCIwal4pSmo4B+FdXV3YuHEjlixZgqVLl+J3v/vdtPbXPuI+8XyjsggvbV+K\nfQ8uw9cri3yeMCbDP1HHxkhw3yp3j+mreV1VXLXH06Xv6OVuj126Iso+g6FHI/x5bSxwqGUEPzrY\nFvLWjc+e6oGrRLIiNxGVc1ImfoEPdlPg2f1wrFH0xjSk8rjPTCUpUStSjltflvGueJ7rE9ZGNw66\ng6KybOFKyfMy3EF4x6gRNh9XVMONzc56/dJwNgh14f4s1AM4yjhnuiQl3I5bQ3e/YJuC8NAzWGzc\nROE4sxEZg0rB4yN94v2NIiYTLpPJ8Jvf/AYNDQ04efIk/vCHP+DSpUsB7YtlWUEgXOKcaBNo8O2y\nJMd9yfLeZdmCk0txahx3u0ukE7e+w91iaqwhPINwq51F/5j7hFyR6/7gq+/XhrRjTNOgHqec7ckY\nAF++piCgY6D9uVdwYP5NOPfFH4g8wvAyPhMOABaanEkiVHm2gptM3602CcohGgd49eBZCsHrkmJj\nkOWcUGixsehWi5NUCbaOEaNgUqaLt8mZdtYxWaxHbQyoTMSfenAXYUlKeJUqzgTjuCDcTEF4yPHn\n9i1WK8GMSxY2Xukf/5KAjfIqApLjvJdtiWHa4X1ubi5ycx2Z5cTERJSVlaG3txdlZWVT3tegzgK9\ns14tKVaKdJFawqwqSML/3DQXerMNN/FWZgMcl91S42IwarTCbHNMWslLDnw5dNZmg6HTnQk3D6pg\nGlQhNit9glfNvP4xEzfpIFMhw69vXYDfHO3E+5cdJ5qX65SChZFcmfHpfiHyxzne4kzr56ViQWbC\nBM/2rf2Pe8BarOjfVwXd974ExdzCKb2+uro67LIz3pgHPYNwyoRHr0g5bn2Rx0hQlqXAeWci4Hyf\nFhtLHRPcL/Ey4YuzPc8L89LjuR7irSoDl8gJZ83D7i8WCzLj0eycpHmhXwuz1Q55jARvNQzilfNK\nqPQWQYvdvCQ5luUlYlGWAlqzFX0aMwa0ZqTFx+C28ixBzTwwLhOeNPEk94wZ7pASbsetoWt8Jtzz\niiOZOjvLQhJgHNHNK0WZM+jZT7+lRYl1AY9MiF+WG8xyFFH33N7ejtraWqxduzaw1/NKUUrS4kQL\n+I8GmA0AACAASURBVBiGQeWcVJ+PF6fGYdR5wu8cNU4rCDf2DYK1CGuqxy5eQeyGqwPeZzDw66oK\nnD/vvcty8EHTMOwscKZ7DFeG9JifmQCtyYofV7XhklKHhyuLPb7IiI1/yXllgB0O7FYrjP1D3Lax\nu3/KQXik8JYJNw9REE4i17K8RC4Ir+sbw8bSNOjMNnQ65wxJGHj9cj4vPZ67itY6bMDG0pkbc6D4\n9eDXlaTCYLGjW22C2cbigtLxO/jDiW6vr+0bM6NvTIUPmjwDxINXRrAyPxHbV+RieV4iGIYJOBM+\nFIUdUjzLUYZ8PDO8GK12/OlkN2x2Fl+5phAJ8uBlcaeCZVk8eaQD1e1q7FqTjzsCaLTAD8Kzezo8\nH+8Sb/FFQY/wSAjCtVot7r77bjz11FNITBR2Mdm9ezeKi4sBACkpKaioqOC+8bpmRFdWVqJjxAhN\nyzkAwJzFN3k8HqxtW/cAEDMXAPDhoY9hKU0LeH+H3n4PjXYdyiWODMRFuw5j77yHe5xB+HsHD+NY\n+yiWrr4G9y7LwYnjx0T/eYYOnURJuwpzv3o/LuhVXp8/kLoQAKBpOQezORnAAhSkxGKO7grO9WmR\nXLoCr9QpcV1MF577pBdDaYsAAD9+4W2YbyjBzTfdELS/x7HqNqBwKQBA21qH6qHYKe9vdekiwG7H\nRbsjoF/ao5zyeCorK2fk+JvudlNjA/Lh4Pp5y5zlKOEwPtqe+W2XcBnPVLdXlC7Hi7WO81NVvwzf\nqLwfTUN6qJ2fDyvWXIt4mdTj9bq2Omha+pFcugKtKmPY/DwTbR891gVkLAYA6NvqkDasQ7fz8+jv\new84khKFFQAcv4+4GAmKl67GiN6CwaZaAEBy6Qrucf72kaPVOHIU2H7LJnz9+iKcP3MSGrUJyaUr\nkJ0on3B8mQkybn/DS7OC/vsIt/OtoauPO5+WSxQwDajCany+to+3j+KgsQCA4/Nz0/z0sBjf2Z4x\n/PuDQwCAFyQMbi3LnHL8c/xYNTQ9Y0guXQFFW7vg7wMAly+ew/6qw9i26YZpj3fUaHX/P60vFjzu\nut3Z6ZgYumvXLgSKYUWYgWexWHDrrbfiU5/6FL7xjW8IHquqqsKqVav82s+vjnTgw2ZH0PjVawsD\n+qYUiL0Ng3jGmWnYujAd31ofeC/Qrn/tQ8O3nhDcl3DrTah87kd4r3EYfzndC53Z0Xbv0Q3F2LxA\n3F6w5uFRHFpxO1iLFcnLF+O6D/7q9XlPH+vC25cc3+x3XZ2Pe5c5usRcGdJj997LABzZpmV5iTjX\nK6wP37wgHY9uCE6/1CGdGTv2NABwtND69wPLAuphrq69iBOfcv9jzP/OFzD/kYdEG2c4OfGpXVDX\nXhTcV/qtnVjwaOAnBiLEsixYqw0SWUyohxIVzFY77vrneVictdJ7ti/Fu41DeLHWkZ28ZXEGHq4s\n9nhd56gRu16/BLAssuQM/vXgSsHjLMvinzX96FIbsXNNPvKSAr/qKQabncWdL9TB5Pw5X9mxFJcG\ndfjhgTaP56bGxeCPdy3mykQsNjuaBvU4369F+4gRqfExyEuKRWaCDMc7RvFRy4igdOW/b5yDp493\ncxm+l7YvQabCdzb8YLMKTx5xZBs3zE3Ff22aK9aPHRGOb90JTV0jty1VJGBzy8EQjsg/T1V34t1G\nR1np2qJk/GTr9C8HGSw2vFTbjziZFJ9ZnhPQZ/L391/BmW53qekf71qE0oyplZp+/a3LaBzUQ2Yy\n4ms//TYwLnw9uWEbbnzia1g/d/rrszz2/hVuXsZPt87D1UW+m0PU1NRg06ZNAb3PtD9RWJbF5z//\neZSXl3sE4FPVIZiUGTfBM8VVwpucyW+RGAgDrzOKS/uZS3julYuCejzAUfIhdhBu6OrjymHGGpph\nt1ohifH8M/doTGDsdhS2NSFvoQyAIwifn5mA1YVJONM9BjsLjwAcAA40q3B7eSYWjZsYJQb+xKuF\nmQkBLyJk7BdeljL2TH3CRnV1eNUo+kITM4PLPKLByVu+AMvoGFb/61dIWVkelPdhbTYwUs9Lx0OH\nT6HnlfdQeN9tyKhcPel+IuW4nYg8RoLybAW3dP3Db1/GgNZdErE42/u5pyA5Fgk2M+760/8hfUiJ\ntrT/xdzbN3KPH2oZ4QJ5CcMIFg0y2+z40YE29I2Z8NjGOVgY4FyUYZ0FVS0q2OwsEmRSKORSlKTF\nYX5GvEeJZeeokQvAMxNkSEuQYXleEiQMBAF0bnc7Hhq8CMkCO7B2OQBAJpVgSW4iluR6rp9ROTcV\nn12Vh2dOdHPlOfwAPEbCeCyCNN5Mr5oZbsft+ImZNp0eVp0eMYrAjouZ0sdruNAiUpvLfReH8Mr5\nAQCOZgk7Vro7zBksNrx0Tgm5lMEd5VlI9lK60TFiEATggGOux1SCcJZluXKU7N4ujwAcAOL1WtT1\nakUJwjUzVI4y7e4ox44dw4svvohDhw5h5cqVWLlyJfbv3z/l/dhZFu0joQnC+R1SOkeN02rPp2/3\nnCyQMdiPwVHP/pUNSvE7kPCXLGetNo/JJS69GhOuOlaFe/72NHT/+SU0/+JZ2K2Og+4zvN7pLp9e\nmoVrS9zfBJ850R2UNoaNk0y88pepX1i/Z+wdCHhf4YxlWWpRGGS9r78PfWsXLKpRdO95Jyjv0fzk\n8zgw/yY0/fxPgvvtVivqdv8Qff8+gJoHH4uqhZj4i7PxA/AYCeNzrohUwuCalgvI6euCzGJG659e\n5h5jWRav17vPA3W9Y4Jz2JHWEZzu1qBbbcJLtYF1WWBZFj882IrnP+nF38704Q8nuvHkkQ58de9l\nHG71/LJ8RTAp03G+U8ilws4vLIt73vg7TG+8i9pd/8WdpyeTlxyLxzbOQaYz2ObXuGYpZJNOjhPU\nhM/Qgj3hwqY3ev1fMw+G/+TM/jF33fSQziL4uweKH6u8el4p2OevP+7EK3VK/LOmHztfu4gPmoY9\nYoM3L3jWak91XRaNyQats4qgoL+Luz8myf2/Eq/XCho7TIewO0oYB+GVlZWw2+04d+4camtrUVtb\ni23btk15P0qtGSbnggApcTFIm8HlydMTYqBwTl7QW+xQ6QM/aPXt3R73SW02pA8pESNhsH15DuKc\ni84MaC2CiTJiGL9kuZ634hf3HJsdA2MmLDvtrG9iWbT85u/45K6vwtDVh4rcRJTzMk0bS9PwxbUF\n+NLaAsicmelLA3p81OL5oTJdE7UgmwrPTPjUg/Bwysr4YtMbYDeYPO6PpmAt2LSNrdxtUxA+hO0W\nK1qf/gfsBhNaf/8ibHp3MsLYO8hd1bDp9Gh/9mVfu+FEwnHrj1UFyYJtmYTBhnmp+O1tCyfscT23\nuYG7bW5s4QKCuj4trvBW0lQZrIKrk/yggJ8MmIrLg3rBip587zV6trhr5i1XPz/T3clldaH7S0a5\nxAjZoON8Zh5UeSQYJqKQS/FwZZHH/RP9/lzGr5oZ7LUjgn3cmodG/P4CY/Bx5VTspdHFZrOzUI4J\nYwoxVo/lJ0j1FjteOuf4/ZzoUONj3gqWGpMNv/64E996p5mbRK02WlF1xfO8Wd+vndIxxW85WjLg\nTnZmrHNfHYzX69A1rq1pIFiWFXzRCOvFesTCLwOZM4NZcMDRPaU41V0b2DEa+EGr45WjDBS666bv\nSdDhT59ejIfW5AsWmWhQBnay98U8rgxB19bl8Zy+MTPSlH1IVQlP5qOn63Fs04NQHTuLRzeUYG1R\nMu6uyMa31xdDwjDIT47Fp5e66/Sf+6RH0NFmumx2Fk28TgFiZsINvUofz4xs3kpRACpH8WXgg6Po\neP41WHX+H7fapnbudjB+r6aBYXdHJbtdsM6AoVN4Za3jL6/DPKIRfQwzjbVPvgJjWXYCti/PwYr8\nRHxxbQFe2rEU/3XjXCzM8n1esFutSL5wgdtm9HronS1j36j3/CJ+kXf+vdDvvq3SWzGkm3qCZH+T\nO0hbnJWAWxa7yw0v9Gu5+UAu/OXq+d1e7lqajasKklCRm4iv5Al/V8Ye3+cylmXRv+8j9L97mAtw\n1han4Kb5wsvz4zuj2M0WdP1zL/r2HuDuS5BLkSBzhAgWG4sxk3DskaTzb2/go6W34NjGz8Lqx6qK\n4zujuIT7gj2DOjPGt5znX20JhN5sE6wpAgBvXxxC67ABTx/nZaR5paMXlDp8ZW8j3qgfwNsXB7k+\n+PMz4rnSDo3JJihBnkjj//4OXbd8DkvPOCZyZnW7O6Nk3ODuxhevd/wPn++bXjbcaLVz81HkUoZL\nnAZDWAbhM1mK4iIsSfHMLPrDMqqBTe3441tkMqiXLeMeK9cOce+xJMd9mTXQkhTToArK/R8LsmaA\nZxmCvsUzCO9RmzCvsZ7bji/O52pRrRotmp94FgUpsfjJ1lJ8cW0BZFL3YbJ9RS7Xv12lt+Krey/j\njfoB2EXIkvCXpM5MkE04aWgy4zPhNq0eFs3UftfjO02EI35mNjbb/YFPmXBP6vOXUfPgd3Hpv3+D\ntmf+5ddrWJaF9rJ7ktz4L7liMI07VvnrDOjHzTGxafXoePaVCfcX7sft8NEz+GjprTh1527Yzb4z\nVgzD4KE1+Xjy5gW4uyLbr7pM9blLYMaE/+cH959F54iRq42uOH0M699/A/HaMVwacHxoq/T/n7z3\nDoyruraH1/SmNurdkixLttyNu2VjTDFgWnAInYSQEJLwCCWENMJLINSEhDwCAcKD0Lvp2GBsY8tV\nkous3nvXaIqml/v9ceeee86dO9LIBXjfb/+jGc2des89Z521117bjz47O+83RmG0o4XbH8QuKjt4\n84oc/KI8H8XhTp5Bjm3AEwxxDDNPg3CTVoWHLijGXy+aBV0Pm111TwLCB7Z8gaM3/x5Hb/othj/b\nTf5/y8pchs2TMuG9r3+MursfxbFb7sPQVvF5Ujb8dMbpGrdcMIi2v70IAHC2dGFgyxfM475ACId6\nbExWWqoHF+LbzoRLwTIAtMXIhIf8AXQ+9ya6X3iX2STLAeVAiMOdHzcT68pEvRovfq8MVy5IR7jP\nFvxBDs8c7MNLh8Xf8vJ56ZifKWa4Y5GkODt60fnMG0BvP857/zWs3boF+oEBAIBCrUJK+RnkWL2T\nfz25WrbphFSKcjr7o3yLQDjlEZ70DYPwEyzOpPXgNnMqtKViVbK9voXcpjt40uxLrBEKBHDgoptx\n5Ae/xvE7/sw8JmXqnO0yINzuRXFDDbk/61c/whmvP07uR9ORAzw7csfafNLRTrjQfv1ZKwbsJ7Z5\nEYJOAa89tg8N9/79hJkHuZTtZAzS/9WgmXBTSYH4f4v1tKePY42hrbvR9OenIzZGX3dYq0SGdHz/\n0Zie4x0cRYDavEnlXqcipPUK9DxCA3Ihuv79Fvy2U9/S/OuKjqdeg99ixfiBoxj+Yu8pfe3RHQcj\n/nf4qxr8rYKX5WV3tuLcD17D0r07sGrHJyQTWStDhjRPE4Tv6bCSZnO5iToyz6/IF2tpDvWI83Ov\nzUMkmMkGNQN46ZhoZp1SorG0ADD06Vfk9uiuQ+R2gl6Nu9blQ6NUQKdWRvTNsB0WJTwD74sOIHTD\nnv+rXuGWA8eYdaT/HbFmrWHYiVu2NOL329rx0y2NRIJAr4EKrfgbeEe+3SB8QA6Ex1ic2fv6x2i8\n9wnU/+avzBjopJ6fmygqBoSxDgA/W5WD9Dgtblqeg6e+MxszUyKbZCUb1TizKIntzh0DCJfOgcsq\nxM8WV1oEfVY6uW9wTQAch2MnyYTTLetPpxQF+BaBcLYo89R3OQt5fZMuXDT73h1jikQaNGtlS06F\neV4xuT9R30Zuz0k3QcjcdFjcESnKKd+ns4+4sNATLRDJgDplNOFDnUPI6u0EAHBKJVLPXo3kcMU9\nwLOrXDD6Z1qRn4h/XlZKGB6A33n+6N0GvFjVD7f/xNKWgh48o68Lhf95EV3PvYW2x184odfynAIQ\n/k1oaz0DIzhwyS2ovOK2mIAWDcINuZlQGflzwvkDCE6cXBryVISrqx9Hb/odOv7nZTTe949v9LP4\nqAVUTqYlF1IA5Lc6YpJSTCekmxMahEuZcAAIOJzoeu6tqK/3bdeE07+psznSiu9kYnTH/oj/pQ30\nEbBd2CyCzazeTrRb3HD7g7JkSNM0deFbm8TxdX5pCmHPlueJ2vbKHjvJGtYPy0tRpEHLoQDA0ys/\nj3EcB2ulmOGUjt0V+Yl45aq5ePnKMhRJQBLdDXLsq0Nk/k/9Gpnw0zVuBz/4krk/fuAYbJ19eL6y\nH3d81EwcNxzeICo6+fWT3ugkzC8ht7/tXTMHZYiwHqu42ZssLHurye2xPVXkdgeFzc4pTsaqfNaq\nb1luAtYXiXKnwmQD/nFJCa5emAHa3OzSsjRoVEosoAquY9GFT1YDkbCgFCqDjqx7qlAIWq8H/eHO\nsXTUDzlx87sNeHRXJ4Khyd/z62rUA3xLQHgwxKHHevo04c72HuxceDF2LroE4wePyR6TR9sUnjAI\nFxdPa3IqcubMgMrAv653eIxIB4xaFYqSw2AJrC4xlqCBV8DmQMgrDjZputzTN4SgpHDPX3GA3FYv\nmgetOQFKnRYac3ixCIWmTLsXmA14QnKh+YMcXjs6hJveacD+rumn7QUmPG1ATL/ajjdN+3WCLg8C\nMgDW/X/AIaX7P+/BeqgGY3uq0PPS+1MeT1fra1PN0CSLE6Rv7NQXzk43bEfqyIIe7dr7uoJOJXsH\nRiKkXHJBS1EAPrUdmKasacrPNcAuMjTwpi1Pc6+7hNzufO6tacurvg0RdHmYzfBES2TXuxMN3+g4\nbJSvsxCpg+J8MqtPPJ9JYyMIhTg0jbhQOyjDhI+6Y5bZ9Vg9qA3P4yoFcG6x2FW4JNWIBB0v97O4\nA2gb4193S604H83NlC9Cl8qhgOhMuLt7AN4hcSxJwTsAmI0aJMmYHtAMr3/cTn7H/+sOKaFAAIMf\n74z4/4sPvoY3jw1BisWEdYv+jZOWzCW3v+1ylAFHJAgPcbFZL080iAXojrpWcpuu+ypI1uOHy7Jg\n8LhQ0FwHUyiA29bkRcg1NColblyWjccvKsGSnHicXWzG5fN4xrrAbECcVrwepDIwaXioMe3Vsdgw\ncSHf5IpgF4i68Oo+FgPwNWwebG8dJ5utaPH/HAgfdPiIV2qyQX3K7WA6nnwFfqsDIbc3qsVYRpwW\nurDEwuYJnJCtj5uWoySnYkaKCXGzi8j/HA0iGz4v88R14VK220uBcrl0udSxJa5K3PGmnreG3KY1\nxfRkHi2EC+3vF5eglCqWGnX68cft7dNikly+IJko4hxi4Zl3YPoSBk+Uz+6ZZnHmN6GtdVKgRA5Q\nSIM+97q0ZGhTxDTz6dAvTzdokOUdHP1GZRTSMU1vmqPFRFN7xP9OdWFkBBPeJc+EF932fRiLeKeL\ngM2Bvrc+lX29b7MmXDoXOVs6T9lrj+6uJN7BiYvmQBFurJQ0Pgatxw2134fkLhHQ6rweGCfsqO61\noz2cclcAxCnL6QuiP0aJ3TaqIHNFfiLMFHhVKRVYmiuChIM9duzrtJHsr16txIWlqbKv6x0ajdj0\nRet5YK06ztz3W6wxu/n4JAzv6A6eqEmh6nIsp1mOcjrGraWiWlwTKaCYtm8vGSu0UcKRfgfc/iCj\nCU9cIvYF8P0fkqMkG0Uc1TZFcWbI64OzXcyaTzS1IxQuFu+wiAC+0GxAfoIWP3v9n7j8padw2+ev\nIiM+eu1WWYYJD19QjHvWF0CnViLo8sDZ0Ip56WImZipdOM2EHzjrAjSsOhMAoE6IQ8aF/G163TO4\n+Nc71C2uf1a3nyE7d07h7Pb/HAin3UjkijJjYayiRcDhZPRNcvIMgG/ckJd0cpIUR4e4wEykpCMr\nXof4uaIkxVEnrwufrkOK1BGDZkPlgBetC3fbnchsaiD3iy5eT24zIHwaabfZ6SY8cUkJ7lqXT/RT\nIQ54oWog5tdoHnVBICUyfeJF6RkcjdlWSghpoRt5rROwKfy6g9a/OWqbpzzeNyKOBW2qGdpkCoSP\nfvPFmdLrbeIUgq7phrS+QK5eQhpybOKp1oV7BiILM7lgEIEJJ3kvhVYDQ24GZvzoe+S4MYkUbTrB\nhUIYrzqOnlc/RMN9T6D6ul+i4Q9PMFm10xHOVsl4aO06ZfIeATgCQPrGcsSViB0eZ1qHcEFoDJDM\nJeaxEXzSOEYY0aIUA2PPSlumRotAiMPnzeJ8eX5pZAO2FfkiCD/UbSMWbwBwSVlqVOJJyoIDgLt3\nSDaFP36oJuJ/cuNXGlwwGEHsjO7itfUsE356x8bpiAFKipJ3/aVQxfGAO3l0GJl9Xbh6YQb+dnEJ\nCsO4wx/kUNk5zsgZk6jmXN8kEx6YcGL4872TkgB0YeaaGeJaIOjCOY5D39ufoe+tz5jrztnWDS4g\nykhDXh+crV0Yd4k+43q1EhnxWtjrWsG1dQIAvHsrEZiIDb8EPV7s3/Rj7Dv7+1jxl4dhmOAJmSlB\nOEWeOBLN6P7hjVi79w2cWfkuwSx0BtgQLs6s7nPAF+S/Y2WvHfQVU9ljn1QG/P8eCJ9ED9753JvY\nXnIuqm/41QkVmvVv+QJBlwjyo4FwILJpz3RjgmLCdTOyoVIqED9HBOGjuw6i87k3UXv3I0j56GOy\nE28cdsIfjH0himDCw4CZ4zhZCzUXtcNt3bYP6gDPaFgzs5E4U/SQ1WVMjwmnQ6lQYGNJCv560Swi\nTznc54jZOJ8uykzzUBd1KDTtiY9mFoVJF5g+E34qNYp9b36K/effhL63Ppv0OJr5dHX2TSk5oDdk\n2ggm/FsAwltZuYEzBlBwukI6jlxTgHA5KQBw6jMM3gF2c8j5A/AMjMDdLW5iDXlZUCiVSNsg2nFZ\n9h2RdReZatz6LDYc2HQzDl70E9Td9TC6nnkTI9v3oevZNzFEOWqcjnC2seMh5PbCHUXjPJ3gQiGM\n7hRBeOqGVYifO4vcvzMzgAs8kQxy0tgwaQACAPMy4pisHm2ZGi2qe+3ETSHZqMay3ISIY87ISSDz\nYuOIi7ii6FQKbJ6fHnG8EFJdNxDu3CiTUaL14ELEorn3WWwRNUDWw/Xwjdu/1q6Zp1oTHvL5mULV\nnCsvBM5cTe4vPF6JqxdnQqlQMI3oqo+0A2GAqstIhT5bbF7nHR2ftF7qdMaxn/wBh2+4G4e+8zPZ\njavTFyTgUaNSMLUIrWE/+r43P8Xx/7ofx2+7HwPvfU4edzRGZvwc9a0RDRSVCgXGD1BF7RzHSFcm\ni763PsNEWA2gqm3ANf96FKmDfaiZQhdOr+cT8YnITdTBNDMfmkTRS58mnzJD/Gf2BEKk8PNgN7tx\n8Yc47J1EksKAcJ8LHU+/Bsv+I7F8zWnHtwKET9Yps/Pp18EFghj5vCImZlAava98yNz3W2xRF9GT\ncUgJeX0IhgcLp1AgpSgHABgmfOyrSjTe+wR6X/4AvQ89jRUt/GD2BlmrqqkiggkPd0wM2CdkJwgn\nZVM4tE1M+dmWnsEcp02jmfAT2/HnJelx7ixRD/lCVX9Mmye6MCpuQqJrH5geg+2NwmJ8U10zg24v\n6n79GGxHG1B39yNRfWr9VntE6pnOnsgFPRZ0qWZoUsTF5OvyCg84XTj20/uwa+nljNsFFwpFMuEy\noPbrCC4YZKQ7gHxjLTrkpADAqf1dOY6TdY1xdfYxshRjfjb/tyAXhvDtoMsNK+VqEUv4bQ5UXXU7\nbEfqZR+PhTk9mZAjQaQbtRMJ+/FmQk5oU5KQML8ECXQWsr5VdhE1j7JzwvxMEwPCY5HU0UzeWUVm\nqJSRdmYJerVs87FNc1InbUwX7XqR2hT67ROM3JE8nzqfAacbdfc8FpHxkO0CGQphbHcla1H4f8wd\nZXTXIbJZ0edmInHJXOwvWUIen3P8MLQcD2ZX06xxvTgeDXmZUGo1ItMaQ72UNIJuL2rvfgTV198N\nV3fs2WE6Ak4XRsKZnonGdlkHM7pTZtlIDzI6RHDcbuHrEPre+IT8b5jCAhMyINxe24IOSg9eGCZI\npbU9sdRthQIBdPzzFeZ/iVYLrnr2L0isqsLgJE0L6fXcmZCEHMqhRQgtxYSXaEUMdKjHDn8whKre\nyOzBZJIUGoTrnnkRTX98ElVX3RGRtTwV8Y2DcJcvyNjJFFBAOOjxMsDJVjO9Ij1bTRPsNZG62mhs\neP5JOKS4egYIs+1ISEJeGr9Li58zk3hwS2NOtwiw6mQKg6KFtOBO0P1FmxyEtDsXDMK3R7TwUpav\nYI5jmPCTaEpw/ZIsprPmge7JNbRH+x041CMeo7WxO1SpjMQzNAr78aao4J6+aGk9n6d/OKYNwdBn\nX2H/hT/Gu797cMpjYwnbsQbS1TLk9cGy97DscXJOGPYpNp50y3ptqhnaFLFK/esozAw4Xai+9i4M\nbPkCnt5Bpu26p384opvn6QZ50cI3ZiXslhDO9slBeDQANFmGoefl97HrjO+g9a//G9Pn8lsdCHki\nFyBXVx8zHowzssntlHVih7ix3VWQRjRtbcDhRNXVd8IuzKMKBTIv3oC080QG0t1zYiAh1nDK9C04\nFbpwhgU/awUUSiXDhNuONsBaXRvxPPMYu6jOy4xjmgG1jbkRmMJJgfYTp3tASIOWpAA8W3nFgowo\nR/NBXy9Kvai9lfpY2w7XkfUHSnFZp5n0zqdfQ89/tqDr2TfR/67Igkab60d3HkAyBcLH3YEpXSVO\nJmLRhAdCHD5rHJUtpJXG4IeiDDXr0rPRMOzCXnMeHAk84Fba7WTczEo1ECcY9bA4JvS5mQD4ehsh\nppslbnn4GfS+/AFGvtiLjidfntZzhXDUt4nnF/IEgqAHz29txNmPP4TGK/8Lixv5jacnEEJ3+wAD\noMcra8h6KLeBc9S1oJPSgxck68FxHCwSe1d7zdTk6OCHO0iRuTohjmSotT4fLn7tOdR+Kb8mcqEQ\nMz6d8QnITYiULGvMIgjPhTifHuyxo3bISewUaWnJkX4Hxt3yG0sahHNH+QxTyOuLqLs4FfGNd8B3\nKQAAIABJREFUg/CXDg+QNvFJejVj1SStArcfmx4Il7LgQkRjXvJPwiHFLbEnFDpwahLjUfK7n0Kf\nk4GE+SVIO0dMh5m7Osnt2mnowqVMuDBIaa0qLUsQ0u6W/UehtPFgdyIuAakUQAWkcpQTB+HpcVpc\nNEcsNHqhqj/q5O0LhPCPveLCvLYgEQHJ96NlJJ7+YexeeQX2nXsjel/7SPY1aWbRVDwD6gR+YQx5\nfVE7TAoRcLpw/LYHYDtch+7n3zklHdKkaWJau0qHnCe0/Xh0JjwUCIisrEIBTXIiwwic7sLMgNON\n6mt/ifED4sQ+0dRBmH6560wuvf51hNzCORUTHg2E+6NoMn3jdjT8/u/w9A2h7fEXYnIviVa/4O7q\nZ+YUAw3C1y4jt8f2VE75HgBfV1N93S8ZP+h5f/0NFj33AGbc9F3xfU8jCOc4TpYAORV1ArRVa+pZ\nKwGAAeGO+layIaRJkaQxcYOfnaBDslEDs0FDOkr6ghzjkyyN6XT5peUBAHBhaUpUb3Ag/HtR10vy\najFzKZXwjB8S55i0s0RyhQbxI1+K9o2ORhF00fU/9Dgb3XkQKoXok8wBsEQBLV9X/H1PN/5W0YN7\nPm1Fx2Tnxe3F0NY95H7WZefg3dphcEolGheK18/ABzxQVygUWBmWpCRYqd9DAOEZ4no2nXop6+E6\ndFJ2otbq6WWuhJCqAFwdkXOXoAenbTiX7v6CgPe293cyQN47OEokb3JMuKOuBR0WcWwXmg1wtnRF\n1MTIEZ10cKEQ2v/xErlfcPOVWPnxswhk8htQJcdh4vnXZJ/rt9hIN2GPwYiARjslE272uUiHy367\nF+9RnXLXFyVhXrgeL8Tx3v5yYfPwbLoyECAKB+DUujkJ8Y2C8NZRF96vGwE4DqkDvfjxolRoqfag\n0gVhqpNNR8DpRv9728h986rF5HY0Jjw7QUdar446/bBPwyGF9va1JqcxgL7wZ9dgffUWrP7iRSx8\n5k+EqVB09UDt4xeGo/2OmP3CpZpwoTjPNyaCrvj5JVDqwgvJ6Dj8NgejAWuZtxg5Ev29jpKjyKYo\npxFXLcogF0LnuAf3f9mBz5rG0GfzMmz0G8eGiE+rUaPEzXMSwUl0rnQKaHj7PrKYDlN6PzpowKXP\nTIM+W9RcTiVJGdjyBQIOfkM0B3qMVVRPenwsId09j+w4IMvIyzHhk0mwaFmExpwIpVrNFmaexq6Z\nAacbh6+/m9UHAkAoRJjWCRkQ7ukbiqlt9KkOuU3lVDaF9IZBcCUBojPh/e98RtL8XDAYky99tPQm\nL0ehmfAccjul/Azi9GA7XE/GqxBy2tqOf73OsGBlD/8SuddcBIDXmwtxOkG4b3RcVt7jPMmFLeQP\nwHZMLDZPDnfQ05oToM+JZJrTzllFbpvHRkiGhO7kR7Phk3XO7Bx3Ew/mqbr8FiUbkBV2koiFBfcO\nj8Fv5bPEqjgjzMvmkcekY8taKRZlZl1+HpQGHqj4RizwWWzw2ycYtyX6+fRcn37uGmL35h0axURD\nG6sLP42SlKk04d1WD75o4T+rP8QxjjTSGKuoIn0SjEV5mJgxg2iA20tEy0G6o/TqyUB4OsWEx0jM\nhHx+1N7xIJOBm2hqP6HiZ7tEligPwvl1Mckizinx3V3I7OOvr4kv9kQ8x1pZg8CEk1z3CrUKKhM/\n9n1jVox0i+OkwKyHRTrfg9/oTTaPjmzfR0C+ymhA/k1XIH52EYyP/xFceB4zVFbL6tJpp7OJ+EQo\nwOM0aWiodS9otWNxjqgXP0hl2VfkJ2L9TDFbvCuKJEVgwhOsFub8nQrpnDS+MRAeDHF4Ym8PuGAI\nm958Hjf88yHob7mTKTRyS/RTjoY2YpszVQx++KV4Ec7MR961F5PHooFwtVLBdHqqPdaOruffQfeL\n70V4bUtjgroobMmpyE2U9zpXm4yImzWDvxMKoczGD3KXP4QP6mLTG0Uw4USOIoIDXWoyjAXiwj3R\n2M74pTYuWIocyWA+mcJMaZgNGlw+L43c39dlw9/2dOPGt+tx0zsNeP3oII70O/DGMfEiv2lZNoyO\nSPaWXjBc1LmTa8gDsMBGl5kKA7UQT1acyXEcev6zhfkf3bTgRILjOIxXsmlwd3e/bFGgdLwDPBCM\nNmkzLetT+YmFzoCcju6OQnQ89Sos+8QUIg12bEd5QBQNXJ0s6DqRiLZwTsaG00x48spF5LYcE85x\nXETmLZYOoXS9A81Cujr74O6hmPB8ESgLmmeAB/uxFAwNfrSD3J7121uQ/4PLxdemr4+BkZjn2OkG\nPe9qU8WFcDpMuNzm1VHXQjbm+txM6CnWMr6sOOL49I3riMZXHfAjzs7PObRtbCmVkZ2scyYN0Cdj\nwQGebf392YW4cHYK/nRuUUTreGnQRcxxJYVEGgGwWeJQIMAwrOYVCxFXPIPcn2juwPj+IwyYoJ9P\nXxu6zDSkrBOZ4pEdBxi2fneH9YSbsU0n/PaJiHnvjWNDjMPFV+1WuIdGYa2ujShUFNxdACB941q8\nUzNCHHAKSsUNNf3dF2TFwahRRgHhqbLPmSza//FSZJ+BQBCOSepiuGAQ45XHIzbW9uMSJlxOjmLn\nfy86uwMACw7tgd41AW1NpBxr/NBx5jOaZuYzdWyJPfw1m6hXw2zUYPygTKfhUIjJrDDfh+PQ9sR/\nyP28Gy6DNrzJK1w0C22zF5DHOp+OZMNpaelEfCLS47TQqSNhq5aqhfKNWbEiL7I4Wq9WYkFmHNYW\nJpEi6dohZ0RTH38wRAhR8zg7h///CoR/0jiKphEX1m57H6W1/CLibO2CjWK7pen5kNcn69srF7Qf\neN61l8BETUpSmyw65pmApXu+wDVPPwr7pT9Aw+8eR/2v/4K9Z12HkZ3yMgIAGG+jLoqcTNmBIkTC\nwjnk9jlBcZC9WzuMkbq2SdsSc6FQBAgQvEsZZjQlEaaZ+eR+53NvERbKak7FUH4hMuKlIJyaaIbG\nTrrt+RULMmQbL/XavHihagD3fNpK9JZz0o3YNCdVdoKj2WsntdmRYxE5jotkwmmQMYlNoe1IAzPZ\n1YecGNtdeVK/g6uzTxYMy40lV3ekb/VkkzbrjMKDGs005Siurn4c/sE9qLvnsWmBL7rte/Evb0LR\nrdeR+wSEU6CLdqn5JnTh0TaVThlGCYh0RjGvEkG4XIbBWl0bseBO1umNHEONYRrouzp7WXeU/Gzm\neSlrRV346FesVaFUW+vuGSCuBAqthpGfAIBSp4UuM3zth0KnrYCZHg/J5WeQRmZ+i21KmRjAM2o7\n5m5C9XW/ZMaqtUoEF0lL5zHPSZg3C9JIXr0IJiqzYR4bhkoBLMoS2bNYizMbh8XH5AovpTEr1Yjb\ny/NxRm4CAk43jtz0W1Re+QvZDZuDWuviSgthyKFAOOUVPtHQRhzA9NnpMORmwlRSID7e3BlBJtCa\ncmYzn5ZM5DwA0POfLShsqCEyhneOD+Oa1+vw3ME+OLyndrMmjNuB97fjy5LzsHvNVQSMDti92NHK\nZme9gyPYc86NOLDpZrQ8+hzz2Bh1Tdjmz8PHjeK1eOEacUx4h8cIgNeqlFiWm8CAcGHjo6WYcF8M\nINzR0MaAT3W8ODbsUQoZQ/4Aqq66Awcv/gkObb6VWPOGAoEIuYirI3KtGHB4oQiFkGhhP1/p8WqU\nHTkIRfh7Ckw3AIwfOsboweNmFyGBknGlDvLvU2Dm9eD0vG8qFvGFPUq9nmXfEdjCG0SFVoOCW64i\nj+Um6lC97hxyv/+9zyPmHvq6cCYkRki6hKAzwP5xm+xxS3LioVUrYTZosDhbvNa/amfnHrtH3GRm\n2Nkx52w5dZaqQnztIJzjOGxvseB/K/sxv3Ivlu5lW8rSLJkcMxjtZDPvEQoRIAAA2VeczwBSV2dv\nVO/pwocfwbpt75MUjvicPlRffSeO3nyvbAMEJyVHiaMYaLlIXCSC8My+bpKizDhcjeqzr8fulVdE\nLcjzWx0RDiheQY5Ca8KTk5gU+hDNgi9ciswEPZHeCKGON5Hin6Dbg+BJygZMWhWe/s5s/M+lJfjR\n8mysyEuAQRM55FQK4PbyfCgVClmwRLOFtN2i32JF0CPpBkoVuqlMRqjjTTHLUXpe2hLxP0/fkGzq\nL9ag9eC0FnV0x8GIY+nxTk9w0SQp0m6ZACSFmZMz4UGPF4d/cA+Gt+5Bz3+2YOTLfZMeT4d3WDxP\nGZvWM2OagHCKNaBrIU61LtzV2Yu6Xz2Ght//DX1vf4aJ5s6IiZKWoyi0IrMXzaaQdkZRx5sYRtU/\nHrm5kas/iab3poNeZBIWzCYyggDFBGqSE6FJYAv+aLZSrjiTjuEvxPOasuYMqE2RjO3XIUmhyY+4\n4hkwzaLY2hgYpo6nXoPfYsXI9n0Y/lzcaNAFl1IQLmXCdZmpMMzIgbFQnBvXqp34zYYCpunIrFQj\nhNmxy+qJyv5OhwmXRte/38LQJ7sw9lUlup59K+JxlgkvYJhwunU9rQdPWjo/fLzoke5s7oiQ1fnG\nrCS7SxMf2vRkpJ61gsid3D0DyH74MXz/6UdQcrwaykAATl8Qbx8fxgNfduJUBxcKofnPTwPgNwqC\nI8gbMt0tl+3+HKEwAdX13Nvk+7h7BshYU+q0eHJCJCaW5SZgaVEKNEk8COMCrEf68tx4xNtEUGbI\nE5jw6dVLNT/wFNEyJ54xF4U/u4Y85jguP5+3PPwM2SzZa5oIeHW2dkdkBVxdfcwcF+I4DDl8iLda\noA6y2Ebj96P8C7F+qvCnV5O1aKKpg6npiZ8zE/HUxjU93L26MNkAd88gWT9VJiNv+RiOaLis95UP\nyO3cqzZBnylmxzUqJdTzy9A7YyYA3pqV1s8DQFcrZdmbkITvRZFw0YWZPosNqSYtilMM0HrcyOjr\nAkIhrMgXjzmLkqR81c6uk3RRZpqVPddBt+eUO6R8rSC8bcyFOz9uwaNfdSGlsQEbPnoj4hh64XbJ\nFKrF1EVwcJToijXJSdClJUMdbyJML+cPyFr8eEcsCNWKrx9UqZC8bhnUlB/l4Idf4rDEs5wLBhHq\nFxeulFkigJILGrDYjzXimsX8hb5kPw+UuUAQva/Jd/aUY4yE1vU0E65NTmTYHjoaFyxjuoQJoVAo\n2LTbKWhMoFIqUJpmwvcWZOD+jTPx5rXz8aszZ2BxdhxZ5G44IwuFyYao7+kdGkPIH0AoEGC09/xj\nLGingY/A7tE+r+4o3eb8Vjsp0gF4aUCZkmcvYpWkBN1ejO2pYlKJtB48+3sXkNuW/YcZiRMXDDLg\nJ+PC9eS2NBUphLRbJgB+cQnXHARsjknZ7eYH/0UYUiCSoQ44nGj/n5eYhhfkvanzpEtPQXxZMelQ\n6O7qh6t7gDDBCo0aaWeLOtxoTPhEUweO3PRbdDwlX6QTLY7f/mf0vLQFXf9+G8f/635UrLsGuxZf\nhnHqt6c3zrRtZbQNFpOiLSmYtBNpwOHEoMxv5BmYHhOuz04jVoR0yP3PvHwhqflwtnQyC4NUWztC\n2UamnbsGcvG1gHCKCTcV5zMgPBaHFPpzjWwXNxaMFOMMCQifV8LcN69cBIVCAVNRLvnfSqUT6wrN\nzHFGrYq4ZYU44Gi/jJbdFyRWtkoFGFOBWGLwQ1EiRGvahaDHYFxpEfRZaeTa9g6NEmA2TunBk5aH\nQXipCMLH9h6WLbwTpHl0t0xdegr0GakovffnjBtLSn8PLnrzf3HLY7/D+k/eQepAL44PTkzpHDOd\nKC8vx+iuQ8x59vQNYXjCR7TgAHD9kkyY7FbMrxLHddDpwsh2/j6dGbLNno2hMH6N16lw57p8mXVO\nvE5zAy6owiSX1xRHNqwMCI+haya9MZz7yN1M9lvO0m/4873o+OerzP+EbKkcCRPy+phrfszlhz/E\nsW4/VIdQoTcIAGRfcYEItDkOgx+L4zBudhESqI1r2mAYhJv1TP2Pefl8JFLzqBy7H/L5mes07/vf\niThmhlmPyrXnkvs9L7/PdFVurBdJkryZWVG7c9Jt6/0WGziOw4oUDX7wxP249ulHsebLjxmJyuoZ\niYSEbB51YYhqctRrF/XttL5eiFPZ5Rc4BSB869atmD17NmbNmoVHHnlE9phgiMMLVf34+ftNqBty\nwuB04OI3/g2VkB4xijpsGoTLAeVYmHAaqNHWXjQbLqftoZ0DhrLy8K9fP4yEJx/E2orXkf3d88Xj\njtQzwMhaVQtFeEKciE9Ebq58C2Ih4stmQqHmd6Ku9h6sS9OgIORCTpcIiEa+2Csrg4hmO+cdsTBM\nuEbChNPfy5KeyaRj6DhVDinRQq9W4pxZyXjkwll47ep5+PfmObh6kcjwyOrtOA7ewRF4egeZrl5A\npCSFZhb1BIRPzYT3vf0Z0ZXGz5uFGT+mOhPujs2Bovq6u1B5xW1MKnGcYsKzN2+EMTwGQ24vo6/z\nDI4S5kSbaoZ5uaiVi5YVYeQoYSZcoVQSzR0gz9oCvNaz69k3mf9Jbc/a/vESmv/8Lxz7yb3M5jfo\n8pCNhkKjhiY5EUqdlmEdB7aIRcCmwjzmsWgNRBr/+CSGPtmFpj89CUd9bA0gPIMjDJMjhHdolFnU\n6IXWvGKh+FmigXDqM8aXFkFLMS3+cRtzbfZv+QJBd3jiphY+71AsTDgrnTLMiMyi0VpxIVQGHTNG\nom0UA04XxvaKLGj6uatljxMYP0B+3j0VQWexTDPzWd3yFHUCXCjEXNujX+7npWcjFiJbVOq1jCMK\nwM//dPpdkPwYi6i1IMoYWE413TnQHXkd0V1+C8wGGDTyVrRy4WzrZnoAOBraWGKH4xjpZVxJAZQa\nNZnTAH7scxzHZNvMyxaEjxdB+ISM/Rwgeo3ToFIAm4U/uwbrDr6Dgp9cRbIzAKB3TmDJ/p244Z8P\nYfnnH6HPduLdrOVCmo109w3irZohAvbnZZhwzaJMrN2/A2pJNlvojD26U8wyVmeL4+EXa/KIvl2X\nKU82mcbF2/YkUYIynW7SgQknKahVaDWILysmNRwAMFHfxmSz3b2DOP6L+yNeR8iW2mvlHbJonEP0\n4BRozNi0nhn7AGDLnwHjjGxm7qAtUuPnzETc7Jlks2ceG4Ha50VBsoFZr8wrFyFhfim572iMLDi1\n7DtM1glDXpZsfcYMsx4dJXMxms7PP8EJF3peeh8AUDPgYAozVy4pjHi+ECq9jnxXLhhEwD6BBf3t\niAvXmC2urECSVpyb43RqLMoWs4t7u0TstKtNvJ00HkmkxJK1m06cFAgPBoO49dZbsXXrVtTX1+P1\n119HQ0Pkjv7329rw+lExnVTSeBx6N5/G02Wm8o4h4ZgIp5ECTpfYsplK4zvqWwm7N7xtD/addyPa\nn2RN4JkmF5Q0hE7xyxVn0o0veopmwWswom7ICV1aMhY8+QdkbT6PPD5CpUPpBiXtpfOIPWG0UOl1\nzIB01TbjcksbFNQk7O4ZkO0uGE07KVTBC6FNZjXhQjQu5LWkdPUwHexkc3pb9KaYNIw3OxBdu+sZ\nGJH1GJam/Gkdrj6LT30xmnAZEM5xHLnwASDvhu8gde0y1If4CcSyt3rKLmnungHi/22vaUL/O9vg\nt0+IDJRSicTFcxj7MFoXztjR5Wcjnpq0HXWtsu8vJ0cB2EpxIdUa8gfgDzdz8o2O4/gvHpD5Diz4\noh0X6OYutBRFl54CRRh40hme/ne2ktumWTNgKsonE7urqz+i0JnjONgOi+xRrD0Bhj8Xrz1jUR5S\nzhRlGjT7Ry+0Zlp73SEvR5Ey4UqdVpzkA0Em20FLUbIuEzWOsTDhtNRKl53OzFdCSPXgQrB+4eJG\nkdaEj+2uJFnBuDkzGcabeY8YmfD+d7ai5tY/xrxJEiLkZ7NYxqI8mGYVkPtTsUu+MSvZpAL83GQ/\n3sxkmhIXzoFSy1r+KZRKEXAolUg5czkAMEx4tDGwmuqieKDbhpCEFKH14AtdIxirqI65foQulAV4\n9o6eb32j46IzislI5jB6LnP3DGKisZ0UrqtMRrKuGPKzSKYkWnh6hxDy+cUaI6WSsXrTZ6Ri9h9v\nw5mH3sXMO26McJpZsu9LdI7E3t9iqtjx/kfM9QwAjp4hfNYk/i7XLM6Ef2QMsw9GdnYd2b4Pfqud\nkd50Fc8GAGyYaca6InGOZOUl4nWqojzCrYlmIkNi3FGmIKfoedSQkwGFUgldWjIB/kG3h6xlIX8A\nR39yLzkHuqw0gnfsNY3wjliYzRqdlaeLM4kzClWUmbCgFNkUZgGA4yULMO7yMyCcfHejAdqcTOzu\nd8IWBsUKjkPaUD9mJOlhociO5JWLoEmMJwQB5w9EuJvQ3XfTL1hH1gk6CswGQKlEVbk4b/a9yTcU\nevnwIAHRAJBZKD93CUGPXf+4DcY2cY7SupwRVsFrC8R1siJsVej0BXGwJ/yeoRC0Q5F44VQbC5wU\nCD906BCKi4tRUFAAjUaDq666Ch988EHEcf37xZO3MCsO39WKhYUzbvouUtZQ/qedfQj5/JKipCwy\nAYS8Pkw0d8Bvc6Dm1j/BXtOE5j8/zeyYaBBuiMaEy4FwKq05mFsAAKij/LvTz1tLbtOTRf9WcdHj\nQbi8MwodCQtnk9u2o/UwVx6KOObVpz5CvcQ/3DMqr/P1jFhYn/DkJGhTzUxBCKdQoGnBUuQm6pAW\nxUrr6wThckFPcGpKB+vpH4KzPfKcefqlIJySo4TlRwIY5x8fjQC0ozsPkgtLFWdE9uXnwlRSQHRm\nfqsjqiREiLE9rOay7W8vwHpILGhKmFsMtcnIFD3RunBaemWckQ19Riq0YYlJ0OWWZet8MnIUILJS\n3LL/CL6ccz6+LDkP23LWYueiSwiApxdqaUEwfQ3SYFEqRRGCBuH0RGWamQ+VQSdmpTgu4lx6B0YI\n6ABir0If2SbabuX/cDOWvPhoBNjnOI4Zy0lLykgmyjs4ioAz0m+YlQLwDIxGJsNgr20m1qlKnRaF\nP79W/E5TaMKDHi+RkClUKuhSzYwVoRBGGSYckPqFV8kCwBFKD55+nrwUBYgNhLc/+Qpqbv0T+t/Z\nhqqr7piWD727u59ksXRZaWGXqALy+FTFunK/5eiX+5iizMQlcyOOAYA5D96JvBu+g4VP3QdTIQ++\njYUUCO/sk60RynOMYePWd1DYVItxdwCNw2yNjKAHTx3sQ+Hdv0bld/8LXc9FarvlgpaiCEFvbKQs\nuABg2CLzIQbopJ29CsqwJEypVsuSMOaVYhbI3TfIZtNSkmQby+nSkjHrnh/jzEPvYOmbf0cwkZ9f\ntD4f+qpjtw2eKoa374toqGXt6oc/yI/r4hQDzsiJR8dTr0IZ3lgOZudjNIs/lyGvD80PPUO6ZDoS\nkjCWnoVUowa3rs5lXpdlwkXs4KXkivakZIyGLRnVifFkrgw6XZParNJuXgZKx59ASaME+Ub/25+J\nhYsqFRY9+wBT1zD21SHGnjB9o4hBaCmd0KiHlqOYCnKRd/2lzGdrmbsYB3vsSJIB4a6cHPz4vSY8\ntLMLA+ninLPYNQKV1UqcyZQ6LZnraTaclqRwoRCGqbk54/x1Ee8HiB3Sm+YvRSg8bztbu3GsdQjH\nBiaIcxHAGkfIhdSUQNoVWLrBW+gexZyaKigDAdQNOWFx+bGnw0rG2zyND5yMM9mpdkg5KRDe19eH\nvDxR8pCbm4u+vsiq3dk1fKr06kUZePiCYgQbxEGVuKgMKqOeTC5cMAhXVx/jjGLIz4rQUXe/8K7I\nRnEck3JzR/HXZeUoLAjggkGmmHMgj19464cmyOKWetYKsnjbaxrhGRiBpa0H3tZOAEBArYZ2+SLE\n69SYKujvM/LlfqbqWAjVwSrc/lEz/nVAvNja2+QXyJbmPmZR1CQnQqFQMJKUnoJZmEhIwpIoLDhw\nYn6opzLo96R/I0/fMFwyHQ6lrgJ0el8XBt8qvY4wxVwwyIDIgNOF+nseI/ezN2+EOs4EhUKBM889\nm/xfSPdzoRAmWrsiFm1p0xR3Vz8a//sf5L5QMJW8ajGj5RUAD8uE84CInrQdtS18dXrVcSJP8crI\nUQBJceboOOp/+zix6wTASHrm/e235Land5CMdanmkN7sMCA8Qx6E0yE4E5kY0MVKUqTMajQbUToC\nThfDeqWft5YH+4KdXygEZ3s3qZkAeLZHk5TAsMvursg5i35/IbXPerDz19rYV+J5z7jwTEYG4B2x\nRC0AB9jFX5eRAoVKJQu45YA5ACTMLyHMmHdolBSZCppwLhRisnTR9ODA1CC841+vo/mBp8TPPjyG\n+t/+NerrSYPOYgnzsLEwl4A+3j8+evMVuazC8PZ9kxZlkvcrzMXcR+9G1mWi9lQdZyIbSM4fkPV0\nb/z1Y5hbsRMXv/5vGCfs2E+lrDmOQ1OYCS9oqRcbojz+v1M2aZpo7ZLNJEzUi2sYzSrGUU4nBolN\n4dCnu8j9jAtZoEM7pACAyqBH5kUbyH1P3xBrT0htqOVCoVIh9czlUC0Xe25MVNVM8ozYIxQIIKMi\nspFNgJrfl+YmwDc6zmQtD5x1ARrmiyReN/VYV/FsxOvVuPecQsRJ1mR63qLXDHePOA5oEK5QKAgp\nAkwuSaHJDLqYlgWs/BzeQ2XRZt7xA5iXzecLY8PR8+pHZKOujjchlcp+0SBcjgk3FuUiYX4pMi46\nCwDQUrYQ42kZ2N9lgz4jNULm1hKfhj57uAdHlrhpWdXbhKY//ZPcT1xcRtawhAXUd6I6Z9qPNZKs\ntCY5kdQqSCMnQQeNUoGgRoOxdHEO2rHtMBShEIwTImE71fhkGtWNWBg8BwAjX4hkqbOjF3Wbf44L\n3noBm198EsqAH/u6bNjRJp7Xco04H9HZ5cnc9U4kpkaLk4RcekEuvqr+ALPm6DA0qse/9pvgqz2K\nOeB3QMedY1BXVMA0awY8fUOoDznh//ATzE/gdz31ISfSNAGsXlCKoU92oT7kxND7HyG3toc8DgCz\nmzuRun4FKioqUFdzFILasMY2gs6KCpSXl8NUnE+OXxxeZIXU7cKULAQnXKgPOaFOSkTBHIaKAAAg\nAElEQVQwNQUIcOisrcKHn4/i0o1nQZMQh57ZWbDXNKFMacLw5xX415cHkBpyokxpQu/MUqyNH0VF\n+P3o15feXxAGLPUhJ7BvHykCbM6MR6B/EGVKE7K72+GpP4gX23QoTbsUZ81MxueV1UgPv19Ao0Gz\nl18YtMd7UDxuJ9/vvDBr15qsxWj4+MaFy2BvOwpVUhaAPNnPV2MbQUf4eO/QWNTPf7ruH+7tRCjk\nQZnShMRFc7Bn1y4AwIyBYTjbu8n3E36vgzVHMUb93gdrj8Ea/vz6jFTy+vrsDB6QhpzgPtuKC266\nAQDwxk/vwXBXK8qUJmiS4jFUXobx8OulrF2G7W+9BwBI2VOFjE3r8fI1P4OrvRtr1pRj+XtPYu/e\nvbxtZFgOQH8+Z6v4eRcs4yeh/Yer0F2aidwafvx9+uyLyNi4FglhT+j6kBNurx0l4EHW7i/5gr+U\n1z9C+5Mv42ANv1lbs3oN3F195PXXhUF4RUUFOrw2CNz/p08/D1tdPfm9yOdTxWHmnTeiLc2ARm0Q\ns30qBN0e7PpsGzQJcViclQ9wHDk+OcyEV1RUYHD/Xgg5ivqAE67w7xVXUoBGTQAhr5d9v4kx5IAH\nE19t5RtozQwzn8L5yapvZz6fKcw2CI8vSs9F+z/+g5YkDTLOX0eKuGrd/EZkxbyFMOZnoaKiAq3J\nOmTzL48dH34MU4G4oDTHK2CoqICpMBeu9h7Uh5zwffIZLin7L/J+QZeHLHwNKh9MbU1Ym5MBTXIC\n+XxnhJnwiv37MBIeb4lnzMW+QwfRHK9EiSMEcBx2ffwZtKlm2fHuGRghr7cq7BpwdGwA9eHXE34P\n9XAvzsHSiOcrVCp0F6fBWsnPF5Z9h3FkoJs8bj/WiKND/Dy5KC0HSYvLol5/q5ctF3//3k6s8weg\n1Kj58/3JTsS98Bk7fpQmDL6/HR8UpiJlzZIpr++c8HxbH3IiXc9hOQClVoPWNAO8/UP89dLWjeP2\nEdnn54c3hPT72w7Xo0HpBRfyo0xpQtLSedOab4xFeTgyyH+uM9p7YJyRQx5fs2YNbEca+PfzAVnd\nHdiXk4ZSH795LFm0HBZ3APa2o3B2iJneY5ZBjP7+IVz5jz9Hff/+tz+DkFNpUHrABYIoU5rgaGgl\nx8cdrCHfd8LIQYAwtW4rusLjw7L/CJkP5uqTkHb2aub94ksLsYP6vcwrF+K4y4Lm8PM9fUPYvfMr\ntITv69KTY/r9ejMMEK6ozr07UVGxMOrx23Z8BbVSgbPXr5v0fMxyBOEdHA2vvwkodfFkQdP4AJxN\nVTCVLkVZhgnv3ftnDDgtKFOa4CsqxFFNEMYEPQR+uCE4Qb7vxMKFuD59DGPNdiCdfb/ijDTy+/bX\nH4eQQzlw7Ahs4d/DkZSMr/bsgTM3AeXl5dBlpOBwN79RWjE8BlNhruz36dm/DwINUh+YgC08PybM\nLxHn09pmOBrasL+Kz4DP1SUi/8bNqKiogNMsZif37q0g3yd+7izU2EfJ/ODq7BNtHe3pUASD6B/t\nxmCIH0/G8Ofjvn8+Su+6GY9XjMHedhQ7OxT4zYYCBOfOQX1HC3n90Yxs2NuOQq9WYt6aecC29/nP\n++WXzHyUlR0PYZvQqPSiKfx57MebyOdJ31NLjk+ZNx9KtVr2/O/ftxfawS7408swnJWLkX4eyI8d\naYRxrgGN4fO5KC0HSq1m0vGpSU4kv2/hoRqC54Tv52ztxva33oM+Ox3mD/cj6HLzj7cfxXnvvYKP\nU2/BseqD4AAkzlyEsqADn4afv2HNBgxt24M6jxUYcEKx7QscOFKN7m5+/vjRj36EE42TAuE5OTno\n6REZjp6eHuTm5kYcd3vAjA2/uhNacwJsRxuw/8+vA+CZkHXnbwQANGytxNiuQyhTmlCijSe6qjKl\nCSUrVpAq9zKlCdhTB3+YeRAGh8CslZeXwzv+IIRa4A2XbCKFeYa8LMzVJ4Hz+eEdHkPA4SQnU2iB\nXqY0IX3NagxmxqGq14GEmYtgKhILiM65cjMaa58AANRt2Yn8UScKwp+hcNM6bLxQZE+FzyN3P+QP\nQKnXokxS13LJrTdh4J1tsB1tgDIUwsKACk1li/BERQ/0ahWyggaUht/PMKsQZfX8oG3s6AY4joBJ\nYdBvfvD3OP7rv2C3S4u6xSuQpFbhuovnR3we+r7hXzyb4B0ejfr5T8f9gNOF2T4VoDSFC/1mkvPr\n6eeZcOG+ELMDGqykXmN2QAt7+BhdVhrKwwz04ZyPYa9pRJnShIUpPAMwVlGN1M+rkRo+fs4DdyD7\nYrEAt0kXJO9nOXAU+869EQVOF6A0YXz/EYzvP4ry8nI46luxN6y9XpiSBSiURBokPF9gwsvLy5F7\nRR8aa/gxlN84gGX3l+PAIy+T45edw7NVCfNKRIeWMOMq3Bcq1YX72tRk8vrpFXVo38577+cc60JO\n+JiCn1yFjffdGi4iVEBtMmAWAEVhMZFfLMktROKCUmINRn7/AREcNX11HAKPvXLxEhSHf3+FSoVV\nZ5zBFEqWKU04ezOfEo0rKaSu107yegBw9JXPmfdzdfYh5A+Qxyuv/AXGvqqECUDxKr64cHhbBTk+\nfWM5eb201TXoOMyD+rnKOCTnFULgq5cWzsKK8nI0bBV/zxK9yKCUl5fDXteCfeT4YqxdxwMIbXIS\neT+hCLrUo0Ra+H+mglyUl6+GsqCYMF1L8ouQRMkk6PHuHRwhrydIps6+7GIEb3+cMKtzNQnYcOlF\nss8HgA2XXITGav67WvYdQfn1fyQL0/Dne8nrp569GgqVatLrT5eZirIwiefpH4ZxRjZKnBwmwgAc\nANasXg19TgYG3uXPV9x/PsOyG6+VfT36fu37DwPgf+/Z68SU+qpFizE8yKetnS2dKN+8Ufb5LXuf\nJc8nwXGYE9QCSi1p0lOeEft8YyrKQ9mB8Hhr6wHOWkke945YEHS5yfvZ+7uxz7YQBectRW6iHrvD\n3sIJMxdh1V6xc2+Z0gT1tir4bQ5oEuNl33/vH56FILza+P1r0f3CuwAAR30bysvvA8dx2HnLQ+T1\nVl8neiuvXX8mTM/zzlmWimry+VLKl0Idb2K/H3W9CceUnr0K6gd5/2p33xAWpZ8DjTCHpKVgaQzz\n9WxzJqpe4cfEsmEblq1cJXt8RacVj7cnIEGvxhKXH2ajJur5qLr6DgIui268Fv3vbIOnj9+cHUjJ\nhxXAnHQTuJ5xmIX57NbrkOTORIgD+g5VIqe7nXxfTqHA7bdfjKSMZNn3E7rHlilNSAyIoLfUrcCE\ncM6TkpExewnKF4k2hcLrCxkEue9z7NUvIOSS1qxZg9zwMfHUfG4/3ozeVz8k9zMuOBPalCSUl5eD\nWx3CzkdfgW/Mypy/hHmzsPiyi4Hf8hkpV0cvzlmzBoEQh7+/VosE2zjmQQ8oeemG2mRkPl9+nQvd\nM/l6mF1t49hnzMRq6vVLls/GdzaVY0FWHJRWG3b+ARHr7eLMfKy45zZy/9yrvgvVAy8A4LOZ56xY\nyW/ef/s0+X0X3yjaM8r9Xnv8udjZNo7hrDycFX6/ur5umPKKyPvrwiTFZNczPT+PfLmfvD8dMy1e\n5Jw9D7uuv5d9vKYK9rffRvu5lwDgGzcpawbI46bifJha8lDWyCPLRWnZWP9rMbN2+PBhnGiclBxl\n6dKlaGlpQWdnJ3w+H958801ccsklkQdyHKmspVMEdPraxFTKd7NylLxsJC4QNdSQ0T4KGtSAw0kA\nENOEAjxIoFkxWtvDpDWXlKEsXTx59YwuXDzpwapjyO0QpTXrrhFPylSh1KgZuYEQmReuZzyV57bz\nv5fLH8Ift7fD6BRTnekLxMrvlCHx96JTJ6bCXAQe+W9sv/RqcCoVZqUaJ5XLaKNUgY8fPIaOp1+b\nlg5ULgITTqYrKh20zEGblsxYCzrbe2SbGEndUZjCTEpDRjukjO46CMuBo6i98yHyv7TzypElAQDa\nVDMp5uV8/gjfdGHjNkoVxaWsXYYiShcM8JM37T6RedEG4qIxtvcwvMNjkhoIXn4QL9NoRGnQEUmU\nECqDHmqT6DBEyybI83RaFPz0aiiUSqhNRuZ4A+M/zP/G0kZZ3v5hIlWJJkcBeHmZ9LtrwpIJOq0u\nlaPQqXggbCMa/gxcMAgr5YXc8Ju/8i2Vt4tSC1oryThDNHdINOz8mKB9oqWNL1hpkCgFYTXh9vBz\nxZSwoDOmtYuTecrSEh8BhCt1Wmas6nMyyIZaLsyrRGmAZf8RRhfO/D6T6MGFkJOkdL/4Hvlf0rL5\nOOOVv2Duw3cT+aDfYkPd3Y/I6tE9AyNEc0yncGlZICNRmqQ4k/4d6RQ/+WxRpCiTBa0Ld0qKM6Xj\nP6Of//z7u/j5j/YHjx9mi7cCNge6/v227HvSUhSlXoui224QH2vpRMgfgLOtm/xu6sR4xM+ZSY4x\nyHx3AMjYdGbE/+IkcpTktUvZ7qh9Q0zjGVqKOFmklM2Ex8TnwgwuJzoOy1jocRz+fagPHHjfZbp1\nuDSGP98rOpooFMi99lLme8bbxpGbqEOiXs34+pesPwN/OKcQ581KRuistcxrJi6cHQHA6ZDThHMc\nx0ix7EkpGHGKa5UuLTbnMHqdor+HIS+T+JMHbA70vCpKUXKpjt5QKDA+L1K+oSmdCY05gUjQgi43\nfCMWfNQwCrs3yEpRCiMlbKuoQuN/7O1BS1YB8/i1m1diRX4iDBoVdGnJyLqcL+rU52Qg7/vfwRmv\n/AXrDr7DyOO0qWa2Xq+pHc72HjK/Kw06pJ65ApPFjHANHS2BSR/oZYoyp9KDA6wchS7KpyW5I5/v\nRc9LW4gTmmCrCwArvtqG+ZX8nLmhOJkpJDfMyGFqWE5lceZJgXC1Wo0nn3wSGzduRFlZGa688krM\nmSOvCxU0z7TVGV2cyHa07IroFqdNSYqozqaLDiea2sFxHFuUmZ8FhZL9itEcUqyHRRF/4pJ5mJsh\nFgXWDYnA1zgjB4pC/jXUAT8xxo8rK446QUYL+vsD/EKiz05ntJtFrfVQc3yxSogDDE6xeI2enM2j\n4gVID0YAONInPieaNaEQchaF7r4hVF75CzT98Uk0/O7xKb9XtOj+zxZsLz4XBy66WVY3KdXI0mBk\norGdbL6kle1C04JQIMB2f6MuXAMF6Pve+ASHLvsZWWg1SfGY+9ivIuRVgiSFDkFnDgCDn+yE3z7B\nNEtJWbcUeT+4nNFoJy2bz7y2PitNtMkLhdD/9lby3RUqFfTZ/HsYC3KI5k6dGI+Zd9yI9VVbsO7A\n25jxoyuIdZhU6ys9/wCQI2mUQIdcO2xXFwtCgm4PKXhi3VHYyVGqCzcygEu8xl3tvWQzFvR4ZTXg\nwv+crd2iBSB4Fqr62ruIZESXmcpoE1mw3ym7aTBS7hhOScMexl2JbhdPa8LDjaKI245SSUAsPUYm\n65rpYTztxefQi1y0okwhEuYWkwJm7+AoXB29KC8vh6uzl7DxCo0aqWFXkMlCCsJDXh8slDfwgifv\ngzrOBHW8CfP//jvy/+FtFRjdwXaA7X9nK3YtvhQ75l+Eyu/9gtFAm2aKi2KsCxv9W+XRgCUcJwLC\nmQZuknoT6fhP7+sBOA77u2xoHnWRLntajxsqa2SxfOczbzB+x0IMUa4oaWevhj4rjVx/nD8AZ2sX\n32I+HOYVC5k1TLoGAgCUSoYcEsJYkEt0zPrsdH6sxJsIiAt5fXA0iGCFLu6eLBQKBZylIoHUu0f8\nvN4RC0Z2HMCBtjH028WitnG3PPFir2vBsVv+ACCchT5/LYz5WczcH2+zYG6GCT6LjWx+VQY9dJmp\nWD0jCb88cwZuuOu7pCAbAFLXTz7epW3ouVAIfouNzDM+rQ4egxGjTvE7MGvjJF7hDAinyBeFQsH4\n1gtAUJ+byXTAfePYEHanFUW8bqUhja/zohyURpq68OoR/v3MDAiPtCem3X4CIQ5jaZkYS+M/X8L8\nEkbzDgAL/nkfNjRsxZlV72HuI3cj7ZzVUFF2lULQc2/Vlbej4Xd/I/dTz1wOlXFyowqhOHOEAuHJ\nwwNIpOwBaWvOaKGRIZ8AoPjOG8nt8YPHmA3y3MfuQWC5WFOw4aM3kGIdw9qCRNbNqSCHJYpPYXHm\nSfuEX3DBBWhqakJrayt+85vfRD3OEgbhdgqEJ9IgfBYLwl0ME54ZcTwAzLzrh8Rj3G91wDc6zkye\nso0vZBxSAhNO1kpu0WzMTjdCaCjZOe7BRLhF75baYRzKLYU0YmGapCEFLJkXh2UI80sI0AxZ7bgp\njtoEUEx4HAXC6S5Z0sF4pJ8C4ZMUZQKALtVMJjO/xYqQP4DRnQeIl+jw53snLTaLFn77BJru54s7\n7DVNaHv8hYhjaOZdn5HKg2hl5BCNn1tMWEkuECSskW9knFTXa1OSGLsymjGUxpwH7mBYczpyvncB\n+QxZm8/D2j2vES/ikNuL/rc+YxbNlLXLoDYZMPP2H5D/0Y1qhKCt7Dopv259rsh8KpRKLN/yFJa9\n+yTWV72HWff8GNqUJBhyMzHngTuwvvp9rPjgaSx46j7mtTUp7PlXqFUo/Pl1iBbSYi8gkgkERDZy\nUiZ8MTum46jrWm0yioAjGBRBdkunrAWjAMpsNZEODHRGLf28cgaoMGC/o4dp0CRcVybaHUPiPMMw\n4RQIpruy+S12nigIbwwNuZlkvNGbHbl25EIwjXoo4E4vsnIe4XQoVCrGctESHot9b4oSktSzVjKE\nRbSQeoVbq+sIUDAW5DAbgpS1S5F3w2XkPs2Yh/wBNIW7HoLjMLa7knQfVWg1DNiPmy2CjbHdlVGL\nM71U1iD17NUMkwlENumJJRgmXOLWI20KZnI6EGezom7Iids+aCIMabpVBArGmflkfQnYJyKcUvxW\nO9OELfNivmCOtqt1NLSRtRIAkleJ5xYANAlxjGsUwDdOkQPQSo0ai59/EPk3bsbi5x8kRbA0G047\nSGhjZMIBQLVQ/L0dlby0w2+fwP7zb0L1NXei5/rbofGKG2eLK3LN8AyN4vANv0LQxZ9zQ14W5j76\nKwDsZiPeZkVZuok5R8aiPOaa16WnMBtNuU0J8/kNOrIZEbpm0uDZnpQMKBSkMJN/D/H3kSvkBfgG\nNWTjrVBAn5XOPC6X/c69+iLyXT5pHMULVQPoLGbn0aBKhS0OHdz+IDNud+6uh8PLz505DnH9pC04\nhShNM8JsoLJqSiWs9/8ec/9yD5a8/FgECaVQKKA1J0xZ+0evb74xK0Yp6930KK4odBSEQbhPb4A1\nmb+uVaEQSjvFDEtMTLg5knwC+Cy3gLW4oNghVZeVhuzNG7HomfsxnJlD3vfsjmOI06mZgn1jQU4E\nRj1V8bV1zLTXNsM7PCZafykUjIG9Lj2FLBQB+wRxc1AZ9IRVpHdcmuQk5F1/Gdv6uLkTbjqFIOO5\nK+eQYjvaSBbT+NlFUJuMMGhUKAp3ceQA/HRLE655vRZPH+hD2+zIVFH6JM4D0UIKwjM2rQfAgy9a\nkjKvowFLc+OhCIVgcInSGGm6UQiaCR1x+tBr4xdSrUqBuemTL8YKlYrtDjhigWWfCDKDThccddPz\nCAaA3pc/YBw6up5/O4KBlPpPKzVq2RSpsTCPYQ4JOKSZxSyW9U1aUoZl7/wDhT+7Fhmb1vMbnaw0\nFPz0mggZihAVFRVIXFyGtRWvY/X2FwkTmHu1qNFteezfhD0xzMgmQCX/pu9i3t9/h7l/uYdp7ytE\nxqb1TPc78t0kThhqkwEpa5bIgihtciLMKxZGyBWkcpTszRsZRlcaNPiKJkcBRI/1yUC4IT+bsYqi\n2QOABRxjFeEWzVHGk8A20Bt3uoufENIFlwH7gSCjURdAuD43U7QpHGJtCl1UFo5JvTIWWFbGp5dO\n/zKWmBI5Ci3FisaEJy4RJT3RHGfooIGaZd9h7Nm9G31viyA8h+rUOllImXC6AVAyxdQJUfBTUes5\nsn0fSeUPb90d8b2FMBXlMTZ4CfNmkXRxwOFkmjzRwTThykpjFn65Jj2xhJGSJrp7BplzI+eYk9Hf\nDQ4g/S50aiWuSRU3j3ElBSi+4wfkfsc/XyXdG0P+AI7efC/5jdTxJpLBii8TyRRHXQvZSAG8m5I0\npGw43V1XGublC1D20F1Md0PWa1wc67TcYqpIXiVaHSqP80C+69k3CThN7GjHpa8+A5Wf/02tEiY8\n6PbiyPfvET3O44zw3nEl2UzQTHiC1YKyDBOv2w+HXDfouY/ejZyrNqHsobuYOoxoQRMv3uGxSBAO\nMHIUusHT4Ec7UXmoGbd/2IyXqgeIHMszMCJmbDNSInzraQwDAFAokHPVJv49PQE8e5Afd+64eDhm\niHPnWFomrEEFtjaNMQRCx3Exk1HmFyU/cky4UqHASqp1e3aCDj/ctBB5110aNUsaS+ReewnmP/H7\nyCyNUhkTLsqM10Gr4oH+cJb4ubNaxHlfuumWC41MBtg0awY0CXFIk9mUzbjpCig1auRmJaH7QnFN\nzz9SBb/VTixzlQYddBmprFrjFHbN/Pra1odC6H7hXcJ4mYpnQB0nAguFQhGxYANhSUl4J5ZxwZkE\nuBTf9UOoTQZG/+ls7mCZcBlrLzk5Ct2kh14AaUnK0ISP7IoH8grhixMZZW1KEjPJxRqmmflkkc3Y\ntJ5hJGkQPrpjP363oRBXFxlJQx9NUjzfKEXG1zWUIH42WooyNyMOWvXUp5yVpIzCso8tOqDb18YS\nIZ8fnf9mWSHOH0DTH/+H+Z8cuKN14UKYivKYSUMA38xCLbNzTilfitI//ByLn38Qq794EWcd+QCz\n77t1yp2+qSgPCfNKyHFZl58HRXhyDVAp55R1onRFoVAg96pNyLvu0qjeuylrz4j4v2ESsBxrMKyY\nQsHoTuVCVo5CAVEhPAPDfHMPwY9eoWBkN/y/FEiiWElplzS6Y+PQJ3xBm6NBBOG0f61wfdKNe+bc\nfzvDBKqMBiSXR/6OtMyBbnYhjCulWs0wzvSk6u6W7zNAT/J+i43Vg1OAjmZt6A1WyyPP4ovCDai5\n7QG+AyTTsl4EHTnfuxDFv/oxiu/+EXK+F7mBk0by6iXktmXfETjqWslmSmNOiJkgiADhFZTMqjwS\nhJsKc8XmSBxHaiS6nn+HHJN/42aU3vtzxJcV85Kq27/PvIZCqUQ+1c66+8X3IvTlAaebYdK1KUmM\nBCtxUWSTnlhCZdCJwCEUYthvqRwFEHXhAN+58ZnLZ6NggmYf85B52TlE5x50e1B93S8x8MGXaPzD\nE0xDpbl/+TVpiR4/R7xGhrftIRsYVZxRti5EKnuMhW1kni8nacHUFnB0FCyfB5+W3xDrxsZgr2tB\n5zNvMMfktzdj01svQBEMwuIWmXDPwAgObb5VzGYplVj07ANM5tplFj9LksOKvCQ9y4TPjASZhrws\nzP/775B/4+aYvgOzzg2OMh2DHWEQbvME4Avw2dXkVYuIhDTk9aH23idQP+zEK0cGsaudnxOj6cGF\nkDLhqWetJOfjg/oRuP38e+Ul6jD3YvG8ClKNt48PQ0fVqSSEfcHnZ8ZBNyi+t9wmBQC+tyADiXo1\nUowa/HZDwbS6vEYLhUKBnCsvxNq9b6D0vltJljrrO+cwhF60UCkVpLcKrQtX+EQpUCxyFLn3SlzM\nb8akSgWVych4qF900wUIaPjxHGrvwvA20c7QOCOHx6e0fC1sHHAq4usD4eA1wUJIpSUAZJsL0H6+\ncaWFKN/9KlZ8+C/k/5C/0KT6T1cXtTDKpHJNM6ndTFs3Jlo6mXb1SUtEAHFBaQo0ShagKRXAhpIU\n5J8vntS0c1ZHaM9jCYVSieXvP4WVnz6HhU//kXksZd1SsuFw1LdB5/dhc66ox9KkmPkW5RIQBABD\nSlGDRRfELM6JizhWLmhGxHLwWISu1TJNED7w/naysNAAanhbBVPUyILwyJbzQhhn5hHdNCAytHSD\nlWidAacT0kpsIbTJici4IHLhS5Xox6eKrEsjC3mn0gDHEvrsdLKJK/zZNbLXFR1SOYrfamc2F0J4\n+kcYzb021SxbNFjy21tgXrkI+T/8LpLXLGEeSz9/HSlKHT94DN4RC1OUmXmJ6GPsbO0CFwzCQTVK\nSjuvHKV/+Ln4ehvLodJH6hSjZYlogBxXKkohHOE+A1woxDLh1PzDMOHjNtmiTIBlwoWNYdDlQfv/\nvAwuGET/W5+i/clXmMwNvalUajUovvNGFN/1w5jAZcK8WSRT4h0YQco28ZrKuuzcKTsnCkFfMxPN\nnYxUIUVyHoXIu0EE0L2vfQxbTRPZpCvUKhT94gYU/vxarNnxEs5p2sZ4dQuRc+WFpL7BUdvCzMcA\nm+HSZ6RCEWbYsjafB9OsGZj165/E9P3kginipYq55DJBBcN9iNOqcPPybDy2aRayE3RMNs9YlAel\nWo3F//sgmbc4fwDHfnIvcUABgOJf3oSsS0UXLZoJpwtYzcsjs1wAC6IT5pdMmuWSC1ldOWIvzASA\n/FQTBvLE6+fYz/6b9O3wacXrsbjhGDa99QKUdQ0IBQIYP1SD/Rt/yJzjOQ/cgbQNK5n5tkcnrhMp\nE1YoFQrWa75o8jktlmA3yywTHkgTr8cxV9grXKlE2f/X3pkHRlWea/w5s+/JZJvsmawkgSQEIvsO\nQaECIggKl6JAtVq9Vi219dLWHVy4VbRai2vxurVVsVQoyL2KUpUq+yIgi2wBEkJCFsh67h+Tc+Y7\nZ84kM8nMZJK8v79mOTNzMvnmO+/3fs/7vI/fKz6esGsHUr93LSRe/PIULl1plgTySgXE5swUqI3u\n67NQkFnf2IIP97nH+fzieGQsmgV9fAw0NguOjHbNixV1TXinwh1rRLYF4beWxEvNLLz0FkiK0OO9\n+QPw57n5yIkxKR7TWdQGPdJvn4ex37yPEZteQ+Fzv/X5tYIu/Hyi8uLBFzmKUiY8sk0eae2fLRn3\nyfOuFQ0DAGBgZhySr3GPv6PPrxFvC8kajdno7mfT3CLZCe0KIQ3CmxhnDdtAhR3l+h4AACAASURB\nVCA8WzkTzmLJSoN9SKGYlZQE4YePy/ScngNRZ7eJX2prQyO+uvY2idyCzYRnRBvx7vwBeG5GDlbP\nysWauf3xtwWFuH+cE+m3zoVKr4NKr0Pq4hs6+tO9ojboETmov8fFVmMxwyLsDLS2omb/96KWCWjT\nbgPQxXoG4cdbXRfdqstNYjU/AMlWVHuwGYKyDzZ5PH/x610+t2fmeR7HXnxLvJ/+s/lIZLJ73/32\nWVFjLpejAMpBuDlDJkdpu0izQYPNh238rpA8T1YcxnEeAWdHOKaOkVRnAy4noEAwaM1TmPjdBvT7\nzc86PFYfFy1m9psqqz3aDwtcKTvfrhRFwJqXiaEfvoD8x+/12GXQx0bBPrQt283zOL9hi0SOEjtx\nhHiRaqqsxsV/7xHlPnpHDAyOGCTPn478J5YibckNyHv0HsVzELpcKv2t4nmyWtzvXEF4w7kLYpt3\nbVSERAYk1YRXo46ZhNktYiWp1KW9hyRNkg6v+JN4XxtpVSx48hVOrXYX+gIS+Y2vUhRAGtw1VVaJ\n52ftn6242AdcUiDhAtlwrgK7bvuN+Jxj6jiftrm1kTZJcH7itfclz7PdWgWZGadWo+gPD2L0528j\naphUN+0PbAB8ab9rx6TlSoOiq03q+VN4b/4AzC50QN2WnGHdOoTsoyXbiaF/f0nxehY/YyIy71sk\necyUnqwos2IlHyyspCF+xiTFY9rDkOwZhHM6raQleofvoVHhUo47q1vHJEA2zZiHb0a5Fxk5+3Zg\n4u9X4H/zpmDbrDtFez9OrUbuI3cjbZFn5vog5/7dGS9WukwX2O9aIRPuL9Id33JJEK5itNwV9W5J\nSuTgAZLr1/h//BWqlhZUXWnGy9vOSDPhCosdTq1GYttv0laQI+5SffxdhajtTrDqMDbDDkNiHMZ9\n+wHG7/47Rk91J3j+1eIOniMryzEpMxLJl6vdHWnjYyTuVx7nwHHQqoMX+mnMJtgK+vmVmOwwCPcl\nE66gCRe66HIcJ2a+tXYbnLfd6HGsJAHEFIlLGj4GQRce0iCcRUnrqCRHUSqulLyGzWQcOCL5EXh7\nbf4TS8ULfXN1jbjVqbGaPTJoFr0G/WLNSLMb4bDqYNa5tm8iCvth/J51GL9nHSLkOq8AYStk2tzu\nPujRYhhQ1vEdbNKgleex6XAlmtsEjPlxZjjt3n+YLOzkxOpxBZoqq1HXQZtpgYpPvxa7mapNRqQu\nnImcB24TC2prvzuKU//j2saWWBR6CcI5rQbG5HhptrGtaKt6J1P0G4AgXPBbViJ6dIlkZW0ryPFp\n641FG2lDzDipfVMgMuFA20Qbaev4QLgyPEbme2YXpWxwcOXMuXadUXxFqH0AXLtjgrxFbTbBlJYo\nkYyVve/WCAvBB8dxSF04E3mP3uP1O5d3CwRcY4fNlrABmJCNlzqjSP8X7CTfeLFa4qjBylG0dpu7\nxXVtPZpr6zxaKLPtufVd0GMKsJIUseFRttOvxajc0lUgWkHuI75Gq5EsSNndgVSF4MobqTdfL94u\n+2izJOEgke0E4LtikSzE2sbA5VNnRV2vIckBtcUV9DRWXEQzIy/ieV6SCWd3nIxJDgz98EWJTNFW\nlIuCZ5Z5LExVGo0kIy/grZg8cdbVyLx3ETLvuUUxmOgIY5JnhlYfG+Vz8z0BVZFnMezF+EQcKhiE\nLVfPBDdtsuS55po68G1b+NqoSJS8+wycP5krPs/Ot3vrgKY2eQB3+QqaLl6S2EiaApEJj5dlwhl9\nvI7JYrMOKQCQ818/hapNShRdfhZFX7tkdRsOXcCZw+7x780tLX/FLzDy0zcx9KOXoNJp0djcir/u\ndS805xS5F3mcWg21QY/p+bEwaV3hWr3ZKu42GK5cxm15NskCRUkPHu4IsUm9xYZaqyyY9rLjL0el\n04q/VQBtvUbcv++Muxdi2McvY+Snbyr+b2InjhDjEhZWtmiRWGn3oCBcnpXi1GrY8j21bhYvmvD2\nMKUmiBe8xgvu7I3eEePVGidm7BAMWfuixwUnYmCeX6s3rc0Crc03iUdnsDHe6Jd2fye5MOnETLjn\nFmKF1ojDFfVYf9Ad1E7J9V3v561Ah5UG+SJJaa6tw9FV7m2d5PnToI20wRAfi4z/XCA+/sPqd8Hz\nvLSFcttCwCjThJucSS4bPyZT0XC2HFfKykX9rdpklLhyBANOpZIUaMqDaV9hXVIA6XccStgFReVW\ndyt4QVMHtMlRfMiEd4RjitvTuGavW69tzcsAp1JJFuNnGUs3j6KmdmA14QL6uGhJoMFafAoWet6c\nUQBAbTKIsgm+scm9/ctxkmM5jpN6hZ+tQJU8CGeQOyh0hqgRngFb0typfgdWSjKuaIWiTJbk+dM8\nXIys+VmS7HxHRBTligEr39iEU2+7XUQaZEWZgUQahHuOAVN6skTHyzr1NFZcFBM4aovJYy7WRUfi\nqr+uQtptc5F007UY/ObTXnc82LEIuAwJIoqUF1AqvQ7Zv1yC7Pt/ApXWU67SEUpyFF/tCVmiBvdH\ni6ze5YtxU8CrVIg26zDhj7/F/y7+GfYMHoEam3uxbCvshxH/fMXr4q6usQXHqxpwKdIdeFV9s1d0\n6tFGRUBn9y3B0B5sEuHKOakm3Mr8DtjiTMAliTIsdhclj9j8D9EJ5ugBd2CmJEcB2qwKczPEsbDx\ncKXoHhNt0qI02/N/Ydap8WBpBoal2jCjfyyMzKKfP10mWfwqOaOEO1nRRtGNrjpFusDSx0a12yuB\nhTUlsBXkSH4fHMchclC+Vyc0tckgNn1jYQ0+2L4GgfIKD0kQLq/wtvRLVwyQhQCLpSNtL6dWK2vJ\nO8goRhT2w/D1r0gcWqLHtH+xCTXsuV3ac8hLJtxzhXjZZMbr35SJrigmrQpj0n3P0ioFVxqrWZKt\nEjqOAa7t2+rdB1H5rx04v3ErTr21Dttv+RX+t/+PRPs+Tq1GGpP1SPvJXKjbsgl135/AxS93uuVK\nKpUot9EnSi+6wpavXHdbvZORohTlKhZD+os3TbhA+h3zkXTjjxA/YyLS75jX7rHeiLt6lLh6NyQ5\nFHVtoYDNDFR9425cxW71+ypH8eWz5B75gDsgYn/Pgi8woFxH4g1thNVjkS0vPDOmJoqZj8YLVWgo\nr5QU5CktiJQaIRkS4zx06RKHlLPlkkx42q1zvR7bWawDssVxlK8yAyoVEmcru/60h3y+5TRq2Ie3\nL/cwJsdLCskBVxbc3wUAO7+c/POHYhE/29RI7nrUVcxZaaIk7Mqps2iqrpEV9yfCVuRe/LE7g1Ip\nSqri36sxm5D30N0o+P0D7Qa68gLmyKsKOhVg+4Le4VnQr/OjKFMgNSEC5xLdv9Xy+CQczneNlVtK\nEqBVq1BbMhibZs7H6qWPIuGDl1Hyzu8xbN2fFK/rwnx74HwdeAA1Nve17cLn7jqHjmpcfIUt9qs/\nclJ0w+B0WtiT3M9VyIJwAKibNkW009M3XEH2D666FX2Fe370pW9ISyuPd3e57Q5nF8RB50UqMjDR\niocnZ+JnI1IQk+P+DmoP/yDdJXD2vCA8xqzDnSNSUJJsRd4I6Q6LL3pwAbZuJ8IHhxw58UythgAr\nNZT3swkEIQnC5dtqShdgwLXClwfPvmQGlbaelZxR5BgSYjHkwxeRtXQJ0u/8D6Qtmdvha0IJG4TX\nHjyGK4zfsS66LUhVmDyvmCz4lnFFGZ9p96sKWmnQ24cNlGiehe58DeWV+GLMfHw5+RZsu/5n2P7j\npdh77+M4v34LWhvc23gJM0slBUQas1GiwTr6nDtjro+xuz1t5Znwtq02ie72TDmqdyh3Yg0mapMB\nBc/8Fwa+9IjP0g85GosZg15fgaS5U1H04kN+By6Bgs3asP83W1E/MfvbUluPuiPuiaezchQAiL92\nnMdjQjZQSZYG+JcJBzyz4fLCM06lgiWPKc7c/72kuElJGqRVyMCZFKxQ2QVAzf4jYnaV02nRb9kd\nSJx9jfi80vzlLyqNBlFM5jlm7FWdkm6wdpWA60ImuHi0RyrjGa6JsCJh5uR2jlYmfvpE8fu9fOIM\nKtu07Ve8FLAGApVWKgWpOXBEYk9oTEuSdGuu3uV26mELBU1dzD7Kg3B7F3TuHaHSaBQWqP5nwp12\nA77Pd4+5Lya5dkSKEy1iNjfK1FbrxHGoT0xCzLihHRYbCx2qayPYINzt1OPN+cNf2CQC263VmORA\njNWdJJTLUQCgvBE41N8d15RWnwB4HtZqd+F6nb3j7/TLE9U4V+t6f5tejak+7lizc86++1bgzF82\nuJ8L0PcTaq7Ni8Hj12QhY5gsCPdBDy4ey/xPIwf571gXK+upwKnVMDDyLUuOE5FDCpE8b5pf9Tbt\nEaJMuHRCaS+jxV6AtZFWn+QeSno6X7W1GrMRWfctQr9ld3SpOCoYaCxmsfkD39KCC1+4ZQK6GFdG\nTr4F2spxuGKQ6pqm5PoXLClNyFEjimHtnyVmrxvKynH5RBn2/+ppRScBAWt+FrJ/fRvyn/iFx3PJ\nbf6oACQG/+wPSZ61EQpytHabqFduqauXfDeBCsLb04QHkuhRJSh4dhnsjD1fqPGWtTGlJUnkEmyT\nnM5mwgFlb2MxE57lmenSx0X7HYDJg1ulxaVcklIvCcIVCrsVMuGsM4r4WcyF4/yGz8XbtgE5UOm0\n6P/kL+H86U1IXTwbKfOnt/+H+Ej8dFcWZ39rHdI6WSwuz1AqWRMqETNhGJJuuhZ6RwwGPHV/u4Vh\n3lAb9XBcO168L+yiNXixcgwUEknKPtkYSE2UJI0u7f5OLEpns49ddeuQy1Hk18xAI/+9d0aOkhJh\nwM6RE7B+1o/xt4V34lhuAXRqDv850r0rwDaHqfTSNVNAmG+FDtWsHEXShjxAmXBJEoExGjAmxyPW\n7F4oyOUorsca8UOWe1xY9+zFrGQdNG0mA1cMRvx88ykcOF/n8VqWvWfdzfeu6Rftc7KMVRfwLS2i\nLAoI3CKlu2CTj4Bv9oQCqYtmQxtpReRVBX5bdwKuRDD7OkOyQ7IjpY+NwrCP/ogB//1rn60wOyI4\n+10y9HHRMGeniRqa9rYJzJmpEKZcX/WxSvpfpexUTySisB/q2/yS2S5dgiZcHjA3WSwSfWZWtNFv\nKyKdgiY8angxVBoN7EMKUPF/XwMADjywEuWbvxSPiRxS6GprbTHB2j8L8deOb3frMHJIIUwZKZJt\nXdff5P58Tq2G3hEt2hAKmXCO42CIjxW9fVnLq854tvd15BlQ8fHUBBgSYsX/EauX7UoQbs5MhaVf\nusRWUugAqxTQ+JsFBzwX50q7RqxHc82Bo1JNuEI9inIm3DMIZxcMbP2EsEBUmwzIffCu9k7fbxJv\nuAZaewRajxz0kIf4ikcQruBlrwSnUqHg9w906jNZooYX49SatQDc35u3pkaBQtIs58D30nbVaYkw\nZ6RAbTGhpbYejRUX0VBWDkNiXEDdOnQxdlhyM1D73VHoYqOCPofJdeFKc35H6DQqxNtNOFDsrodZ\nMCgBSRHuZJbd6A5mL17u2Fe5qaVVzITXRCgX4wUqyFSbDNDYLJIAFnDtCsYwQbiSHKW8rglnUjPR\nrNFC09yE+qMnMaPpPIRf+qXIKFRebsYDG47g1dl5sJuUs/+Hyt0N7Ni+JB0RO3E4il9bjuMvvSvp\n26Ey6HxSAYQzxtREyf/FHzlKzNghmLDv4y7JURNmluJMW7Mz+eI4GITMHSX3d3fBlJGC1EWzPVY6\nLOwWsq+DSSkT7s0ns6fhLfgQ5Ci6GGkQro6Uaoqn9PN/ctWYjZIqY43VLDaNYLdJ2QA85cczMeyj\nP6LkrZUY+KdHkHn3wg61e4LJvxz5jy5mvGuS18XYJW3R9QoFbdqoSK8Bpb90pAnvTShlwnXRka7u\nk14KB7siRwGk2XBjSoK466U2GTyKmtgiZV+ROx0pLRrYAKx6xz6xuJdTqxUbRfmaCZfovBknFHb8\nBhpOpULc5JGYevuijg/2Apv4UBsNksZLoYAt5qz6di9aLjeg4bx7i9+frJivsN02a/Z972Fzy6lU\nisWZQjMpIDCB4cCXH0PmvYsw+H9WKnrfBxJ5EN4ZOQoApEW6ZRsZUUbMKpDOFWwm/GJ9+5nwUaNG\n4VBFPRpaXFlpjZd5J1CacEA5wDMmxyOaCZor65tElzGBiromtGi1OOV0L+JPvf138XZ9lGuuqWts\nwduM5pulpZXH4QvuTr3+JsscU8Zi6IcvYNTnbyHttrmIGNQfeY/d69WQoqfAcZzkN+lvsqer9WAx\n44ci856bETNhOLLvv7VL7+ULIQvCYyeNwJh/vavoHcwSP308LDnp0ERYfU73m9KTxRbU4mO9JBNu\nK/AWhAuFmdLJ0xzrDhL0GhUmZHVucmUnJ7Y1upLjgTE1Ef1+17EftRJJN0zxcFaQ/+jyHr0Xxa8t\nx/ANr0j0qUoFbRED87pNV92TMSQ6xCY6AsJC1psEoLMXboGE60vFojh5UbRckhJRFIBMeAdyFLba\n3ZDkUCyM0yp40ZqV5ChesjfhvktjciaJLeGdd8zrVCfKrmBMcogLgdbLDSj/ZKu4iNFFRwblfNgx\ncGn3QbTUuwIjjdUs7nywxZlV3+5zNXVifOIDocO1ZKUh+5dLgmZ5yyL3sPanWybL+ExXMsioVeHe\nManQyJrb+ZsJ313mzkqnZCvr7ANZeKgU4BlTXEWlkQbX75+HKxAX4Hke5W06cVaSUvHpNvF2Tn/3\n7vw/DlTgXI2nrvxE1RU0tHXjjDZpEW3u3Ni2ZDuR99DdGP7x6oBJ27qbxFmumhJOp+2081hn4TgO\n2fffipK3VvauTLivaCxmjPzsTUzYs07RdksJlU4ryUapTUaffCV7At52DQQXDa3dJlmARDiiMDTF\nBhUHLCiOF33N/YWdlFkP4oiBedIOfByHglXLfCreUsKQGIeYsVdJHpNfENRGPRxTxnpka5U0woHM\nNIZKEx4OqHRajwuSIMdQWuxoI61dztZZsp0oeecZ5D58N/r99k7pc7LizM5kwnXRkRIfcaVAQxtp\nU+7K6qWmRKfgXqO066b0nWlslpDoNbsybjmOw6A3n8bEg/9E9tIlATwr32EX+mUffiLeDoYeHHAl\nMoTaGsGRBXA5bAkL+kjGqvPEa39D1fZ9aL3iCqx00ZGS7ns9AQ9NeCcX1GMy7Hjthjy8eoNyB0ZJ\nJtwHTTgbhPfr75nxNiQ5Alq7pbSzInw3rCTlAhOE1ze1iu3ly3KY6w2jK3fmpSI/zlXg19TKY812\ntwe5wKEKtxQlJzaw3St7Osnzp2P4hlcw5sv3fHKZ6cmEXRAOuC4E/mY82KwXO3n2dLQRVo+svtZu\nEzPT8tb1uuhIPHJ1Jj5cWIQ5RcrtiX1BaFOtMujgmOouVFAb9JItaudtN3apYx0AJM39keS+rxow\nuX0hEDpnlN6IfLITAlGl4KerUhSB6JGD4Lx1rkcQw2456+Oi/aqQZ4mf5nLgMSQ5vGY1LLmej3vr\nTyC3kNQ7lLvT6R1edmn86EPQXXAc161BJVuUWP7Jv8TbwdCDC1j7Z3k8xsoh464ZLRYEttTWY9dP\nf+c+LoDyiFDhqQnv/K5WUoRBIt9gYbXQHWXCW1p57DvnLmQsSo/x+L0FUooCKM9jghQu1uxONpUz\nDinna923VZlOxYSfKTkBi65yzyGffF+JExevSI45yOjBA91CvqfDcRwiBuYpdh3tbYT/FcFHWP1n\noLoOhgvyLKD8R89KUgTNqkHTtX9txt0LUfzqcgz/+GWP7b9+v7sTtoIcJN4wJSCaqbhrRktaJvt6\nsVXMhAcwCO9LmnDAs7mEIAtQ0t53Nij2Ffb/aB9a1OlFde4jP8dVf3seIze/Id3BYWB14QLeakrk\nmXBTuvJxaqPeo4gzVAvEnj5u2boT1i4z0I16WNgCXQE2CFcb9Bjw1P3ifbaxS090ozCmxIs7qNqo\niE7vZHaEP5nwuNxBuNImz4izaBFv1XsEYYH+rj3mMZVKHGfeijPZ2zFWPaLHSHdyAddcWphgRUmy\n67rWygOvfyvNhh9mMuH9KBPeZ+k1QXgUY6UVTI/V7kAuSZG36mYr2wPV7EWl1cAxdayHfy3gspgc\nsel1FD73m4BsDaoNemT/8icAxyFiUH+f9b/yi7IhOb5TVluEC6+ZcIXgp7MaUl+JKM5HvwfvQuLs\nq5Gz7I5Ov49Kq0H0yEHt+rgrjXF5y3oBuSa8PX2qfEcnmEWZvQlTerLi+ApqEK64EJOOgagRxUhe\nMMPjuJ7oy6yxmJH9q9tgciah37LO1fP4gkWnhrZNJ365qRWXm1q8HruHkaIUxruKtOW7cKYuutDI\nkf9GDQmxYi2ItyCczYrHmnWKQbgx2bV4uLnEPYa+OF4luqE0tbTiaBeKMoneQ5eC8KVLlyIvLw9F\nRUW4/vrrUV1dHajz8pvokYMwcPWjyF/xC0nntd6AvLmR4IwiwGbjOuowGq6kLZ6NSYc2Yti6l3yu\nbpa7dgQ609iXNOGAZxBuTHFdQHTRkeBk8rCu2BP6SvpPb0Lh878L+s6WkkzFV024kjOKgDxoDFVR\nZk8ftxzHKSZSgilHsTFuDAJKY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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "\n", - "import pymc as pm\n", - "x_t = pm.rnormal(0, 1, 200)\n", - "x_t[0] = 0\n", - "y_t = np.zeros(200)\n", - "for i in range(1, 200):\n", - " y_t[i] = pm.rnormal(y_t[i - 1], 1)\n", - "\n", - "plt.plot(y_t, label=\"$y_t$\", lw=3)\n", - "plt.plot(x_t, label=\"$x_t$\", lw=3)\n", - "plt.xlabel(\"time, $t$\")\n", - "plt.legend()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "One way to think of autocorrelation is \"If I know the position of the series at time $s$, can it help me know where I am at time $t$?\" In the series $x_t$, the answer is No. By construction, $x_t$ are random variables. If I told you that $x_2 = 0.5$, could you give me a better guess about $x_3$? No.\n", - "\n", - "On the other hand, $y_t$ is autocorrelated. By construction, if I knew that $y_2 = 10$, I can be very confident that $y_3$ will not be very far from 10. Similarly, I can even make a (less confident guess) about $y_4$: it will probably not be near 0 or 20, but a value of 5 is not too unlikely. I can make a similar argument about $y_5$, but again, I am less confident. Taking this to its logical conclusion, we must concede that as $k$, the lag between time points, increases the autocorrelation decreases. We can visualize this:\n" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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jsXXr1lLjKcrLV+p3Q0XlqlWrFi5fvoygoCDcvn0b9erVw/Dhw/Hf//5XnUZWVhbHPZBN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\naWruK5afblT6KDkVBZl3S6WvT7mlniPdz4nlJ7a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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def autocorr(x):\n", - " # from http://tinyurl.com/afz57c4\n", - " result = np.correlate(x, x, mode='full')\n", - " result = result / np.max(result)\n", - " return result[result.size / 2:]\n", - "\n", - "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", - "\n", - "x = np.arange(1, 200)\n", - "plt.bar(x, autocorr(y_t)[1:], width=1, label=\"$y_t$\",\n", - " edgecolor=colors[0], color=colors[0])\n", - "plt.bar(x, autocorr(x_t)[1:], width=1, label=\"$x_t$\",\n", - " color=colors[1], edgecolor=colors[1])\n", - "\n", - "plt.legend(title=\"Autocorrelation\")\n", - "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", - "plt.xlabel(\"k (lag)\")\n", - "plt.title(\"Autocorrelation plot of $y_t$ and $x_t$ for differing $k$ lags.\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that as $k$ increases, the autocorrelation of $y_t$ decreases from a very high point. Compare with the autocorrelation of $x_t$ which looks like noise (which it really is), hence we can conclude no autocorrelation exists in this series. \n", - "\n", - "\n", - "####How does this relate to MCMC convergence?\n", - "\n", - "By the nature of the MCMC algorithm, we will always be returned samples that exhibit autocorrelation (this is because of the step `from your current position, move to a position near you`).\n", - "\n", - "A chain that is [Isn't meandering exploring?] exploring the space well will exhibit very high autocorrelation. Visually, if the trace seems to meander like a river, and not settle down, the chain will have high autocorrelation.\n", - "\n", - "This does not imply that a converged MCMC has low autocorrelation. Hence low autocorrelation is not necessary for convergence, but it is sufficient. PyMC has a built-in autocorrelation plotting function in the `Matplot` module. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###Thinning\n", - "\n", - "Another issue can arise if there is high-autocorrelation between posterior samples. Many post-processing algorithms require samples to be *independent* of each other. This can be solved, or at least reduced, by only returning to the user every $n$th sample, thus removing some autocorrelation. Below we perform an autocorrelation plot for $y_t$ with differing levels of thinning:" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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v3+aN9Swd612lgXmyfMyRNDBPhtM48S8ru1EqjXdTqISEBJw4cQIJCQkYMmQI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\nSGRkJCqVio4dO/L+++8DZfn4kZGRuLu706pVq3JjKapy/zF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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "max_x = 200 / 3 + 1\n", - "x = np.arange(1, max_x)\n", - "\n", - "plt.bar(x, autocorr(y_t)[1:max_x], edgecolor=colors[0],\n", - " label=\"no thinning\", color=colors[0], width=1)\n", - "plt.bar(x, autocorr(y_t[::2])[1:max_x], edgecolor=colors[1],\n", - " label=\"keeping every 2nd sample\", color=colors[1], width=1)\n", - "plt.bar(x, autocorr(y_t[::3])[1:max_x], width=1, edgecolor=colors[2],\n", - " label=\"keeping every 3rd sample\", color=colors[2])\n", - "\n", - "plt.autoscale(tight=True)\n", - "plt.legend(title=\"Autocorrelation plot for $y_t$\", loc=\"lower left\")\n", - "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", - "plt.xlabel(\"k (lag)\")\n", - "plt.title(\"Autocorrelation of $y_t$ (no thinning vs. thinning) \\\n", - "at differing $k$ lags.\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With more thinning, the autocorrelation drops quicker. There is a tradeoff though: higher thinning requires more MCMC iterations to achieve the same number of returned samples. For example, 10 000 samples unthinned is 100 000 with a thinning of 10 (though the latter has less autocorrelation). \n", - "\n", - "What is a good amount of thinning? The returned samples will always exhibit some autocorrelation, regardless of how much thinning is done. So long as the autocorrelation tends to zero, you are probably ok. Typically thinning of more than 10 is not necessary.\n", - "\n", - "PyMC exposes a `thinning` parameter in the call to `sample`, for example: `sample( 10000, burn = 5000, thinning = 5)`. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### `pymc.Matplot.plot()`\n", - "\n", - "It seems silly to have to manually create histograms, autocorrelation plots and trace plots each time we perform MCMC. The authors of PyMC have included a visualization tool for just this purpose. \n", - "\n", - "As the title suggests, the `pymc.Matplot` module contains a poorly named function `plot`, which I prefer to import as `mcplot` so there is no conflict with other namespaces. `plot`, or `mcplot` as I suggest, accepts an `MCMC` object and will return posterior distributions, traces and auto-correlations for each variable (up to 10 variables). \n", - "\n", - "Below we use the tool to plot the centers of the clusters, after sampling 25 000 more times and `thinning = 10`." - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[****************100%******************] 25000 of 25000 completePlotting centers_0\n", - "Plotting centers_1\n", - "\n" - ] - }, - { - "data": { - "image/png": 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dcfFva3SvJltdTssOttj5C9NT6+18iYmJnD2dCQSol/POpuDephsSSfX7L9iT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9KfS0X4eFCLEmXaWq4qvSQ7K8NniZYXRJiT9pPKl/G+Denb3IXnOpdcjNHUxc7kcvYEhkPoWBme\n6v6MEDpWNb89fanwvjB+fn506NCBAQMG0KFDBxo1asTVq1c5c+YMcXFxnDhxgvfff58ff/yxxL3/\nN3cOPZo1IycJfjjjTMeOHdVDe6oH1qJjN6CkTk57RSI5idngqXl98ftVx9p0du6k2PDEmCd0uv/v\nI4fJuBJXQqfHrdNTPO3jxl+XTuHtag901np/VsJplJKpmvVDHQDe8s7g+oNcevXuQ/tGdYmOjqat\nvBBwLNV+XY97e7nwrFsKdzLzCc9TjvT0trqBp5Mtv91vqL6+qI5VdsJpCiSpQu1dy3UEO+9K21v0\n2LPdk3wR3IrnF2/ROH/xnxgcUtLJadhO6/3adKymd/dgT1ZjMvMKTEbnqSLHXt7evBgUoPV8yqV/\nSM7MA1xNwt7nGqTi4WTDpbs5nD8Rw7HzcbSoZw9dXkFQsxH5OjUP0WfGpVwdKxWBgYGEhIRgafk4\nr+OTTz5h6NCh2NnZsWjRIn755ReuXr3KW2+9xbZt2zTu11UH5mZ6LlO3XtQo2/GCL/YV1BBJvP+Q\nGX9c0ijr0KgOi4e10bmOwWtOliib0Mmd57s05tTtTJ5oWEennKyipGbnUyiVLvWgrc2KcmCaMthL\nycpn4q/nAXiphyfjOjYstX5rmQXyCu4TFNSqHiHxSi0xmcXjbYYcbS3JzCvQy3aVntlnYYkaK3/m\n9GnKUJ/6fHQggWM3Msqtx8vFjtXjnuCn47fZfPqOXrZUJ78914H/bDynUabqRyj5XhyY1pnrD3KZ\n9rvy34quemrFmdnTkx/+vqWHxY8Z0c6NWb2baj2nrw6MqSF0rEyHQwkP+CzsaqXr0VXHqkEda+b1\n99JZWqcoHk62NHKs2M4eAtNB38+vckesFAoFwcHBnD59muDgYD777DPmzZuHpaUlQUFBdOumHGGy\nt7cnICAAhUJRqSFIbWFeRYMqUC5F/yioBT+fSGJU+waExz/gDf9metulor17HSxlFjzZxEmv+93q\nVF47qzQ8nGwZ5vM496xo8KZt0kjjy1ifWSULC5aNaMOeS/eY1t2DcRvO6lGJJqVpzfTxckZmYcGH\nA1swfN3pMusI9K7HvP5eADRx0fxQa9ewDhdSsitkk08DBy7dLXvj5MriYm+t87VBrZSab7Iiz2r1\nWB+e+rHsqY6PB7XAp0Ednt30OIAb3aFhpQOrVvVNZxGDQGBo7mbLeesv/VbffjuyjQisaiHlJsNY\nWVkREhLC/fv3OXjwIN27dyc8PJyQkBDeffdd9XUrV64kMjKSI0eO0LVrV70NMtDeygD0be7C6rFP\n8LSPG18Na41nBfcELI6rgxXdmjgZZZ5392Q/9arK+g7av4TX/acd43zdtZ5TpeN8NLAF4zo2ZOdk\nP55vmKo+72JX4VlhAHwa1mFuQDOc9Ly/OJZa8ob+muJHvUc+21rJ0JZeVzR/wkpmoc4/GtjKVeO6\nOX20j6yUxsyenhqLEaqSpSOUo6ll5YI86+fO3ABl0GhRJBrWlr/3Wt/HvjraWtLbywXXUt6dyiBS\nvQyPyLEyPNWdY2XMnC6RY2Vcyg2skpKS6NKlC/b29hQWKsUwZ8+eTWBgIC+++KK67OTJkwwePJgB\nAwawZ88e/S0yZGRlYLp4OBp8BWJxXunVhEGtXUuU21jJGN2hIUtHtGHVWB+sK5i8r7q6bwsXXurh\niZ2VDFmROlrVd+DlInIYuqBSyy+OcyWCrO5NlSOBRb2zLjaMNT+o7FWb3vUfLxiQWVhoqPO3cLXT\n2ZalI9owukND9JgB0IsnGtbB00l78L9qrA9z+jRlctfG6tWnrg5lP+eiK2eL0qrI8wGY2LmRxjPT\nhRWjH8uLiLjKvJkzZ47I2alhiD4zLgbRsQL43//+x44dOwgLC2Po0KF6G+ThbItbHWvauJne9ELB\noy/YqtTSGNW+AW/389Iom9X7sdTAEw3r4GhrhUcFR99aa3meRf2wsIAxZWiBvVPMJoCuxaZD1Rpj\njeuydWJHdXlFhFufeTTiVlYA27OZE68Uk18oqlHTr4VmwFdYZH7ZwsKC4WWsSi3KEw2VCw10TEM0\nCBLa9Xaa17Nn2BNuGisB7a0t2TyhA79P6lji+uIUfZofBilXjdo+Wr35/JON+WF06Tps2qhIgCqo\nOEKTyPBUt46VuetmGaPNWqVjlZiYSG5uLuPGjWP06NGkpFRcFVeFlcyC9ePb8+3INnwR7M03w3VP\nNq9qCqtr6KIIM3t6MqJdSR2j+UEteKqNK062ZQctG55tzxfB3nRoVLfM68oadXitb1OCtIyiFeeb\nEW2Y1t2D6d09cbazYryfO4Nau/JHOV/8M3t68t2otnwyqCUepYzYaNhqYcGo9prPRGMAr5gzZcVF\nz/ppnzotSvV2e8Uaq1/HGkdb7SNXpQ1qNna05adn2vHrfztU1Dg1VT1ya2iWLFmCv78/AIsWLcLf\n3///t3fmcVFW3QP/DrIILqCgmGgquOAChAG5hEFgarmWZiZmuWRuZWbWr7Jscc/MtMyl8n1LzVcr\nRUVMWRQ3BJfcMEFUxAVRZFWEYZ7fHzQTA8M+CzNzv5+PH+fZ7jnnuZdnztx7nnMICQlBLpcDsGHD\nBnr37s2gQYPIyckxpKoCgcDI0Uoeq7S0NC5evMhvv/3GpEmTmDdvXq2UqmchQyYrDhDv4tygVm1p\nk6J/vqH1uc7r+Yhmh6iVfX3e6dOm0kLSzRtalxtoX9IO5ffksFLJKFvZ2/Cce/EMT2Wrj80bWvOi\np7PqTcnxvi1596k25X4JLxvUgRc9mzOwsxMdnezo2cZe43lV4aNOJQLSS/kmFbkq43xbVtp2dSas\n1r5QvZkfTdQ0NsPmn8SsE/yKqwGUvO+l+8DF3qZaM4kVUdd9rIcPH/LXX38hk8lIT08nOjqamJgY\nPD092bZtG4WFhaxevZqYmBjGjBnD6tWrDa2yiLHSASLGSrcy9YHJxFiVpmQeq5ycHFq0aIG9vT2+\nvr7Ur1+fwMBAEhISNF47ZcoUFi5cyMKFC1m1apXaTTp48GCd2x7llE5X5wYEtW9C9qVTdHqYrDf5\nE1pmMNQ+Dbd/3rgq73zll1r2pVPVlnfmzL9v8aWeP87Bgwd53c9F1V7JB8PBgwf5oGMu28d60sim\nHo4ZF6olr3R7bfISuZd4igl+LljVsyhz/rWz8WXkl26/5PEzZ86otiUktfPnBLWD1DO80OTfmdSS\n+oR4tyijX8n7KSFpPK5pu80/CWHLO75ueOdy7+/BgwdVTlxN+nN62yzWvuDOi57OkHpW7fi9xJOV\nXl8V+8o7X9mesqzVlClTmDKlbuSw+uGHHxg7diySJBEfH09AQAAAwcHBHDlyhKSkJDw8PLCwsFDt\nE/yLiNcxPkSfGRat5LHy9vamf//+/Pnnn8TFxfHTTz/x/fffq11v7Hlg5ApJFTRcl/j1r1v8GHez\n2jm6lCjzI43waM7EJ4qdqv/9lca6uBtA8YzVjyO6qF1TpJCwkFVvOahkHqZZfR4lqH3TCrPnL4y6\nQuSl4hxZJfM5ldfmnxO8VdsbRnWlWQVpLU5cz+b93Zdo72jLd8PckSSJjPtyFkZf4a+buWptAny5\n/yp/JmYAxcH1FeXR+nOCNzeyH/Lq/86r9r0X0IZF0cVFuXePe4zQ8+lqKQ5a29vwwz/3+GhKFh//\nmcwbPVwqjHmrKsp7oswPVhEX0+9z934hOxLSiU/NoV2T+ly+l49rU1uSMx6UsVPZ9uyn2pS7VGzo\nPFaFhYWEhISwefNm/P39mTJlCtnZ2UyaNImkpCQWLFjAhAkTCA0NZcGCBcjlcvr160dEhHpuI2N/\nfpkS+s5jVRtWDOlIp2Z1Z9VFUD0Mnsdq4sSJBAQEUK9ePdavX19tReo6ddGpAhjh4YxbU7saL5l+\nM7gjEUn3COn+b9mUF72cVY6VJqtrUk5IiYWMSp0qALsa5C5TUtlPhe4ujVn7grsqv4xMJsOxgRUu\n9jYqx6pkfytKXPtFPzc+2nNJ5Vy5N7OjiZ0VR65mqc4pHScmAzaP7oYkFd+7oV2b0d2lEc0bWhOd\nnEmP1v8u1fZ41J6dr3phreWyQFXpMWVaiZ5t7JErJOrJinP4NG9oXWHi2rq8FPjzzz/z8ssvq7bt\n7e1JTU0FIDs7GwcHB+zt7cnOzlbbp4kpU6bw6KOPqtrRVDlCbOtnW1uVA5ToqjIBdKwT90tsV21b\n+TklJQWACRMmUBOqPGNVW0zpF9/BgweN5u2EiqjIDuUX6aMO9VXLV7VB2d664Z151KHyN8ruPSjk\ni4grDOnqRJ92mtM6KNvs1MyOkY7pfHah2Lnc9HK3cnN9VcTXB1MIu3AXgD3jH1PNyK06ksof59KB\n4pmako7VnvGPsevCXb45dE11vKRuAF8P6lgtx1eb40uph0N9S/5XyYxVVdpR8ucEb6Zuu0DinQds\nGtUNxwaa77ehZ6zef/99Tp06hUwmIzY2lhkzZnDs2DF27tzJ4sWLcXV1ZejQoQQFBREVFcXWrVtJ\nSUlh1qxZau3o+/lliGdMeTKVsTraXlqqqY01nbHKvnRK7U09Xc9YZV86xX9mvqi3GauS91NXfVaR\nTH2gb3k6m7G6efMmzz33HAkJCeTl5WFhYcH06dM5e/Ysrq6urF27Fot/UkCfOHECHx8f5HK5ap/A\nuNHWZMSsPo9yPfthlZwqgCa2Viwd2KFaMsb7tiTjQWGNnCpQn+kqucw52rsFt3ILeO6frPal0zdo\nws3Rlkt3i5fP6sILGLqYVfpmcCfy5QqtBcHrgoULF6o+9+nTh48//pjFixfj7+9PmzZtmDlzJpaW\nlkycOBF/f3+aNm3Kxo0bDahx3UPE6hgfos8MS6WOlTKP1bBhw8rksfrqq6/YuXMngwcPBuC7777j\n8ccf17nShsYUZqugYjs6N7cj4fZ9VcLO2vJMOckqtYEk6bZPGte35NO+/yYl9WjRkPjUnAoduADX\nJirHqrpo0xZl2SL35tp37upZyOq0U1WaAwcOADB79mxmz56tdiwkJISQkBBDqKURkZNI+4g8VsYv\n01i+eyt1rGxsbLCx+TdmpHQeq7179zJ48GDOnTtH69atuXTpkl4TKgp0wxf93DiemkOvWqRAMDYe\nb9WI3X/fpUWjilNYDPdoTlM7K3xctON06pIFA9zY8/ddjbnQqsP3w9w5dDWTTs3scKiv/bI4AoFA\nYCrUOo9VVlZx0O7y5cuZNm2a6jxTpmSgmzFTkR2NbCwJcGui9SBqXaBMr1Bb/Ns68OVz7fl2aKcK\nz7OqZ0G/jo6quCIbS+2Od22Or2YNrAnp/kitazm6Otoypvsj+LW211vtRHPGEM+Y8mSKPFbGIa/k\n/RR5rAxLtZ+2JfNYdevWDWdnZ5KSkmjcuDGOjsXLPeXNWIm3aurW9pkzZ+qUPtXdzr6USGO3x5Ak\nVDm5DKHPU65N2LAjgq7ODYDi4PWCq6fJvpSKY0fvOnO/9LGt/Fzbt2oEdQcRr2N8iD4zLFrJY5Wa\nmsrXX3+NnZ0dx44d44UXXmDNmjVq15vSW4GCuoHyTTVlPqq6xtlbubjY29DE1nyXzgz9VqC2EM+v\nuoPIYyXQFzV9flW6ziOXywkODlblsTp27BiBgYEEBwdjY2ODr68vw4YNY//+/ezevRsvL68yyUEF\nAnOkW4uGZu1UCQQCgTlSqWNlaWnJvn37yMjIYO/evfj5+REVFcW+fft4//33y5wfGRlp8qkWjGWd\ntzJMxQ4J07EFTMsWQc0QMVbaR8RY6VamPjCWZ2OlHtDNmzfp3r07tra2KBTFOainT59OYGAg48eP\nR6FQkJOTQ3BwME899RSDBg0iNze3klaNm5I19owZU7HD0c7KZGwB0+kXXfHKK6+we/duQ6thNoi6\nc8aH6DPDUqljpcxj1aNHjzJ5rLp27crOnTuxtrZmw4YN7N+/nyFDhphkSZuSKN+ENHaM3Y7lgzvi\n386Bt55sbfS2lMSUbNEFa9euJT09nZEjR7J8+XLy8vIMrZLWETmJtI/IY2X8MuqSMP4AACAASURB\nVI0lj1WljpWNjY1a7azSeawOHz6MjY0Nzs7OQPHSoaVl7V7tFgiqQufmDZgT1K7CgssC0+Pu3bsk\nJydjb2+Ps7Mz48aNM7RKAoFAoKLWeawyMzNVx3Nzc1mzZo1a0VNTRPkqubFjKnaAsMWcWLp0KWPG\njGHNmjW89NJLJrnkIWKstI+IsdKtTH1gLDFWtc5j1aJFC6A4d9X48eOZP38+jRuXzUidm5vLiRMn\naq9xHWDChAkmYYup2AHClrqKLuItAwICcHNzA2DXrl0899xzWpch+BdTdFxNHdFnhqVajpUy5dWc\nOXOYM2eOKo8VwMcff0zv3r0JCAjQeO2QIUNqp6lAIBAA+/fvZ9CgQQDExMSYpGMl4mW0j4ixMn6Z\nJhNjVZU8Vjdu3GDx4sX88ccfBAYGijxWAoFAZ6SnpxMREUFkZCRpaWmGVkcgEAjUqHTGSpnHqiRR\nUVFq2y1btuThw4fa1UwgEAg08M0337Bx40YkSeLrr782tDo64eDBg3r/dV6eTGWsjraXl/RtY/al\nU3qdRSqOseqoN3kl76eu+qwimfrAEH8XNUG8vicQCIyKlJQUsrKyePjwIcuXL+fjjz82tEomjS6+\nnOVFCi7eyUO6nFn5yaU4npqtdX1MDRFjZVj0kiL97bffpk+fPsyYMUMf4rTClStXcHZ2JjAwkP79\n+wOwZMkS/P39CQkJQS6XA7BhwwZ69+7NoEGDyMnJMaTKamhK7FpV/SMjI+nVqxdPP/00169fN5gN\nSjTZYm9vT2BgIE8//bTqzdS6bktsbCy9e/fG39+fmTNnAsbbJ5ps0VeffPXVVwwcOJCXXnqJkSNH\nas+oOoSpx8tIwClZWz6PuFztf+EXM2okU8RYGb9MY5itAj04VidOnCAvL48DBw5QUFBAfHy8rkVq\njWeeeYaoqCjCw8O5ffs20dHRxMTE4OnpybZt2ygsLGT16tXExMQwZswYVq9ebWiVVZRM7ApUS/8v\nvviCvXv3snDhQhYsWGBIM4CytgB4enoSFRVFZGQkDg4ORmFL27ZtiYqKIiYmhtu3b3PgwAGj7ZPS\ntpw9e1ZvfdKtWze6detGp06d6NSpk7ZNEwgEglqhc8cqNjaWZ555BoDg4GCOHDmia5FaIyoqij59\n+vD1119z/Phx1RuPSjuSkpLw8PDAwsKiztlWMrGrJEnEx8dXSf8HDx5ga2tLgwYN8PPz49y5cwa0\nopjSSWoBEhIS6NOnD//3f/8HQGJiYp23xdnZGWvr4mSmVlZWnDt3zmj7pLQt9erV01ufREVFMWjQ\nIEaMGMGIESMqPPfcuXP07t2bPn36MHnyZMA4Zp7NIY/VrQv6TSki8ljpVqY+MNk8VtUlMzMTV1dX\noHipoC58KVSFli1bkpiYiLW1NUOGDCEnJ4fmzZsD0LhxYzIzM8nMzFTl7FLuq6tkZWWV0VWT/iX3\nARQVFRlE38pISkrCwcGBN954gx07duDk5GQ0tpw+fZr09HQcHBxUBcuNtU+UtnTu3FlvffLrr7+S\nkJCAr68vqampFZ7bqVMnDh06BMC4ceOIi4tTzRIuXryYbdu2MWTIENXM2tatW1m9ejWzZs2qtl6m\niojXMT5EnxkWnc9Y2dvbk51dHGyYlZVVZuahrmJtbY2trS316tVj4MCBuLm5qezIzs7GwcFBzTbl\nvrqITCbTqGtl+wDq1atnEJ0rQ3mvhw4dytmzZ43GloyMDKZPn86PP/5o9H1S0hbQX5+8/fbbqnqk\n8+fPr/DckuW1Hjx4QFxcnFHMPJtDvEwL9+56lSdirIxfpoix+oeePXsSEREBQEREBD179tS1SK1Q\nMmP0oUOHaN++vaqUz759++jZsycdO3bk7NmzKBQK1b66iCRJ+Pj4VEl/Ozs7Hjx4QF5eHseOHaNr\n164G1l4dSZK4f/++aqbj4MGDtG/f3ihskcvlhISE8OWXX9K8eXOj7pPStuizTxo2bKiqTWpra1vp\n+aGhoXh4eGBjY0OTJk2qNHMrEAgENUXnS4He3t7Ur1+fPn364O3tjY+Pj65FaoWYmBjmzJmDjY0N\nffr0wc/Pjz59+uDv70+bNm2YOXMmlpaWTJw4EX9/f5o2bcrGjRsNrbYKuVxO//79VYld582bV2X9\nP/zwQ/r27YutrS3/+c9/DGyJZlsmT55Mw4YNcXV15fPPP0cmk9V5W7Zs2UJ8fDyzZ88GYMGCBUbb\nJ5psmTp1ql76xMnJiZiYGN555x3VUmpFDB48mMGDB/Pmm2/SoEED1fJhXZ55Noc8VrcunABHd622\nWREij5VuZeoDY8ljJZOUdWoEAoHASLhw4QIKhYIuXbpUeF5BQYEqyP6jjz6iY8eO/O9//2Pnzp0s\nXrwYV1dXhg4dSlBQEFFRUWzdupWUlJQyMVYRERGsW7eORx99FCgOcfDw8FA95JVBtdraXrVqlU7b\n17R95swZVYC/ruVFHzjAF5ujsPAeDPwb6K10fHSxff9GEi38h6u2L65+BwCfxRE6k7flyw/o1KyB\nyfVfySDyJ5980mTkKT+npKQAxXVbg4KCqC7CsRIIBEbFqFGjgOKYKYBt27aVe25oaChfffUVkiTR\nrl07fvjhB5YuXcqOHTto06YN69evx9LSkl9++YVVq1apZtYaNWqk1k5ERATdu+s3JsiUKSxS8M7O\nRC6k3zeYDvGzi78wfRZH6EzGiiEd6dSsgc7aF+iWEydO1MixEpnXBQKBUbFp0yagON5u2bJlFZ6r\nXAYsyezZs1VLmEpCQkIICQnRrqICs8e6nl5ycAvqGHpzrP744w+116wFAoF5UJNffBVx7tw5ZDIZ\nhYWFRpO+pbqIGCvtY4gYq0XRtjS2qf6br893a06PNvbVukbEWNUdKnWsxo0bx65du2jevDlnzpzR\neM6bb77J7t27sbOzY/369Xh7e5c5p3HjxmY7lT5lyhS+++47Q6thMMzZfnO2HYqn0rXN1q1bgeLE\nsSJfj+4R97jmJGc8qNF1fVyb1Equ6DPDUuk85WuvvUZ4eHi5x8PCwkhKSiIxMZE1a9aogucE/6IM\neDVXzNl+c7ZdV/j4+ODj44OHhwepqans2rXL0CppHXPISSTyWGkXcxgzxjBbBVVwrPz9/WnSpHzv\nOTQ0lLFjxwLwxBNPkJmZSVpamvY0FAgEghKsW7eOhIQELly4wLp167hz546hVRIIBAIVtY6su379\nOq1bt1Ztt2rVqtIyE+aGvX311spNDXO235xt1xXu7u7MmjWLd955h06dOql+2JkSolag9hG1AnUr\nUx+YVa3A0hkbZDKZNpo1GTw8PAytgkExZ/vN2XZdMn78eGQymSoDu0B3iHgd40P0mWGptWPl4uLC\ntWvXVNupqam4uLhoPHfKlCl6S7BXl7b1mUCtLm3//fffLFy4UO2lhbqkn9jWT4I9bTNv3jxSU1Nx\ncHDAxsZG6+3XBcwhXqaFe3cy9ZjHSsRYGb9MY4mxqlKC0CtXrjBo0CCNbwWGhYWxcuVKwsLCOHr0\nKDNmzODo0aNlzhMJ9syPo0eP8uyzz+Ln51fhCxAC06WmCfYq4s033yQvL48ffviB119/nTVr1mi1\nfU2I55d2MZcEoTXlzd6tGdjZydBqmD01fX5VGmM1atQoevXqxd9//03r1q358ccfWb16NatXrwbg\n2WefxdXVlfbt2zNp0iSzfrW8PIxlXVhXKOuwmSPm3ve6wMLCgjZt2gDUibp+ukDEWGkfEWOlW5n6\nwFiep5UuBSqzHFfEypUrtaKMQCAQVIaNjQ3nz59nxYoV3Lt3z9DqmDwiXsf4EH1mWERJGz1gLOvC\nusKcM+6be99rG0mSGD58OHfu3EGSJKZMmWJolXSCOcTLiBgr7WIOY8ZYnqfCsRIIBEaDTCYjKiqq\nTK0/gUAgqCuICpF6wFjWhXWFiLESaIvt27ezfft2goKCGDFiBCNGjDC0SjpBxFhpHxFjpVuZ+sBY\nnqeVzliFh4czY8YMioqKmDBhAu+9957a8Tt37hASEsKtW7eQy+XMmjWLV199VVf6CgQCMyY8PJxD\nhw4xefJkVq1aZWh1zAIRr2N8iD4zLBXOWBUVFTFt2jTCw8M5f/48mzZtIiEhQe2clStX4u3tzalT\np4iOjuadd95BLpfrVGljw1jWhXWFiLESaIuUlBR27dpFSkoKYWFhhIWFGVolnWAO8TKiVqB2MYcx\nYyzP0wodq2PHjtG+fXvatm2LlZUVL730Etu3b1c755FHHlEt9WRnZ+Po6IilpQjdEggE2mfEiBHc\nuXOHF198kfT0dNLT0w2tkkAgEKhRoWOlqQ7g9evX1c6ZOHEi586do2XLlnh5ebF8+XLdaGrEGMu6\nsK4QMVYCbfHqq68yduxYtX+miIix0j4ixkq3MvWBsTxPK5xaqkrNv/nz5/PYY48RHR3NpUuX6Nu3\nL3/99ReNGjXSmpKVkZ2dTWRkJEOHDtVam0eOHGHmzJlkZmaWWf4UCAQCc0HE6xgfos8MS4WOVek6\ngNeuXaNVq1Zq5xw+fJgPP/wQADc3N9q1a8fff/+Nj49PmfZ0VSswMzOTdevW4eTkVOn5vXv3RiaT\nVdp+Tk4OX3zxBfPnz6+1fuXVCpQkCX9//3K3ayqvrmyfP38eKI6xqgv6iG3TqBVYHWJjY5k5cyYW\nFhb4+vry1VdfsWTJEkJDQ2nTpg3r16/H0tKSDRs28N1339G0aVM2btyo1x+GmjCHeBmRx0q7mMOY\nMZYYqwprBcrlcjp16kRERAQtW7bEz8+PTZs20blzZ9U5M2fOxN7enk8++YS0tDQef/xxTp8+TdOm\nTdXaqqzW1oMHD5g+fTppaWlYWlryxx9/cPLkSebOnYtcLmfAgAFMmzaNhQsXcvXqVTIyMrh//z5b\ntmxh4cKFbNy4kc6dO7N48WKuXbvGsmXLKCoqYuLEibzwwgtMnTqVBg0akJSUxIcffsgHH3xA/fr1\nad++PUuXLi1Xr6CgICIiytaSio6OZunSpTx48IBBgwbx1ltvabQhJiaGzz//HIDx48czcuRINV3G\njh3Lr7/+ipWVFf369WP06NHl95aRIWoFCnRRK7A6pKWl0aRJE6ytrQkJCeH1119n0aJF7Nq1i8WL\nF+Pq6sqQIUMICgoiOjqarVu3kpKSwqxZs9TaEbUCtYuoFVgxolZg3UAntQItLS1ZuXIl/fr1o0uX\nLowcOZLOnTur1Qr84IMPiI+Px8vLi+DgYBYvXlzGqaoK//3vf+nevTs7duzgjz/+AOCzzz7j559/\nZteuXRw+fJj09HRkMhlubm5s3rwZHx8foqOjGT9+PL169WL79u107NiRpUuXsn37dnbt2sW6detQ\nKBQAeHl58fvvv5OQkMDIkSPZvn07X375ZbV1BXjiiSfYsWMHf/75Jzt27CA/P1+jDZ9//jlvv/02\nYWFhrFmzhvz8fDVdHB0dycnJ4b///a9JOVUlETFWAkPh7OyMtbU1AFZWVpw7d46AgAAAgoODOXLk\nCElJSXh4eGBhYaHaZ2hEjJX2ETFWupWpD4zleVrp63sDBgxgwIABavsmTZqk+uzk5MSOHTtqrUhi\nYiIhISFq+86fP6/al5WVpQqc9/T0BIqXKjMzM9WuuXPnDpcuXeL5558Hir/U79y5A4C3tzcAQ4cO\nZcmSJUyaNImnn36akSNHVlvfU6dOsXjxYuRyOdeuXePOnTsabVAoFDRq1AhLS0vatWvHrVu31HSR\nyWQ89ph+p4wFAnPj9OnTpKen4+DggIVF8e/Jxo0bk5mZSWZmpioliHKf4F9EvI7xIfrMsNSZvAgd\nO3bk8OHDPPbYYygUCiwsLOjatSvr16+ncePGqn179uxRu06SJCwtLVWzUo6OjnTo0IHffvsNKysr\n5HK5Kv2DMhjf0tKSTz/9FIBevXrVyLFasWIFy5Yt49FHHyUwMBBJktRskCQJmUyGTCajS5cuFBYW\nkpycTIsWLdR0kSRJ9aA3VUQeK4EhycjIYPr06WzZsoX4+HhSU1OB4h9dDg4O2Nvbq6WMcXBw0NiO\nrmJENW0r9xkiRk4f8g4dUpennN1RxiXparu0PF3Lr2n7CSdicbhrX2f7z1S3lZ9rGyNaYYyVNqks\nRiE/P5+pU6dy+/ZtVXzSX3/9xdy5c1EoFFhbW/Pzzz+zfPlyunfvTt++fVm3bh0NGzZk5MiRvPji\nizRo0ICPP/6YK1eusGzZMiwsLHBycuKHH35g6tSpTJ8+HXd3d/744w/WrVsHQPfu3VUxUCW5ePEi\n7733HidPnsTb25vPPvsMDw8P1fFNmzbx7bff0qVLF27cuMH333+Pk5NTGRsOHDjA559/jkwm47XX\nXmPUqFFquhw6dIg///xT5eiZEiLGSmDoGCu5XM7gwYP59NNP8fX15fbt24wbN46dO3eqYqyGDh1K\nUFAQUVFRIsZKT4gYq4oRMVZ1g5o+v+qMY2XKlPzlaU4oHSt3d3cOHz5saHUMgrn2vRJDO1abNm3i\nrbfeomvXrgAsWLCAAwcOsGPHDrW3An/55RdWrVpV7luB+n5+GWLclCdTGaujzeWlwiIFo7/cTKaj\nu9barIzsS6fU3tTTtWNVWl51qIljVbL/dNFnlcnUB/qWV9PnV51ZCjQkq1evZteuXartLl26sHDh\nQgNqJBAItMGoUaMYNWqU2r4ePXowe/ZstX0hISFl4iMFxYh4HeND9JlhqXURZihOPfD2229TWFiI\nk5MT0dHRutBVZ0yaNEktIF/bmPOMBYgYK4GguphDTiKRx0q7mMOYMZbnaYWOlbII8759+3BxccHX\n15fBgwer5bHKzMxk6tSp7Nmzh1atWqnewBMIBAKBaXMr5yGXM/KrfZ2lBdy9X6gDjQQCw1OhY1Wy\nCDOgKsJc0rHauHEjL7zwgioju5OTCLgrjbnH2Zh7Hitz7ntBzTCWGKuch0V8sje5RvJqE4Mk5JVF\nxFjVHSp0rDQVYY6NjVU7JzExkcLCQgIDA8nJyeGtt95izJgxutFWIBAIBHpFxOsYH6LPDEutizAX\nFhZy4sQJIiIiuH//Pj179qRHjx506NChzLn6zANTl7bLqxVo6tuiVqD5bSs/15VagcaKOcTLmHrM\nk4ixMn55NaXCdAtHjx5l7ty5qhxECxYswMLCQi2AfdGiRTx48IC5c+cCxQ/S/v37M3z4cLW2zDnd\ngrki8lgJDJ1uQVuI55dmEu/cZ+q2vw2tRo0QeawElaGTWoE+Pj4kJiZy5coVCgoK2Lx5M4MHD1Y7\nZ8iQIRw8eJCioiLu379PbGwsXbp0qbYipoyx1DfSFeYeYyUQVBdzqBVo6rX7RK1A45dXUypcCixZ\nhLmoqIjx48erijBDcZoCd3d3+vfvj6enJxYWFkycOFE4VgKBQGAiiHgd40P0mWGpdRFmgFmzZpUp\nASH4F2NZF9YVIo+VQFA9zCFextRjnkSMlfHLqymmXf1XIBAIBAKBQI8Ix0oPGMu6sK4QMVYCQfUQ\nMVbax9TliRiruoOoFSgQCASCchHxOsaH6DPDUumMVXh4OO7u7nTo0IFFixaVe15cXByWlpb8/vvv\nWlXQFDCWdWFdIWKsBILqYQ7xMqYe8yRirIxfXk2p0LFS1goMDw/n/PnzbNq0iYSEBI3nvffee/Tv\n358K0mIJBAKBQCAQmDS1rhUIsGLFCoYPH05cXJzOFDVmjKW+ka4w9xgrc+57Qc0wllqBtcHUa/fV\nRt6W02n8nZ5XrWuunonHw6cHI7ya8981qwBRK9BQ1LpW4PXr19m+fTuRkZHExcVVqQyOQCAQCIwD\nEa+jf27mFHAzJ6Na12SnZnO36T1GeDYXfWZgal0rcMaMGSxcuBCZTIYkSRUuBYpagXVDH31ti1qB\n5ret/CxqBdYOc4iXMfWYJ1OXByLGqjxqXSvQ1dVV5UzduXMHOzs71q5dW6b0jai1ZX6IWoECQ9cK\nvHnzJs899xwJCQnk5eVhYWHBkiVLCA0NpU2bNqxfvx5LS0s2bNjAd999R9OmTdm4cSONGjVSa0c8\nvzQjagXWLZo1sOLboZ1wsLUytComgcFqBSYnJ3P58mUuX77M8OHDWbVqVZlzzB1jyb2hK8w9xkpg\nOJo2bUpkZCQ9evQA4Pbt20RHRxMTE4Onpyfbtm2jsLCQ1atXExMTw5gxY1QluwyJyGOlfcxJnshj\nZVhqXStQINBEdHQ0mzZtAiA9PZ1PP/2UDz74ACsr8UtKoD9sbGywsbEBQJIk4uPjCQgIACA4OJgN\nGzbQtWtXPDw8sLCwIDg4mIkTJxpQ47qHiNcxPkSfGRat1ApU8tNPP2lHKxPDWNaFtcnRo0fZsmUL\nABkZGSxfvpzZs2ebnWNljn1fl8nKylLlVWvcuDGZmZlkZmaW2WdoRIyVkFfX5YGIsSoPkXldoBWy\nsrJITk6mcePGLF26lIiIsnELwcHBfPbZZzRt2hQbGxu6dOliAE0F5opMJsPe3p7U1FSgeInawcEB\ne3t71XK1cp8mzPXlm4q2nd2L486Uy1DKL3dj2VZSV/Sp7XYzT1+g7owPY9tWfq7tyzcVBq9rE3MO\n/tRW7o3c3FwKCgqws7Ojfv361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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from pymc.Matplot import plot as mcplot\n", - "\n", - "mcmc.sample(25000, 0, 10)\n", - "mcplot(mcmc.trace(\"centers\", 2), common_scale=False)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There are really two figures here, one for each unknown in the `centers` variable. In each figure, the subfigure in the top left corner is the trace of the variable. This is useful for inspecting that possible \"meandering\" property that is a result of non-convergence." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The largest plot on the right-hand side is the histograms of the samples, plus a few extra features. The thickest vertical line represents the posterior mean, which is a good summary of posterior distribution. The interval between the two dashed vertical lines in each the posterior distributions represent the *95% credible interval*, not to be confused with a *95% confidence interval*. I won't get into the latter, but the former can be interpreted as \"there is a 95% chance the parameter of interest lies in this interval\". (Changing default parameters in the call to `mcplot` provides alternatives to 95%.) When communicating your results to others, it is incredibly important to state this interval. One of our purposes for studying Bayesian methods is to have a clear understanding of our uncertainty in unknowns. Combined with the posterior mean, the 95% credible interval provides a reliable interval to communicate the likely location of the unknown (provided by the mean) *and* the uncertainty (represented by the width of the interval)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The plots titled `center_0_acorr` and `center_1_acorr` are the generated autocorrelation plots. They look different than the ones I have displayed above, but the only difference is that 0-lag is centered in the middle of the figure, whereas I have 0 centered to the left. \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Useful tips for MCMC\n", - "\n", - "Bayesian inference would be the *de facto* method if it weren't for MCMC's computational difficulties. In fact, MCMC is what turns most users off practical Bayesian inference. Below I present some good heuristics to help convergence and speed up the MCMC engine:\n", - "\n", - "### Intelligent starting values\n", - "\n", - "It would be great to start the MCMC algorithm off near the posterior distribution, so that it will take little time to start sampling correctly. We can aid the algorithm by telling where we *think* the posterior distribution will be by specifying the `value` parameter in the `Stochastic` variable creation. In many cases we can produce a reasonable guess for the parameter. For example, if we have data from a Normal distribution, and we wish to estimate the $\\mu$ parameter, then a good starting value would be the *mean* of the data. \n", - "\n", - " mu = pm.Uniform( \"mu\", 0, 100, value = data.mean() )\n", - "\n", - "For most parameters in models, there is a frequentist estimate of it. These estimates are a good starting value for our MCMC algorithms. Of course, this is not always possible for some variables, but including as many appropriate initial values is always a good idea. Even if your guesses are wrong, the MCMC will still converge to the proper distribution, so there is little to lose.\n", - "\n", - "This is what using `MAP` tries to do, by giving good initial values to the MCMC. So why bother specifying user-defined values? Well, even giving `MAP` good values will help it find the maximum a-posterior. \n", - "\n", - "Also important, *bad initial values* are a source of major bugs in PyMC and can hurt convergence.\n", - "\n", - "#### Priors\n", - "\n", - "If the priors are poorly chosen, the MCMC algorithm may not converge, or at least have difficulty converging. Consider what may happen if the prior chosen does not even contain the true parameter: the prior assigns 0 probability to the unknown, hence the posterior will assign 0 probability as well. This can cause pathological results.\n", - "\n", - "For this reason, it is best to carefully choose the priors. Often, lack of convergence or evidence of samples crowding to boundaries implies something is wrong with the chosen priors (see *Folk Theorem of Statistical Computing* below). \n", - "\n", - "#### Covariance matrices and eliminating parameters\n", - "\n", - "### The Folk Theorem of Statistical Computing\n", - "\n", - "> *If you are having computational problems, probably your model is wrong.*\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Conclusion\n", - "\n", - "PyMC provides a very strong backend to performing Bayesian inference, mostly because it has abstracted the inner mechanics of MCMC from the user. Despite this, some care must be applied to ensure your inference is not being biased by the iterative nature of MCMC. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "\n", - "1. Flaxman, Abraham. \"Powell's Methods for Maximization in PyMC.\" Healthy Algorithms. N.p., 9 02 2012. Web. 28 Feb 2013. ." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.11" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/Chapter4_TheGreatestTheoremNeverTold/Ch4_LawOfLargeNumbers_PyMC2.ipynb b/Chapter4_TheGreatestTheoremNeverTold/Ch4_LawOfLargeNumbers_PyMC2.ipynb new file mode 100644 index 00000000..80f48f1e --- /dev/null +++ b/Chapter4_TheGreatestTheoremNeverTold/Ch4_LawOfLargeNumbers_PyMC2.ipynb @@ -0,0 +1,1204 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4\n", + "______\n", + "\n", + "## The greatest theorem never told\n", + "\n", + "\n", + "This chapter focuses on an idea that is always bouncing around our minds, but is rarely made explicit outside books devoted to statistics. In fact, we've been using this simple idea in every example thus far. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Law of Large Numbers\n", + "\n", + "Let $Z_i$ be $N$ independent samples from some probability distribution. According to *the Law of Large numbers*, so long as the expected value $E[Z]$ is finite, the following holds,\n", + "\n", + "$$\\frac{1}{N} \\sum_{i=1}^N Z_i \\rightarrow E[ Z ], \\;\\;\\; N \\rightarrow \\infty.$$\n", + "\n", + "In words:\n", + "\n", + "> The average of a sequence of random variables from the same distribution converges to the expected value of that distribution.\n", + "\n", + "This may seem like a boring result, but it will be the most useful tool you use." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Intuition \n", + "\n", + "If the above Law is somewhat surprising, it can be made clearer by examining a simple example. \n", + "\n", + "Consider a random variable $Z$ that can take only two values, $c_1$ and $c_2$. Suppose we have a large number of samples of $Z$, denoting a specific sample $Z_i$. The Law says that we can approximate the expected value of $Z$ by averaging over all samples. Consider the average:\n", + "\n", + "\n", + "$$ \\frac{1}{N} \\sum_{i=1}^N \\;Z_i $$\n", + "\n", + "\n", + "By construction, $Z_i$ can only take on $c_1$ or $c_2$, hence we can partition the sum over these two values:\n", + "\n", + "\\begin{align}\n", + "\\frac{1}{N} \\sum_{i=1}^N \\;Z_i\n", + "& =\\frac{1}{N} \\big( \\sum_{ Z_i = c_1}c_1 + \\sum_{Z_i=c_2}c_2 \\big) \\\\\\\\[5pt]\n", + "& = c_1 \\sum_{ Z_i = c_1}\\frac{1}{N} + c_2 \\sum_{ Z_i = c_2}\\frac{1}{N} \\\\\\\\[5pt]\n", + "& = c_1 \\times \\text{ (approximate frequency of $c_1$) } \\\\\\\\ \n", + "& \\;\\;\\;\\;\\;\\;\\;\\;\\; + c_2 \\times \\text{ (approximate frequency of $c_2$) } \\\\\\\\[5pt]\n", + "& \\approx c_1 \\times P(Z = c_1) + c_2 \\times P(Z = c_2 ) \\\\\\\\[5pt]\n", + "& = E[Z]\n", + "\\end{align}\n", + "\n", + "\n", + "Equality holds in the limit, but we can get closer and closer by using more and more samples in the average. This Law holds for almost *any distribution*, minus some important cases we will encounter later.\n", + "\n", + "##### Example\n", + "____\n", + "\n", + "\n", + "Below is a diagram of the Law of Large numbers in action for three different sequences of Poisson random variables. \n", + "\n", + " We sample `sample_size = 100000` Poisson random variables with parameter $\\lambda = 4.5$. (Recall the expected value of a Poisson random variable is equal to its parameter.) We calculate the average for the first $n$ samples, for $n=1$ to `sample_size`. " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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UXpRQUVs5u6SlpXkGrQMHDqRVq1asX7+eFi1acMkll3i+gq9cuZKYmBi6dOnC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wcFpW6uff+5BOMp/vJfTwBw+Q1LePjPu7jubY08dv9egsMxZs8rweOzs+GqBezf2c0jf8n8m9/1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\ny96P1voJrfWPpn2UL8PofRZe6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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "from IPython.core.pylabtools import figsize\n", + "import matplotlib.pyplot as plt\n", + "\n", + "figsize(12.5, 5)\n", + "import pymc as pm\n", + "\n", + "sample_size = 100000\n", + "expected_value = lambda_ = 4.5\n", + "poi = pm.rpoisson\n", + "N_samples = range(1, sample_size, 100)\n", + "\n", + "for k in range(3):\n", + "\n", + " samples = poi(lambda_, size=sample_size)\n", + "\n", + " partial_average = [samples[:i].mean() for i in N_samples]\n", + "\n", + " plt.plot(N_samples, partial_average, lw=1.5, label=\"average \\\n", + "of $n$ samples; seq. %d\" % k)\n", + "\n", + "\n", + "plt.plot(N_samples, expected_value * np.ones_like(partial_average),\n", + " ls=\"--\", label=\"true expected value\", c=\"k\")\n", + "\n", + "plt.ylim(4.35, 4.65)\n", + "plt.title(\"Convergence of the average of \\n random variables to its \\\n", + "expected value\")\n", + "plt.ylabel(\"average of $n$ samples\")\n", + "plt.xlabel(\"# of samples, $n$\")\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above plot, it is clear that when the sample size is small, there is greater variation in the average (compare how *jagged and jumpy* the average is initially, then *smooths* out). All three paths *approach* the value 4.5, but just flirt with it as $N$ gets large. Mathematicians and statistician have another name for *flirting*: convergence. \n", + "\n", + "Another very relevant question we can ask is *how quickly am I converging to the expected value?* Let's plot something new. For a specific $N$, let's do the above trials thousands of times and compute how far away we are from the true expected value, on average. But wait — *compute on average*? This is simply the law of large numbers again! For example, we are interested in, for a specific $N$, the quantity:\n", + "\n", + "$$D(N) = \\sqrt{ \\;E\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\;\\;\\right] \\;\\;}$$\n", + "\n", + "The above formulae is interpretable as a distance away from the true value (on average), for some $N$. (We take the square root so the dimensions of the above quantity and our random variables are the same). As the above is an expected value, it can be approximated using the law of large numbers: instead of averaging $Z_i$, we calculate the following multiple times and average them:\n", + "\n", + "$$ Y_k = \\left( \\;\\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\; \\right)^2 $$\n", + "\n", + "By computing the above many, $N_y$, times (remember, it is random), and averaging them:\n", + "\n", + "$$ \\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k \\rightarrow E[ Y_k ] = E\\;\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\right]$$\n", + "\n", + "Finally, taking the square root:\n", + "\n", + "$$ \\sqrt{\\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k} \\approx D(N) $$ " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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nc/DgQY4cOeI6lq+vL9deey0fffSR641RmzZt+OSTT1zLBR33vvvu45NPPnGd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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "N_Y = 250 # use this many to approximate D(N)\n", + "N_array = np.arange(1000, 50000, 2500) # use this many samples in the approx. to the variance.\n", + "D_N_results = np.zeros(len(N_array))\n", + "\n", + "lambda_ = 4.5\n", + "expected_value = lambda_ # for X ~ Poi(lambda) , E[ X ] = lambda\n", + "\n", + "\n", + "def D_N(n):\n", + " \"\"\"\n", + " This function approx. D_n, the average variance of using n samples.\n", + " \"\"\"\n", + " Z = poi(lambda_, size=(n, N_Y))\n", + " average_Z = Z.mean(axis=0)\n", + " return np.sqrt(((average_Z - expected_value) ** 2).mean())\n", + "\n", + "\n", + "for i, n in enumerate(N_array):\n", + " D_N_results[i] = D_N(n)\n", + "\n", + "\n", + "plt.xlabel(\"$N$\")\n", + "plt.ylabel(\"expected squared-distance from true value\")\n", + "plt.plot(N_array, D_N_results, lw=3,\n", + " label=\"expected distance between\\n\\\n", + "expected value and \\naverage of $N$ random variables.\")\n", + "plt.plot(N_array, np.sqrt(expected_value) / np.sqrt(N_array), lw=2, ls=\"--\",\n", + " label=r\"$\\frac{\\sqrt{\\lambda}}{\\sqrt{N}}$\")\n", + "plt.legend()\n", + "plt.title(\"How 'fast' is the sample average converging? \");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, the expected distance between our sample average and the actual expected value shrinks as $N$ grows large. But also notice that the *rate* of convergence decreases, that is, we need only 10 000 additional samples to move from 0.020 to 0.015, a difference of 0.005, but *20 000* more samples to again decrease from 0.015 to 0.010, again only a 0.005 decrease.\n", + "\n", + "\n", + "It turns out we can measure this rate of convergence. Above I have plotted a second line, the function $\\sqrt{\\lambda}/\\sqrt{N}$. This was not chosen arbitrarily. In most cases, given a sequence of random variable distributed like $Z$, the rate of converge to $E[Z]$ of the Law of Large Numbers is \n", + "\n", + "$$ \\frac{ \\sqrt{ \\; Var(Z) \\; } }{\\sqrt{N} }$$\n", + "\n", + "This is useful to know: for a given large $N$, we know (on average) how far away we are from the estimate. On the other hand, in a Bayesian setting, this can seem like a useless result: Bayesian analysis is OK with uncertainty so what's the *statistical* point of adding extra precise digits? Though drawing samples can be so computationally cheap that having a *larger* $N$ is fine too. \n", + "\n", + "### How do we compute $Var(Z)$ though?\n", + "\n", + "The variance is simply another expected value that can be approximated! Consider the following, once we have the expected value (by using the Law of Large Numbers to estimate it, denote it $\\mu$), we can estimate the variance:\n", + "\n", + "$$ \\frac{1}{N}\\sum_{i=1}^N \\;(Z_i - \\mu)^2 \\rightarrow E[ \\;( Z - \\mu)^2 \\;] = Var( Z )$$\n", + "\n", + "### Expected values and probabilities \n", + "There is an even less explicit relationship between expected value and estimating probabilities. Define the *indicator function*\n", + "\n", + "$$\\mathbb{1}_A(x) = \n", + "\\begin{cases} 1 & x \\in A \\\\\\\\\n", + " 0 & else\n", + "\\end{cases}\n", + "$$\n", + "Then, by the law of large numbers, if we have many samples $X_i$, we can estimate the probability of an event $A$, denoted $P(A)$, by:\n", + "\n", + "$$ \\frac{1}{N} \\sum_{i=1}^N \\mathbb{1}_A(X_i) \\rightarrow E[\\mathbb{1}_A(X)] = P(A) $$\n", + "\n", + "Again, this is fairly obvious after a moments thought: the indicator function is only 1 if the event occurs, so we are summing only the times the event occurs and dividing by the total number of trials (consider how we usually approximate probabilities using frequencies). For example, suppose we wish to estimate the probability that a $Z \\sim Exp(.5)$ is greater than 10, and we have many samples from a $Exp(.5)$ distribution. \n", + "\n", + "\n", + "$$ P( Z > 10 ) = \\frac{1}{N} \\sum_{i=1}^N \\mathbb{1}_{z > 10 }(Z_i) $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0061\n" + ] + } + ], + "source": [ + "import pymc as pm\n", + "N = 10000\n", + "print(np.mean([pm.rexponential(0.5) > 10 for i in range(N)]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### What does this all have to do with Bayesian statistics? \n", + "\n", + "\n", + "*Point estimates*, to be introduced in the next chapter, in Bayesian inference are computed using expected values. In more analytical Bayesian inference, we would have been required to evaluate complicated expected values represented as multi-dimensional integrals. No longer. If we can sample from the posterior distribution directly, we simply need to evaluate averages. Much easier. If accuracy is a priority, plots like the ones above show how fast you are converging. And if further accuracy is desired, just take more samples from the posterior. \n", + "\n", + "When is enough enough? When can you stop drawing samples from the posterior? That is the practitioners decision, and also dependent on the variance of the samples (recall from above a high variance means the average will converge slower). \n", + "\n", + "We also should understand when the Law of Large Numbers fails. As the name implies, and comparing the graphs above for small $N$, the Law is only true for large sample sizes. Without this, the asymptotic result is not reliable. Knowing in what situations the Law fails can give us *confidence in how unconfident we should be*. The next section deals with this issue." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Disorder of Small Numbers\n", + "\n", + "The Law of Large Numbers is only valid as $N$ gets *infinitely* large: never truly attainable. While the law is a powerful tool, it is foolhardy to apply it liberally. Our next example illustrates this.\n", + "\n", + "\n", + "##### Example: Aggregated geographic data\n", + "\n", + "\n", + "Often data comes in aggregated form. For instance, data may be grouped by state, county, or city level. Of course, the population numbers vary per geographic area. If the data is an average of some characteristic of each the geographic areas, we must be conscious of the Law of Large Numbers and how it can *fail* for areas with small populations.\n", + "\n", + "We will observe this on a toy dataset. Suppose there are five thousand counties in our dataset. Furthermore, population number in each state are uniformly distributed between 100 and 1500. The way the population numbers are generated is irrelevant to the discussion, so we do not justify this. We are interested in measuring the average height of individuals per county. Unbeknownst to us, height does **not** vary across county, and each individual, regardless of the county he or she is currently living in, has the same distribution of what their height may be:\n", + "\n", + "$$ \\text{height} \\sim \\text{Normal}(150, 15 ) $$\n", + "\n", + "We aggregate the individuals at the county level, so we only have data for the *average in the county*. What might our dataset look like?" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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fj40bN3LXXXfx7W9/m74+47yNJFfiK0M4HOa8887jnHPOYfv27axcuZKnn346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vS7DpmcjWlprJ0T5nmhkqJdH9LtjPDdkFufWWc8dnl095Az58p0miM8N0RRRyytF3j4sXRKGkd9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\nBsZE5MtAJ9Ba99FtEcEa89tRc343aLcaCbNHdDBbRAu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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "std_height = 15\n", + "mean_height = 150\n", + "\n", + "n_counties = 5000\n", + "pop_generator = pm.rdiscrete_uniform\n", + "norm = pm.rnormal\n", + "\n", + "# generate some artificial population numbers\n", + "population = pop_generator(100, 1500, size=n_counties)\n", + "\n", + "average_across_county = np.zeros(n_counties)\n", + "for i in range(n_counties):\n", + " # generate some individuals and take the mean\n", + " average_across_county[i] = norm(mean_height, 1. / std_height ** 2,\n", + " size=population[i]).mean()\n", + "\n", + "# located the counties with the apparently most extreme average heights.\n", + "i_min = np.argmin(average_across_county)\n", + "i_max = np.argmax(average_across_county)\n", + "\n", + "# plot population size vs. recorded average\n", + "plt.scatter(population, average_across_county, alpha=0.5, c=\"#7A68A6\")\n", + "plt.scatter([population[i_min], population[i_max]],\n", + " [average_across_county[i_min], average_across_county[i_max]],\n", + " s=60, marker=\"o\", facecolors=\"none\",\n", + " edgecolors=\"#A60628\", linewidths=1.5,\n", + " label=\"extreme heights\")\n", + "\n", + "plt.xlim(100, 1500)\n", + "plt.title(\"Average height vs. County Population\")\n", + "plt.xlabel(\"County Population\")\n", + "plt.ylabel(\"Average height in county\")\n", + "plt.plot([100, 1500], [150, 150], color=\"k\", label=\"true expected \\\n", + "height\", ls=\"--\")\n", + "plt.legend(scatterpoints=1);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What do we observe? *Without accounting for population sizes* we run the risk of making an enormous inference error: if we ignored population size, we would say that the county with the shortest and tallest individuals have been correctly circled. But this inference is wrong for the following reason. These two counties do *not* necessarily have the most extreme heights. The error results from the calculated average of smaller populations not being a good reflection of the true expected value of the population (which in truth should be $\\mu =150$). The sample size/population size/$N$, whatever you wish to call it, is simply too small to invoke the Law of Large Numbers effectively. \n", + "\n", + "We provide more damning evidence against this inference. Recall the population numbers were uniformly distributed over 100 to 1500. Our intuition should tell us that the counties with the most extreme population heights should also be uniformly spread over 100 to 1500, and certainly independent of the county's population. Not so. Below are the population sizes of the counties with the most extreme heights." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Population sizes of 10 'shortest' counties: \n", + "[100 103 138 182 194 100 118 161 156 186]\n", + "\n", + "Population sizes of 10 'tallest' counties: \n", + "[100 147 132 193 270 130 414 101 150 109]\n" + ] + } + ], + "source": [ + "print(\"Population sizes of 10 'shortest' counties: \")\n", + "print(population[np.argsort(average_across_county)[:10]])\n", + "print(\"\\nPopulation sizes of 10 'tallest' counties: \")\n", + "print(population[np.argsort(-average_across_county)[:10]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not at all uniform over 100 to 1500. This is an absolute failure of the Law of Large Numbers. \n", + "\n", + "##### Example: Kaggle's *U.S. Census Return Rate Challenge*\n", + "\n", + "Below is data from the 2010 US census, which partitions populations beyond counties to the level of block groups (which are aggregates of city blocks or equivalents). The dataset is from a Kaggle machine learning competition some colleagues and I participated in. The objective was to predict the census letter mail-back rate of a group block, measured between 0 and 100, using census variables (median income, number of females in the block-group, number of trailer parks, average number of children etc.). Below we plot the census mail-back rate versus block group population:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Vi+dbDIViPxakET+TN2GqlzubLjBbHPLE9qVimUK+PO7lPtC9c+lzun4iUT8r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O7eyCr6aQqF0gJWXmfzbpfeNG11frnMeOjhyAKzC0UESaQxl6e9P2I88JFkAfLZ9e1sDqnP5tnf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\n4w7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SiIiIhFCOPvFP5P0+BvxSmcZWNSvVlq+HmbOtZwvpiwu0tDbS198OGLMzc8ylF3P3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\n5LGp3PbgUBe79vRWcUQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 6.5)\n", + "data = np.genfromtxt(\"./data/census_data.csv\", skip_header=1,\n", + " delimiter=\",\")\n", + "plt.scatter(data[:, 1], data[:, 0], alpha=0.5, c=\"#7A68A6\")\n", + "plt.title(\"Census mail-back rate vs Population\")\n", + "plt.ylabel(\"Mail-back rate\")\n", + "plt.xlabel(\"population of block-group\")\n", + "plt.xlim(-100, 15e3)\n", + "plt.ylim(-5, 105)\n", + "\n", + "i_min = np.argmin(data[:, 0])\n", + "i_max = np.argmax(data[:, 0])\n", + "\n", + "plt.scatter([data[i_min, 1], data[i_max, 1]],\n", + " [data[i_min, 0], data[i_max, 0]],\n", + " s=60, marker=\"o\", facecolors=\"none\",\n", + " edgecolors=\"#A60628\", linewidths=1.5,\n", + " label=\"most extreme points\")\n", + "\n", + "plt.legend(scatterpoints=1);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above is a classic phenomenon in statistics. I say *classic* referring to the \"shape\" of the scatter plot above. It follows a classic triangular form, that tightens as we increase the sample size (as the Law of Large Numbers becomes more exact). \n", + "\n", + "I am perhaps overstressing the point and maybe I should have titled the book *\"You don't have big data problems!\"*, but here again is an example of the trouble with *small datasets*, not big ones. Simply, small datasets cannot be processed using the Law of Large Numbers. Compare with applying the Law without hassle to big datasets (ex. big data). I mentioned earlier that paradoxically big data prediction problems are solved by relatively simple algorithms. The paradox is partially resolved by understanding that the Law of Large Numbers creates solutions that are *stable*, i.e. adding or subtracting a few data points will not affect the solution much. On the other hand, adding or removing data points to a small dataset can create very different results. \n", + "\n", + "For further reading on the hidden dangers of the Law of Large Numbers, I would highly recommend the excellent manuscript [The Most Dangerous Equation](http://nsm.uh.edu/~dgraur/niv/TheMostDangerousEquation.pdf). " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: How to order Reddit submissions\n", + "\n", + "You may have disagreed with the original statement that the Law of Large numbers is known to everyone, but only implicitly in our subconscious decision making. Consider ratings on online products: how often do you trust an average 5-star rating if there is only 1 reviewer? 2 reviewers? 3 reviewers? We implicitly understand that with such few reviewers that the average rating is **not** a good reflection of the true value of the product.\n", + "\n", + "This has created flaws in how we sort items, and more generally, how we compare items. Many people have realized that sorting online search results by their rating, whether the objects be books, videos, or online comments, return poor results. Often the seemingly top videos or comments have perfect ratings only from a few enthusiastic fans, and truly more quality videos or comments are hidden in later pages with *falsely-substandard* ratings of around 4.8. How can we correct this?\n", + "\n", + "Consider the popular site Reddit (I purposefully did not link to the website as you would never come back). The site hosts links to stories or images, and a very popular part of the site are the comments associated with each link. Redditors can vote up or down on each submission (called upvotes and downvotes). Reddit, by default, will sort submissions to a given subreddit by Hot, that is, the submissions that have the most upvotes recently.\n", + "\n", + "\n", + "\n", + "\n", + "How would you determine which submissions are the best? There are a number of ways to achieve this:\n", + "\n", + "1. *Popularity*: A submission is considered good if it has many upvotes. A problem with this model is that a submission with hundreds of upvotes, but thousands of downvotes. While being very popular, the submission is likely more controversial than best.\n", + "2. *Difference*: Using the *difference* of upvotes and downvotes. This solves the above problem, but fails when we consider the temporal nature of submission. Depending on when a submission is posted, the website may be experiencing high or low traffic. The difference method will bias the Top submissions to be the those made during high traffic periods, which have accumulated more upvotes than submissions that were not so graced, but are not necessarily the best.\n", + "3. *Time adjusted*: Consider using Difference divided by the age of the submission. This creates a *rate*, something like *difference per second*, or *per minute*. An immediate counter-example is, if we use per second, a 1 second old submission with 1 upvote would be better than a 100 second old submission with 99 upvotes. One can avoid this by only considering at least t second old submission. But what is a good t value? Does this mean no submission younger than t is good? We end up comparing unstable quantities with stable quantities (young vs. old submissions).\n", + "3. *Ratio*: Rank submissions by the ratio of upvotes to total number of votes (upvotes plus downvotes). This solves the temporal issue, such that new submissions who score well can be considered Top just as likely as older submissions, provided they have many upvotes to total votes. The problem here is that a submission with a single upvote (ratio = 1.0) will beat a submission with 999 upvotes and 1 downvote (ratio = 0.999), but clearly the latter submission is *more likely* to be better.\n", + "\n", + "I used the phrase *more likely* for good reason. It is possible that the former submission, with a single upvote, is in fact a better submission than the latter with 999 upvotes. The hesitation to agree with this is because we have not seen the other 999 potential votes the former submission might get. Perhaps it will achieve an additional 999 upvotes and 0 downvotes and be considered better than the latter, though not likely.\n", + "\n", + "What we really want is an estimate of the *true upvote ratio*. Note that the true upvote ratio is not the same as the observed upvote ratio: the true upvote ratio is hidden, and we only observe upvotes vs. downvotes (one can think of the true upvote ratio as \"what is the underlying probability someone gives this submission a upvote, versus a downvote\"). So the 999 upvote/1 downvote submission probably has a true upvote ratio close to 1, which we can assert with confidence thanks to the Law of Large Numbers, but on the other hand we are much less certain about the true upvote ratio of the submission with only a single upvote. Sounds like a Bayesian problem to me.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One way to determine a prior on the upvote ratio is to look at the historical distribution of upvote ratios. This can be accomplished by scraping Reddit's submissions and determining a distribution. There are a few problems with this technique though:\n", + "\n", + "1. Skewed data: The vast majority of submissions have very few votes, hence there will be many submissions with ratios near the extremes (see the \"triangular plot\" in the above Kaggle dataset), effectively skewing our distribution to the extremes. One could try to only use submissions with votes greater than some threshold. Again, problems are encountered. There is a tradeoff between number of submissions available to use and a higher threshold with associated ratio precision. \n", + "2. Biased data: Reddit is composed of different subpages, called subreddits. Two examples are *r/aww*, which posts pics of cute animals, and *r/politics*. It is very likely that the user behaviour towards submissions of these two subreddits are very different: visitors are likely to be more friendly and affectionate in the former, and would therefore upvote submissions more, compared to the latter, where submissions are likely to be controversial and disagreed upon. Therefore not all submissions are the same. \n", + "\n", + "\n", + "In light of these, I think it is better to use a `Uniform` prior.\n", + "\n", + "\n", + "With our prior in place, we can find the posterior of the true upvote ratio. The Python script `top_showerthoughts_submissions.py` will scrape the best posts from the `showerthoughts` community on Reddit. This is a text-only community so the title of each post *is* the post. Below is the top post as well as some other sample posts:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Post contents: \n", + "\n", + "Toilet paper should be free and have advertising printed on it.\n" + ] + } + ], + "source": [ + "# adding a number to the end of the %run call with get the ith top photo.\n", + "%run top_showerthoughts_submissions.py 2\n", + "\n", + "print(\"Post contents: \\n\")\n", + "print(top_post)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Some Submissions (out of 98 total) \n", + "-----------\n", + "\"You will never feel how long time is until you have allergies and snot slowly dripping out of your nostrils, while sitting in a classroom with no tissues.\"\n", + "upvotes/downvotes: [71 6] \n", + "\n", + "\"What if porn ads weren't fake and all these years I've been missing out on these local mums in my area that want to fuck?\"\n", + "upvotes/downvotes: [43 11] \n", + "\n", + "\"You'll be real lucky to find a Penny in Canada.\"\n", + "upvotes/downvotes: [28 11] \n", + "\n", + "\"\"Smells Like Teen Spirit\" is as old to listeners of today as \"Yellow Submarine\" was to listeners of 1991.\"\n", + "upvotes/downvotes: [92 10] \n", + "\n" + ] + } + ], + "source": [ + "\"\"\"\n", + "contents: an array of the text from the last 100 top submissions to a subreddit\n", + "votes: a 2d numpy array of upvotes, downvotes for each submission.\n", + "\"\"\"\n", + "n_submissions = len(votes)\n", + "submissions = np.random.randint( n_submissions, size=4)\n", + "print(\"Some Submissions (out of %d total) \\n-----------\"%n_submissions)\n", + "for i in submissions:\n", + " print('\"' + contents[i] + '\"')\n", + " print(\"upvotes/downvotes: \",votes[i,:], \"\\n\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " For a given true upvote ratio $p$ and $N$ votes, the number of upvotes will look like a Binomial random variable with parameters $p$ and $N$. (This is because of the equivalence between upvote ratio and probability of upvoting versus downvoting, out of $N$ possible votes/trials). We create a function that performs Bayesian inference on $p$, for a particular comment's upvote/downvote pair." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pymc as pm\n", + "\n", + "\n", + "def posterior_upvote_ratio(upvotes, downvotes, samples=20000):\n", + " \"\"\"\n", + " This function accepts the number of upvotes and downvotes a particular submission received, \n", + " and the number of posterior samples to return to the user. Assumes a uniform prior.\n", + " \"\"\"\n", + " N = upvotes + downvotes\n", + " upvote_ratio = pm.Uniform(\"upvote_ratio\", 0, 1)\n", + " observations = pm.Binomial(\"obs\", N, upvote_ratio, value=upvotes, observed=True)\n", + " # do the fitting; first do a MAP as it is cheap and useful.\n", + " map_ = pm.MAP([upvote_ratio, observations]).fit()\n", + " mcmc = pm.MCMC([upvote_ratio, observations])\n", + " mcmc.sample(samples, samples / 4)\n", + " return mcmc.trace(\"upvote_ratio\")[:]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below are the resulting posterior distributions." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'figsize' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfigsize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m11.\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mposteriors\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mcolours\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m\"#348ABD\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"#A60628\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"#7A68A6\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"#467821\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"#CF4457\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubmissions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msubmissions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mNameError\u001b[0m: name 'figsize' is not defined" + ] + } + ], + "source": [ + "figsize(11., 8)\n", + "posteriors = []\n", + "colours = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\", \"#CF4457\"]\n", + "for i in range(len(submissions)):\n", + " j = submissions[i]\n", + " posteriors.append(posterior_upvote_ratio(votes[j, 0], votes[j, 1]))\n", + " plt.hist(posteriors[i], bins=18, normed=True, alpha=.9,\n", + " histtype=\"step\", color=colours[i % 5], lw=3,\n", + " label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n", + " plt.hist(posteriors[i], bins=18, normed=True, alpha=.2,\n", + " histtype=\"stepfilled\", color=colours[i], lw=3, )\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim(0, 1)\n", + "plt.title(\"Posterior distributions of upvote ratios on different submissions\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some distributions are very tight, others have very long tails (relatively speaking), expressing our uncertainty with what the true upvote ratio might be.\n", + "\n", + "### Sorting!\n", + "\n", + "We have been ignoring the goal of this exercise: how do we sort the submissions from *best to worst*? Of course, we cannot sort distributions, we must sort scalar numbers. There are many ways to distill a distribution down to a scalar: expressing the distribution through its expected value, or mean, is one way. Choosing the mean is a bad choice though. This is because the mean does not take into account the uncertainty of distributions.\n", + "\n", + "I suggest using the *95% least plausible value*, defined as the value such that there is only a 5% chance the true parameter is lower (think of the lower bound on the 95% credible region). Below are the posterior distributions with the 95% least-plausible value plotted:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 1 3 2] [0.95553912986585299, 0.94130501756135543, 0.80681345969724116, 0.88775207639838272]\n" + ] + }, + { + "data": { + "image/png": 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rcampqYwaNQpXV1eCgoI4evSoFnf27Fm6dOmCu7s7QUFB/Pbbbwby6Q+h5TQs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IyLmRgXM7EGsvoxA0lEREREjnAtbJ9i3ZC5GBszMS5mYlzMxBrI6scMJBERERE5whpIn2LdkLkY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\nnr6/qTQQROvGDclf5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N = posteriors[0].shape[0]\n", + "lower_limits = []\n", + "\n", + "for i in range(len(submissions)):\n", + " j = submissions[i]\n", + " plt.hist(posteriors[i], bins=20, normed=True, alpha=.9,\n", + " histtype=\"step\", color=colours[i], lw=3,\n", + " label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n", + " plt.hist(posteriors[i], bins=20, normed=True, alpha=.2,\n", + " histtype=\"stepfilled\", color=colours[i], lw=3, )\n", + " v = np.sort(posteriors[i])[int(0.05 * N)]\n", + " # plt.vlines( v, 0, 15 , color = \"k\", alpha = 1, linewidths=3 )\n", + " plt.vlines(v, 0, 10, color=colours[i], linestyles=\"--\", linewidths=3)\n", + " lower_limits.append(v)\n", + " plt.legend(loc=\"upper left\")\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(\"Posterior distributions of upvote ratios on different submissions\");\n", + "order = np.argsort(-np.array(lower_limits))\n", + "print(order, lower_limits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The best submissions, according to our procedure, are the submissions that are *most-likely* to score a high percentage of upvotes. Visually those are the submissions with the 95% least plausible value close to 1.\n", + "\n", + "Why is sorting based on this quantity a good idea? By ordering by the 95% least plausible value, we are being the most conservative with what we think is best. That is, even in the worst case scenario, when we have severely overestimated the upvote ratio, we can be sure the best comments are still on top. Under this ordering, we impose the following very natural properties:\n", + "\n", + "1. given two submissions with the same observed upvote ratio, we will assign the submission with more votes as better (since we are more confident it has a higher ratio).\n", + "2. given two submissions with the same number of votes, we still assign the submission with more upvotes as *better*.\n", + "\n", + "### But this is too slow for real-time!\n", + "\n", + "I agree, computing the posterior of every submission takes a long time, and by the time you have computed it, likely the data has changed. I delay the mathematics to the appendix, but I suggest using the following formula to compute the lower bound very fast.\n", + "\n", + "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", + "\n", + "where \n", + "\\begin{align}\n", + "& a = 1 + u \\\\\\\\\n", + "& b = 1 + d \\\\\\\\\n", + "\\end{align}\n", + "\n", + "$u$ is the number of upvotes, and $d$ is the number of downvotes. The formula is a shortcut in Bayesian inference, which will be further explained in Chapter 6 when we discuss priors in more detail.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Approximate lower bounds:\n", + "[ 0.9335036 0.95310536 0.94166971 0.90854227 0.88683909 0.85564276\n", + " 0.85607414 0.93758888 0.95697574 0.91015237 0.9112593 0.91305389\n", + " 0.91341024 0.83335231 0.87543995 0.87081169 0.92748782 0.90747915\n", + " 0.89063214 0.89804044 0.91295322 0.78329196 0.91901344 0.79950031\n", + " 0.84776174 0.83540757 0.77406294 0.81391583 0.7296015 0.79338766\n", + " 0.82895671 0.85331368 0.81849519 0.72362912 0.83662174 0.81019924\n", + " 0.78564811 0.84570434 0.8400282 0.76944053 0.85827725 0.74417233\n", + " 0.8189683 0.8027221 0.79190256 0.9033107 0.81639188 0.76627386\n", + " 0.8010596 0.63657302 0.62988646 0.75041771 0.85355829 0.84522753\n", + " 0.75627191 0.8458571 0.80877728 0.66764706 0.69623887 0.71480224\n", + " 0.72921035 0.86797314 0.73955911 0.90742546 0.80364062 0.72331349\n", + " 0.79249393 0.72708753 0.81109538 0.66235556 0.80480879 0.72039455\n", + " 0.73945971 0.83846154 0.69 0.70597731 0.68175931 0.59412132\n", + " 0.6011942 0.73158407 0.69121436 0.68134548 0.87746603 0.79809005\n", + " 0.6296728 0.87152685 0.81814153 0.86498277 0.81018384 0.54207776\n", + " 0.6296728 0.74107856 0.53025484 0.71034959 0.80149882 0.85773646\n", + " 0.58343356 0.62971097]\n", + "\n", + "\n", + "Top 40 Sorted according to approximate lower bounds:\n", + "\n", + "\n", + "586 18 Someone should develop an AI specifically for reading Terms & Conditions and flagging dubious parts.\n", + "-------------\n", + "2354 98 Porn is the only industry where it is not only acceptable but standard to separate people based on race, sex and sexual preference.\n", + "-------------\n", + "1924 101 All polls are biased towards people who are willing to take polls\n", + "-------------\n", + "949 50 They should charge less for drinks in the drive-thru because you can't refill them.\n", + "-------------\n", + "3726 238 When I was in elementary school and going through the DARE program, I was positive a gang of older kids was going to corner me and force me to smoke pot. Then I became an adult and realized nobody is giving free drugs to somebody that doesn't want them.\n", + "-------------\n", + "164 7 \"Noted\" is the professional way of saying \"K\".\n", + "-------------\n", + "100 4 The best answer to the interview question \"What is your greatest weakness?\" is \"interviews\".\n", + "-------------\n", + "267 17 At some point every parent has stopped wiping their child's butt and hoped for the best.\n", + "-------------\n", + "291 19 You've been doing weird cameos in your friends' dreams since kindergarten.\n", + "-------------\n", + "121 6 Is it really fair to say a person over 85 has heart failure? Technically, that heart has done exceptionally well.\n", + "-------------\n", + "523 39 I wonder if America's internet is censored in a similar way that North Korea's is, but we have no idea of it happening.\n", + "-------------\n", + "539 41 It's surreal to think that the sun and moon and stars we gaze up at are the same objects that have been observed for millenia, by everyone in the history of humanity from cavemen to Aristotle to Jesus to George Washington.\n", + "-------------\n", + "1509 131 Kenny's family is poor because they're always paying for his funeral.\n", + "-------------\n", + "164 10 Black hair ties are probably the most popular bracelets in the world.\n", + "-------------\n", + "26 0 Now that I am a parent of multiple children I have realized that my parents were lying through their teeth when they said they didn't have a favorite.\n", + "-------------\n", + "41 1 If I was as careful with my whole paycheck as I am with my last $20 I'd be a whole lot better off\n", + "-------------\n", + "125 8 Surfing the internet without ads feels like a summer evening without mosquitoes\n", + "-------------\n", + "157 12 I wonder if Superman ever put a pair of glasses on Lois Lane's dog, and she was like \"what's this Clark? Did you get me a new dog?\"\n", + "-------------\n", + "1411 157 My life is really like Rihanna's song, \"just work work work work work\" and the rest of it I can't really understand.\n", + "-------------\n", + "19 0 Binoculars are like walkie talkies for the deaf.\n", + "-------------\n", + "221 22 I'm honestly slightly concerned how often Reddit commenters make me laugh compared to my real life friends.\n", + "-------------\n", + "18 0 Living on the coast is having the window seat of the land you live on.\n", + "-------------\n", + "188 19 I have not been thankful enough in the last few years that the Black Eyed Peas are no longer ever on the radio\n", + "-------------\n", + "29 1 Rewatching Mr. Bean, I've realised that the character is an eccentric genius and not a blithering idiot.\n", + "-------------\n", + "17 0 Sitting on a cold toilet seat or a warm toilet seat both suck for different reasons.\n", + "-------------\n", + "54 4 You will never feel how long time is until you have allergies and snot slowly dripping out of your nostrils, while sitting in a classroom with no tissues.\n", + "-------------\n", + "16 0 I sneer at people who read tabloids, but every time I look someone up on Wikipedia the first thing I look for is what controversies they've been involved in.\n", + "-------------\n", + "1485 222 Kid's menus at restaurants should be smaller portions of the same adult dishes at lower prices and not the junk food that they usually offer.\n", + "-------------\n", + "1417 212 Eventually once all phones are waterproof we'll be able to push people into pools again\n", + "-------------\n", + "35 2 Childhood and adolescence are thinking that no one has ever felt the way you do and that no one has ever experienced the things that you have. Adulthood is realizing that almost everyone has felt and experienced something similar.\n", + "-------------\n", + "60 5 Myspace is so outdated that jokes about it being outdated has become outdated\n", + "-------------\n", + "87 9 Yahoo!® is the RadioShack® of the Internet.\n", + "-------------\n", + "33 2 People who \"tell it like it is\" rarely do so to say something nice\n", + "-------------\n", + "49 4 The world must have been a spookier place altogether when candles and gas lamps were the only sources of light at night besides the moon and the stars.\n", + "-------------\n", + "41 3 Closing your eyes after turning off your alarm is a very dangerous game.\n", + "-------------\n", + "47 4 As a kid, seeing someone step on a banana peel and not slip was a disappointment.\n", + "-------------\n", + "23 1 The phonebook was the biggest invasion of privacy that everyone was oddly ok with.\n", + "-------------\n", + "53 5 I'm actually the most productive when I procrastinate because I'm doing everything I possibly can to avoid the main task at hand.\n", + "-------------\n", + "86 10 \"Smells Like Teen Spirit\" is as old to listeners of today as \"Yellow Submarine\" was to listeners of 1991.\n", + "-------------\n", + "240 36 if an ocean didnt stop immigrants from coming to America what makes us think a wall will?\n", + "-------------\n" + ] + } + ], + "source": [ + "def intervals(u, d):\n", + " a = 1. + u\n", + " b = 1. + d\n", + " mu = a / (a + b)\n", + " std_err = 1.65 * np.sqrt((a * b) / ((a + b) ** 2 * (a + b + 1.)))\n", + " return (mu, std_err)\n", + "\n", + "print(\"Approximate lower bounds:\")\n", + "posterior_mean, std_err = intervals(votes[:, 0], votes[:, 1])\n", + "lb = posterior_mean - std_err\n", + "print(lb)\n", + "print(\"\\n\")\n", + "print(\"Top 40 Sorted according to approximate lower bounds:\")\n", + "print(\"\\n\")\n", + "order = np.argsort(-lb)\n", + "ordered_contents = []\n", + "for i in order[:40]:\n", + " ordered_contents.append(contents[i])\n", + " print(votes[i, 0], votes[i, 1], contents[i])\n", + " print(\"-------------\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can view the ordering visually by plotting the posterior mean and bounds, and sorting by the lower bound. In the plot below, notice that the left error-bar is sorted (as we suggested this is the best way to determine an ordering), so the means, indicated by dots, do not follow any strong pattern. " + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Rh/U5yn2NEJ0aQYhA/W+MZBwL/ASYaGb3ZNWZzIZIyaTopzvjvbuAB6IP68eT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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "r_order = order[::-1][-40:]\n", + "plt.errorbar(posterior_mean[r_order], np.arange(len(r_order)),\n", + " xerr=std_err[r_order], capsize=0, fmt=\"o\",\n", + " color=\"#7A68A6\")\n", + "plt.xlim(0.3, 1)\n", + "plt.yticks(np.arange(len(r_order) - 1, -1, -1), map(lambda x: x[:30].replace(\"\\n\", \"\"), ordered_contents));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the graphic above, you can see why sorting by mean would be sub-optimal." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Extension to Starred rating systems\n", + "\n", + "The above procedure works well for upvote-downvotes schemes, but what about systems that use star ratings, e.g. 5 star rating systems. Similar problems apply with simply taking the average: an item with two perfect ratings would beat an item with thousands of perfect ratings, but a single sub-perfect rating. \n", + "\n", + "\n", + "We can consider the upvote-downvote problem above as binary: 0 is a downvote, 1 if an upvote. A $N$-star rating system can be seen as a more continuous version of above, and we can set $n$ stars rewarded is equivalent to rewarding $\\frac{n}{N}$. For example, in a 5-star system, a 2 star rating corresponds to 0.4. A perfect rating is a 1. We can use the same formula as before, but with $a,b$ defined differently:\n", + "\n", + "\n", + "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", + "\n", + "where \n", + "\n", + "\\begin{align}\n", + "& a = 1 + S \\\\\\\\\n", + "& b = 1 + N - S \\\\\\\\\n", + "\\end{align}\n", + "\n", + "where $N$ is the number of users who rated, and $S$ is the sum of all the ratings, under the equivalence scheme mentioned above. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Counting Github stars\n", + "\n", + "What is the average number of stars a Github repository has? How would you calculate this? There are over 6 million repositories, so there is more than enough data to invoke the Law of Large numbers. Let's start pulling some data. TODO" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "While the Law of Large Numbers is cool, it is only true so much as its name implies: with large sample sizes only. We have seen how our inference can be affected by not considering *how the data is shaped*. \n", + "\n", + "1. By (cheaply) drawing many samples from the posterior distributions, we can ensure that the Law of Large Number applies as we approximate expected values (which we will do in the next chapter).\n", + "\n", + "2. Bayesian inference understands that with small sample sizes, we can observe wild randomness. Our posterior distribution will reflect this by being more spread rather than tightly concentrated. Thus, our inference should be correctable.\n", + "\n", + "3. There are major implications of not considering the sample size, and trying to sort objects that are unstable leads to pathological orderings. The method provided above solves this problem.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Appendix\n", + "\n", + "##### Derivation of sorting comments formula\n", + "\n", + "Basically what we are doing is using a Beta prior (with parameters $a=1, b=1$, which is a uniform distribution), and using a Binomial likelihood with observations $u, N = u+d$. This means our posterior is a Beta distribution with parameters $a' = 1 + u, b' = 1 + (N - u) = 1+d$. We then need to find the value, $x$, such that 0.05 probability is less than $x$. This is usually done by inverting the CDF ([Cumulative Distribution Function](http://en.wikipedia.org/wiki/Cumulative_Distribution_Function)), but the CDF of the beta, for integer parameters, is known but is a large sum [3]. \n", + "\n", + "We instead use a Normal approximation. The mean of the Beta is $\\mu = a'/(a'+b')$ and the variance is \n", + "\n", + "$$\\sigma^2 = \\frac{a'b'}{ (a' + b')^2(a'+b'+1) }$$\n", + "\n", + "Hence we solve the following equation for $x$ and have an approximate lower bound. \n", + "\n", + "$$ 0.05 = \\Phi\\left( \\frac{(x - \\mu)}{\\sigma}\\right) $$ \n", + "\n", + "$\\Phi$ being the [cumulative distribution for the normal distribution](http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution)\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Exercises\n", + "\n", + "1\\. How would you estimate the quantity $E\\left[ \\cos{X} \\right]$, where $X \\sim \\text{Exp}(4)$? What about $E\\left[ \\cos{X} | X \\lt 1\\right]$, i.e. the expected value *given* we know $X$ is less than 1? Would you need more samples than the original samples size to be equally accurate?" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Enter code here\n", + "import scipy.stats as stats\n", + "exp = stats.expon(scale=4)\n", + "N = int(1e5)\n", + "X = exp.rvs(N)\n", + "# ..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. The following table was located in the paper \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression\" [2]. The table ranks football field-goal kickers by their percent of non-misses. What mistake have the researchers made?\n", + "\n", + "-----\n", + "\n", + "#### Kicker Careers Ranked by Make Percentage\n", + "
Rank Kicker Make % Number of Kicks
1 Garrett Hartley 87.7 57
2 Matt Stover 86.8 335
3 Robbie Gould 86.2 224
4 Rob Bironas 86.1 223
5 Shayne Graham 85.4 254
51 Dave Rayner 72.2 90
52 Nick Novak 71.9 64
53 Tim Seder 71.0 62
54 Jose Cortez 70.7 75
55 Wade Richey 66.1 56
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In August 2013, [a popular post](http://bpodgursky.wordpress.com/2013/08/21/average-income-per-programming-language/) on the average income per programmer of different languages was trending. Here's the summary chart: (reproduced without permission, cause when you lie with stats, you gunna get the hammer). What do you notice about the extremes?\n", + "\n", + "------\n", + "\n", + "#### Average household income by programming language\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
LanguageAverage Household Income ($)Data Points
Puppet87,589.29112
Haskell89,973.82191
PHP94,031.19978
CoffeeScript94,890.80435
VimL94,967.11532
Shell96,930.54979
Lua96,930.69101
Erlang97,306.55168
Clojure97,500.00269
Python97,578.872314
JavaScript97,598.753443
Emacs Lisp97,774.65355
C#97,823.31665
Ruby98,238.743242
C++99,147.93845
CSS99,881.40527
Perl100,295.45990
C100,766.512120
Go101,158.01231
Scala101,460.91243
ColdFusion101,536.70109
Objective-C101,801.60562
Groovy102,650.86116
Java103,179.391402
XSLT106,199.19123
ActionScript108,119.47113
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "1. Wainer, Howard. *The Most Dangerous Equation*. American Scientist, Volume 95.\n", + "2. Clarck, Torin K., Aaron W. Johnson, and Alexander J. Stimpson. \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression.\" (2013): n. page. [Web](http://www.sloansportsconference.com/wp-content/uploads/2013/Going%20for%20Three%20Predicting%20the%20Likelihood%20of%20Field%20Goal%20Success%20with%20Logistic%20Regression.pdf). 20 Feb. 2013.\n", + "3. http://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [conda env:bayes]", + "language": "python", + "name": "conda-env-bayes-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter4_TheGreatestTheoremNeverTold/Ch4_LawOfLargeNumbers_PyMC3.ipynb b/Chapter4_TheGreatestTheoremNeverTold/Ch4_LawOfLargeNumbers_PyMC3.ipynb new file mode 100644 index 00000000..d002f51b --- /dev/null +++ b/Chapter4_TheGreatestTheoremNeverTold/Ch4_LawOfLargeNumbers_PyMC3.ipynb @@ -0,0 +1,1199 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4\n", + "`Original content created by Cam Davidson-Pilon`\n", + "\n", + "`Ported to Python 3 and PyMC3 by Max Margenot (@clean_utensils) and Thomas Wiecki (@twiecki) at Quantopian (@quantopian)`\n", + "\n", + "______\n", + "\n", + "## The greatest theorem never told\n", + "\n", + "\n", + "This chapter focuses on an idea that is always bouncing around our minds, but is rarely made explicit outside books devoted to statistics. In fact, we've been using this simple idea in every example thus far. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Law of Large Numbers\n", + "\n", + "Let $Z_i$ be $N$ independent samples from some probability distribution. According to *the Law of Large numbers*, so long as the expected value $E[Z]$ is finite, the following holds,\n", + "\n", + "$$\\frac{1}{N} \\sum_{i=1}^N Z_i \\rightarrow E[ Z ], \\;\\;\\; N \\rightarrow \\infty.$$\n", + "\n", + "In words:\n", + "\n", + "> The average of a sequence of random variables from the same distribution converges to the expected value of that distribution.\n", + "\n", + "This may seem like a boring result, but it will be the most useful tool you use." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Intuition \n", + "\n", + "If the above Law is somewhat surprising, it can be made more clear by examining a simple example. \n", + "\n", + "Consider a random variable $Z$ that can take only two values, $c_1$ and $c_2$. Suppose we have a large number of samples of $Z$, denoting a specific sample $Z_i$. The Law says that we can approximate the expected value of $Z$ by averaging over all samples. Consider the average:\n", + "\n", + "\n", + "$$ \\frac{1}{N} \\sum_{i=1}^N \\;Z_i $$\n", + "\n", + "\n", + "By construction, $Z_i$ can only take on $c_1$ or $c_2$, hence we can partition the sum over these two values:\n", + "\n", + "\\begin{align}\n", + "\\frac{1}{N} \\sum_{i=1}^N \\;Z_i\n", + "& =\\frac{1}{N} \\big( \\sum_{ Z_i = c_1}c_1 + \\sum_{Z_i=c_2}c_2 \\big) \\\\\\\\[5pt]\n", + "& = c_1 \\sum_{ Z_i = c_1}\\frac{1}{N} + c_2 \\sum_{ Z_i = c_2}\\frac{1}{N} \\\\\\\\[5pt]\n", + "& = c_1 \\times \\text{ (approximate frequency of $c_1$) } \\\\\\\\ \n", + "& \\;\\;\\;\\;\\;\\;\\;\\;\\; + c_2 \\times \\text{ (approximate frequency of $c_2$) } \\\\\\\\[5pt]\n", + "& \\approx c_1 \\times P(Z = c_1) + c_2 \\times P(Z = c_2 ) \\\\\\\\[5pt]\n", + "& = E[Z]\n", + "\\end{align}\n", + "\n", + "\n", + "Equality holds in the limit, but we can get closer and closer by using more and more samples in the average. This Law holds for almost *any distribution*, minus some important cases we will encounter later.\n", + "\n", + "##### Example\n", + "____\n", + "\n", + "\n", + "Below is a diagram of the Law of Large numbers in action for three different sequences of Poisson random variables. \n", + "\n", + " We sample `sample_size = 100000` Poisson random variables with parameter $\\lambda = 4.5$. (Recall the expected value of a Poisson random variable is equal to it's parameter.) We calculate the average for the first $n$ samples, for $n=1$ to `sample_size`. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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9ls/befMWqzfe9isuv+TkZFJTU8nLy2PYsGEEBweTmJhIy5Yt/boGp0+f5uqr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\nMC8aNWNfLABk161TLRYkSZKkQY19sdDpd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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "from IPython.core.pylabtools import figsize\n", + "import matplotlib.pyplot as plt\n", + "\n", + "figsize( 12.5, 5 )\n", + "\n", + "sample_size = 100000\n", + "expected_value = lambda_ = 4.5\n", + "poi = np.random.poisson\n", + "N_samples = range(1,sample_size,100)\n", + "\n", + "for k in range(3):\n", + "\n", + " samples = poi( lambda_, sample_size ) \n", + " \n", + " partial_average = [ samples[:i].mean() for i in N_samples ]\n", + " \n", + " plt.plot( N_samples, partial_average, lw=1.5,label=\"average \\\n", + "of $n$ samples; seq. %d\"%k)\n", + " \n", + "\n", + "plt.plot( N_samples, expected_value*np.ones_like( partial_average), \n", + " ls = \"--\", label = \"true expected value\", c = \"k\" )\n", + "\n", + "plt.ylim( 4.35, 4.65) \n", + "plt.title( \"Convergence of the average of \\n random variables to its \\\n", + "expected value\" )\n", + "plt.ylabel( \"average of $n$ samples\" )\n", + "plt.xlabel( \"# of samples, $n$\")\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above plot, it is clear that when the sample size is small, there is greater variation in the average (compare how *jagged and jumpy* the average is initially, then *smooths* out). All three paths *approach* the value 4.5, but just flirt with it as $N$ gets large. Mathematicians and statistician have another name for *flirting*: convergence. \n", + "\n", + "Another very relevant question we can ask is *how quickly am I converging to the expected value?* Let's plot something new. For a specific $N$, let's do the above trials thousands of times and compute how far away we are from the true expected value, on average. But wait — *compute on average*? This is simply the law of large numbers again! For example, we are interested in, for a specific $N$, the quantity:\n", + "\n", + "$$D(N) = \\sqrt{ \\;E\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\;\\;\\right] \\;\\;}$$\n", + "\n", + "The above formulae is interpretable as a distance away from the true value (on average), for some $N$. (We take the square root so the dimensions of the above quantity and our random variables are the same). As the above is an expected value, it can be approximated using the law of large numbers: instead of averaging $Z_i$, we calculate the following multiple times and average them:\n", + "\n", + "$$ Y_k = \\left( \\;\\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\; \\right)^2 $$\n", + "\n", + "By computing the above many, $N_y$, times (remember, it is random), and averaging them:\n", + "\n", + "$$ \\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k \\rightarrow E[ Y_k ] = E\\;\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\right]$$\n", + "\n", + "Finally, taking the square root:\n", + "\n", + "$$ \\sqrt{\\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k} \\approx D(N) $$ " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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evZk9ezZ//vknaWlprrbuuVm0aJGr0lK5cmXKlSuHt7d3rjGePHmSChUqUK1a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\nLK+//jpfffUVR44coU6dOtx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POhO42RhzNK98LncfArCaDaVNncSXO61Zi6N3H9MKQSmg\n7XxVQWh5UU5pWVFKlTZOmwy9jtVkaCRwnf3vX4ELnvDnoS2wzRizxxhzDpgD9MqRphcwE8AY8ytQ\nTURq2dukAPFedjdeG+j6efWe45zL0GZDSimllFKq5HN6g30XcKcxZpEx5k9jzCKgD3B3AfIKAPa6\nLSfY6/JKs88tjQEWi8jvIjLcUybF0YcAoNFf/KhZ2QeAk2czWJ90sljiUM5pO19VEFpelFNaVpRS\npY3TeQg8DTd6OYch7WiMSRKRGlgVgzhjzAX/6y5btoyYmBiCgoIAqFatGtdee63rFW7Wf9RFsXxj\ncHU+WbAYgBW7/Lk+sGqR5qfLuqzLuqzLJW85S0mJx33Z39+funXropQq2aKjo9m4cSPHjx8HID4+\nnuuvv56uXbsWSX5ijMk/kcjbWE1+XgbigfpYfQpijDGPOcpIpB3wkjGmh738NGDcOxaLyIfAUmPM\nl/byFqCzMWZ/jmO9CKQYY/6RM5+ffvrJtGrVyklIhe6P5JOM/d82AKpVLMecgdfg7VXip25QSil1\nhUhMTCyVFQJ/f388TYVkjEFEOHTo0GWOSqmi4en3NDY2lq5duxbJjaXTNwRPYVUA3sfqVLwPqw/A\nKwXI63eggYjUB5KAe4ABOdJ8A4wGvrQrEMeMMftFxA/wMsacFJFKwK1YlZMSpWmtStRPPULgyhUc\nrBPIxr8GE163SnGHpZRSSpVau3fv5rfffiMsLKy4Q1GqzMq3D4GIeGPNQ/CqMaaBMcbPGNPQGPO8\nMeaM04yMMRnAw8Ai4A9gjjEmTkRGiMiDdprvgF0ish2YDoyyd68FRIvIWuAX4L92P4YLFFcfAgAv\nETqm7eeG5YsI/2WZTlJWwmk7X1UQWl6UU1pWCte2bdu0MqBUEcu3QmDfyP/DGHP6UjMzxiw0xjS2\nKxRT7HXTjTEz3NI8bFc8rjPGxNrrdhljwo0xLY0x12btWxK16NeV9HI+BO7Zwdq1O8l00CRLKaWU\nUhdKS0ujUqVKruUtW7bw6quvFmNESpVNTkcZ+q+I3FGkkRSS4piHwN11YTWJb94CgFq//Urc/tRi\njUd5pmOFq4LQ8qKc0rJyaTZt2uT6efXq1bRv39613KRJE+Lj4zlzxnEDBaWUA04rBBWBeSLys4h8\nJiIzsz5FGVxp5O0l+Nx6MwBNNsSwXJsNKaWUUo6kpKTw5ZdfukZWyczMvKAzcbdu3fjuu++KIzyl\nyiynFYJNwKvAUmA7sMPtU6IUZx+CLOF9OnO6oi81kxJYH7MNJyM5qctP2/mqgtDyopzSsnLxqlSp\nwpAhQ4iKiiI2NpbWrVtfkKZ8+fIsXry4GKJTquzyOMqQiEw1xjxpL64wxiy5TDGVei2D/Zk1YCj7\nqtfgWMXqbD2URuMalfLfUSmllLrChYWF8dFHH1GvXj1yDiM+c+ZMbrjhBpYsWcKJEyeoWrVqMUWp\nVNmS1xuCB91+nl/UgRSW4u5DAFDOS6jboxPH/GsCsGKXNhsqibSdryoILS/KKS0rl65JkybUqlUr\n27r58+cTGBhI48aNueuuu4iKiiqm6JQqe/Kah2C9iMwDNgMVRGRibomMMS8USWSlXKeQ6izedgSA\n6N3HGNamrsdJVZRSSil13uDBgy9Y17t3b9fPHTp0oEOHDpczJKXKtLwqBP2w3hLUBwSol0uaEtc4\nft26dRe8YiwOrQKq4OfjRdq5TBJPnGXnkVOE+fsVd1jKTXR0tD7JU45peVFOleaysrB27jfZPZJX\nOU7vKa1SquTyWCEwxhzAnolYRMoZY4ZetqjKgPLeXtwQVI2lO44CVrMhrRAopZRSufP398/1TXpB\nBuY4fPhwYYak1BUjrzcELqWpMlAS+hBk6RRcnaXbj1BrXzzrTx+F6+sWd0jKTWl9gqeKh5YX5VRp\nLisFfbpfmG8DPN3Me6oo5KTNcpW6eI4qBOriXF+vKjesXkLH775iY+sO7Lm3PfWv8i3usJRSSqlS\nY968eXTp0qW4w1CqTHM6D0GpURLmIchSsZwXVW9uB0DDP9ayYuuhYo5IudOxwlVBaHlRTmlZKTy7\nd+8mKCiouMNQqswrcxWCkub6js05UCeQiqdPsf27FcUdjlJKKVVqbNu2jbCwMAAOHjzI2LFjeeON\nNwDrAeCwYcNISEgozhCVKhMcVwhEpImIPC8i77sttyi60C5OSepDAHBDvapsDW8DwFUrV7Hv+Jli\njkhlKc3tfNXlp+VFOaVlpXCkpaVRqdL5ST1r1KhBREQEa9asAaB+/fo8/PDDBAYGFleISpUZjioE\nInIXsBwIAAbZqysD/yiiuMoMv/Le+HbrDEDYlo1Eb04q5oiUUkqpkmnTpk2un1evXk379u1dy6dO\nnaJixYrcfPPNLF68mI0bN9KiRYl7LqlUqeT0DcFEoJsxZiSQYa9bD1xXJFFdgpLUhyBL2zZhrG9z\nI9biN/sAACAASURBVCtvuZ3Vu3XW4pJC2/mqgtDyopzSsnJxUlJS+PLLLzl+/DgAmZmZ2UYO2rBh\nAy1atODuu+9mzpw5pKen4+3tXVzhKlWmOB1lqCawwf7ZuP1b4iYmK4naBVXjrT4DSc80kGrYn3KW\nWlXKF3dYSimlVIlRpUoVhgwZQlRUFOHh4bRu3Trb9lOnTlG+fHnKly+Pj48PR48eLaZIlSp7nL4h\nWMP5pkJZ7gF+K9xwLl1J60MAUKVCOcLrVnYtr9C3BCWCtvNVBaHlRTmlZeXihYWFsW3bNg4fPszV\nV1/tWv/LL78we/ZsDh48CMC9995L7dq1iytMpcocp28IxgCLRGQYUElEfgAaAbcWWWRlTKfg6sQk\npAAQvesY/a6tWcwRKaWUUiVPkyZNqFWrVrZ17dq1o127dq7lTp06Xe6wlCrTHL0hMMZsAZoA7wPP\nAR8D1xpjthVhbBelJPYhAOgQXB0vuynk5gOpHEo9W7wBKW3nqwpEy4tySsvKpRk8eLB2FlbqMnM6\nylAAUMEY8x9jzFRjzBzAR0TqFm14ZUe1iuVoUcduNpSZycqtB4s3IKWUUkoppXDeh2A+kHOg30Dg\n68IN59KVxD4EWToFV6fJ+t8Z/sbz7P1obnGHc8XTdr6qILS8KKe0rCilShunFYJGxpiN7ivs5SaF\nH1LZ1TG4OufKV6DKiWNUW7mSo6fOFXdISimllFLqCue0QnBQRBq4r7CXDxd+SJempPYhALjazwe/\njtdzuqIvNZL3sernjfnvpIqMtvNVBaHlRTmlZUUpVdo4rRD8G4gSkdtFpJmI3AHMAz4qSGYi0kNE\ntojIVhEZ7yHNNBHZJiLrRCQ8xzYvEYkVkW8Kkm9JcmOjGmxr3hKAhKhFxRyNUkoppZS60jmtEEwB\nPgfeAH4HptrLU5xmJCJewHtAd6A5MEBEmuRI0xMIM8Y0BEYAH+Y4zKPA5rzyKcl9CMBqNrSlxfUA\nVF+5kuPabKjYaDtfVRBaXpRTWlaUUqWN02FHM+3RhZoYYyrZ/75hjMksQF5tgW3GmD3GmHPAHKBX\njjS9gJn/396dh0lVXokf/57aet+bfRcEXFBARBQUE9yNGmM0LonRya4mmYn5jSYzk2UyS8yu2dRR\nYzRGkxjXaIyJGiIuyKogi4BCszZ003tXdW3n98e93VRveAsoqpo+n+e5T9371lt1324PbZ2677mv\ne87FQJmIDAMQkdHABaR5VSLXDC0OUTT7RFpLymgtKeP1VVuzPSRjjDGDhN/vp729PdvDMMb0o729\nHb/ff9jP63VhMkRkCnAiUJzarqr3eXyLUUDqp99tOEnC/vpsd9tqgR8D/w8o299JVq5cycyZMz0O\nKTvmTazkV//8DWJ5+ZzSoJyb7QENUosWLbJv8oxnFi/Gq1yOlaFDh7J7924aGxuzPRTjampqoqxs\nvx9tzCDi9/sZOvTwL17rKSEQka8D3wDeBFK/WlCc+oKMEpELgVpVXSkiZwLSX9+FCxeydOlSxo4d\nC0BZWRnTpk3r+uPcWeyVzeO8thixvHIAXlr4Mn8LbeesD5yRM+OzYzu2Yzu24wM/7pQr47Hj3D4G\nOOaYY3JmPHacO8erVq2iqakJgJqaGmbNmsWCBQvIBFHV9+8kshs4S1XfOuATicwBvqWq57nHtwKq\nqrel9LkTeElVf+cerwPm49QOfByIAwVACfCYql7b8zwvvPCC5voVAoAbHl/HxvowALeeOY4PTqrM\n8oiMMcYYY0yuWr58OQsWLOj3S/GD4bWoOAysO8hzLQEmicg4EQkBVwI97xb0FHAtdCUQjapaq6pf\nV9WxqnqU+7oX+0oGBpJ548u79l9+zy7dGmOMMcaY7PCaEPwH8FMRGeHe+rNr83oiVU0ANwHPA28D\nj6jqWhH5nIh81u3zLPCeiGwE7gJuSOunIbfXIUh1+oR9CcGSbc2EY4ksjmZw6nl535j9sXgxXlms\nmHRYvJhcEPDY73738dMpbYJTQ+C5FFpVnwOm9Gi7q8fxTe/zHguBhV7PmavGlOczriKf9rc3MG3Z\nq7yet4cPXH12todljDHGGGMGGa8JwYSMjuIQyvV1CFKdPr6ctU+vZ/rif7CTDrCE4LDqLNwxxguL\nF+OVxYpJh8WLyQVe1yHY0t+W6QEeyU6fUM76aSehIpQuW05bQ0u2h2SMMcYYYwYZzzUAInKxiPxQ\nRH4tIg90bpkc3IEYKDUEAOMr8ikbM5zt4yYSiMdY8sjz2R7SoGLzNk06LF6MVxYrJh0WLyYXeEoI\nROSbOEW+PuByoB44F7Db4xwEEeH0CeWsPWEWALuf+FuWR2SMMcYYYwYbr1cI/gk4W1X/BYi6jxcB\n4zM1sAM1kGoIAOZNKGfD8TNI+HwUrX6bcENztoc0aNi8TZMOixfjlcWKSYfFi8kFXouKy1V1tbsf\nFZGgqr4hIvMzNbDB4uiqAsqGVvKnqz7NztHjGdKqzK7I9qiMMcYYY8xg4fUKwSYROc7dXw18QUQ+\nATRkZlgHbiDVEMC+aUObjjmR9pIyFr3XlO0hDRo2b9Okw+LFeGWxYtJh8WJygdeE4N+BKnf/VuBL\nwPeBmzMxqMEmddXiV7c0kkhqFkdjjDHGGGMGE1E9sj58vvDCCzpz5sxsDyMtSVU+/vDb1LXHALjt\n/EnMGFWS5VEZY4wxxphcsXz5chYsWCCZeG+vdxna20/77kM7nMHJJ8LclKsEf91QT/0ry9j64BMc\naQmbMcYYY4zJLV6nDAV7NohIEPAf2uEcvIFWQ9Dp9AllXfv/WL2DV67/d97+f99j9T//N4n2SBZH\nduSyeZsmHRYvxiuLFZMOixeTC/abEIjIyyLyDyBfRP6RugHrgVcPyygHgeOGFXPC8GIAovkFvHD2\nJcSCQbb/7llev+iztG/eluURGmOMMcaYI9F+awhE5JOAAL8EPp/ylAK1wIuqGsvoCNM0EGsIOkXi\nSe5fuoPHV+9Bgepd27no4f+jon4PvpIipv/iWww9e262h2mMMcYYYw6zTNYQ7HcdAlX9NYCIvK6q\n6zIxALNPfsDH5+eM5vQJ5fzwHzVsYxQPfeEWzn3sQSatfYvFO9q4UBWfZCQWjDHGGGPMIOS1hmCG\niBwDICJTRGShiLwkIlMzOLYDMlBrCFIdN6yYX146lStOGEq8oICnr/oMj3zmK/w0NoRbnt3IjuaO\nbA/xiGDzNk06LF6MVxYrJh0WLyYXeE0I/gvovNPQD4AlwELgF5kYlIG8gI9Pzx7Fjy+azLiKAnaO\nPQqAN3e28rnH1vH46t0k7Q5ExhhjjDHmIHlah0BEmlW1VETygZ3AcCAG1KlqZYbHmJaBXEPQn2gi\nyUPLd/G7t2pJXbPs+GFFfKEizKS5JyA2jcgYY4wx5oiV9XUIgD0iMgk4H1iiqh1APk7BscmwkN/H\n9SeP5I5LpjChIr+rvfmVZWy4/Ab+dNUtdLS0ZXGExhhjjDFmoPKaEHwHWAbcC3zfbTsLeDMTgzoY\nR0INQX8mVxfysw9P4eMzhuMXCEY7iAdDBP++iKfO+CQblr+T7SEOKDZv06TD4sV4ZbFi0mHxYnKB\np4RAVe8HRgCjVfWvbvPrwJUZGpfpR9Dv49qTRvCzD0+B0+fw28//K/VDhlOycwdrP/w5/vizx0kk\nrbbAGGOMMcZ4028NgYiIuk+KSL+Jg6omMzS2A3Ik1hD0J55UHnmzlj+8vpkPPPYQU1cto62ohEX/\nfRtfOmcKEyoLsj1EY4wxxhhzCGRrHYImoNTdj+MsRpZK3DZ/BsZlPAj4hI/PGM7ccWX8YHgZO/70\nHPVDR7C1VbnxifV8fMZwrjhxGAGflXoYY4wxxpi+7W/K0HEp+xOAo3psnW055UiuIejPhMoC7rhk\nKjO+eBW7jnaWhognlfuX7eRLT67n3fpwlkeYm2zepkmHxYvxymLFpMPixeSC/U0F2pqyv6W/LZ2T\nich5IrJORN4RkVv66XOHiGwQkZUiMt1tyxORxSKyQkRWicg30znvYOD3CVdNH84vLp3C1CGFXe0b\n68Pc+NgaHli6g1gip2Z3GWOMMcaYHLC/GoIH6T1NqBdVvdbTiZw6hHeABcAOnMXNrlTVdSl9zgdu\nUtULReQU4HZVneM+V6iq7SLiB14BvqSqb/Q8z2CqIehPIqk8tno39y/bSSyhzHnxGYbs2s76T32a\nL597DEdXF77/mxhjjDHGmJyRrXUINgKb3K0J+DBOvcA293WXAI1pnGs2sMG9shADHnHfI9UlwAMA\nqroYKBORYe5xu9snD6f2wW6l0w+/T7j8hGHceelUTixSZr72d45e8yZz/+c7fOuuF/nV0h1E7WqB\nMcYYY4xh/1OGvt25AZOBC1X1GlX9uqp+HLgQmJLGuUYBW1OOt7lt++uzvbOPiPhEZAWwC/irqi7p\n6ySDsYagP2PK8/nux2agd/6QuuGjqKjfzZV3fp+V9z/NjU+sZ/2ewb2Ymc3bNOmweDFeWayYdFi8\nmFywv7sMpZqDs+5AqsXAqYd2OP1zb286Q0RKgSdE5FhVXdOz38KFC1m6dCljx44FoKysjGnTpjFv\n3jxg3z+8wXL82quvMKQIZj13D3+94b9pXPQXxv3+F+wKt/PlxjOZmdzC2ZMr+cD8M3JivHZsx3Zs\nxwP9uFOujMeOc/u4U66Mx45z53jVqlU0NTUBUFNTw6xZs1iwYAGZ0G8NQbdOIn/HmfP/DVUNi0gB\n8G1gjqqe4elEInOAb6nqee7xrYCq6m0pfe4EXlLV37nH64D5qlrb473+A2hT1R/1PI/VEPQvkUzy\n7A8eJvyrR3j4szfTVlIGwJiyPG4+YxzHDivK8giNMcYYY0xfslVDkOo6YC7QJCK1ODUF8wBPBcWu\nJcAkERknIiGcVY6f6tHnqc73dBOIRlWtFZFqESlz2wuAs4F1mLT4fT4u+tdrmPvyb5k0ed9sra1N\nHfzL0+9w9+LtdMSttsAYY4wxZjDxlBCo6mZVPQ2YCFwMTFLV01R1s9cTqWoCuAl4HngbeERV14rI\n50Tks26fZ4H3RGQjcBdwg/vyEcBLIrISZ6rSX9y+vVgNwfsbVV3CbRdM4ktzx1AQdEJAgUdX7ebz\nj61j9a7W7A7wMOl5udaY/bF4MV5ZrJh0WLyYXBBIp7OqbhWRa1T1uwdyMlV9jh6FyKp6V4/jm/p4\n3SrA5gEdQj4RPnRMNSePLuXHi2pYsbWJOS/9mRWnnsnNf+rgkuOGcP2sERQEbSFqY4wxxpgjmaca\ngm4vEGlW1dIMjeegWQ1B+lSV5/79l8i9v6GpvIqnr/40u0eOZURJiH+eN5YZo0qyPURjjDHGmEEt\nF2oIUmVkICZ7RIQzP38phdOmUNZYz5V3/5Djl77KzpYot/x5I999aTMN4Vi2h2mMMcYYYzLgQBKC\n3xzyURxCVkNwYArGjGDu03cy+hOXEIjHOeeJhzj78YdAlRc3NfCpP6zlmXV1JNO8opTLbN6mSYfF\ni/HKYsWkw+LF5IK0EwJV/UImBmKyz5+fx/Hfv4Vpt/87khdiDB0gzgWh1miC2xdt5StPb+C9veEs\nj9QYY4wxxhwq/dYQiMiDODef2S9VTefWoxlnNQSHRsvaTSRjcTZUjuCnr2xlZ0u067mAJvnIicO5\nZsZwKzo2xhhjjDkMslVDsBHY5G5NwIcBP7DNfd0lQGMmBmWyr+SYiZSdMIVZo0u5+7JjuGr6MAI+\nJwbPfvQBol/9Fv/5rUd47d29WR6pMcYYY4w5GP0mBKr67c4NmAxcqKrXqOrXVfXjwIX0uIVoLrAa\ngkMvL+Dj+lkjufPSqZxYEeSodas46p23mX/vz9l+7jXc+/nvs/2dmmwPM202b9Okw+LFeGWxYtJh\n8WJygdcagjnA6z3aFgOnHtrhmFw2tiKf733kOPL/cA+vf+ij7K0eRnFLE6OeeJxlZ32Sx5dtJZE8\ncoqOjTHGGGMGA0/rEIjI34ElwDdUNSwiBcC3gTmqekZmh5geqyE4PJoice5ZvI23n3+DE5YsIpJf\nwIsXX8mkqgL+ed5YJg8pzPYQjTHGGGOOGJmsIfC6UvF1wG+BJhFpACqApcA1mRiUyX1l+QFunj+e\ntyZXcccr06hpcO48tLE+zJeeWs9FxwzhulkjiK5YTbShiSFnnYYvkNbC2MYYY4wx5jDwNGVIVTer\n6mnAROBiYJKqnqaq72V0dAfAaggOrxNGlPDLS6dw3ayRhPxO0ppUeHLNHj796FqW/PfdrLjuVhbO\n+ggbbvs/wtt2ZXnE+9i8TZMOixfjlcWKSYfFi8kFntchEJEq4ExgvqrWiMhIERmdsZGZASPo93H1\njOHcfdkxnDSqpKu9vi3Ki1VH0T58OB276tj041+x8OTLWHbNzUR27cniiI0xxhhjTCevNQTzgT/i\nTBOaq6olbttXVfWiDI8xLVZDkF2qyt/fbeTO17fREI53NjKhZiMXblhG3quvEywp4swVT+ILBbM7\nWGOMMcaYASIXagh+AnxMVV9wawjAucvQ7EwMygxcIsIHJlZw8ugS7lu6k2fW1qEivDfuaH427mgm\nn38Z11fH+0wGktEY+MRqDYwxxhhjDiOvU4bGq+oL7n7nJYUo3hOKw8ZqCHJDcV6AL80dw08unsxR\nlQVd7e/EgnxtZwE/frmG5ki822u2PfIMC0++jA3fu+ew1BrYvE2TDosX45XFikmHxYvJBV4TgjUi\ncm6PtrOAVYd4POYIc8zQIn7+4Sl8dvZI8gP7wu3P6+v51KNr+duGvXROW6tf+AYdO/ew6Uf3sXD2\nR1n28a+y+y8vk4zH+3t7Y4wxxhhzkLzWEMwB/gQ8A1wBPABcBFyiqksyOsI0WQ1B7trdGuXnr23j\ntS1N3dqnjyzmS3PHMKo0j72vrmDrg09Q+8zf0ZiTCJz86B1UzZuVjSEbY4wxxuSETNYQeEoIAERk\nJPBxYBywFfiNqm7LxKAOhiUEue+VzY38/LVt1LXFutqCPuFjJw7jyhOHEQr4iNY1sP33f6b+5aWc\n9NAPEF/3i1mqSuPS1ZSdONWKk40xxhhzxMtkQvC+U4ZExO+uVFyvqt9T1RtV9bu5mAyA1RAMBHPH\nl3PvR4/hsuOH4HPDOpZUfrNiF59/fB0rdrQQqq5gwg1XM+vhH/VKBgDaN29n8UWf429TzmHJFV9m\n0+2/pnHZapIx79OLbN6mSYfFi/HKYsWkw+LF5IL3TQhUNQFM8NLXGK8Kgn4+N2c0P//wFKYMKexq\n39bUwS3PbuS2v2+mIRzr9/XRugaKp0wgGe6g/h9L2PC/d/H6hZ9lyeVfPBzDN8YYY4w5YnitIfgn\n4Azgm8A29t1pCFVNZmx0B8CmDA08iaTyzLo67luyg/bYvnAqyfPzqZNHct6UKnzS9xWyjj172fvq\nCva+spy9ry5jyNnzmPrNm3r1a6/ZSby5hZJjJ/V5xcEYY4wxJpdlvYZARDo/paV2FkBV1Z+JgR0o\nSwgGrvr2GHe+vo2F7zZ2az9uWBE3nTaaoyoLkH4Sg06aSCD+3iH5zv/eybu3P0CwopTKU2dQedpM\nKuedRPGUCe/7nsYYY4wx2ZYLC5NNyMTJM2HlypVYQjAwVRUG+bcPTuDcyc389JWt7GyJAvB2bRtf\neHw9Qb9QVRikqjBIdWGQyiLnsboo6LaHqCoKkt/He/sLC8gfNYzI9lpqn11I7bMLWZNs46M/+DZj\nr/3w4f1BzYC0aNEi5s2bl+1hmAHAYsWkw+LF5AJPCYGqbjkUJxOR83BWPfYB96rqbX30uQM4H2gD\nrlPVlSIyGudWp8OAJPB/qnrHoRiTyT2zRpdy92XH8NsVu/jDqt3Ek86FqVhC2dUSZZebKPSnOOSn\nqmhf4lBVFKTq7AuouuRiqvfWEVi5msiSlWx48SUqTzmxz/eoX7SMgjHDKRg70q4gGGOMMeaIls5t\nRy8G5gPVONOFAFDVaz2+3ge8AywAdgBLgCtVdV1Kn/OBm1T1QhE5BbhdVeeIyHBguJscFAPLcNZA\nWNfzPDZl6MiypSHMPW/sYNWu1m71BQfLJ1CRH3CuLhSFnOTBTSIqCwI0nH8Nibq95I8aRuXck6ia\ndxKVc2dSMGrYIRuDMcYYY4xXWZ8yJCLfBD4PPAJcDtwFXA38Lo1zzQY2dF5tEJFHgEuA1A/1l+Bc\nCUBVF4tImYgMU9VdwC63vVVE1gKjerzWHIHGVRTwnXMnAhCOJahvj1HX5mx722PUtafuR9nbHu+6\norA/SYX6cJz6cBzqwt2eC3ZEOG/oGMa0RWB7LTt+/yw7fv8s6vOx7aH7KassIT/oIz/gbl37/u7H\nQR9Bn9gVBmOMMcbkNK81BP8EnK2qq0XkelX9FxF5GPj3NM41CmdBs07bcJKE/fXZ7rbVdjaIyHhg\nOrC4r5NYDcGRqyDoZ3SZn9FlfVUJOJKqNEXi1LfFnOShPbZv332sb4/RFInTvGklpROn93qPWF4+\nT1/9WUgmGVK7nTHvbmDMu+vxJxI8tqkFNrV061/Y2sx5jz5A3fCR7Bk2ij3DR9EwZBiJQBCfkJIk\n+PtIIvra39evINhH0uHuh/yWbBxONs/XeGWxYtJh8WJygdeEoFxVV7v7UREJquobIjI/UwPriztd\n6FHgy6ra2lefhQsXsnTpUsaOHQtAWVkZ06ZN6/rH1rkAiB0fmcevvvJK1/Ek9/ky4NrTu/effepp\nPPdCI82ROpoicUYcexL1bTGWv/EazZE4oXEnUNceY1N7PZuGV1I69wsANG9yFr7rTCSaN62kcNsW\nxm9cy/iNa1mTbGMcMCVQwrtTp/HQKbNT+sf7fP2BHvsE/DveZlJVAZee+0Gmjyxm9bLFOfXfw47t\neDAed8qV8dhxbh93ypXx2HHuHK9atYqmpiYAampqmDVrFgsWLCATvN52dDnwCVV9W0ReBJ4AGoDv\nqOp4TycSmQN8S1XPc49vxblt6W0pfe4EXlLV37nH64D5qlorIgHgT8CfVfX2/s5jNQTmUFFV2mNJ\n6tqi3a4utHQkiMSTRGLOY7yxmYK16yioqaFo61ZKt2+jtG4370w7iWeuuL7X+w7ZsZXjVixmz/CR\n1A0fRf2QEcRDoUMy5olVBcwYWcKMkSUcP7yIgmBO3RXYGGOMMQco6zUEOFODqtz9rwEPAcXADWmc\nawkwSUTGATuBK4GrevR5CrgR+J2bQDSqaud0ofuANftLBow5lESEopCfolAB4yoK3qd396lH8bYw\nH2xr58bqyq7EwUkikuy5fxVNr73U1Vd9PnTkCNovOIeGCy/Y19ft7+wnUvadLZboncxvqg+zqT7M\no6t2E/AJxw4tYsYoJ0GYMqQQv8+mGBljjDGmO08Jgao+m7K/GJiU7olUNSEiNwHPs++2o2tF5HPO\n03q3qj4rIheIyEbc244CiMhc4BpglYiswFkg7euq+lzP81gNgfFq0aLMzdsMFBUQKHKSiOK8AMV5\n+54bev6p1OVBy5pNtKzZSNvGGnTbdmZUBpl4yqhe71X/ynLaNm6h5NhJlBxzFIHiIgCiiSTr97Sz\nYnsLK3a0sHZ3G6n11PGk8tauVt7a1cqvl+2kMOjjxBElTB9ZzMxRJYwtz7cahDRkMl7MkcVixaTD\n4sXkAk8JgYgc1d9zqvqu15O5H+Cn9Gi7q8fxTX287hXA5j6YI0LpcUdTetzRXcfJjiitGzYTrCjr\ns//Ox/7Ctoee7jouGDeSkmMnMe7TVzBt7kymDS/m2pNG0BZNsGpXa1eCsLkh0u192mNJXqtp4rUa\nZz5iZWGAmSNLmD6yhBmjShhSdGimLRljjDFmYPFaQ5DE+VY+9etEBVDVnPqgbjUE5kiz4/HnqXtx\nMS1rN9L6zmY0GgNgxq/+l2Hn967r33LfH4nsqEVHDmdrUQVr/SW80RFidzix3/OMKcvrml504ohi\nivO8zig0xhhjTKZlvYZAVX2px+5CYd8EXs7EoIwx+4y89BxGXnoOAMlYnLZNNbSs3Uj5rGl99t/5\n+PM0LlnVdTwZmBIMMO6e29gwZhIrdrSwckcrrVEnQZBEAvX72drUwdamDp5aU4dPYHJ1oVOgPKqE\nY4cVEfL7+jyfMcYYYwa2A/oKUFV3icg/46w8/NtDO6SDYzUExquBOG/TFwxQMvUoSqb2O4uPCTdc\nTcuaTbRv3k64Zgftm7fTUVvH6IkjmTppCBcdO4REUtlY386KHS34Pn8z/rp6GiuqaawcQlNlNY2V\n1bw7dRrr9rTz8Ju15PmF44YXM9NNECZWFeAbZPUHAzFeTHZYrJh0WLyYXHAwcwKmAIWHaiDGmENj\n2Pnze00lSrRH8OUFu479PmHKkCKmDCnixdYmoi3NFLU0M6pmX0nQPV/5NtF8pzC6I6Es397C8u0t\nTL5vGf7SYkYdO4Fjp41n5thyRpSErEDZGGOMGaC81hC8jFsz4CoEjgP+U1X/N0NjOyBWQ2BMejSR\nILx9N+Ga7bRvdrbm97YTufUrrNjt3MVoe3OH21m56TtfIRSNApDw+WgpryQ8ZCjv3fwVCksKKc7z\nUxxyt7wARUEfJfkB99hpLwz5B90VBmOMMeZgZL2GALinx3Eb8KaqbjjE4zHGHGbi91M4dgSFY0dQ\nNW9Wt+dOP9pZfmR3a5QVO1pY8V49m084icK6PZTtraOkuZHyvXUUNzfycG0Ednd0f+9Eghv+51/Z\nVlxKa2kZLaXltJaW01pWzsbTP0hxj0ShOBTYt9/tsXu/UMDqGYwxxphDxWtR8a8zPZBDxWoIjFc2\nb9O7ocUhzp1cxbmTq9BzfsDmhggrdrTw2nv1bFm7BX9DA/TxjX9RWwt5HRHyOiJU1O/uao8UFLJy\nzpm0xqLd+geiUc7746+pK61wEwj3sayC5srqrn4hv3RdgehMFIpCfkrchGFIcYiRJXmMLM2juih4\nSBZks3gxXlmsmHRYvJhc4HUdgv/00k9Vv3FwwzHG5DoRYUJlARMqC/jI8UOJXziVjXXtNITjGaec\ncwAAIABJREFUtEbjtHYkaI26W0clb9x9N/Fd9eiePVC3l2B9PfF4ss/3Lm5uZPLbK3u1t5aUcfct\n/9N1HE0oe8NxWhpbmbx6ObWdVx5Ky+nIL+iWnAR9wrCSECNL8xhRksfIUne/NI/hJSG7e5IxxphB\nz+uUoaOBy4AlwBZgLDAb+CPQufrR+xcjHAbTp0/P9hDMAGHfyBwaAZ8wdWhRWq9JJJW2aIKWjoT7\nGHce91bSXvAVYrV1JGvroK4eX3094aISRpfldSUbcXdJ5rK9dZz7+EPd3jsaCrFjzFE8dv0XAYgl\nlW1NHWxr6iDYEWHY9hrai0toLy6hI7+QIV2JQuoWYkRJHoWhfcusWLwYryxWTDosXkwu8JoQCHCV\nqv6xq0HkI8Dlqnp9RkZmjDli+X1CaX6A0vwef4KOqoBZ4/p8zXXuo6rSkVBaO+LUry+idstZRHft\nIb67Ht1dRygSoToExw4tYmdLBw3heNd7VNfu4Ir7bu86Tvh8hItK2DbhaJ69ovefsiHEmBhupHxE\nFUPGDGFEZTGjyvIYURKiLD9gd1YyxhhzRPCaEJwPXNOj7SngV4d2OAfPagiMVzZvc2ASEfIDQn4g\nRPXMyUy5Z9+MRlUl3tJGMtLBR4c6BdHt0QQ7WzrY2Rxl1xuttB8zFd3bSKC5mbxwO8UtTeRF2vs8\nV8HGjZx2/88AWJNso6SwmhXFJTwx6RgWX3pl19Sjke6UpGG+ONUdbQwbO5RQabElDIOU/W0x6bB4\nMbnAa0KwEbgRuCOl7QvApkM+ImOMOUAiQrC0GEqLu9oKQ34mVhUysaoQJpwOHzu967lIe4QdNXso\naw4zvLCcnS1RdjZ3sL25g9qWKCrC7hGjKWxtIdkcJj/ibHXDRtEeS7KxPszG+nDX+01c+yaXPHQ3\na4BEIECstIxkSTFtM2fQ9ImryPP7yAv4CAXE2W9pJrizllBlGXlVpeSXlZKXH+zqlxcQQp2v8Ysl\nGMYYYzLC6zoEM4DHcRKI7cBoIAZ8RFWXZ3SEabJ1CIwxh0IiqdS1xdjR0sHO5g52NIbZvbOBvTvq\n2B1JsKusutdrJq59k/l/fozC1hZC0X23YF0zfTbPffSTvfpPXfkGFzza/SZukfwC1k6fzUsfuqJX\n/yGNdYzcWUOyuBgtKYGyErS0hEBRIXlBv5s8OElEfsBHKOAjzy+EAj4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27wN+axTf175D\n4bLeU7ye+PjneXfqtF7tZz3xW0Zt2UTC7ycRCJDwO9srZ1/U7QpKp2lLXqGivtbt5yfhD5D0+9l4\n7HSaKqt79R+6vYa8SDvJHv2byyuJ5fWeooZqrztxDaQ7efabEKhqV+SKyF+AC1X15ZS2ecB/ZHZ4\n6Vu4cCFLly5l7FjnEmJZWRnTpk3r+uO8aJFzizY7tmM7tmM7tuNMHHfKlfHYcW4fd+r5/PKt7/Xu\nXxRinpsMpPavKAjSeupYKk4dy7x581BVnnnh79S2RLlk4nQ2N0R44/VX2dUSJX+8U4b56PRpMH1a\nVwF886aVSFIpCY2Cf9TQvMmZ3jR5+mzGlefDtGOoOn4iC048gaqAsGzVSpLxGKXTJncbz2lz59IU\njrNydBVtH5jJUaXDiYQ7WLVjM/FonD+91czGrStp3Oi8f+f5Jzc1MLQowNRACf54nA0dDfiSCRL+\nQNf4UvvXbVtHoLaGY33ONLY1yTYAzv7ER4meMJRNby1BgKOnz8Ynws77XyL4zsZe/WeffjzJ2aN4\nZ+ViRIRjZ54CwDuf/x98697p1f/4H3yPwGlTeHv5YnzAtJPn4ENYev1nSa7fyLH55UggwOavXEtF\nZDgw4YDjY9WqVTQ1NQFQU1PDrFmzWLBgAZngaR0CEWkCqlU1ltIWBOpVtbT/V3Z7jznAt1T1PPf4\nVkBTC4tF5E7gJVX9nXu8DpivqrXu8Tjg6f0VFds6BMYYY4wxvSVVqW2NsnlvhM0NzqKCmxsibG2M\nEEt6/zbbJzCyNI/xFc5djhoj8a5v++vaYmm9V38EqCwMMqQoyJDikPNYFGJIsfNY3tJEYSyCxGJO\n0XtHlGQ0Rum0KYQqy3q9364/vUR4yw6SsRjJaJxkLIZGY4z+xCUUT+o9I339f/2CppVr0VicZDTm\n9o9z3A9uoaKP1c/f+OgX2btoWdfxGa//nsLxow/695Aqk+sQeE0I/g4sAb6hqmERKQC+DcxR1d4T\nzfp+Dz+wHqeoeCfwBnCVqq5N6XMBcKOqXugmED9R1Tkpz4/HSQh6XztyWUJgjDHGGONdIqnsaO5g\nc4OzmOBmN1HY1hThEHy271NZfqDrw/7QHh/2hxQ5K5MHDvHigpmkqk7y4CYcwdIixN/3quoHKhcW\nJrsO+C3QJCINQAWwFLjG64lUNSEiNwHPs++2o2tF5HPO03q3qj4rIheIyEbc2452vl5EfgucCVSJ\nSA3wTVX9Vc/zWA2B8WrRIpvna7yzeDFeWayYdORCvPh9wpjyfMaU53P6hH01B9FEku1NHWxOSRK2\nNITZ2Rzd711nikP+fr/Zd7YgocCRtXq1iHQVT1P0/v1zjaeEQFU3A6eJyBhgJLBTVXuXvr//+zwH\nTOnRdleP45v6ee3V6Z7PGGOMMcYcmJDfx4TKgl63+I3Ek9Q0OslBXVuM8gJnas9Q94N/ZyGyGTg8\nTRkCEJEq4AJghKp+T0RGAj5V3ZbJAabLpgwZY4wxxpgjTSanDHm6XiMi83Hm/1/DvjsLHY2zcJgx\nxhhjjDFmgPI6gesnwMfcOwTF3bbF9F5HIOtWruy9CqAxfel5yzdj9sfixXhlsWLSYfFicoHXhGC8\nqr7g7nfOMYrivSjZGGOMMcYYk4O8JgRrROTcHm1nAb3XyM6y6dOnZ3sIZoDI9l0dzMBi8WK8slgx\n6bB4MbnA6zf8NwN/EpFngAIRuQu4CLgkYyMzxhhjjDHGZJynKwSq+jpwAvA2cB/wHjBbVZdkcGwH\nxGoIjFc2b9Okw+LFeGWxYtJh8WJygacrBCLyVVX9AfC9Hu1fUdUfZWRkxhhjjDHGmIzztA6BiDSr\namkf7XtVtTIjIztAtg6BMcYYY4w50mRyHYL9XiEQkQ+6u34R+QCQOoijgJZMDMoYY4wxxhhzeLxf\nDcG97paPUzvQeXwP8Cngixkd3QGwGgLjlc3bNOmweDFeWayYdFi8mFyw3ysEqjoBQEQeUNVrD8+Q\njDHGGGOMMYeL1xqC6UC9qm5NaRsDVKrqmxkcX9qshsAYY4wxxhxpMllD4HVhst8AwR5tIeDBQzsc\nY4wxxhhjzOHkNSEYq6rvpjao6iZg/CEf0UGyGgLjlc3bNOmweDFeWayYdFi8mFzgNSHYJiLd5uG4\nxzsO/ZCMMcYYY4wxh4vXGoLPAN/AWZhsEzAR+Crw36p6d0ZHmCarITDGGGOMMUearK1D0ElV/09E\nGnFuNToG2ArcrKqPZmJQxhhjjDHGmMPD65QhVPUPqnqeqh7nPuZkMmA1BMYrm7dp0mHxYryyWDHp\nsHgxucBTQiCOz4jICyLyltt2hohckdnhGWOMMcYYYzLJaw3Bd4CzgZ8Ad6pquYgcBfxBVU/K8BjT\nYjUExhhjjDHmSJML6xBcB3xIVR8BOjOI94CjMjEoY4wxxhhjzOHhNSHwA63ufmdCUJzSljOshsB4\nZfM2TTosXoxXFismHRYvJhd4TQieBX4kInng1BQA3wGeTudkInKeiKwTkXdE5JZ++twhIhtEZKWI\nTE/ntQAbN25MZ0hmEFu1alW2h2AGEIsX45XFikmHxYvxKpNfentNCL4CjACagDKcKwPjgH4/mPck\nIj7gZ8C5wHHAVSIytUef84GJqno08DngTq+v7dTW1uZ1SGaQa2pqyvYQzABi8WK8slgx6bB4MV69\n+eabGXtvr+sQNAOXishQnERgq6ruSvNcs4ENqroFQEQeAS4B1qX0uQR4wD3nYhEpE5FhwAQPrzXG\nGGOMMcakyfM6BCJSjnOnoTOBBSJSkea5RuEsaNZpm9vmpY+X1wKwa1e6eYoZrGpqarI9BDOAWLwY\nryxWTDosXkwu8HSFQEQ+CDwGrAe2AGOBn4vIZar6QgbHl/atlSZOnMiXv/zlruMTTzyR6dOn7+cV\nZrCaNWsWy5cvz/YwzABh8WK8slgx6bB4Mf1ZuXJlt2lCRUVFGTuX13UI1gDfUtXfp7RdDnxHVfuc\ny9/He8xx3+M89/hWQFX1tpQ+dwIvqerv3ON1wHycKUP7fa0xxhhjjDEmfV6nDI0E/tij7XFgeBrn\nWgJMEpFxIhICrgSe6tHnKeBa6EogGlW11uNrjTHGGGOMMWnymhA8CNzYo+0LuAXAXqhqArgJeB54\nG3hEVdeKyOdE5LNun2eB90RkI3AXcMP+Xuv13MYYY4wxxpi+eZ0ytAg4BagFtuMU9A4FFrNvoTJU\n9YzMDNMYY4wxxhiTCV6vEPwf8Gng34BfuI+fAe4B7k3ZssbrwmXmyCIi94pIrYi8ldJWISLPi8h6\nEfmLiJSlPPc1d+G7tSJyTkr7TBF5y42fn6S0h0TkEfc1r4nI2MP305lDSURGi8iLIvK2iKwSkS+5\n7RYvphcRyRORxSKywo2Xb7rtFi+mTyLiE5HlIvKUe2yxYvokIptF5E3378sbblt240VVB/yGk9hs\nxFkjIQisBKZme1y2HZb/9vOA6cBbKW23Af/q7t8CfNfdPxZYgXN3rfFuzHReJVsMnOzuPwuc6+5/\nAfiFu/8xnOlqWf+5bTugWBkOTHf3i3HumjbV4sW2/cRMofvoB17HWU/H4sW2/uLlX4DfAE+5xxYr\ntvUXK+8CFT3ashovnq4QiMg9IlLYo22EiDzn5fWHQdeiZ6oaAzoXLjNHOFVdBDT0aL4E+LW7/2vg\nw+7+xTj/KOKquhnYAMwWkeFAiaoucfs9kPKa1Pd6FFhwyH8Ic1io6i5VXenutwJrgdFYvJh+qGq7\nu5uH8z9jxeLF9EFERgMX4Myc6GSxYvoj9J6lk9V48TplqBh4S0ROBRCRK4G3cDKWXOB54TIzKAxV\n5+5UqLOi9lC3vWecdNbDjMKJmU6p8dP1GnWK2xtFpDJzQzeHg4iMx7my9DowzOLF9MWdArIC2AX8\n1f0fr8WL6cuPgf9HSl0lFiumfwr8VUSWiMin3basxounhclU9UoRuQZ4UkTWAyOAS91vZ43Jde9f\nOe9d2ovlmdwiIsU435h8WVVbRaRnfFi8GABUNQnMEJFS4HEROY7e8WHxMsiJyIVAraquFJEz99PV\nYsV0mquqO0VkCPC8+9k6q39bvF4hACcjiQBHAe/hzGHKFdtxVk/uNNptM4NTrYgMA3Avqe1227cD\nY1L6dcZJf+3dXiMifqBUVfdmbugmk0QkgJMMPKiqT7rNFi9mv1S1Gfg7cB4WL6a3ucDFIvIu8DDw\nQRF5ENhlsWL6oqo73cc9wBM4U9+z+rfFaw3BD3Dm5X8Zp6BhJc4Uosu9vP4wsIXLBjehe/b7FHCd\nu/9J4MmU9ivd6vsJwCTgDffSXJOIzBYRwVkcL/U1n3T3LwdezNhPYQ6H+4A1qnp7SpvFi+lFRKo7\n7/IhIgXA2Th1JxYvphtV/bqqjlXVo3A+f7yoqp8AnsZixfQgIoXulWpEpAg4B1hFtv+2eKyGfgZn\nblNq2xnAe9mu1E4Zz3k4dw3ZANya7fHYdtj+u/8W2AF0ADXA9UAF8Dc3Hp4HylP6fw3n6tZa4JyU\n9pPcf5AbgNtT2vOA37vtrwPjs/0z23bAsTIXSOB8obECWO7+3ai0eLGtj3iZ5sbISpyauX9z2y1e\nbNtf3Mxn312GLFZs6ytGJqT8f2hV52fWbMeLp4XJ+iMiJaracsBvYIwxxhhjjMkqzzUEInK2iNwn\nIk+7x7OAkzM2MmOMMcYYY0zGea0h+CLwS+AdnKlCAGHgvzI0LmOMMcYYY8xh4GnKkIhsAhao6mYR\naVDVCrdqebeqVmV8lMYYY4wxxpiM8DplqIR9iyJ0ZhBBIHrIR2SMMcYYY4w5bLwmBP8Abu3R9iXg\npUM7HGOMMcYYY8zh5HXK0Aic++lW4yyH/C7QAnxInfugGmOMMcYYYwYgz7cddRc9OBmOfIJ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize( 12.5, 4)\n", + "\n", + "N_Y = 250 #use this many to approximate D(N)\n", + "N_array = np.arange( 1000, 50000, 2500 ) #use this many samples in the approx. to the variance.\n", + "D_N_results = np.zeros( len( N_array ) )\n", + "\n", + "lambda_ = 4.5 \n", + "expected_value = lambda_ #for X ~ Poi(lambda) , E[ X ] = lambda\n", + "\n", + "def D_N( n ):\n", + " \"\"\"\n", + " This function approx. D_n, the average variance of using n samples.\n", + " \"\"\"\n", + " Z = poi( lambda_, (n, N_Y) )\n", + " average_Z = Z.mean(axis=0)\n", + " return np.sqrt( ( (average_Z - expected_value)**2 ).mean() )\n", + " \n", + " \n", + "for i,n in enumerate(N_array):\n", + " D_N_results[i] = D_N(n)\n", + "\n", + "\n", + "plt.xlabel( \"$N$\" )\n", + "plt.ylabel( \"expected squared-distance from true value\" )\n", + "plt.plot(N_array, D_N_results, lw = 3, \n", + " label=\"expected distance between\\n\\\n", + "expected value and \\naverage of $N$ random variables.\")\n", + "plt.plot( N_array, np.sqrt(expected_value)/np.sqrt(N_array), lw = 2, ls = \"--\", \n", + " label = r\"$\\frac{\\sqrt{\\lambda}}{\\sqrt{N}}$\" )\n", + "plt.legend()\n", + "plt.title( \"How 'fast' is the sample average converging? \" );" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, the expected distance between our sample average and the actual expected value shrinks as $N$ grows large. But also notice that the *rate* of convergence decreases, that is, we need only 10 000 additional samples to move from 0.020 to 0.015, a difference of 0.005, but *20 000* more samples to again decrease from 0.015 to 0.010, again only a 0.005 decrease.\n", + "\n", + "\n", + "It turns out we can measure this rate of convergence. Above I have plotted a second line, the function $\\sqrt{\\lambda}/\\sqrt{N}$. This was not chosen arbitrarily. In most cases, given a sequence of random variable distributed like $Z$, the rate of convergence to $E[Z]$ of the Law of Large Numbers is \n", + "\n", + "$$ \\frac{ \\sqrt{ \\; Var(Z) \\; } }{\\sqrt{N} }$$\n", + "\n", + "This is useful to know: for a given large $N$, we know (on average) how far away we are from the estimate. On the other hand, in a Bayesian setting, this can seem like a useless result: Bayesian analysis is OK with uncertainty so what's the *statistical* point of adding extra precise digits? Though drawing samples can be so computationally cheap that having a *larger* $N$ is fine too. \n", + "\n", + "### How do we compute $Var(Z)$ though?\n", + "\n", + "The variance is simply another expected value that can be approximated! Consider the following, once we have the expected value (by using the Law of Large Numbers to estimate it, denote it $\\mu$), we can estimate the variance:\n", + "\n", + "$$ \\frac{1}{N}\\sum_{i=1}^N \\;(Z_i - \\mu)^2 \\rightarrow E[ \\;( Z - \\mu)^2 \\;] = Var( Z )$$\n", + "\n", + "### Expected values and probabilities \n", + "There is an even less explicit relationship between expected value and estimating probabilities. Define the *indicator function*\n", + "\n", + "$$\\mathbb{1}_A(x) = \n", + "\\begin{cases} 1 & x \\in A \\\\\\\\\n", + " 0 & else\n", + "\\end{cases}\n", + "$$\n", + "Then, by the law of large numbers, if we have many samples $X_i$, we can estimate the probability of an event $A$, denoted $P(A)$, by:\n", + "\n", + "$$ \\frac{1}{N} \\sum_{i=1}^N \\mathbb{1}_A(X_i) \\rightarrow E[\\mathbb{1}_A(X)] = P(A) $$\n", + "\n", + "Again, this is fairly obvious after a moments thought: the indicator function is only 1 if the event occurs, so we are summing only the times the event occurs and dividing by the total number of trials (consider how we usually approximate probabilities using frequencies). For example, suppose we wish to estimate the probability that a $Z \\sim Exp(.5)$ is greater than 5, and we have many samples from a $Exp(.5)$ distribution. \n", + "\n", + "\n", + "$$ P( Z > 5 ) = \\sum_{i=1}^N \\mathbb{1}_{z > 5 }(Z_i) $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0001\n" + ] + } + ], + "source": [ + "N = 10000\n", + "print( np.mean( [ np.random.exponential( 0.5 ) > 5 for i in range(N) ] ) )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### What does this all have to do with Bayesian statistics? \n", + "\n", + "\n", + "*Point estimates*, to be introduced in the next chapter, in Bayesian inference are computed using expected values. In more analytical Bayesian inference, we would have been required to evaluate complicated expected values represented as multi-dimensional integrals. No longer. If we can sample from the posterior distribution directly, we simply need to evaluate averages. Much easier. If accuracy is a priority, plots like the ones above show how fast you are converging. And if further accuracy is desired, just take more samples from the posterior. \n", + "\n", + "When is enough enough? When can you stop drawing samples from the posterior? That is the practitioners decision, and also dependent on the variance of the samples (recall from above a high variance means the average will converge slower). \n", + "\n", + "We also should understand when the Law of Large Numbers fails. As the name implies, and comparing the graphs above for small $N$, the Law is only true for large sample sizes. Without this, the asymptotic result is not reliable. Knowing in what situations the Law fails can give us *confidence in how unconfident we should be*. The next section deals with this issue." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Disorder of Small Numbers\n", + "\n", + "The Law of Large Numbers is only valid as $N$ gets *infinitely* large: never truly attainable. While the law is a powerful tool, it is foolhardy to apply it liberally. Our next example illustrates this.\n", + "\n", + "\n", + "##### Example: Aggregated geographic data\n", + "\n", + "\n", + "Often data comes in aggregated form. For instance, data may be grouped by state, county, or city level. Of course, the population numbers vary per geographic area. If the data is an average of some characteristic of each the geographic areas, we must be conscious of the Law of Large Numbers and how it can *fail* for areas with small populations.\n", + "\n", + "We will observe this on a toy dataset. Suppose there are five thousand counties in our dataset. Furthermore, population number in each state are uniformly distributed between 100 and 1500. The way the population numbers are generated is irrelevant to the discussion, so we do not justify this. We are interested in measuring the average height of individuals per county. Unbeknownst to us, height does **not** vary across county, and each individual, regardless of the county he or she is currently living in, has the same distribution of what their height may be:\n", + "\n", + "$$ \\text{height} \\sim \\text{Normal}(150, 15 ) $$\n", + "\n", + "We aggregate the individuals at the county level, so we only have data for the *average in the county*. What might our dataset look like?" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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8cq677jq2bNnCsmXLePvtt5k6dSolJSWA5Y1etmwZS5YsYerUqaxZs4aOjg6+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\noua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cyWHfichtP8eo27mymerPdiZC0ViQannJ0ef3+33OCg/07toqSFdGQRAE4f6mX4f+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\n4CzwlW2M4b7g6aef3us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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize( 12.5, 4) \n", + "std_height = 15\n", + "mean_height = 150\n", + "\n", + "n_counties = 5000\n", + "pop_generator = np.random.randint\n", + "norm = np.random.normal\n", + "\n", + "#generate some artificial population numbers\n", + "population = pop_generator(100, 1500, n_counties )\n", + "\n", + "average_across_county = np.zeros( n_counties )\n", + "for i in range( n_counties ):\n", + " #generate some individuals and take the mean\n", + " average_across_county[i] = norm(mean_height, 1./std_height,\n", + " population[i] ).mean()\n", + " \n", + "#located the counties with the apparently most extreme average heights.\n", + "i_min = np.argmin( average_across_county )\n", + "i_max = np.argmax( average_across_county )\n", + "\n", + "#plot population size vs. recorded average\n", + "plt.scatter( population, average_across_county, alpha = 0.5, c=\"#7A68A6\")\n", + "plt.scatter( [ population[i_min], population[i_max] ], \n", + " [average_across_county[i_min], average_across_county[i_max] ],\n", + " s = 60, marker = \"o\", facecolors = \"none\",\n", + " edgecolors = \"#A60628\", linewidths = 1.5, \n", + " label=\"extreme heights\")\n", + "\n", + "plt.xlim( 100, 1500 )\n", + "plt.title( \"Average height vs. County Population\")\n", + "plt.xlabel(\"County Population\")\n", + "plt.ylabel(\"Average height in county\")\n", + "plt.plot( [100, 1500], [150, 150], color = \"k\", label = \"true expected \\\n", + "height\", ls=\"--\" )\n", + "plt.legend(scatterpoints = 1);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What do we observe? *Without accounting for population sizes* we run the risk of making an enormous inference error: if we ignored population size, we would say that the county with the shortest and tallest individuals have been correctly circled. But this inference is wrong for the following reason. These two counties do *not* necessarily have the most extreme heights. The error results from the calculated average of smaller populations not being a good reflection of the true expected value of the population (which in truth should be $\\mu =150$). The sample size/population size/$N$, whatever you wish to call it, is simply too small to invoke the Law of Large Numbers effectively. \n", + "\n", + "We provide more damning evidence against this inference. Recall the population numbers were uniformly distributed over 100 to 1500. Our intuition should tell us that the counties with the most extreme population heights should also be uniformly spread over 100 to 4000, and certainly independent of the county's population. Not so. Below are the population sizes of the counties with the most extreme heights." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Population sizes of 10 'shortest' counties: \n", + "[109 135 135 133 109 157 175 120 105 131] \n", + "\n", + "Population sizes of 10 'tallest' counties: \n", + "[122 133 313 109 124 280 106 198 326 216]\n" + ] + } + ], + "source": [ + "print(\"Population sizes of 10 'shortest' counties: \")\n", + "print(population[ np.argsort( average_across_county )[:10] ], '\\n')\n", + "print(\"Population sizes of 10 'tallest' counties: \")\n", + "print(population[ np.argsort( -average_across_county )[:10] ])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not at all uniform over 100 to 1500. This is an absolute failure of the Law of Large Numbers. \n", + "\n", + "##### Example: Kaggle's *U.S. Census Return Rate Challenge*\n", + "\n", + "Below is data from the 2010 US census, which partitions populations beyond counties to the level of block groups (which are aggregates of city blocks or equivalents). The dataset is from a Kaggle machine learning competition some colleagues and I participated in. The objective was to predict the census letter mail-back rate of a group block, measured between 0 and 100, using census variables (median income, number of females in the block-group, number of trailer parks, average number of children etc.). Below we plot the census mail-back rate versus block group population:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Vi+dbDIViPxakET+TN2GqlzubLjBbHPLE9qVimUK+PO7lPtC9c+lzun4iUT8r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O7eyCr6aQqF0gJWXmfzbpfeNG11frnMeOjhyAKzC0UESaQxl6e9P2I88JFkAfLZ9e1sDqnP5tnf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\n4w7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SiIiIhFCOPvFP5P0+BvxSmcZWNSvVlq+HmbOtZwvpiwu0tDbS198OGLMzc8ylF3P3\ny9a4r3ZCuFJ3l/we8PnGR6cr8lo3q0q9d0RERERKVXKfeDN7m5n9o5k9GP/vL1mNLj+WUve0Um35\nesykosm6mZG+sABENel9/Usnedkyl+yEcLle7uUZ09pfq2ec8ZHpoj3ws5JYZ7aSSr13VmOzZV5t\nyjss5R2eMg9LeYeXxMxL7RP/CeC1wB8Aw8Au4D3APuB9FRtdBVXqYjfFjhuV0zh9Ax0sLmbo7e/I\n1biHuHLmel5rsVXnbA/87LcHpZRkJYkulCQiIiLVVmpN/Bhwk7ufzNu3A7jP3fsqOL7LWnNN/Aq1\n5WuRLYtJpS6CG3V10NoWHXditGAinFcPX9gfvhK93NfzWoePjnPy2NP96ndc3YVn4MH7n6KxsYEt\nbY3sGOqCvDaWNfoFTdmU+70jIiIiUkw5+sRPxz+F+86vZ2DVVO4rh16yYp03GV9ptT3ElTPX81oL\nV5k9AyeOTXJ+Kupj37mthRPxc8DmqA/XVWdFRESk2patiTez3dkfojKavzGzV5jZdWb2SuBL1OiF\nnkLXPXnGOTM6zbnJWSbGUoyeOsfp41NkMtGVUpdMhKPKmrjG/PwlK7o4l61BD6knrwf+vv0DuDnN\nWxrJLjxfTM/zyNEHcvevRn34ZpTE2r5aprzDUt7hKfOwlHd4Scx8pZX4o0RTzvwl/J8suM/LgD8u\n96A2momxFKnpNNPnLzJ26jxbWhsZ27aF449PMHRN35LVdhxOnTxLZtFpamng7Pgsre1NQLSKbVC0\n88la2hqWoxXiJavOI3B6/hy7r+0jfXGB7Vd0ctddj+fuH7I+XK0eRUREZLMqqSa+lq21Jr6cho+O\nM3LqHIYx8tQ52tqbODs5yzXP7OdZz9t5yX2zNebuzvmpC2ztjnrHDw51AeRur6s3era309zcsGTy\nD6X1mS+st19rb/p8hfXg3dvbmBibqUp9eCVen4iIiEitKEdNfI6Z/YS7f2/9w0qOtvZm6urqmBpL\nMfzYOC2tTWzr2cLWba1F75vVvKWRxpn5orcBNDTWM/zYBK3tTZybmqVvoIO5xajXfCldbCrS+caX\nfjVTzfrwEJ19RERERGpRyX3i8/z3so+izELXPfX0t9Pe0UwGuPHHdrJ7Xx/PfPZV7HhGd9H7ZmvM\nr97Tw7NfsDNXb97T377k9vaO5lypTWNjA+mLC7nj5E/4l+vlXolWiMX62lerzmwzt3pMYm1fLVPe\nYSnv8JR5WMo7vCRmvuqVeJYuxArxanR/B5NnZgCo31JH/xWd1NVd+hmp+Mr10tXj7O3jI9O5Y7a2\nN3HVri7MuKSLzXJXEK1E55tauNBRVojOPiIiIiK1aNU18WZ22N33V2g8q1YLNfFQnt7hhSdqllpv\nXtjLfXCoi117etf9mooJ0ddeRERERMpcE19LE/haslJteKldVIr1mi+l3jxkWUm0+t3P1MQsiwuZ\nqGOmu7rCiIiIiAS0Up/4t5XyE3Kwpaq1uqdideTFrLVUpbCXeyXLSswMwzhzOir1efTwCN/4+j9W\n7PmkuFp7jyed8g5LeYenzMNS3uElMfOVVuJ/voTHO/AXZRpLYpXaRaVwBb21rZnxkekVV/Czq/wh\nWzwWvp70hfll7ikiIiIilaA+8QGUWkdeWFcPzpHDo7nbi/VBr0avdNXFi4iIiFTemmrizcw8nuGb\n2bJlN+6eWf8Qk63ULiqFdfXDR8eX3F5sBb8avdLVFUZERESkulbqE38u7/cFYL7gJ7uv5tRa3VN2\ncr5rTy+9Ax0llbt4xsHh3NQss6k5oPgJq9XolV74er73vbVf+2u5Hveyslp7jyed8g5LeYenzMNS\n3uElMfOVauKvz/v96koPRJaaGEtx6uRZ+gY6SF9c4KpdXUVXvDf6qvjEWIrHHh6lobGe9IVJBqe7\n2bWnR91uRERERFagmvgaFbL3ezUNHx1nbGSaJx4ewx06u1p43ot2V7yuX0RERKTWlaVPvJndCrwE\n6CXvqq3u/pZ1j3CTKaVvfDXKZKqhrb2Z9IVJsp8lGxsbgtT1i4iIiGxkK9XE55jZh4A/i+//OmAC\neBVwtlwDMbM6M7vPzL4Wb3eZ2bfM7IiZfdPMtpZ6rFqveyqlb/xKvd9rrY58PXn39LczONRNZ1cL\nPdvbaW1vSuwHlnKq9fd40ijvsJR3eMo8LOUdXhIzL3Ul/m3AK9z9sJm91d1/zcw+D/xWGcfyLuAh\noDPe/gDwbXf/hJm9H/hgvG/DK6WjzEpXgL3kyq5Uvq1kpZgZu/b00NbRvGHr+kVERERCK6km3szO\nufvW+Pcx4Cp3n8/fv65BmA0CtwO/D7zb3W81s0eAl7j7qJkNAP/D3a8tfOxGrIlfb5/1zVIvLyIi\nIrKZlaMm/nEzu97dHwQOA283sylg6jKPK9UngfcC+R8I+t19FMDdR8xse5meq+rW21Fms9TLi4iI\niEhxpU7ifwvoiX//IPBXQDvwf6x3AGb2GmDU3e83s5eucNeiXxnccccd3HbbbezcuROArVujzwFv\nf/vbgadroG655ZYa3O6Ito+u7vHuzrX7n81sKs3hh+7j4cdGeNHAi6r2eg4dOrRB8k7OdnZfrYwn\n6dvZfbUynqRvZ/fVyng2w3Zh9tUeT9K3lXf47U996lPccMMNNTOelf79O3jwIMePHwfg5ptv5sCB\nAxRT9RaTZvYR4M1EF4/aQlQE/rfAzcBL88pp7nL36wofX6yc5uDBg7lQpPKUd3jKPCzlHZbyDk+Z\nh6W8w9uoma9UTrPiJN7Mdl7u4O5+fB1jK3y+lwC/HtfEfwKYcPePxye2drn7JSe2bsSaeBERERGR\ny1lPTfwxni5jKXYAB+rXPrQVfQz4azN7GzAM/FyFnkdEREREZEO5XJ/4B4DHiGridwGNBT9N5RyM\nu3/X3W+Nf59095e7+z53f6W7l9yTPr+uSCpPeYenzMNS3mEp7/CUeVjKO7wkZr7iJN7dnwP8LNAN\nfA/4e+ANQJO7L7r7YuWHWD21dlElERERERFYxYmtZlYHvAL4ReBfAS9z9/sqN7TSVLImvrCf+979\nlb+okmecibEUM3ntJ82KlkKJiIiISIKVo088wDXAS4AXAj+kfD3ia1YpV1Ytt0pcjVUfDERERESS\nZcVyGjPrNrN3mNkPgK8AKeDF7v6T7v5kkBGuQbnqnqpxUaXiHxzWJ/vB4OSxKY4cHmF8NLXsfddS\nQpTEOrNap8zDUt5hKe/wlHlYyju8JGZ+uZX4U8CTwGeAe+J9e8xsT/YO7v6dCo2t6tZ7ZdW1qMQH\nh9V8o1CJbwJEREREpLwu1yf+GMtcKTXm7r673INajaT1iXd3xkdTSz44rLf0pbC2f9/+AXqXmZgP\nHx3n5LGnK6UGh7rYtad3Xc8vIiIiIqu35pp4dx+qyIhkWWYWr3yXb/V7Nd8oVKOESERERERW53J9\n4jekJNY9rUf2g8GuPb30DnSsuLLf09/O3v0DDA51sW//QEklRMo7PGUelvIOS3mHp8zDUt7hJTHz\n1XSnkU2gEt8EiIiIiEh5ldwnvlYlrSZeRERERATK1yd+U1OvdRERERGpFaqJL9Fqeq1vNkmsM6t1\nyjws5R2W8g5PmYelvMNLYuZaiS/Req/eutaVfH0DICIiIiKFVBNfotX0Wi/l8Xv3l3YRpbU+TkRE\nREQ2NtXEl8F6r9661pX89X4DICIiIiLJo5r4Eq2m13oxa72I0ka4+FIS68xqnTIPS3mHpbzDU+Zh\nKe/wkph5olbis/Xjo0+dY3xkuuL146upV1/rSv56vwEQERERkeRJVE186Ppx1auLiIiISKWsVBOf\nqHKa4vXjyXk+ERERERFI2CQ+Wy9+6MF7l2xX+vmW294sklhnVuuUeVjKOyzlHZ4yD0t5h5fEzBNV\nE5+tHx+Z6GDf/oGK14+rXl1EREREqiFRNfG1SBdrEhEREZG1UJ/4KpoYSy09+RWd/CoiIiIi65Oo\nmvisWqp72gwnv9ZS3puFMg9LeYelvMNT5mEp7/CSmHkiJ/G1RCe/ioiIiEi5qSa+jIrVvwOMj6aW\nnPyqmngRERERuRzVxAeyXP17VAOvOngRERERKY9EltNUq+5pM9S/F5PEOrNap8zDUt5hKe/wlHlY\nyju8JGaeyEl8taj+XURERERCUE18Gbm76t9FREREpCxUEx+Iman+XUREREQqLlHlNJ5xxkem+fIX\nv8H4yDSV/pYh+3zDR8eDPF+tSmKdWa1T5mEp77CUd3jKPCzlHV4SM0/USny2O8yZkWmOHB6p+NVR\ndTVWEREREamGRNXEDx8d5+Sxqdxtg0Nd7NrTW7HnDv18IiIiIrJ5rFQTn6hymtDdYdSNRkRERESq\nIVGT+J7+dvbuH2Bk4lH27R/IXTG10s83ONQV5PlqVRLrzGqdMg9LeYelvMNT5mEp7/CSmHmiauKz\n3WH6r9pKb4DadHWjEREREZFqSFRNvIiIiIhIUmyamngRERERkc0gkZP4JNY91TLlHZ4yD0t5h6W8\nw1PmYSnv8JKYeSIn8SIiIiIiSaaaeBERERGRGqSaeBERERGRBEnkJD6JdU+1THmHp8zDUt5hKe/w\nlHlYyju8JGaeqD7xSeYZZ2IsxUwqTVt7Mz397ZgV/XZFRERERBJONfEbxPjINEcOj+S29+4fiC80\nJSIiIiJJpJr4BJhJpZdszxZsi4iIiMjmkchJ/Eaue/KMMz4yzfDRccZHpsl+U9LW3rzkfoXb1bSR\n896olHlYyjss5R2eMg9LeYeXxMxVE19jJsZSS8tmiMpmevrb2csAs3k18SIiIiKyOakmvsYMHx3n\n5LGp3PbgUBe79vRWcUQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize( 12.5, 6.5 )\n", + "data = np.genfromtxt( \"./data/census_data.csv\", skip_header=1, \n", + " delimiter= \",\")\n", + "plt.scatter( data[:,1], data[:,0], alpha = 0.5, c=\"#7A68A6\")\n", + "plt.title(\"Census mail-back rate vs Population\")\n", + "plt.ylabel(\"Mail-back rate\")\n", + "plt.xlabel(\"population of block-group\")\n", + "plt.xlim(-100, 15e3 )\n", + "plt.ylim( -5, 105)\n", + "\n", + "i_min = np.argmin( data[:,0] )\n", + "i_max = np.argmax( data[:,0] )\n", + " \n", + "plt.scatter( [ data[i_min,1], data[i_max, 1] ], \n", + " [ data[i_min,0], data[i_max,0] ],\n", + " s = 60, marker = \"o\", facecolors = \"none\",\n", + " edgecolors = \"#A60628\", linewidths = 1.5, \n", + " label=\"most extreme points\")\n", + "\n", + "plt.legend(scatterpoints = 1);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above is a classic phenomenon in statistics. I say *classic* referring to the \"shape\" of the scatter plot above. It follows a classic triangular form, that tightens as we increase the sample size (as the Law of Large Numbers becomes more exact). \n", + "\n", + "I am perhaps overstressing the point and maybe I should have titled the book *\"You don't have big data problems!\"*, but here again is an example of the trouble with *small datasets*, not big ones. Simply, small datasets cannot be processed using the Law of Large Numbers. Compare with applying the Law without hassle to big datasets (ex. big data). I mentioned earlier that paradoxically big data prediction problems are solved by relatively simple algorithms. The paradox is partially resolved by understanding that the Law of Large Numbers creates solutions that are *stable*, i.e. adding or subtracting a few data points will not affect the solution much. On the other hand, adding or removing data points to a small dataset can create very different results. \n", + "\n", + "For further reading on the hidden dangers of the Law of Large Numbers, I would highly recommend the excellent manuscript [The Most Dangerous Equation](http://nsm.uh.edu/~dgraur/niv/TheMostDangerousEquation.pdf). " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: How to order Reddit submissions\n", + "\n", + "You may have disagreed with the original statement that the Law of Large numbers is known to everyone, but only implicitly in our subconscious decision making. Consider ratings on online products: how often do you trust an average 5-star rating if there is only 1 reviewer? 2 reviewers? 3 reviewers? We implicitly understand that with such few reviewers that the average rating is **not** a good reflection of the true value of the product.\n", + "\n", + "This has created flaws in how we sort items, and more generally, how we compare items. Many people have realized that sorting online search results by their rating, whether the objects be books, videos, or online comments, return poor results. Often the seemingly top videos or comments have perfect ratings only from a few enthusiastic fans, and truly more quality videos or comments are hidden in later pages with *falsely-substandard* ratings of around 4.8. How can we correct this?\n", + "\n", + "Consider the popular site Reddit (I purposefully did not link to the website as you would never come back). The site hosts links to stories or images, called submissions, for people to comment on. Redditors can vote up or down on each submission (called upvotes and downvotes). Reddit, by default, will sort submissions to a given subreddit by Hot, that is, the submissions that have the most upvotes recently.\n", + "\n", + "\n", + "\n", + "\n", + "How would you determine which submissions are the best? There are a number of ways to achieve this:\n", + "\n", + "1. *Popularity*: A submission is considered good if it has many upvotes. A problem with this model is that a submission with hundreds of upvotes, but thousands of downvotes. While being very *popular*, the submission is likely more controversial than best.\n", + "2. *Difference*: Using the *difference* of upvotes and downvotes. This solves the above problem, but fails when we consider the temporal nature of submission. Depending on when a submission is posted, the website may be experiencing high or low traffic. The difference method will bias the *Top* submissions to be the those made during high traffic periods, which have accumulated more upvotes than submissions that were not so graced, but are not necessarily the best.\n", + "3. *Time adjusted*: Consider using Difference divided by the age of the submission. This creates a *rate*, something like *difference per second*, or *per minute*. An immediate counter-example is, if we use per second, a 1 second old submission with 1 upvote would be better than a 100 second old submission with 99 upvotes. One can avoid this by only considering at least t second old submission. But what is a good t value? Does this mean no submission younger than t is good? We end up comparing unstable quantities with stable quantities (young vs. old submissions).\n", + "3. *Ratio*: Rank submissions by the ratio of upvotes to total number of votes (upvotes plus downvotes). This solves the temporal issue, such that new submissions who score well can be considered Top just as likely as older submissions, provided they have many upvotes to total votes. The problem here is that a submission with a single upvote (ratio = 1.0) will beat a submission with 999 upvotes and 1 downvote (ratio = 0.999), but clearly the latter submission is *more likely* to be better.\n", + "\n", + "I used the phrase *more likely* for good reason. It is possible that the former submission, with a single upvote, is in fact a better submission than the later with 999 upvotes. The hesitation to agree with this is because we have not seen the other 999 potential votes the former submission might get. Perhaps it will achieve an additional 999 upvotes and 0 downvotes and be considered better than the latter, though not likely.\n", + "\n", + "What we really want is an estimate of the *true upvote ratio*. Note that the true upvote ratio is not the same as the observed upvote ratio: the true upvote ratio is hidden, and we only observe upvotes vs. downvotes (one can think of the true upvote ratio as \"what is the underlying probability someone gives this submission a upvote, versus a downvote\"). So the 999 upvote/1 downvote submission probably has a true upvote ratio close to 1, which we can assert with confidence thanks to the Law of Large Numbers, but on the other hand we are much less certain about the true upvote ratio of the submission with only a single upvote. Sounds like a Bayesian problem to me.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One way to determine a prior on the upvote ratio is to look at the historical distribution of upvote ratios. This can be accomplished by scraping Reddit's submissions and determining a distribution. There are a few problems with this technique though:\n", + "\n", + "1. Skewed data: The vast majority of submissions have very few votes, hence there will be many submissions with ratios near the extremes (see the \"triangular plot\" in the above Kaggle dataset), effectively skewing our distribution to the extremes. One could try to only use submissions with votes greater than some threshold. Again, problems are encountered. There is a tradeoff between number of submissions available to use and a higher threshold with associated ratio precision. \n", + "2. Biased data: Reddit is composed of different subpages, called subreddits. Two examples are *r/aww*, which posts pics of cute animals, and *r/politics*. It is very likely that the user behaviour towards submissions of these two subreddits are very different: visitors are likely friendly and affectionate in the former, and would therefore upvote submissions more, compared to the latter, where submissions are likely to be controversial and disagreed upon. Therefore not all submissions are the same. \n", + "\n", + "\n", + "In light of these, I think it is better to use a `Uniform` prior.\n", + "\n", + "\n", + "With our prior in place, we can find the posterior of the true upvote ratio. The Python script `top_showerthoughts_submissions.py` will scrape the best posts from the `showerthoughts` community on Reddit. This is a text-only community so the title of each post *is* the post. Below is the top post as well as some other sample posts:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Post contents: \n", + "\n", + "Toilet paper should be free and have advertising printed on it.\n" + ] + } + ], + "source": [ + "#adding a number to the end of the %run call with get the ith top post.\n", + "%run top_showerthoughts_submissions.py 2\n", + "\n", + "print(\"Post contents: \\n\")\n", + "print(top_post)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Some Submissions (out of 98 total) \n", + "-----------\n", + "\"Rappers from the 90's used guns when they had beef rappers today use Twitter.\"\n", + "upvotes/downvotes: [32 3] \n", + "\n", + "\"All polls are biased towards people who are willing to take polls\"\n", + "upvotes/downvotes: [1918 101] \n", + "\n", + "\"Taco Bell should give customers an extra tortilla so they can make a burrito out of all the stuff that spilled out of the other burritos they ate.\"\n", + "upvotes/downvotes: [79 17] \n", + "\n", + "\"There should be an /r/alanismorissette where it's just examples of people using \"ironic\" incorrectly\"\n", + "upvotes/downvotes: [33 6] \n", + "\n" + ] + } + ], + "source": [ + "\"\"\"\n", + "contents: an array of the text from the last 100 top submissions to a subreddit\n", + "votes: a 2d numpy array of upvotes, downvotes for each submission.\n", + "\"\"\"\n", + "n_submissions = len(votes)\n", + "submissions = np.random.randint( n_submissions, size=4)\n", + "print(\"Some Submissions (out of %d total) \\n-----------\"%n_submissions)\n", + "for i in submissions:\n", + " print('\"' + contents[i] + '\"')\n", + " print(\"upvotes/downvotes: \",votes[i,:], \"\\n\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " For a given true upvote ratio $p$ and $N$ votes, the number of upvotes will look like a Binomial random variable with parameters $p$ and $N$. (This is because of the equivalence between upvote ratio and probability of upvoting versus downvoting, out of $N$ possible votes/trials). We create a function that performs Bayesian inference on $p$, for a particular submission's upvote/downvote pair." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pymc3 as pm\n", + "\n", + "def posterior_upvote_ratio( upvotes, downvotes, samples = 20000):\n", + " \"\"\"\n", + " This function accepts the number of upvotes and downvotes a particular submission recieved, \n", + " and the number of posterior samples to return to the user. Assumes a uniform prior.\n", + " \"\"\"\n", + " N = upvotes + downvotes\n", + " with pm.Model() as model:\n", + " upvote_ratio = pm.Uniform(\"upvote_ratio\", 0, 1)\n", + " observations = pm.Binomial( \"obs\", N, upvote_ratio, observed=upvotes)\n", + " \n", + " trace = pm.sample(samples, step=pm.Metropolis())\n", + " \n", + " burned_trace = trace[int(samples/4):]\n", + " return burned_trace[\"upvote_ratio\"]\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below are the resulting posterior distributions." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to upvote_ratio and added transformed upvote_ratio_interval_ to model.\n", + " [-------100%-------] 20000 of 20000 in 1.4 sec. | SPS: 14595.5 | ETA: 0.0Applied interval-transform to upvote_ratio and added transformed upvote_ratio_interval_ to model.\n", + " [-------100%-------] 20000 of 20000 in 1.3 sec. | SPS: 15189.5 | ETA: 0.0Applied interval-transform to upvote_ratio and added transformed upvote_ratio_interval_ to model.\n", + " [-------100%-------] 20000 of 20000 in 1.3 sec. | SPS: 15429.0 | ETA: 0.0Applied interval-transform to upvote_ratio and added transformed upvote_ratio_interval_ to model.\n", + " [-------100%-------] 20000 of 20000 in 1.3 sec. | SPS: 15146.5 | ETA: 0.0" + ] + }, + { + "data": { + "image/png": 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biGr7c0FfBHOi6cl4BXgZ1fbuX9QtO47z4JtR90C1f/xbF9c21BV4JtNHnY6qgdqpnkE1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\n4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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize( 11., 8)\n", + "posteriors = []\n", + "colours = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\", \"#CF4457\"]\n", + "for i in range(len(submissions)):\n", + " j = submissions[i]\n", + " posteriors.append( posterior_upvote_ratio( votes[j, 0], votes[j,1] ) )\n", + " plt.hist( posteriors[i], bins = 10, normed = True, alpha = .9, \n", + " histtype=\"step\",color = colours[i%5], lw = 3,\n", + " label = '(%d up:%d down)\\n%s...'%(votes[j, 0], votes[j,1], contents[j][:50]) )\n", + " plt.hist( posteriors[i], bins = 10, normed = True, alpha = .2, \n", + " histtype=\"stepfilled\",color = colours[i], lw = 3, )\n", + " \n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim( 0, 1)\n", + "plt.title(\"Posterior distributions of upvote ratios on different submissions\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some distributions are very tight, others have very long tails (relatively speaking), expressing our uncertainty with what the true upvote ratio might be.\n", + "\n", + "### Sorting!\n", + "\n", + "We have been ignoring the goal of this exercise: how do we sort the submissions from *best to worst*? Of course, we cannot sort distributions, we must sort scalar numbers. There are many ways to distill a distribution down to a scalar: expressing the distribution through its expected value, or mean, is one way. Choosing the mean is a bad choice though. This is because the mean does not take into account the uncertainty of distributions.\n", + "\n", + "I suggest using the *95% least plausible value*, defined as the value such that there is only a 5% chance the true parameter is lower (think of the lower bound on the 95% credible region). Below are the posterior distributions with the 95% least-plausible value plotted:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 0 2 3] [0.80034320917496615, 0.94092009444598201, 0.74660503350561902, 0.72190353389632911]\n" + ] + }, + { + "data": { + "image/png": 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45JNPTMoSHh5O48aNAXBxcaFHjx6AOgT2ww8/4OXlpe10c/ToUdq0aYOLiwtt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\npgJ+dfAf8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N = posteriors[0].shape[0]\n", + "lower_limits = []\n", + "\n", + "for i in range(len(submissions)):\n", + " j = submissions[i]\n", + " plt.hist( posteriors[i], bins = 20, normed = True, alpha = .9, \n", + " histtype=\"step\",color = colours[i], lw = 3,\n", + " label = '(%d up:%d down)\\n%s...'%(votes[j, 0], votes[j,1], contents[j][:50]) )\n", + " plt.hist( posteriors[i], bins = 20, normed = True, alpha = .2, \n", + " histtype=\"stepfilled\",color = colours[i], lw = 3, )\n", + " v = np.sort( posteriors[i] )[ int(0.05*N) ]\n", + " #plt.vlines( v, 0, 15 , color = \"k\", alpha = 1, linewidths=3 )\n", + " plt.vlines( v, 0, 10 , color = colours[i], linestyles = \"--\", linewidths=3 )\n", + " lower_limits.append(v)\n", + " plt.legend(loc=\"upper left\")\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(\"Posterior distributions of upvote ratios on different submissions\");\n", + "order = np.argsort( -np.array( lower_limits ) )\n", + "print(order, lower_limits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The best submissions, according to our procedure, are the submissions that are *most-likely* to score a high percentage of upvotes. Visually those are the submissions with the 95% least plausible value close to 1.\n", + "\n", + "Why is sorting based on this quantity a good idea? By ordering by the 95% least plausible value, we are being the most conservative with what we think is best. That is, even in the worst case scenario, when we have severely overestimated the upvote ratio, we can be sure the best submissions are still on top. Under this ordering, we impose the following very natural properties:\n", + "\n", + "1. given two submissions with the same observed upvote ratio, we will assign the submission with more votes as better (since we are more confident it has a higher ratio).\n", + "2. given two submissions with the same number of votes, we still assign the submission with more upvotes as *better*.\n", + "\n", + "### But this is too slow for real-time!\n", + "\n", + "I agree, computing the posterior of every submission takes a long time, and by the time you have computed it, likely the data has changed. I delay the mathematics to the appendix, but I suggest using the following formula to compute the lower bound very fast.\n", + "\n", + "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", + "\n", + "where \n", + "\\begin{align}\n", + "& a = 1 + u \\\\\\\\\n", + "& b = 1 + d \\\\\\\\\n", + "\\end{align}\n", + "\n", + "$u$ is the number of upvotes, and $d$ is the number of downvotes. The formula is a shortcut in Bayesian inference, which will be further explained in Chapter 6 when we discuss priors in more detail.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Approximate lower bounds:\n", + "[ 0.93349005 0.9532194 0.94149718 0.90859764 0.88705356 0.8558795\n", + " 0.85644927 0.93752679 0.95767101 0.91131012 0.910073 0.915999\n", + " 0.9140058 0.83276025 0.87593961 0.87436674 0.92830849 0.90642832\n", + " 0.89187973 0.89950891 0.91295322 0.78607629 0.90250203 0.79950031\n", + " 0.85219422 0.83703439 0.7619808 0.81301134 0.7313114 0.79137561\n", + " 0.82701445 0.85542404 0.82309334 0.75211374 0.82934814 0.82674958\n", + " 0.80933194 0.87448152 0.85350205 0.75460106 0.82934814 0.74417233\n", + " 0.79924258 0.8189683 0.75460106 0.90744016 0.83838023 0.78802791\n", + " 0.78400654 0.64638659 0.62047936 0.76137738 0.81365241 0.83838023\n", + " 0.78457533 0.84980627 0.79249393 0.69020315 0.69593922 0.70758151\n", + " 0.70268831 0.91620627 0.73346864 0.86382644 0.80877728 0.72708753\n", + " 0.79822085 0.68333632 0.81699014 0.65100453 0.79809005 0.74702492\n", + " 0.77318569 0.83221179 0.66500492 0.68134548 0.7249286 0.59412132\n", + " 0.58191312 0.73142963 0.73142963 0.66251028 0.87152685 0.74107856\n", + " 0.60935684 0.87152685 0.77484517 0.88783675 0.81814153 0.54569789\n", + " 0.6122496 0.75613569 0.53511973 0.74556767 0.81814153 0.85773646\n", + " 0.6122496 0.64814153]\n", + "\n", + "\n", + "Top 40 Sorted according to approximate lower bounds:\n", + "\n", + "\n", + "596 18 Someone should develop an AI specifically for reading Terms & Conditions and flagging dubious parts.\n", + "-------------\n", + "2360 98 Porn is the only industry where it is not only acceptable but standard to separate people based on race, sex and sexual preference.\n", + "-------------\n", + "1918 101 All polls are biased towards people who are willing to take polls\n", + "-------------\n", + "948 50 They should charge less for drinks in the drive-thru because you can't refill them.\n", + "-------------\n", + "3740 239 When I was in elementary school and going through the DARE program, I was positive a gang of older kids was going to corner me and force me to smoke pot. Then I became an adult and realized nobody is giving free drugs to somebody that doesn't want them.\n", + "-------------\n", + "166 7 \"Noted\" is the professional way of saying \"K\".\n", + "-------------\n", + "29 0 Rewatching Mr. Bean, I've realised that the character is an eccentric genius and not a blithering idiot.\n", + "-------------\n", + "289 18 You've been doing weird cameos in your friends' dreams since kindergarten.\n", + "-------------\n", + "269 17 At some point every parent has stopped wiping their child's butt and hoped for the best.\n", + "-------------\n", + "121 6 Is it really fair to say a person over 85 has heart failure? Technically, that heart has done exceptionally well.\n", + "-------------\n", + "535 40 It's surreal to think that the sun and moon and stars we gaze up at are the same objects that have been observed for millenia, by everyone in the history of humanity from cavemen to Aristotle to Jesus to George Washington.\n", + "-------------\n", + "527 40 I wonder if America's internet is censored in a similar way that North Korea's is, but we have no idea of it happening.\n", + "-------------\n", + "1510 131 Kenny's family is poor because they're always paying for his funeral.\n", + "-------------\n", + "43 1 If I was as careful with my whole paycheck as I am with my last $20 I'd be a whole lot better off\n", + "-------------\n", + "162 10 Black hair ties are probably the most popular bracelets in the world.\n", + "-------------\n", + "107 6 The best answer to the interview question \"What is your greatest weakness?\" is \"interviews\".\n", + "-------------\n", + "127 8 Surfing the internet without ads feels like a summer evening without mosquitoes\n", + "-------------\n", + "159 12 I wonder if Superman ever put a pair of glasses on Lois Lane's dog, and she was like \"what's this Clark? Did you get me a new dog?\"\n", + "-------------\n", + "21 0 Sitting on a cold toilet seat or a warm toilet seat both suck for different reasons.\n", + "-------------\n", + "1414 157 My life is really like Rihanna's song, \"just work work work work work\" and the rest of it I can't really understand.\n", + "-------------\n", + "222 22 I'm honestly slightly concerned how often Reddit commenters make me laugh compared to my real life friends.\n", + "-------------\n", + "52 3 The world must have been a spookier place altogether when candles and gas lamps were the only sources of light at night besides the moon and the stars.\n", + "-------------\n", + "194 19 I have not been thankful enough in the last few years that the Black Eyed Peas are no longer ever on the radio\n", + "-------------\n", + "18 0 Living on the coast is having the window seat of the land you live on.\n", + "-------------\n", + "18 0 Binoculars are like walkie talkies for the deaf.\n", + "-------------\n", + "28 1 Now that I am a parent of multiple children I have realized that my parents were lying through their teeth when they said they didn't have a favorite.\n", + "-------------\n", + "16 0 I sneer at people who read tabloids, but every time I look someone up on Wikipedia the first thing I look for is what controversies they've been involved in.\n", + "-------------\n", + "1559 233 Kid's menus at restaurants should be smaller portions of the same adult dishes at lower prices and not the junk food that they usually offer.\n", + "-------------\n", + "1426 213 Eventually once all phones are waterproof we'll be able to push people into pools again\n", + "-------------\n", + "61 5 Myspace is so outdated that jokes about it being outdated has become outdated\n", + "-------------\n", + "52 4 As a kid, seeing someone step on a banana peel and not slip was a disappointment.\n", + "-------------\n", + "90 9 Yahoo!® is the RadioShack® of the Internet.\n", + "-------------\n", + "34 2 People who \"tell it like it is\" rarely do so to say something nice\n", + "-------------\n", + "39 3 Closing your eyes after turning off your alarm is a very dangerous game.\n", + "-------------\n", + "39 3 Your known 'first word' is the first word your parents heard you speak. In reality, it may have been a completely different word you said when you were alone.\n", + "-------------\n", + "87 10 \"Smells Like Teen Spirit\" is as old to listeners of today as \"Yellow Submarine\" was to listeners of 1991.\n", + "-------------\n", + "239 36 if an ocean didnt stop immigrants from coming to America what makes us think a wall will?\n", + "-------------\n", + "22 1 The phonebook was the biggest invasion of privacy that everyone was oddly ok with.\n", + "-------------\n", + "57 6 I'm actually the most productive when I procrastinate because I'm doing everything I possibly can to avoid the main task at hand.\n", + "-------------\n", + "57 6 You will never feel how long time is until you have allergies and snot slowly dripping out of your nostrils, while sitting in a classroom with no tissues.\n", + "-------------\n" + ] + } + ], + "source": [ + "def intervals(u,d):\n", + " a = 1. + u\n", + " b = 1. + d\n", + " mu = a/(a+b)\n", + " std_err = 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1.) ) )\n", + " return ( mu, std_err )\n", + "\n", + "print(\"Approximate lower bounds:\")\n", + "posterior_mean, std_err = intervals(votes[:,0],votes[:,1])\n", + "lb = posterior_mean - std_err\n", + "print(lb)\n", + "print(\"\\n\")\n", + "print(\"Top 40 Sorted according to approximate lower bounds:\")\n", + "print(\"\\n\")\n", + "order = np.argsort( -lb )\n", + "ordered_contents = []\n", + "for i in order[:40]:\n", + " ordered_contents.append( contents[i] )\n", + " print(votes[i,0], votes[i,1], contents[i])\n", + " print(\"-------------\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can view the ordering visually by plotting the posterior mean and bounds, and sorting by the lower bound. In the plot below, notice that the left error-bar is sorted (as we suggested this is the best way to determine an ordering), so the means, indicated by dots, do not follow any strong pattern. " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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4D7jNzPrEticRfsU/V9IKQnTiHUlnABea2UVZY3cDbk30PxMYZGa5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "r_order = order[::-1][-40:]\n", + "plt.errorbar( posterior_mean[r_order], np.arange( len(r_order) ), \n", + " xerr=std_err[r_order], capsize=0, fmt=\"o\",\n", + " color = \"#7A68A6\")\n", + "plt.xlim( 0.3, 1)\n", + "plt.yticks( np.arange( len(r_order)-1,-1,-1 ), map( lambda x: x[:30].replace(\"\\n\",\"\"), ordered_contents) );" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the graphic above, you can see why sorting by mean would be sub-optimal." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Extension to Starred rating systems\n", + "\n", + "The above procedure works well for upvote-downvotes schemes, but what about systems that use star ratings, e.g. 5 star rating systems. Similar problems apply with simply taking the average: an item with two perfect ratings would beat an item with thousands of perfect ratings, but a single sub-perfect rating. \n", + "\n", + "\n", + "We can consider the upvote-downvote problem above as binary: 0 is a downvote, 1 if an upvote. A $N$-star rating system can be seen as a more continuous version of above, and we can set $n$ stars rewarded is equivalent to rewarding $\\frac{n}{N}$. For example, in a 5-star system, a 2 star rating corresponds to 0.4. A perfect rating is a 1. We can use the same formula as before, but with $a,b$ defined differently:\n", + "\n", + "\n", + "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", + "\n", + "where \n", + "\n", + "\\begin{align}\n", + "& a = 1 + S \\\\\\\\\n", + "& b = 1 + N - S \\\\\\\\\n", + "\\end{align}\n", + "\n", + "where $N$ is the number of users who rated, and $S$ is the sum of all the ratings, under the equivalence scheme mentioned above. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Counting Github stars\n", + "\n", + "What is the average number of stars a Github repository has? How would you calculate this? There are over 6 million respositories, so there is more than enough data to invoke the Law of Large numbers. Let's start pulling some data. TODO" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "While the Law of Large Numbers is cool, it is only true so much as its name implies: with large sample sizes only. We have seen how our inference can be affected by not considering *how the data is shaped*. \n", + "\n", + "1. By (cheaply) drawing many samples from the posterior distributions, we can ensure that the Law of Large Number applies as we approximate expected values (which we will do in the next chapter).\n", + "\n", + "2. Bayesian inference understands that with small sample sizes, we can observe wild randomness. Our posterior distribution will reflect this by being more spread rather than tightly concentrated. Thus, our inference should be correctable.\n", + "\n", + "3. There are major implications of not considering the sample size, and trying to sort objects that are unstable leads to pathological orderings. The method provided above solves this problem.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Appendix\n", + "\n", + "##### Derivation of sorting submissions formula\n", + "\n", + "Basically what we are doing is using a Beta prior (with parameters $a=1, b=1$, which is a uniform distribution), and using a Binomial likelihood with observations $u, N = u+d$. This means our posterior is a Beta distribution with parameters $a' = 1 + u, b' = 1 + (N - u) = 1+d$. We then need to find the value, $x$, such that 0.05 probability is less than $x$. This is usually done by inverting the CDF ([Cumulative Distribution Function](http://en.wikipedia.org/wiki/Cumulative_Distribution_Function)), but the CDF of the beta, for integer parameters, is known but is a large sum [3]. \n", + "\n", + "We instead use a Normal approximation. The mean of the Beta is $\\mu = a'/(a'+b')$ and the variance is \n", + "\n", + "$$\\sigma^2 = \\frac{a'b'}{ (a' + b')^2(a'+b'+1) }$$\n", + "\n", + "Hence we solve the following equation for $x$ and have an approximate lower bound. \n", + "\n", + "$$ 0.05 = \\Phi\\left( \\frac{(x - \\mu)}{\\sigma}\\right) $$ \n", + "\n", + "$\\Phi$ being the [cumulative distribution for the normal distribution](http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution)\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Exercises\n", + "\n", + "1\\. How would you estimate the quantity $E\\left[ \\cos{X} \\right]$, where $X \\sim \\text{Exp}(4)$? What about $E\\left[ \\cos{X} | X \\lt 1\\right]$, i.e. the expected value *given* we know $X$ is less than 1? Would you need more samples than the original samples size to be equally accurate?" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "## Enter code here\n", + "import scipy.stats as stats\n", + "exp = stats.expon( scale=4 )\n", + "N = 1e5\n", + "X = exp.rvs( int(N) )\n", + "## ..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. The following table was located in the paper \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression\" [2]. The table ranks football field-goal kickers by their percent of non-misses. What mistake have the researchers made?\n", + "\n", + "-----\n", + "\n", + "#### Kicker Careers Ranked by Make Percentage\n", + "
Rank Kicker Make % Number of Kicks
1 Garrett Hartley 87.7 57
2 Matt Stover 86.8 335
3 Robbie Gould 86.2 224
4 Rob Bironas 86.1 223
5 Shayne Graham 85.4 254
51 Dave Rayner 72.2 90
52 Nick Novak 71.9 64
53 Tim Seder 71.0 62
54 Jose Cortez 70.7 75
55 Wade Richey 66.1 56
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In August 2013, [a popular post](http://bpodgursky.wordpress.com/2013/08/21/average-income-per-programming-language/) on the average income per programmer of different languages was trending. Here's the summary chart: (reproduced without permission, cause when you lie with stats, you gunna get the hammer). What do you notice about the extremes?\n", + "\n", + "------\n", + "\n", + "#### Average household income by programming language\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
LanguageAverage Household Income ($)Data Points
Puppet87,589.29112
Haskell89,973.82191
PHP94,031.19978
CoffeeScript94,890.80435
VimL94,967.11532
Shell96,930.54979
Lua96,930.69101
Erlang97,306.55168
Clojure97,500.00269
Python97,578.872314
JavaScript97,598.753443
Emacs Lisp97,774.65355
C#97,823.31665
Ruby98,238.743242
C++99,147.93845
CSS99,881.40527
Perl100,295.45990
C100,766.512120
Go101,158.01231
Scala101,460.91243
ColdFusion101,536.70109
Objective-C101,801.60562
Groovy102,650.86116
Java103,179.391402
XSLT106,199.19123
ActionScript108,119.47113
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "1. Wainer, Howard. *The Most Dangerous Equation*. American Scientist, Volume 95.\n", + "2. Clarck, Torin K., Aaron W. Johnson, and Alexander J. Stimpson. \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression.\" (2013): n. page. [Web](http://www.sloansportsconference.com/wp-content/uploads/2013/Going%20for%20Three%20Predicting%20the%20Likelihood%20of%20Field%20Goal%20Success%20with%20Logistic%20Regression.pdf). 20 Feb. 2013.\n", + "3. http://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.core.display import HTML\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter4_TheGreatestTheoremNeverTold/Chapter4.ipynb b/Chapter4_TheGreatestTheoremNeverTold/Chapter4.ipynb deleted file mode 100644 index 613ad3ce..00000000 --- a/Chapter4_TheGreatestTheoremNeverTold/Chapter4.ipynb +++ /dev/null @@ -1,1226 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#Chapter 4\n", - "______\n", - "\n", - "##The greatest theorem never told\n", - "\n", - "\n", - "This chapter focuses on an idea that is always bouncing around our minds, but is rarely made explicit outside books devoted to statistics. In fact, we've been using this simple idea in every example thus far. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###The Law of Large Numbers\n", - "\n", - "Let $Z_i$ be $N$ independent samples from some probability distribution. According to *the Law of Large numbers*, so long as the expected value $E[Z]$ is finite, the following holds,\n", - "\n", - "$$\\frac{1}{N} \\sum_{i=1}^N Z_i \\rightarrow E[ Z ], \\;\\;\\; N \\rightarrow \\infty.$$\n", - "\n", - "In words:\n", - "\n", - "> The average of a sequence of random variables from the same distribution converges to the expected value of that distribution.\n", - "\n", - "This may seem like a boring result, but it will be the most useful tool you use." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Intuition \n", - "\n", - "If the above Law is somewhat surprising, it can be made clearer by examining a simple example. \n", - "\n", - "Consider a random variable $Z$ that can take only two values, $c_1$ and $c_2$. Suppose we have a large number of samples of $Z$, denoting a specific sample $Z_i$. The Law says that we can approximate the expected value of $Z$ by averaging over all samples. Consider the average:\n", - "\n", - "\n", - "$$ \\frac{1}{N} \\sum_{i=1}^N \\;Z_i $$\n", - "\n", - "\n", - "By construction, $Z_i$ can only take on $c_1$ or $c_2$, hence we can partition the sum over these two values:\n", - "\n", - "\\begin{align}\n", - "\\frac{1}{N} \\sum_{i=1}^N \\;Z_i\n", - "& =\\frac{1}{N} \\big( \\sum_{ Z_i = c_1}c_1 + \\sum_{Z_i=c_2}c_2 \\big) \\\\\\\\[5pt]\n", - "& = c_1 \\sum_{ Z_i = c_1}\\frac{1}{N} + c_2 \\sum_{ Z_i = c_2}\\frac{1}{N} \\\\\\\\[5pt]\n", - "& = c_1 \\times \\text{ (approximate frequency of $c_1$) } \\\\\\\\ \n", - "& \\;\\;\\;\\;\\;\\;\\;\\;\\; + c_2 \\times \\text{ (approximate frequency of $c_2$) } \\\\\\\\[5pt]\n", - "& \\approx c_1 \\times P(Z = c_1) + c_2 \\times P(Z = c_2 ) \\\\\\\\[5pt]\n", - "& = E[Z]\n", - "\\end{align}\n", - "\n", - "\n", - "Equality holds in the limit, but we can get closer and closer by using more and more samples in the average. This Law holds for almost *any distribution*, minus some important cases we will encounter later.\n", - "\n", - "##### Example\n", - "____\n", - "\n", - "\n", - "Below is a diagram of the Law of Large numbers in action for three different sequences of Poisson random variables. \n", - "\n", - " We sample `sample_size = 100000` Poisson random variables with parameter $\\lambda = 4.5$. (Recall the expected value of a Poisson random variable is equal to its parameter.) We calculate the average for the first $n$ samples, for $n=1$ to `sample_size`. " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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aNmxIgYGBtGTJEpJIJGKZiIgIjYHMREQnT54kiURC165dE+dt2bKFWrZsSTKZ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\ndp0RZxJQE/71BlaRFdhBXmAVWYG3sVUSC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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%matplotlib inline\n", - "import numpy as np\n", - "from IPython.core.pylabtools import figsize\n", - "import matplotlib.pyplot as plt\n", - "\n", - "figsize(12.5, 5)\n", - "import pymc as pm\n", - "\n", - "sample_size = 100000\n", - "expected_value = lambda_ = 4.5\n", - "poi = pm.rpoisson\n", - "N_samples = range(1, sample_size, 100)\n", - "\n", - "for k in range(3):\n", - "\n", - " samples = poi(lambda_, size=sample_size)\n", - "\n", - " partial_average = [samples[:i].mean() for i in N_samples]\n", - "\n", - " plt.plot(N_samples, partial_average, lw=1.5, label=\"average \\\n", - "of $n$ samples; seq. %d\" % k)\n", - "\n", - "\n", - "plt.plot(N_samples, expected_value * np.ones_like(partial_average),\n", - " ls=\"--\", label=\"true expected value\", c=\"k\")\n", - "\n", - "plt.ylim(4.35, 4.65)\n", - "plt.title(\"Convergence of the average of \\n random variables to its \\\n", - "expected value\")\n", - "plt.ylabel(\"average of $n$ samples\")\n", - "plt.xlabel(\"# of samples, $n$\")\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Looking at the above plot, it is clear that when the sample size is small, there is greater variation in the average (compare how *jagged and jumpy* the average is initially, then *smooths* out). All three paths *approach* the value 4.5, but just flirt with it as $N$ gets large. Mathematicians and statistician have another name for *flirting*: convergence. \n", - "\n", - "Another very relevant question we can ask is *how quickly am I converging to the expected value?* Let's plot something new. For a specific $N$, let's do the above trials thousands of times and compute how far away we are from the true expected value, on average. But wait — *compute on average*? This is simply the law of large numbers again! For example, we are interested in, for a specific $N$, the quantity:\n", - "\n", - "$$D(N) = \\sqrt{ \\;E\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\;\\;\\right] \\;\\;}$$\n", - "\n", - "The above formulae is interpretable as a distance away from the true value (on average), for some $N$. (We take the square root so the dimensions of the above quantity and our random variables are the same). As the above is an expected value, it can be approximated using the law of large numbers: instead of averaging $Z_i$, we calculate the following multiple times and average them:\n", - "\n", - "$$ Y_k = \\left( \\;\\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\; \\right)^2 $$\n", - "\n", - "By computing the above many, $N_y$, times (remember, it is random), and averaging them:\n", - "\n", - "$$ \\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k \\rightarrow E[ Y_k ] = E\\;\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\right]$$\n", - "\n", - "Finally, taking the square root:\n", - "\n", - "$$ \\sqrt{\\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k} \\approx D(N) $$ " - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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kSZIkSXrj5ObmEhAQQIMGDTh//jxbtmxh8eLF7Nu3DzMzMxYsWEBwcDC3bt1i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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "\n", - "N_Y = 250 # use this many to approximate D(N)\n", - "N_array = np.arange(1000, 50000, 2500) # use this many samples in the approx. to the variance.\n", - "D_N_results = np.zeros(len(N_array))\n", - "\n", - "lambda_ = 4.5\n", - "expected_value = lambda_ # for X ~ Poi(lambda) , E[ X ] = lambda\n", - "\n", - "\n", - "def D_N(n):\n", - " \"\"\"\n", - " This function approx. D_n, the average variance of using n samples.\n", - " \"\"\"\n", - " Z = poi(lambda_, size=(n, N_Y))\n", - " average_Z = Z.mean(axis=0)\n", - " return np.sqrt(((average_Z - expected_value) ** 2).mean())\n", - "\n", - "\n", - "for i, n in enumerate(N_array):\n", - " D_N_results[i] = D_N(n)\n", - "\n", - "\n", - "plt.xlabel(\"$N$\")\n", - "plt.ylabel(\"expected squared-distance from true value\")\n", - "plt.plot(N_array, D_N_results, lw=3,\n", - " label=\"expected distance between\\n\\\n", - "expected value and \\naverage of $N$ random variables.\")\n", - "plt.plot(N_array, np.sqrt(expected_value) / np.sqrt(N_array), lw=2, ls=\"--\",\n", - " label=r\"$\\frac{\\sqrt{\\lambda}}{\\sqrt{N}}$\")\n", - "plt.legend()\n", - "plt.title(\"How 'fast' is the sample average converging? \");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As expected, the expected distance between our sample average and the actual expected value shrinks as $N$ grows large. But also notice that the *rate* of convergence decreases, that is, we need only 10 000 additional samples to move from 0.020 to 0.015, a difference of 0.005, but *20 000* more samples to again decrease from 0.015 to 0.010, again only a 0.005 decrease.\n", - "\n", - "\n", - "It turns out we can measure this rate of convergence. Above I have plotted a second line, the function $\\sqrt{\\lambda}/\\sqrt{N}$. This was not chosen arbitrarily. In most cases, given a sequence of random variable distributed like $Z$, the rate of converge to $E[Z]$ of the Law of Large Numbers is \n", - "\n", - "$$ \\frac{ \\sqrt{ \\; Var(Z) \\; } }{\\sqrt{N} }$$\n", - "\n", - "This is useful to know: for a given large $N$, we know (on average) how far away we are from the estimate. On the other hand, in a Bayesian setting, this can seem like a useless result: Bayesian analysis is OK with uncertainty so what's the *statistical* point of adding extra precise digits? Though drawing samples can be so computationally cheap that having a *larger* $N$ is fine too. \n", - "\n", - "### How do we compute $Var(Z)$ though?\n", - "\n", - "The variance is simply another expected value that can be approximated! Consider the following, once we have the expected value (by using the Law of Large Numbers to estimate it, denote it $\\mu$), we can estimate the variance:\n", - "\n", - "$$ \\frac{1}{N}\\sum_{i=1}^N \\;(Z_i - \\mu)^2 \\rightarrow E[ \\;( Z - \\mu)^2 \\;] = Var( Z )$$\n", - "\n", - "### Expected values and probabilities \n", - "There is an even less explicit relationship between expected value and estimating probabilities. Define the *indicator function*\n", - "\n", - "$$\\mathbb{1}_A(x) = \n", - "\\begin{cases} 1 & x \\in A \\\\\\\\\n", - " 0 & else\n", - "\\end{cases}\n", - "$$\n", - "Then, by the law of large numbers, if we have many samples $X_i$, we can estimate the probability of an event $A$, denoted $P(A)$, by:\n", - "\n", - "$$ \\frac{1}{N} \\sum_{i=1}^N \\mathbb{1}_A(X_i) \\rightarrow E[\\mathbb{1}_A(X)] = P(A) $$\n", - "\n", - "Again, this is fairly obvious after a moments thought: the indicator function is only 1 if the event occurs, so we are summing only the times the event occurs and dividing by the total number of trials (consider how we usually approximate probabilities using frequencies). For example, suppose we wish to estimate the probability that a $Z \\sim Exp(.5)$ is greater than 10, and we have many samples from a $Exp(.5)$ distribution. \n", - "\n", - "\n", - "$$ P( Z > 10 ) = \\frac{1}{N} \\sum_{i=1}^N \\mathbb{1}_{z > 10 }(Z_i) $$\n" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0069\n" - ] - } - ], - "source": [ - "import pymc as pm\n", - "N = 10000\n", - "print np.mean([pm.rexponential(0.5) > 10 for i in range(N)])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### What does this all have to do with Bayesian statistics? \n", - "\n", - "\n", - "*Point estimates*, to be introduced in the next chapter, in Bayesian inference are computed using expected values. In more analytical Bayesian inference, we would have been required to evaluate complicated expected values represented as multi-dimensional integrals. No longer. If we can sample from the posterior distribution directly, we simply need to evaluate averages. Much easier. If accuracy is a priority, plots like the ones above show how fast you are converging. And if further accuracy is desired, just take more samples from the posterior. \n", - "\n", - "When is enough enough? When can you stop drawing samples from the posterior? That is the practitioners decision, and also dependent on the variance of the samples (recall from above a high variance means the average will converge slower). \n", - "\n", - "We also should understand when the Law of Large Numbers fails. As the name implies, and comparing the graphs above for small $N$, the Law is only true for large sample sizes. Without this, the asymptotic result is not reliable. Knowing in what situations the Law fails can give us *confidence in how unconfident we should be*. The next section deals with this issue." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The Disorder of Small Numbers\n", - "\n", - "The Law of Large Numbers is only valid as $N$ gets *infinitely* large: never truly attainable. While the law is a powerful tool, it is foolhardy to apply it liberally. Our next example illustrates this.\n", - "\n", - "\n", - "##### Example: Aggregated geographic data\n", - "\n", - "\n", - "Often data comes in aggregated form. For instance, data may be grouped by state, county, or city level. Of course, the population numbers vary per geographic area. If the data is an average of some characteristic of each the geographic areas, we must be conscious of the Law of Large Numbers and how it can *fail* for areas with small populations.\n", - "\n", - "We will observe this on a toy dataset. Suppose there are five thousand counties in our dataset. Furthermore, population number in each state are uniformly distributed between 100 and 1500. The way the population numbers are generated is irrelevant to the discussion, so we do not justify this. We are interested in measuring the average height of individuals per county. Unbeknownst to us, height does **not** vary across county, and each individual, regardless of the county he or she is currently living in, has the same distribution of what their height may be:\n", - "\n", - "$$ \\text{height} \\sim \\text{Normal}(150, 15 ) $$\n", - "\n", - "We aggregate the individuals at the county level, so we only have data for the *average in the county*. What might our dataset look like?" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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QarU4cuQIKioqUFlZiXnz5mHVqlXYsGEDcnNzsW3bNrvzP/74Y6jVamRlZWHT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htjmO9PmT+0mp0KDz/fxHVFY+76803f6tTqJZUn315iVQ1UVeH+ZzdlYZWqwcMvt4gCkRVx9nr2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FvaPbtIZRFrIXKS6c//5jCYNWfcj2wS3u3nd5+um3Eome//l2W2MWVzLcuf8yI2fK5cqb582f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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "std_height = 15\n", - "mean_height = 150\n", - "\n", - "n_counties = 5000\n", - "pop_generator = pm.rdiscrete_uniform\n", - "norm = pm.rnormal\n", - "\n", - "# generate some artificial population numbers\n", - "population = pop_generator(100, 1500, size=n_counties)\n", - "\n", - "average_across_county = np.zeros(n_counties)\n", - "for i in range(n_counties):\n", - " # generate some individuals and take the mean\n", - " average_across_county[i] = norm(mean_height, 1. / std_height ** 2,\n", - " size=population[i]).mean()\n", - "\n", - "# located the counties with the apparently most extreme average heights.\n", - "i_min = np.argmin(average_across_county)\n", - "i_max = np.argmax(average_across_county)\n", - "\n", - "# plot population size vs. recorded average\n", - "plt.scatter(population, average_across_county, alpha=0.5, c=\"#7A68A6\")\n", - "plt.scatter([population[i_min], population[i_max]],\n", - " [average_across_county[i_min], average_across_county[i_max]],\n", - " s=60, marker=\"o\", facecolors=\"none\",\n", - " edgecolors=\"#A60628\", linewidths=1.5,\n", - " label=\"extreme heights\")\n", - "\n", - "plt.xlim(100, 1500)\n", - "plt.title(\"Average height vs. County Population\")\n", - "plt.xlabel(\"County Population\")\n", - "plt.ylabel(\"Average height in county\")\n", - "plt.plot([100, 1500], [150, 150], color=\"k\", label=\"true expected \\\n", - "height\", ls=\"--\")\n", - "plt.legend(scatterpoints=1);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What do we observe? *Without accounting for population sizes* we run the risk of making an enormous inference error: if we ignored population size, we would say that the county with the shortest and tallest individuals have been correctly circled. But this inference is wrong for the following reason. These two counties do *not* necessarily have the most extreme heights. The error results from the calculated average of smaller populations not being a good reflection of the true expected value of the population (which in truth should be $\\mu =150$). The sample size/population size/$N$, whatever you wish to call it, is simply too small to invoke the Law of Large Numbers effectively. \n", - "\n", - "We provide more damning evidence against this inference. Recall the population numbers were uniformly distributed over 100 to 1500. Our intuition should tell us that the counties with the most extreme population heights should also be uniformly spread over 100 to 1500, and certainly independent of the county's population. Not so. Below are the population sizes of the counties with the most extreme heights." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Population sizes of 10 'shortest' counties: \n", - "[111 103 102 109 110 257 164 144 169 260]\n", - "\n", - "Population sizes of 10 'tallest' counties: \n", - "[252 107 162 141 141 256 144 112 210 342]\n" - ] - } - ], - "source": [ - "print \"Population sizes of 10 'shortest' counties: \"\n", - "print population[np.argsort(average_across_county)[:10]]\n", - "print\n", - "print \"Population sizes of 10 'tallest' counties: \"\n", - "print population[np.argsort(-average_across_county)[:10]]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Not at all uniform over 100 to 1500. This is an absolute failure of the Law of Large Numbers. \n", - "\n", - "##### Example: Kaggle's *U.S. Census Return Rate Challenge*\n", - "\n", - "Below is data from the 2010 US census, which partitions populations beyond counties to the level of block groups (which are aggregates of city blocks or equivalents). The dataset is from a Kaggle machine learning competition some colleagues and I participated in. The objective was to predict the census letter mail-back rate of a group block, measured between 0 and 100, using census variables (median income, number of females in the block-group, number of trailer parks, average number of children etc.). Below we plot the census mail-back rate versus block group population:" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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CwsIhMQiHswOkXV1drFq1ape2bv8lYHdtqaysJJlM4na76e/vHzGew9neVwUw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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 6.5)\n", - "data = np.genfromtxt(\"./data/census_data.csv\", skip_header=1,\n", - " delimiter=\",\")\n", - "plt.scatter(data[:, 1], data[:, 0], alpha=0.5, c=\"#7A68A6\")\n", - "plt.title(\"Census mail-back rate vs Population\")\n", - "plt.ylabel(\"Mail-back rate\")\n", - "plt.xlabel(\"population of block-group\")\n", - "plt.xlim(-100, 15e3)\n", - "plt.ylim(-5, 105)\n", - "\n", - "i_min = np.argmin(data[:, 0])\n", - "i_max = np.argmax(data[:, 0])\n", - "\n", - "plt.scatter([data[i_min, 1], data[i_max, 1]],\n", - " [data[i_min, 0], data[i_max, 0]],\n", - " s=60, marker=\"o\", facecolors=\"none\",\n", - " edgecolors=\"#A60628\", linewidths=1.5,\n", - " label=\"most extreme points\")\n", - "\n", - "plt.legend(scatterpoints=1);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above is a classic phenomenon in statistics. I say *classic* referring to the \"shape\" of the scatter plot above. It follows a classic triangular form, that tightens as we increase the sample size (as the Law of Large Numbers becomes more exact). \n", - "\n", - "I am perhaps overstressing the point and maybe I should have titled the book *\"You don't have big data problems!\"*, but here again is an example of the trouble with *small datasets*, not big ones. Simply, small datasets cannot be processed using the Law of Large Numbers. Compare with applying the Law without hassle to big datasets (ex. big data). I mentioned earlier that paradoxically big data prediction problems are solved by relatively simple algorithms. The paradox is partially resolved by understanding that the Law of Large Numbers creates solutions that are *stable*, i.e. adding or subtracting a few data points will not affect the solution much. On the other hand, adding or removing data points to a small dataset can create very different results. \n", - "\n", - "For further reading on the hidden dangers of the Law of Large Numbers, I would highly recommend the excellent manuscript [The Most Dangerous Equation](http://nsm.uh.edu/~dgraur/niv/TheMostDangerousEquation.pdf). " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: How to order Reddit comments\n", - "\n", - "You may have disagreed with the original statement that the Law of Large numbers is known to everyone, but only implicitly in our subconscious decision making. Consider ratings on online products: how often do you trust an average 5-star rating if there is only 1 reviewer? 2 reviewers? 3 reviewers? We implicitly understand that with such few reviewers that the average rating is **not** a good reflection of the true value of the product.\n", - "\n", - "This has created flaws in how we sort items, and more generally, how we compare items. Many people have realized that sorting online search results by their rating, whether the objects be books, videos, or online comments, return poor results. Often the seemingly top videos or comments have perfect ratings only from a few enthusiastic fans, and truly more quality videos or comments are hidden in later pages with *falsely-substandard* ratings of around 4.8. How can we correct this?\n", - "\n", - "Consider the popular site Reddit (I purposefully did not link to the website as you would never come back). The site hosts links to stories or images, and a very popular part of the site are the comments associated with each link. Redditors can vote up or down on each comment (called upvotes and downvotes). Reddit, by default, will sort comments by Top, that is, the best comments.\n", - "\n", - "\n", - "\n", - "\n", - "How would you determine which comments are the best? There are a number of ways to achieve this:\n", - "\n", - "1. *Popularity*: A comment is considered good if it has many upvotes. A problem with this model is that a comment with hundreds of upvotes, but thousands of downvotes. While being very *popular*, the comment is likely more controversial than best.\n", - "2. *Difference*: Using the *difference* of upvotes and downvotes. This solves the above problem, but fails when we consider the temporal nature of comments. Comments can be posted many hours after the original link submission. The difference method will bias the *Top* comments to be the oldest comments, which have accumulated more upvotes than newer comments, but are not necessarily the best.\n", - "3. *Time adjusted*: Consider using Difference divided by the age of the comment. This creates a *rate*, something like *difference per second*, or *per minute*. An immediate counter example is, if we use per second, a 1 second old comment with 1 upvote would be better than a 100 second old comment with 99 upvotes. One can avoid this by only considering at least t second old comments. But what is a good t value? Does this mean no comment younger than t is good? We end up comparing unstable quantities with stable quantities (young vs. old comments).\n", - "3. *Ratio*: Rank comments by the ratio of upvotes to total number of votes (upvotes plus downvotes). This solves the temporal issue, such that new comments who score well can be considered Top just as likely as older comments, provided they have many upvotes to total votes. The problem here is that a comment with a single upvote (ratio = 1.0) will beat a comment with 999 upvotes and 1 downvote (ratio = 0.999), but clearly the latter comment is *more likely* to be better.\n", - "\n", - "I used the phrase *more likely* for good reason. It is possible that the former comment, with a single upvote, is in fact a better comment than the later with 999 upvotes. The hesitation to agree with this is because we have not seen the other 999 potential votes the former comment might get. Perhaps it will achieve an additional 999 upvotes and 0 downvotes and be considered better than the latter, though not likely.\n", - "\n", - "What we really want is an estimate of the *true upvote ratio*. Note that the true upvote ratio is not the same as the observed upvote ratio: the true upvote ratio is hidden, and we only observe upvotes vs. downvotes (one can think of the true upvote ratio as \"what is the underlying probability someone gives this comment a upvote, versus a downvote\"). So the 999 upvote/1 downvote comment probably has a true upvote ratio close to 1, which we can assert with confidence thanks to the Law of Large Numbers, but on the other hand we are much less certain about the true upvote ratio of the comment with only a single upvote. Sounds like a Bayesian problem to me.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "One way to determine a prior on the upvote ratio is to look at the historical distribution of upvote ratios. This can be accomplished by scraping Reddit's comments and determining a distribution. There are a few problems with this technique though:\n", - "\n", - "1. Skewed data: The vast majority of comments have very few votes, hence there will be many comments with ratios near the extremes (see the \"triangular plot\" in the above Kaggle dataset), effectively skewing our distribution to the extremes. One could try to only use comments with votes greater than some threshold. Again, problems are encountered. There is a tradeoff between number of comments available to use and a higher threshold with associated ratio precision. \n", - "2. Biased data: Reddit is composed of different subpages, called subreddits. Two examples are *r/aww*, which posts pics of cute animals, and *r/politics*. It is very likely that the user behaviour towards comments of these two subreddits are very different: visitors are likely to be more friendly and affectionate in the former, and would therefore upvote comments more, compared to the latter, where comments are likely to be controversial and disagreed upon. Therefore not all comments are the same. \n", - "\n", - "\n", - "In light of these, I think it is better to use a `Uniform` prior.\n", - "\n", - "\n", - "With our prior in place, we can find the posterior of the true upvote ratio. The Python script `comments_for_top_reddit_pic.py` will scrape the comments from the current top picture on Reddit. Below is the picture, and some comments:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Title of submission: \n", - "Frozen mining truck\n", - "http://i.imgur.com/OYsHKlH.jpg\n" - ] - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.core.display import Image\n", - "# adding a number to the end of the %run call with get the ith top photo.\n", - "%run top_pic_comments.py 2\n", - "\n", - "Image(top_post_url)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Some Comments (out of 77 total) \n", - "-----------\n", - "\"Do these trucks remind anyone else of Sly Cooper?\"\n", - "upvotes/downvotes: [2 0]\n", - "\n", - "\"Dammit Elsa I told you not to drink and drive.\"\n", - "upvotes/downvotes: [7 0]\n", - "\n", - "\"I've seen this picture before in a Duratray (the dump box supplier) brochure. If I recall it was either at Ekati or Diavik... In which case the truck could be either a Komatsu or a CAT... anyone care to comment?\"\n", - "upvotes/downvotes: [2 0]\n", - "\n", - "\"Actually it does not look frozen just covered in a layer of wind packed snow.\"\n", - "upvotes/downvotes: [120 18]\n", - "\n" - ] - } - ], - "source": [ - "\"\"\"\n", - "contents: an array of the text from all comments on the pic\n", - "votes: a 2d numpy array of upvotes, downvotes for each comment.\n", - "\"\"\"\n", - "n_comments = len(contents)\n", - "comments = np.random.randint(n_comments, size=4)\n", - "print \"Some Comments (out of %d total) \\n-----------\" % n_comments\n", - "for i in comments:\n", - " print '\"' + contents[i] + '\"'\n", - " print\"upvotes/downvotes: \", votes[i, :]\n", - " print" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " For a given true upvote ratio $p$ and $N$ votes, the number of upvotes will look like a Binomial random variable with parameters $p$ and $N$. (This is because of the equivalence between upvote ratio and probability of upvoting versus downvoting, out of $N$ possible votes/trials). We create a function that performs Bayesian inference on $p$, for a particular comment's upvote/downvote pair." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import pymc as pm\n", - "\n", - "\n", - "def posterior_upvote_ratio(upvotes, downvotes, samples=20000):\n", - " \"\"\"\n", - " This function accepts the number of upvotes and downvotes a particular comment received, \n", - " and the number of posterior samples to return to the user. Assumes a uniform prior.\n", - " \"\"\"\n", - " N = upvotes + downvotes\n", - " upvote_ratio = pm.Uniform(\"upvote_ratio\", 0, 1)\n", - " observations = pm.Binomial(\"obs\", N, upvote_ratio, value=upvotes, observed=True)\n", - " # do the fitting; first do a MAP as it is cheap and useful.\n", - " map_ = pm.MAP([upvote_ratio, observations]).fit()\n", - " mcmc = pm.MCMC([upvote_ratio, observations])\n", - " mcmc.sample(samples, samples / 4)\n", - " return mcmc.trace(\"upvote_ratio\")[:]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below are the resulting posterior distributions." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[****************100%******************] 20000 of 20000 complete\n" - ] - }, - { - "data": { - "image/png": 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z5gyqq6uhra0Ne3t7BAcH4/nz57C0tGzyMzeUmZmJ3r17tzg9RVEURVGdFw0U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\nx4pSd7Xmp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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(11., 8)\n", - "posteriors = []\n", - "colours = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\", \"#CF4457\"]\n", - "for i in range(len(comments)):\n", - " j = comments[i]\n", - " posteriors.append(posterior_upvote_ratio(votes[j, 0], votes[j, 1]))\n", - " plt.hist(posteriors[i], bins=18, normed=True, alpha=.9,\n", - " histtype=\"step\", color=colours[i % 5], lw=3,\n", - " label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n", - " plt.hist(posteriors[i], bins=18, normed=True, alpha=.2,\n", - " histtype=\"stepfilled\", color=colours[i], lw=3, )\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.xlim(0, 1)\n", - "plt.title(\"Posterior distributions of upvote ratios on different comments\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Some distributions are very tight, others have very long tails (relatively speaking), expressing our uncertainty with what the true upvote ratio might be.\n", - "\n", - "### Sorting!\n", - "\n", - "We have been ignoring the goal of this exercise: how do we sort the comments from *best to worst*? Of course, we cannot sort distributions, we must sort scalar numbers. There are many ways to distill a distribution down to a scalar: expressing the distribution through its expected value, or mean, is one way. Choosing the mean is a bad choice though. This is because the mean does not take into account the uncertainty of distributions.\n", - "\n", - "I suggest using the *95% least plausible value*, defined as the value such that there is only a 5% chance the true parameter is lower (think of the lower bound on the 95% credible region). Below are the posterior distributions with the 95% least-plausible value plotted:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[3 1 2 0] [0.36980613417267094, 0.68407203257290061, 0.37551825562169117, 0.8177566237850703]\n" - ] - }, - { - "data": { - "image/png": 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G3759AdR3XIqKim9+gf9Pe+bVGCsrK+Tm5mLr1q2QlZXFV199hf79++P58+cdJhOHwxEx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\nTHZVS5y91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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "N = posteriors[0].shape[0]\n", - "lower_limits = []\n", - "\n", - "for i in range(len(comments)):\n", - " j = comments[i]\n", - " plt.hist(posteriors[i], bins=20, normed=True, alpha=.9,\n", - " histtype=\"step\", color=colours[i], lw=3,\n", - " label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n", - " plt.hist(posteriors[i], bins=20, normed=True, alpha=.2,\n", - " histtype=\"stepfilled\", color=colours[i], lw=3, )\n", - " v = np.sort(posteriors[i])[int(0.05 * N)]\n", - " # plt.vlines( v, 0, 15 , color = \"k\", alpha = 1, linewidths=3 )\n", - " plt.vlines(v, 0, 10, color=colours[i], linestyles=\"--\", linewidths=3)\n", - " lower_limits.append(v)\n", - " plt.legend(loc=\"upper left\")\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.title(\"Posterior distributions of upvote ratios on different comments\");\n", - "order = np.argsort(-np.array(lower_limits))\n", - "print order, lower_limits" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The best comments, according to our procedure, are the comments that are *most-likely* to score a high percentage of upvotes. Visually those are the comments with the 95% least plausible value close to 1.\n", - "\n", - "Why is sorting based on this quantity a good idea? By ordering by the 95% least plausible value, we are being the most conservative with what we think is best. That is, even in the worst case scenario, when we have severely overestimated the upvote ratio, we can be sure the best comments are still on top. Under this ordering, we impose the following very natural properties:\n", - "\n", - "1. given two comments with the same observed upvote ratio, we will assign the comment with more votes as better (since we are more confident it has a higher ratio).\n", - "2. given two comments with the same number of votes, we still assign the comment with more upvotes as *better*.\n", - "\n", - "### But this is too slow for real-time!\n", - "\n", - "I agree, computing the posterior of every comment takes a long time, and by the time you have computed it, likely the data has changed. I delay the mathematics to the appendix, but I suggest using the following formula to compute the lower bound very fast.\n", - "\n", - "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", - "\n", - "where \n", - "\\begin{align}\n", - "& a = 1 + u \\\\\\\\\n", - "& b = 1 + d \\\\\\\\\n", - "\\end{align}\n", - "\n", - "$u$ is the number of upvotes, and $d$ is the number of downvotes. The formula is a shortcut in Bayesian inference, which will be further explained in Chapter 6 when we discuss priors in more detail.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Approximate lower bounds:\n", - "[ 0.83167764 0.8041293 0.8166957 0.77375237 0.72491057 0.71705212\n", - " 0.72440529 0.73158407 0.67107394 0.6931046 0.66235556 0.6530083\n", - " 0.70806405 0.60091591 0.60091591 0.66278557 0.60091591 0.60091591\n", - " 0.53055613 0.53055613 0.53055613 0.53055613 0.53055613 0.43047887\n", - " 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887\n", - " 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887\n", - " 0.43047887 0.43047887 0.43047887 0.47201974 0.45074913 0.35873239\n", - " 0.3726793 0.42069919 0.33529412 0.27775794 0.27775794 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.13104878 0.13104878 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794]\n", - "\n", - "Top 40 Sorted according to approximate lower bounds:\n", - "\n", - "327 52 Can you imagine having to start that? I've fired up much smaller equipment when its around 0° out and its still a pain. It would probably take a crew of guys hours to get that going. Do they have built in heaters to make it easier? You'd think they would just let them idle overnight if they planned on running it the next day though.\n", - "-------------\n", - "120 18 Actually it does not look frozen just covered in a layer of wind packed snow.\n", - "-------------\n", - "70 10 That's actually just the skin of a mining truck. They shed it periodically like snakes do.\n", - "-------------\n", - "76 14 The model just hasn't been textured yet!\n", - "-------------\n", - "21 3 No worries, [this](http://imgur.com/KeSYJud) will help.\n", - "-------------\n", - "7 0 Dammit Elsa I told you not to drink and drive.\n", - "-------------\n", - "88 23 Speaking of mining...[BAGGER 288!](http://www.youtube.com/watch?v=azEvfD4C6ow)\n", - "-------------\n", - "112 32 Wonder why OP has 31,944 link karma but so few submissions? /u/zkool may have the worst case of karma addiction I'm aware of.\n", - "\n", - "title | points | age | /r/ | comnts\n", - ":--|:--|:--|:--|:--\n", - "[Frozen mining truck](http://www.reddit.com/r/pics/comments/1mrqvh/frozen_mining_truck/) | 2507 | 4^mos | pics | 164\n", - "[Frozen mining truck](http://www.reddit.com/r/pics/comments/1cutbw/frozen_mining_truck/) | 16 | 9^mos | pics | 4\n", - "[Frozen mining truck](http://www.reddit.com/r/pics/comments/vvcrv/frozen_mining_truck/) | 439 | 1^yr | pics | 21\n", - "[Meanwhile, in New Zealand...](http://www.reddit.com/r/pics/comments/ir1pl/meanwhile_in_new_zealand/) | 39 | 2^yrs | pics | 12\n", - "[Blizzardy day](http://www.reddit.com/r/pics/comments/1uiu3y/blizzardy_day/) | 7 | 19^dys | pics | 3\n", - "\n", - "*[Source: karmadecay](http://karmadecay.com/r/pics/comments/1w454i/frozen_mining_truck/)*\n", - "-------------\n", - "11 1 This is what it's typically like, living in Alberta.\n", - "-------------\n", - "6 0 That'd be a haul truck. Looks like a CAT 793. We run em at the site I work at, 240ton carrying capacity. \n", - "-------------\n", - "22 5 Taken in Fort Mcmurray Ab!\n", - "-------------\n", - "9 1 \"EXCLUSIVE: First look at \"Hoth\" from the upcoming 'Star Wars: Episode VII'\"\n", - "-------------\n", - "32 9 This is the most fun thing to drive in GTA V.\n", - "-------------\n", - "5 0 it reminds me of the movie \"moon\" with sam rockwell.\n", - "-------------\n", - "4 0 Also frozen drill rig.\n", - "-------------\n", - "4 0 There's just something awesome about a land vehicle so huge that it warrants a set of stairs on the front of it. I find myself wishing I were licensed to drive it.\n", - "-------------\n", - "4 0 Heaters all over the components needing heat: \n", - "http://www.arctic-fox.com/fuel-fluid-warming-products/diesel-fired-coolant-pre-heaters\n", - "-------------\n", - "4 0 Or it is just an amazing snow sculpture!\n", - "-------------\n", - "3 0 I have to tell people about these awful conditions... Too bad I'm Snowden.\n", - "-------------\n", - "3 0 Someone let it go\n", - "-------------\n", - "3 0 Elsa, you can't do that to people's trucks.\n", - "-------------\n", - "3 0 woo Alberta represent\n", - "-------------\n", - "3 0 Just thaw it with love\n", - "-------------\n", - "6 2 Looks like the drill next to it is an IR DM30 or DM45. Good rigs. \n", - "-------------\n", - "4 1 That's the best snow sculpture I've ever seen. \n", - "-------------\n", - "2 0 [These](http://i.imgur.com/xYuwk5I.jpg) are used for removing the ice.\n", - "-------------\n", - "2 0 Nigger\n", - "-------------\n", - "2 0 Please someone post frozen Bagger 288\n", - "-------------\n", - "2 0 It's kind of cool there are trucks so big they need both a ladder and a staircase to get into them.\n", - "-------------\n", - "2 0 Eight miners are just out of frame hiding inside a tauntaun.\n", - "-------------\n", - "2 0 http://imgur.com/gallery/Fxv3Oh7\n", - "-------------\n", - "2 0 BRAZZERS.\n", - "-------------\n", - "2 0 It would take a god damn week just to warm that thing up.\n", - "-------------\n", - "2 0 Maybe /r/Bitcoin can use some of their mining equipment to heat this guy up!\n", - "-------------\n", - "2 0 Checkmate Jackie Chan\n", - "-------------\n", - "2 0 I've seen this picture before in a Duratray (the dump box supplier) brochure. If I recall it was either at Ekati or Diavik... In which case the truck could be either a Komatsu or a CAT... anyone care to comment?\n", - "-------------\n", - "2 0 The Texas snow has really hit hard!\n", - "-------------\n", - "2 0 I'm going to take a wild guess and say the diesel is gelled.\n", - "-------------\n", - "2 0 Do these trucks remind anyone else of Sly Cooper?\n", - "-------------\n", - "2 0 cool\n", - "-------------\n" - ] - } - ], - "source": [ - "def intervals(u, d):\n", - " a = 1. + u\n", - " b = 1. + d\n", - " mu = a / (a + b)\n", - " std_err = 1.65 * np.sqrt((a * b) / ((a + b) ** 2 * (a + b + 1.)))\n", - " return (mu, std_err)\n", - "\n", - "print \"Approximate lower bounds:\"\n", - "posterior_mean, std_err = intervals(votes[:, 0], votes[:, 1])\n", - "lb = posterior_mean - std_err\n", - "print lb\n", - "print\n", - "print \"Top 40 Sorted according to approximate lower bounds:\"\n", - "print\n", - "order = np.argsort(-lb)\n", - "ordered_contents = []\n", - "for i in order[:40]:\n", - " ordered_contents.append(contents[i])\n", - " print votes[i, 0], votes[i, 1], contents[i]\n", - " print \"-------------\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can view the ordering visually by plotting the posterior mean and bounds, and sorting by the lower bound. In the plot below, notice that the left error-bar is sorted (as we suggested this is the best way to determine an ordering), so the means, indicated by dots, do not follow any strong pattern. " - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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Ojhw/fhw/Pz9iYmIICwsjPj6e4OBglft+/Pgx5ubmrFixgq1bt0q7qpdV9j4/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/xz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\nnRwcHDhz5ky5Nffq1QsAJycntm7dCkB8fLzUGOjSpQvm5ublnrt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AAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "r_order = order[::-1][-40:]\n", - "plt.errorbar(posterior_mean[r_order], np.arange(len(r_order)),\n", - " xerr=std_err[r_order], xuplims=True, capsize=0, fmt=\"o\",\n", - " color=\"#7A68A6\")\n", - "plt.xlim(0.3, 1)\n", - "plt.yticks(np.arange(len(r_order) - 1, -1, -1), map(lambda x: x[:30].replace(\"\\n\", \"\"), ordered_contents));" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the graphic above, you can see why sorting by mean would be sub-optimal." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Extension to Starred rating systems\n", - "\n", - "The above procedure works well for upvote-downvotes schemes, but what about systems that use star ratings, e.g. 5 star rating systems. Similar problems apply with simply taking the average: an item with two perfect ratings would beat an item with thousands of perfect ratings, but a single sub-perfect rating. \n", - "\n", - "\n", - "We can consider the upvote-downvote problem above as binary: 0 is a downvote, 1 if an upvote. A $N$-star rating system can be seen as a more continuous version of above, and we can set $n$ stars rewarded is equivalent to rewarding $\\frac{n}{N}$. For example, in a 5-star system, a 2 star rating corresponds to 0.4. A perfect rating is a 1. We can use the same formula as before, but with $a,b$ defined differently:\n", - "\n", - "\n", - "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", - "\n", - "where \n", - "\n", - "\\begin{align}\n", - "& a = 1 + S \\\\\\\\\n", - "& b = 1 + N - S \\\\\\\\\n", - "\\end{align}\n", - "\n", - "where $N$ is the number of users who rated, and $S$ is the sum of all the ratings, under the equivalence scheme mentioned above. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Counting Github stars\n", - "\n", - "What is the average number of stars a Github repository has? How would you calculate this? There are over 6 million repositories, so there is more than enough data to invoke the Law of Large numbers. Let's start pulling some data. TODO" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Conclusion\n", - "\n", - "While the Law of Large Numbers is cool, it is only true so much as its name implies: with large sample sizes only. We have seen how our inference can be affected by not considering *how the data is shaped*. \n", - "\n", - "1. By (cheaply) drawing many samples from the posterior distributions, we can ensure that the Law of Large Number applies as we approximate expected values (which we will do in the next chapter).\n", - "\n", - "2. Bayesian inference understands that with small sample sizes, we can observe wild randomness. Our posterior distribution will reflect this by being more spread rather than tightly concentrated. Thus, our inference should be correctable.\n", - "\n", - "3. There are major implications of not considering the sample size, and trying to sort objects that are unstable leads to pathological orderings. The method provided above solves this problem.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Appendix\n", - "\n", - "##### Derivation of sorting comments formula\n", - "\n", - "Basically what we are doing is using a Beta prior (with parameters $a=1, b=1$, which is a uniform distribution), and using a Binomial likelihood with observations $u, N = u+d$. This means our posterior is a Beta distribution with parameters $a' = 1 + u, b' = 1 + (N - u) = 1+d$. We then need to find the value, $x$, such that 0.05 probability is less than $x$. This is usually done by inverting the CDF ([Cumulative Distribution Function](http://en.wikipedia.org/wiki/Cumulative_Distribution_Function)), but the CDF of the beta, for integer parameters, is known but is a large sum [3]. \n", - "\n", - "We instead use a Normal approximation. The mean of the Beta is $\\mu = a'/(a'+b')$ and the variance is \n", - "\n", - "$$\\sigma^2 = \\frac{a'b'}{ (a' + b')^2(a'+b'+1) }$$\n", - "\n", - "Hence we solve the following equation for $x$ and have an approximate lower bound. \n", - "\n", - "$$ 0.05 = \\Phi\\left( \\frac{(x - \\mu)}{\\sigma}\\right) $$ \n", - "\n", - "$\\Phi$ being the [cumulative distribution for the normal distribution](http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution)\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Exercises\n", - "\n", - "1\\. How would you estimate the quantity $E\\left[ \\cos{X} \\right]$, where $X \\sim \\text{Exp}(4)$? What about $E\\left[ \\cos{X} | X \\lt 1\\right]$, i.e. the expected value *given* we know $X$ is less than 1? Would you need more samples than the original samples size to be equally accurate?" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Enter code here\n", - "import scipy.stats as stats\n", - "exp = stats.expon(scale=4)\n", - "N = 1e5\n", - "X = exp.rvs(N)\n", - "# ..." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\\. The following table was located in the paper \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression\" [2]. The table ranks football field-goal kickers by their percent of non-misses. What mistake have the researchers made?\n", - "\n", - "-----\n", - "\n", - "#### Kicker Careers Ranked by Make Percentage\n", - "
Rank Kicker Make % Number of Kicks
1 Garrett Hartley 87.7 57
2 Matt Stover 86.8 335
3 Robbie Gould 86.2 224
4 Rob Bironas 86.1 223
5 Shayne Graham 85.4 254
51 Dave Rayner 72.2 90
52 Nick Novak 71.9 64
53 Tim Seder 71.0 62
54 Jose Cortez 70.7 75
55 Wade Richey 66.1 56
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In August 2013, [a popular post](http://bpodgursky.wordpress.com/2013/08/21/average-income-per-programming-language/) on the average income per programmer of different languages was trending. Here's the summary chart: (reproduced without permission, cause when you lie with stats, you gunna get the hammer). What do you notice about the extremes?\n", - "\n", - "------\n", - "\n", - "#### Average household income by programming language\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
LanguageAverage Household Income ($)Data Points
Puppet87,589.29112
Haskell89,973.82191
PHP94,031.19978
CoffeeScript94,890.80435
VimL94,967.11532
Shell96,930.54979
Lua96,930.69101
Erlang97,306.55168
Clojure97,500.00269
Python97,578.872314
JavaScript97,598.753443
Emacs Lisp97,774.65355
C#97,823.31665
Ruby98,238.743242
C++99,147.93845
CSS99,881.40527
Perl100,295.45990
C100,766.512120
Go101,158.01231
Scala101,460.91243
ColdFusion101,536.70109
Objective-C101,801.60562
Groovy102,650.86116
Java103,179.391402
XSLT106,199.19123
ActionScript108,119.47113
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "\n", - "1. Wainer, Howard. *The Most Dangerous Equation*. American Scientist, Volume 95.\n", - "2. Clarck, Torin K., Aaron W. Johnson, and Alexander J. Stimpson. \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression.\" (2013): n. page. [Web](http://www.sloansportsconference.com/wp-content/uploads/2013/Going%20for%20Three%20Predicting%20the%20Likelihood%20of%20Field%20Goal%20Success%20with%20Logistic%20Regression.pdf). 20 Feb. 2013.\n", - "3. http://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.10" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/Chapter4_TheGreatestTheoremNeverTold/top_pic_comments.py b/Chapter4_TheGreatestTheoremNeverTold/top_pic_comments.py deleted file mode 100644 index 75b95d3e..00000000 --- a/Chapter4_TheGreatestTheoremNeverTold/top_pic_comments.py +++ /dev/null @@ -1,63 +0,0 @@ -import sys - -import numpy as np -from IPython.core.display import Image - -import praw - - -reddit = praw.Reddit("BayesianMethodsForHackers") -subreddit = reddit.get_subreddit( "pics" ) - -top_submissions = subreddit.get_top() - - -n_pic = int( sys.argv[1] ) if len(sys.argv) > 1 else 1 - -i = 0 -while i < n_pic: - top_submission = top_submissions.next() - while "i.imgur.com" not in top_submission.url: - #make sure it is linking to an image, not a webpage. - top_submission = top_submissions.next() - i+=1 - -print "Title of submission: \n", top_submission.title -top_post_url = top_submission.url -#top_submission.replace_more_comments(limit=5, threshold=0) -print top_post_url - -upvotes = [] -downvotes = [] -contents = [] -_all_comments = top_submission.comments -all_comments=[] -for comment in _all_comments: - try: - upvotes.append( comment.ups ) - downvotes.append( comment.downs ) - contents.append( comment.body ) - except Exception as e: - continue - -votes = np.array( [ upvotes, downvotes] ).T - - - - - - - - - - - - - - - - - - - - diff --git a/Chapter4_TheGreatestTheoremNeverTold/top_showerthoughts_submissions.py b/Chapter4_TheGreatestTheoremNeverTold/top_showerthoughts_submissions.py new file mode 100644 index 00000000..90df9644 --- /dev/null +++ b/Chapter4_TheGreatestTheoremNeverTold/top_showerthoughts_submissions.py @@ -0,0 +1,36 @@ +import sys + +import numpy as np +from IPython.core.display import Image + +import praw + + +reddit = praw.Reddit("BayesianMethodsForHackers") +subreddit = reddit.get_subreddit("showerthoughts") + +top_submissions = subreddit.get_top(limit=100) + +n_sub = int( sys.argv[1] ) if sys.argv[1] else 1 + +i = 0 +while i < n_sub: + top_submission = next(top_submissions) + i+=1 + +top_post = top_submission.title + +upvotes = [] +downvotes = [] +contents = [] + +for sub in top_submissions: + try: + ratio = reddit.get_submission(sub.permalink).upvote_ratio + ups = int(round((ratio*sub.score)/(2*ratio - 1)) if ratio != 0.5 else round(sub.score/2)) + upvotes.append(ups) + downvotes.append(ups - sub.score) + contents.append(sub.title) + except Exception as e: + continue +votes = np.array( [ upvotes, downvotes] ).T \ No newline at end of file diff --git a/Chapter5_LossFunctions/Ch5_LossFunctions_PyMC2.ipynb b/Chapter5_LossFunctions/Ch5_LossFunctions_PyMC2.ipynb new file mode 100644 index 00000000..5da1d68a --- /dev/null +++ b/Chapter5_LossFunctions/Ch5_LossFunctions_PyMC2.ipynb @@ -0,0 +1,1481 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5\n", + "____\n", + "### Would you rather lose an arm or a leg?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Statisticians can be a sour bunch. Instead of considering their winnings, they only measure how much they have lost. In fact, they consider their wins as *negative losses*. But what's interesting is *how they measure their losses.*\n", + "\n", + "For example, consider the following example:\n", + "\n", + "> A meteorologist is predicting the probability of a possible hurricane striking his city. He estimates, with 95% confidence, that the probability of it *not* striking is between 99% - 100%. He is very happy with his precision and advises the city that a major evacuation is unnecessary. Unfortunately, the hurricane does strike and the city is flooded. \n", + "\n", + "This stylized example shows the flaw in using a pure accuracy metric to measure outcomes. Using a measure that emphasizes estimation accuracy, while an appealing and *objective* thing to do, misses the point of why you are even performing the statistical inference in the first place: results of inference. The author Nassim Taleb of *The Black Swan* and *Antifragility* stresses the importance of the *payoffs* of decisions, *not the accuracy*. Taleb distills this quite succinctly: \"I would rather be vaguely right than very wrong.\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loss Functions\n", + "\n", + "We introduce what statisticians and decision theorists call *loss functions*. A loss function is a function of the true parameter, and an estimate of that parameter\n", + "\n", + "$$L( \\theta, \\hat{\\theta} ) = f( \\theta, \\hat{\\theta} )$$\n", + "\n", + "The important point of loss functions is that it measures how *bad* our current estimate is: the larger the loss, the worse the estimate is according to the loss function. A simple, and very common, example of a loss function is the *squared-error loss*:\n", + "\n", + "$$L( \\theta, \\hat{\\theta} ) = ( \\theta - \\hat{\\theta} )^2$$\n", + "\n", + "The squared-error loss function is used in estimators like linear regression, UMVUEs and many areas of machine learning. We can also consider an asymmetric squared-error loss function, something like:\n", + "\n", + "$$L( \\theta, \\hat{\\theta} ) = \\begin{cases} ( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\lt \\theta \\\\\\\\ c( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\ge \\theta, \\;\\; 0\\lt c \\lt 1 \\end{cases}$$\n", + "\n", + "\n", + "which represents that estimating a value larger than the true estimate is preferable to estimating a value below. A situation where this might be useful is in estimating web traffic for the next month, where an over-estimated outlook is preferred so as to avoid an underallocation of server resources. \n", + "\n", + "A negative property about the squared-error loss is that it puts a disproportionate emphasis on large outliers. This is because the loss increases quadratically, and not linearly, as the estimate moves away. That is, the penalty of being three units away is much less than being five units away, but the penalty is not much greater than being one unit away, though in both cases the magnitude of difference is the same:\n", + "\n", + "$$\\frac{1^2}{3^2} \\lt \\frac{3^2}{5^2}, \\;\\; \\text{although} \\;\\; 3-1 = 5-3$$\n", + "\n", + "This loss function imposes that large errors are *very* bad. A more *robust* loss function that increases linearly with the difference is the *absolute-loss*\n", + "\n", + "$$L( \\theta, \\hat{\\theta} ) = | \\theta - \\hat{\\theta} |$$\n", + "\n", + "Other popular loss functions include:\n", + "\n", + "- $L( \\theta, \\hat{\\theta} ) = \\mathbb{1}_{ \\hat{\\theta} \\neq \\theta }$ is the zero-one loss often used in machine learning classification algorithms.\n", + "- $L( \\theta, \\hat{\\theta} ) = -\\hat{\\theta}\\log( \\theta ) - (1-\\hat{ \\theta})\\log( 1 - \\theta ), \\; \\; \\hat{\\theta} \\in {0,1}, \\; \\theta \\in [0,1]$, called the *log-loss*, also used in machine learning. \n", + "\n", + "Historically, loss functions have been motivated from 1) mathematical convenience, and 2) they are robust to application, i.e., they are objective measures of loss. The first reason has really held back the full breadth of loss functions. With computers being agnostic to mathematical convenience, we are free to design our own loss functions, which we take full advantage of later in this Chapter.\n", + "\n", + "With respect to the second point, the above loss functions are indeed objective, in that they are most often a function of the difference between estimate and true parameter, independent of signage or payoff of choosing that estimate. This last point, its independence of payoff, causes quite pathological results though. Consider our hurricane example above: the statistician equivalently predicted that the probability of the hurricane striking was between 0% to 1%. But if he had ignored being precise and instead focused on outcomes (99% chance of no flood, 1% chance of flood), he might have advised differently. \n", + "\n", + "By shifting our focus from trying to be incredibly precise about parameter estimation to focusing on the outcomes of our parameter estimation, we can customize our estimates to be optimized for our application. This requires us to design new loss functions that reflect our goals and outcomes. Some examples of more interesting loss functions:\n", + "\n", + "\n", + "- $L( \\theta, \\hat{\\theta} ) = \\frac{ | \\theta - \\hat{\\theta} | }{ \\theta(1-\\theta) }, \\; \\; \\hat{\\theta}, \\theta \\in [0,1]$ emphasizes an estimate closer to 0 or 1 since if the true value $\\theta$ is near 0 or 1, the loss will be *very* large unless $\\hat{\\theta}$ is similarly close to 0 or 1. \n", + "This loss function might be used by a political pundit who's job requires him or her to give confident \"Yes/No\" answers. This loss reflects that if the true parameter is close to 1 (for example, if a political outcome is very likely to occur), he or she would want to strongly agree as to not look like a skeptic. \n", + "\n", + "- $L( \\theta, \\hat{\\theta} ) = 1 - \\exp \\left( -(\\theta - \\hat{\\theta} )^2 \\right)$ is bounded between 0 and 1 and reflects that the user is indifferent to sufficiently-far-away estimates. It is similar to the zero-one loss above, but not quite as penalizing to estimates that are close to the true parameter. \n", + "- Complicated non-linear loss functions can programmed: \n", + "\n", + " def loss(true_value, estimate):\n", + " if estimate*true_value > 0:\n", + " return abs(estimate - true_value)\n", + " else:\n", + " return abs(estimate)*(estimate - true_value)**2\n", + " \n", + "\n", + "\n", + "- Another example is from the book *The Signal and The Noise*. Weather forecasters have a interesting loss function for their predictions. [2]\n", + "\n", + "\n", + "> People notice one type of mistake — the failure to predict rain — more than other, false alarms. If it rains when it isn't supposed to, they curse the weatherman for ruining their picnic, whereas an unexpectedly sunny day is taken as a serendipitous bonus.\n", + "\n", + "> [The Weather Channel's bias] is limited to slightly exaggerating the probability of rain when it is unlikely to occur — saying there is a 20 percent change when they know it is really a 5 or 10 percent chance — covering their butts in the case of an unexpected sprinkle.\n", + "\n", + "\n", + "As you can see, loss functions can be used for good and evil: with great power, comes great — well you know.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loss functions in the real world\n", + "\n", + "So far we have been under the unrealistic assumption that we know the true parameter. Of course if we knew the true parameter, bothering to guess an estimate is pointless. Hence a loss function is really only practical when the true parameter is unknown. \n", + "\n", + "In Bayesian inference, we have a mindset that the unknown parameters are really random variables with prior and posterior distributions. Concerning the posterior distribution, a value drawn from it is a *possible* realization of what the true parameter could be. Given that realization, we can compute a loss associated with an estimate. As we have a whole distribution of what the unknown parameter could be (the posterior), we should be more interested in computing the *expected loss* given an estimate. This expected loss is a better estimate of the true loss than comparing the given loss from only a single sample from the posterior.\n", + "\n", + "First it will be useful to explain a *Bayesian point estimate*. The systems and machinery present in the modern world are not built to accept posterior distributions as input. It is also rude to hand someone over a distribution when all they asked for was an estimate. In the course of an individual's day, when faced with uncertainty we still act by distilling our uncertainty down to a single action. Similarly, we need to distill our posterior distribution down to a single value (or vector in the multivariate case). If the value is chosen intelligently, we can avoid the flaw of frequentist methodologies that mask the uncertainty and provide a more informative result.The value chosen, if from a Bayesian posterior, is a Bayesian point estimate. \n", + "\n", + "Suppose $P(\\theta | X)$ is the posterior distribution of $\\theta$ after observing data $X$, then the following function is understandable as the *expected loss of choosing estimate $\\hat{\\theta}$ to estimate $\\theta$*:\n", + "\n", + "$$ l(\\hat{\\theta} ) = E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", + "\n", + "This is also known as the *risk* of estimate $\\hat{\\theta}$. The subscript $\\theta$ under the expectation symbol is used to denote that $\\theta$ is the unknown (random) variable in the expectation, something that at first can be difficult to consider.\n", + "\n", + "We spent all of last chapter discussing how to approximate expected values. Given $N$ samples $\\theta_i,\\; i=1,...,N$ from the posterior distribution, and a loss function $L$, we can approximate the expected loss of using estimate $\\hat{\\theta}$ by the Law of Large Numbers:\n", + "\n", + "$$\\frac{1}{N} \\sum_{i=1}^N \\;L(\\theta_i, \\hat{\\theta} ) \\approx E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] = l(\\hat{\\theta} ) $$\n", + "\n", + "Notice that measuring your loss via an *expected value* uses more information from the distribution than the MAP estimate which, if you recall, will only find the maximum value of the distribution and ignore the shape of the distribution. Ignoring information can over-expose yourself to tail risks, like the unlikely hurricane, and leaves your estimate ignorant of how ignorant you really are about the parameter.\n", + "\n", + "Similarly, compare this with frequentist methods, that traditionally only aim to minimize the error, and do not consider the *loss associated with the result of that error*. Compound this with the fact that frequentist methods are almost guaranteed to never be absolutely accurate. Bayesian point estimates fix this by planning ahead: your estimate is going to be wrong, you might as well err on the right side of wrong." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Optimizing for the *Showcase* on *The Price is Right*\n", + "\n", + "Bless you if you are ever chosen as a contestant on the Price is Right, for here we will show you how to optimize your final price on the *Showcase*. For those who forget the rules:\n", + "\n", + "\n", + "1. Two contestants compete in *The Showcase*. \n", + "2. Each contestant is shown a unique suite of prizes.\n", + "3. After the viewing, the contestants are asked to bid on the price for their unique suite of prizes.\n", + "4. If a bid price is over the actual price, the bid's owner is disqualified from winning.\n", + "5. If a bid price is under the true price by less than $250, the winner is awarded both prizes.\n", + "\n", + "The difficulty in the game is balancing your uncertainty in the prices, keeping your bid low enough so as to not bid over, and trying to bid close to the price.\n", + "\n", + "Suppose we have recorded the *Showcases* from previous *The Price is Right* episodes and have *prior* beliefs about what distribution the true price follows. For simplicity, suppose it follows a Normal:\n", + "\n", + "\n", + "$$\\text{True Price} \\sim \\text{Normal}(\\mu_p, \\sigma_p )$$\n", + "\n", + "\n", + "In a later chapter, we will actually use *real Price is Right Showcase data* to form the historical prior, but this requires some advanced PyMC use so we will not use it here. For now, we will assume $\\mu_p = 35 000$ and $\\sigma_p = 7500$.\n", + "\n", + "We need a model of how we should be playing the *Showcase*. For each prize in the prize suite, we have an idea of what it might cost, but this guess could differ significantly from the true price. (Couple this with increased pressure being onstage and you can see why some bids are so wildly off). Let's suppose your beliefs about the prices of prizes also follow Normal distributions:\n", + "\n", + "$$ \\text{Prize}_i \\sim \\text{Normal}(\\mu_i, \\sigma_i ),\\;\\; i=1,2$$\n", + "\n", + "This is really why Bayesian analysis is great: we can specify what we think a fair price is through the $\\mu_i$ parameter, and express uncertainty of our guess in the $\\sigma_i$ parameter. \n", + "\n", + "We'll assume two prizes per suite for brevity, but this can be extended to any number. \n", + "The true price of the prize suite is then given by $\\text{Prize}_1 + \\text{Prize}_2 + \\epsilon$, \n", + "where $\\epsilon$ is some error term.\n", + "\n", + "We are interested in the updated $\\text{True Price}$ given we have observed both prizes and have belief distributions about them. We can perform this using PyMC. \n", + "\n", + "Lets make some values concrete. Suppose there are two prizes in the observed prize suite: \n", + "\n", + "1. A trip to wonderful Toronto, Canada! \n", + "2. A lovely new snowblower!\n", + "\n", + "We have some guesses about the true prices of these objects, but we are also pretty uncertain about them. I can express this uncertainty through the parameters of the Normals:\n", + "\n", + "\n", + "\\begin{align}\n", + "& \\text{snowblower} \\sim \\text{Normal}(3 000, 500 )\\\\\\\\\n", + "& \\text{Toronto} \\sim \\text{Normal}(12 000, 3000 )\\\\\\\\\n", + "\\end{align}\n", + "\n", + "For example, I believe that the true price of the trip to Toronto is 12 000 dollars, and that there is a 68.2% chance the price falls 1 standard deviation away from this, i.e. my confidence is that there is a 68.2% chance the trip is in [9 000, 15 000].\n", + "\n", + "We can create some PyMC code to perform inference on the true price of the suite." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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lkz5MeyjNX/68jqZqL7n8uVw4v47Ino1A+X9ftaxlu5Y3b95MOBwGoK2tjbPP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XcDnwD2icgecpffvsTZbYr3WeBfABe5FUd+P53PRRXNt9G+ok7vb4F/ExE7cIzchpxWtL+oMYwx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\nffd1+zRMnyoX65w+Mcf46UU816dWdSkt1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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import scipy.stats as stats\n", + "from IPython.core.pylabtools import figsize\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "figsize(12.5, 9)\n", + "\n", + "norm_pdf = stats.norm.pdf\n", + "\n", + "plt.subplot(311)\n", + "x = np.linspace(0, 60000, 200)\n", + "sp1 = plt.fill_between(x, 0, norm_pdf(x, 35000, 7500),\n", + " color=\"#348ABD\", lw=3, alpha=0.6,\n", + " label=\"historical total prices\")\n", + "p1 = plt.Rectangle((0, 0), 1, 1, fc=sp1.get_facecolor()[0])\n", + "plt.legend([p1], [sp1.get_label()])\n", + "\n", + "plt.subplot(312)\n", + "x = np.linspace(0, 10000, 200)\n", + "sp2 = plt.fill_between(x, 0, norm_pdf(x, 3000, 500),\n", + " color=\"#A60628\", lw=3, alpha=0.6,\n", + " label=\"snowblower price guess\")\n", + "\n", + "p2 = plt.Rectangle((0, 0), 1, 1, fc=sp2.get_facecolor()[0])\n", + "plt.legend([p2], [sp2.get_label()])\n", + "\n", + "plt.subplot(313)\n", + "x = np.linspace(0, 25000, 200)\n", + "sp3 = plt.fill_between(x, 0, norm_pdf(x, 12000, 3000),\n", + " color=\"#7A68A6\", lw=3, alpha=0.6,\n", + " label=\"Trip price guess\")\n", + "plt.autoscale(tight=True)\n", + "p3 = plt.Rectangle((0, 0), 1, 1, fc=sp3.get_facecolor()[0])\n", + "plt.legend([p3], [sp3.get_label()]);" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 50000 of 50000 complete in 8.0 sec" + ] + } + ], + "source": [ + "import pymc as pm\n", + "\n", + "data_mu = [3e3, 12e3]\n", + "\n", + "data_std = [5e2, 3e3]\n", + "\n", + "mu_prior = 35e3\n", + "std_prior = 75e2\n", + "\n", + "true_price = pm.Normal(\"true_price\", mu_prior, 1.0 / std_prior ** 2)\n", + "\n", + "\n", + "prize_1 = pm.Normal(\"first_prize\", data_mu[0], 1.0 / data_std[0] ** 2)\n", + "prize_2 = pm.Normal(\"second_prize\", data_mu[1], 1.0 / data_std[1] ** 2)\n", + "price_estimate = prize_1 + prize_2\n", + "\n", + "\n", + "@pm.potential\n", + "def error(true_price=true_price, price_estimate=price_estimate):\n", + " return pm.normal_like(true_price, price_estimate, 1 / (3e3) ** 2)\n", + "\n", + "\n", + "mcmc = pm.MCMC([true_price, prize_1, prize_2, price_estimate, error])\n", + "mcmc.sample(50000, 10000)\n", + "\n", + "price_trace = mcmc.trace(\"true_price\")[:]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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X+7dd4ZzbE7StrXPuLOdcY+dcvHMu3Tn3nXOujnOus3Ouu3Ouh3Pu71VzGrzh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\n5WRQYIwxfmbBgLkdLS0tvP766zQ0NPDuu++iqgA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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "import scipy.stats as stats\n", + "\n", + "x = np.linspace(5000, 40000)\n", + "plt.plot(x, stats.norm.pdf(x, 35000, 7500), c=\"k\", lw=2,\n", + " label=\"prior dist. of suite price\")\n", + "\n", + "_hist = plt.hist(price_trace, bins=35, normed=True, histtype=\"stepfilled\")\n", + "plt.title(\"Posterior of the true price estimate\")\n", + "plt.vlines(mu_prior, 0, 1.1 * np.max(_hist[0]), label=\"prior's mean\",\n", + " linestyles=\"--\")\n", + "plt.vlines(price_trace.mean(), 0, 1.1 * np.max(_hist[0]),\n", + " label=\"posterior's mean\", linestyles=\"-.\")\n", + "plt.legend(loc=\"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that because of our two observed prizes and subsequent guesses (including uncertainty about those guesses), we shifted our mean price estimate down about $15 000 dollars from the previous mean price.\n", + "\n", + "A frequentist, seeing the two prizes and having the same beliefs about their prices, would bid $\\mu_1 + \\mu_2 = 35000$, regardless of any uncertainty. Meanwhile, the *naive Bayesian* would simply pick the mean of the posterior distribution. But we have more information about our eventual outcomes; we should incorporate this into our bid. We will use the loss function above to find the *best* bid (*best* according to our loss).\n", + "\n", + "What might a contestant's loss function look like? I would think it would look something like:\n", + "\n", + " def showcase_loss(guess, true_price, risk=80000):\n", + " if true_price < guess:\n", + " return risk\n", + " elif abs(true_price - guess) <= 250:\n", + " return -2*np.abs(true_price)\n", + " else:\n", + " return np.abs(true_price - guess - 250)\n", + "\n", + "where `risk` is a parameter that defines of how bad it is if your guess is over the true price. A lower `risk` means that you are more comfortable with the idea of going over. If we do bid under and the difference is less than $250, we receive both prizes (modeled here as receiving twice the original prize). Otherwise, when we bid under the `true_price` we want to be as close as possible, hence the `else` loss is a increasing function of the distance between the guess and true price." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For every possible bid, we calculate the *expected loss* associated with that bid. We vary the `risk` parameter to see how it affects our loss:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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zj3/8g1GjRpXY5rbbbqNnz5589tlnDB06lL/85S/Ex8cTExNDXFwc33zzTakB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XOIvOGFgEyGdz5l1UX87sMHKK7Mo3tyBj//wd8JDgpttuM1VVlxDZ8t2kvu8XIAouNCGDGhB70y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\nIEKsdRGJpa0kli4J18FSc/fqBZU0bYwhVfDoTxfpyxTpT5foz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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 7)\n", + "# numpy friendly showdown_loss\n", + "\n", + "\n", + "def showdown_loss(guess, true_price, risk=80000):\n", + " loss = np.zeros_like(true_price)\n", + " ix = true_price < guess\n", + " loss[~ix] = np.abs(guess - true_price[~ix])\n", + " close_mask = [abs(true_price - guess) <= 250]\n", + " loss[close_mask] = -2 * true_price[close_mask]\n", + " loss[ix] = risk\n", + " return loss\n", + "\n", + "\n", + "guesses = np.linspace(5000, 50000, 70)\n", + "risks = np.linspace(30000, 150000, 6)\n", + "expected_loss = lambda guess, risk: \\\n", + " showdown_loss(guess, price_trace, risk).mean()\n", + "\n", + "for _p in risks:\n", + " results = [expected_loss(_g, _p) for _g in guesses]\n", + " plt.plot(guesses, results, label=\"%d\" % _p)\n", + "\n", + "plt.title(\"Expected loss of different guesses, \\nvarious risk-levels of \\\n", + "overestimating\")\n", + "plt.legend(loc=\"upper left\", title=\"Risk parameter\")\n", + "plt.xlabel(\"price bid\")\n", + "plt.ylabel(\"expected loss\")\n", + "plt.xlim(5000, 30000);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Minimizing our losses\n", + "\n", + "It would be wise to choose the estimate that minimizes our expected loss. This corresponds to the minimum point on each of the curves above. More formally, we would like to minimize our expected loss by finding the solution to\n", + "\n", + "$$ \\text{arg} \\min_{\\hat{\\theta}} \\;\\;E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", + "\n", + "The minimum of the expected loss is called the *Bayes action*. We can solve for the Bayes action using Scipy's optimization routines. The function in `fmin` in `scipy.optimize` module uses an intelligent search to find a minimum (not necessarily a *global* minimum) of any uni- or multivariate function. For most purposes, `fmin` will provide you with a good answer. \n", + "\n", + "We'll compute the minimum loss for the *Showcase* example above:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum at risk 30000: 14068.38\n", + "minimum at risk 54000: 12967.09\n", + "minimum at risk 78000: 12031.03\n", + "minimum at risk 102000: 11991.21\n", + "minimum at risk 126000: 11803.17\n", + "minimum at risk 150000: 11803.17\n" + ] + }, + { + "data": { + "image/png": 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4qWxlwUlNbV8G31NS20rfngxARLuGxabxBA7baTLXzwEg/PIyb9NRZVm57VuW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import scipy.optimize as sop\n", + "\n", + "ax = plt.subplot(111)\n", + "\n", + "\n", + "for _p in risks:\n", + " _color = next(ax._get_lines.prop_cycler)\n", + " _min_results = sop.fmin(expected_loss, 15000, args=(_p,),disp = False)\n", + " _results = [expected_loss(_g, _p) for _g in guesses]\n", + " plt.plot(guesses, _results , color = _color['color'])\n", + " plt.scatter(_min_results, 0, s = 60, \\\n", + " color= _color['color'], label = \"%d\"%_p)\n", + " plt.vlines(_min_results, 0, 120000, color = _color['color'], linestyles=\"--\")\n", + " print(\"minimum at risk %d: %.2f\" % (_p, _min_results))\n", + "\n", + "plt.title(\"Expected loss & Bayes actions of different guesses, \\n \\\n", + "various risk-levels of overestimating\")\n", + "plt.legend(loc=\"upper left\", scatterpoints=1, title=\"Bayes action at risk:\")\n", + "plt.xlabel(\"price guess\")\n", + "plt.ylabel(\"expected loss\")\n", + "plt.xlim(7000, 30000)\n", + "plt.ylim(-1000, 80000);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As intuition suggests, as we decrease the risk threshold (care about overbidding less), we increase our bid, willing to edge closer to the true price. It is interesting how far away our optimized loss is from the posterior mean, which was about 20 000. \n", + "\n", + "Suffice to say, in higher dimensions being able to eyeball the minimum expected loss is impossible. Hence why we require use of Scipy's `fmin` function.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "______\n", + "\n", + "### Shortcuts\n", + "\n", + "For some loss functions, the Bayes action is known in closed form. We list some of them below:\n", + "\n", + "- If using the mean-squared loss, the Bayes action is the mean of the posterior distribution, i.e. the value \n", + "$$ E_{\\theta}\\left[ \\theta \\right] $$\n", + "\n", + "> minimizes $E_{\\theta}\\left[ \\; (\\theta - \\hat{\\theta})^2 \\; \\right]$. Computationally this requires us to calculate the average of the posterior samples [See chapter 4 on The Law of Large Numbers]\n", + "\n", + "- Whereas the *median* of the posterior distribution minimizes the expected absolute-loss. The sample median of the posterior samples is an appropriate and very accurate approximation to the true median.\n", + "\n", + "- In fact, it is possible to show that the MAP estimate is the solution to using a loss function that shrinks to the zero-one loss.\n", + "\n", + "\n", + "Maybe it is clear now why the first-introduced loss functions are used most often in the mathematics of Bayesian inference: no complicated optimizations are necessary. Luckily, we have machines to do the complications for us. \n", + "\n", + "## Machine Learning via Bayesian Methods\n", + "\n", + "Whereas frequentist methods strive to achieve the best precision about all possible parameters, machine learning cares to achieve the best *prediction* among all possible parameters. Of course, one way to achieve accurate predictions is to aim for accurate predictions, but often your prediction measure and what frequentist methods are optimizing for are very different. \n", + "\n", + "For example, least-squares linear regression is the most simple active machine learning algorithm. I say active as it engages in some learning, whereas predicting the sample mean is technically *simpler*, but is learning very little if anything. The loss that determines the coefficients of the regressors is a squared-error loss. On the other hand, if your prediction loss function (or score function, which is the negative loss) is not a squared-error, like AUC, ROC, precision, etc., your least-squares line will not be optimal for the prediction loss function. This can lead to prediction results that are suboptimal. \n", + "\n", + "Finding Bayes actions is equivalent to finding parameters that optimize *not parameter accuracy* but an arbitrary performance measure, however we wish to define performance (loss functions, AUC, ROC, precision/recall etc.).\n", + "\n", + "The next two examples demonstrate these ideas. The first example is a linear model where we can choose to predict using the least-squares loss or a novel, outcome-sensitive loss. \n", + "\n", + "The second example is adapted from a Kaggle data science project. The loss function associated with our predictions is incredibly complicated. \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Financial prediction\n", + "\n", + "\n", + "Suppose the future return of a stock price is very small, say 0.01 (or 1%). We have a model that predicts the stock's future price, and our profit and loss is directly tied to us acting on the prediction. How should we measure the loss associated with the model's predictions, and subsequent future predictions? A squared-error loss is agnostic to the signage and would penalize a prediction of -0.01 equally as bad a prediction of 0.03:\n", + "\n", + "$$ (0.01 - (-0.01))^2 = (0.01 - 0.03)^2 = 0.004$$\n", + "\n", + "If you had made a bet based on your model's prediction, you would have earned money with a prediction of 0.03, and lost money with a prediction of -0.01, yet our loss did not capture this. We need a better loss that takes into account the *sign* of the prediction and true value. We design a new loss that is better for financial applications below:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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qjP+a0sXLmd4+zfX0B3vTKLOytyAKhUJhKWRZGb/tP6qnXXp1ofF9zvUokUKh\nUChqQqP6FqC2uZnPvykvhnmxPy2X4lLJqYtX+PlUToVoQIqKNFT/07pA6dZyKN1ahksHTxDa9D4A\nbJvY8UB4WD1LZH3Ux7P72L8O12p7P0d0rtX2FArFndNgZ/4BPJs14ekO7nr601/SKSgqrUeJFA0R\nFxcXfTdKheJeoKy4hKyfr7ukuPbvTiNHh3qUSKFQKBQ1xeqM/5r4/JvydAc3HnBsDMClayWsPHTe\nEmJZBcr/VHEvop7b2idnz0GKL+Vy+LyBRo4OuPbtVt8iWSXq2bU8w4YNY+XKlYC2i/CYMWNuq52n\nn36aNWvW1KZoAMyYMYN33nlHT3/66ae0adMGb29vLl26VOv91SWdOnVi586dNy+oqHWszu3nVmna\n2JYXu3vx1rYUADacuMDgNg/gfZ99/QqmUCgUdyElBVe4sCVWTz/4SC9s7ZvUo0SK2qQhu+mMGTOm\nRsZ/VFQUKSkpfPTRR/q5r776yiIymRr+JSUlzJ07l02bNtGuXbsbyqamptKpUycuXLhQo92DFRUp\nKipi+vTpfPfddzg6OvLnP/+Zl19+ucrya9euZf78+fz22288/PDDREdH07y5tpZ00qRJxMTEYGdn\np5c/e/bsXRP21Oqejlvx+S+nv/99tPdwAqBUwkexaVhbCNTaQPlOK+5F1HNbu1zYtIfSa4UAhLXv\nhEvPW//NVdQM9ezeGqWl1u22m5mZSWFhIa1btzabL6VECFGt/WLtOroTFi5cSEpKCseOHWPDhg1E\nR0ezdetWs2Xj4+OZPn06y5YtIyEhAXt7e2bMmFGhzOTJkzEYDPpxtxj+YIXG/+0ghODlnl7YGO/L\nwXN5xBly61cohUKhuMsovJBDzt7rrpXuTz6MqGLHVIWiNnB1dWX58uV06dKF4OBg/vrXv+p5q1ev\nZvDgwbz++usEBgYSFRUFwMqVKwkLCyMgIICnnnqKtLQ0vc62bdvo0aMHfn5+zJo1q4KhvHr1aoYM\nGaKn4+PjGTVqFAEBAbRt25b33nuPLVu2sGjRItavX4+3tzf9+/cHKroPSSn55z//SceOHWnTpg2T\nJk0iN1ezKVJTU3F1deXLL7+kQ4cOBAcH8+6771Z5/ZMmTeKtt94iKSmJsDBtUb2fnx8jR468oeyT\nTz6p53t7e3PgwIEKOgoKCiIqKoqoqCgiIyP1euUylZWVAZCbm8vkyZNp164doaGhLFiwwOyAIiMj\nAy8vLy62qgJzAAAgAElEQVRfvqyfO3r0KEFBQZSWlpKSksKIESMIDAwkODiYl156SddDVddZzp49\newgNDa3Q17PPPktwcDBdunSpcrO2O2HNmjX85S9/wdnZmeDgYMaPH8/q1avNlo2JiWHw4MGEhYXh\n4ODAnDlz+P777ykouDfCxlud8X+rPv/lBLg6MKTNA3p6aVwaRSVltSWWVaD8TxX3Iuq5rT0yN+5A\nSu130dG/FUdyMupZIutGPbsaGzduZPv27Wzbto0ff/xRN7IBDh48iL+/P6dOnWLGjBls3LiRxYsX\ns3LlSk6fPk3Pnj2JiIgAIDs7m2effZa5c+eSmJiIr68v+/btq9BX+exsfn4+o0eP5tFHHyU+Pp4D\nBw7Qr18/wsPDmTZtGiNHjsRgMLBjx44b5P3iiy9Ys2YN33//PYcOHSIvL49Zs2ZVKLNv3z4OHDjA\n+vXrefvttzl9+nS1OggICGDv3r2A5j6yfv36G8r88MMPer7BYKBbt24VdHTy5El9drryLLRpetKk\nSdjZ2XHo0CF27NjB9u3b+fzzz2/oz8PDg+7du/Ptt9/q52JiYhg+fDi2trZIKZk2bRoJCQnExcWR\nnp6uD9BqQrlMUkrGjh1Lhw4diI+PZ8OGDSxbtoxt27aZrbd48WL8/Pzw9/fHz8+vwmd/f3+zdS5f\nvkxGRgYhISH6udDQUBISEsyWT0hIqFDW19cXOzs7kpKS9HOffvopgYGBhIeH891339X4uusCqzP+\n74TnunrSrIk2i3U+r4iY41n1LJGiIZCTk1Phx1OhuBspOJNK7vFTetrjyQF31WtshfUyZcoUnJ2d\n8fLyIjIykpiYGD3P09OTP/3pT9jY2NCkSRM+++wzpk6dSmBgIDY2NkydOpXjx4+TlpbG5s2badu2\nLU8++SS2trZMnDgRNzc3s33+97//xd3dnYkTJ2JnZ4ejoyNdunSpkbwxMTG8/PLLtGrVCgcHB954\n4w3WrVunz6wLIZg1axZ2dnaEhIQQEhLC8ePHa6yPm7klV86vrKPqyMrKYvPmzSxYsAB7e3tcXV2J\njIxk3bp1ZsuPGjWqwv1Yt26dvm7Cz8+P/v3706hRI1xcXJg4caI+gLkVDh48SHZ2NjNmzMDW1hZv\nb2+eeeaZKmWaMmUKycnJnDlzhuTk5Aqfz5w5Y7ZOfn4+Qgicna/vVdKsWTPy8/PNli8oKKhQtnL5\nyMhIDhw4wKlTp3jttdeYNGkS+/fvv+VrtxRWt+D3dnz+y3G2b8SzXT15f6/2inDVr5kMDHDBvZnd\nTWo2DJT/qeVQurUcSrd3jpSSjO+vz7Ld1zmEpq086dPKsx6lsn7Us6vRokUL/XOrVq3IyLj+xsnL\ny6tC2dTUVGbPns3cuXOB637w58+f191UTKmcLufcuXP4+vrelrznz5+nZcuWFWQuKSkhK+v6hKLp\noMPBwcGi7iJVXaM50tLSKC4upm3btoCmPyllhesxZdiwYcyePZusrCxOnz6Nra2t7p504cIFZs+e\nTWxsLAUFBZSVlXHffffdsvxpaWmcP39en7WXUlJWVkavXr1uua2qcHLS1n3m5eXh6qrt95Sbm6uf\nr4yjoyN5eXkVzuXl5enl27dvr59/9NFHeeqpp/j+++/p3r17rcl8J1id8X+nPNHmATYmXORMzjUK\nS8r4MDaNeY+Zf02kUCgUDYHcX+O5mqqFQbaxtcVtUN96lkjRkDh37py+yDUtLQ0PDw89r/Lbp5Yt\nW/Lqq68yevToG9pJSkqq4P9f3rY5vLy8zLrWmOuzMp6enhX6SU1NpXHjxri5uVXZX21QlVyVzzs4\nOHDlyhU9XXkwZW9vT1JSUo3e7DVv3pwBAwawbt06Tp06xahRo/S8+fPnY2NjQ2xsLM7OzmzcuPEG\n96dyHB0duXr1apUy+fr61njmfNGiRSxatKjKfIPBYPY63N3dOX78uL6O4/jx47Rp08ZsG23atOHE\niRN6Ojk5meLiYgICAsyWv9lC7LrG6tx+btfnvxxbG8Hk3t56OtZwmb1n7+1YurWF8j+1HEq3lkPp\n9s4oKy4h88frsbhd+z2EnYsWzk7p1rIo/WpER0dz+fJl0tLSWLp0aQUDszLPPfcc7777ru6rnZub\nyzfffAPAY489xsmTJ/nhhx8oLS1l6dKlFWbjTXn88cfJyspi2bJlFBUVkZ+fz8GDBwFt1t5gMFRp\nzI0aNYqPPvoIg8FAfn4+b775JqNGjdLDb96JEVhdXVdXV2xsbEhOTq62jfbt2xMbG0taWhq5ubks\nXrxYz3N3d2fAgAHMmTOHvLw8pJSkpKRU664zatQo1qxZw3fffVchVGp+fj6Ojo44OTmRnp5OdHR0\nlW2EhoayadMmLl26RGZmJsuWLdPzunbtipOTE0uWLOHatWuUlpYSHx/P4cPmd6OeNm1ahSg7lY+q\n+N3vfsc777zD5cuXOXnyJP/5z38YO3as2bJjxozhp59+Ii4ujoKCAv7+978zdOhQHB0dAfj2228p\nKChASsnWrVv5+uuvKywmr2+szvivDdq5OzKkjaue/mBvGleLVXgshULR8MjefYCi37RoHo0cmvLA\ngLB6lkjR0BgyZAgDBgxgwIABDBo0iHHjxlVZ9oknnmDq1KlERETg6+tLnz592LJlC6Dtpv7vf/+b\nefPmERgYSEpKiu6iUhknJydiYmL46aefaNOmDd27d2fPnj0ADB8+HCklAQEBDBw4EKg4uz5u3Die\nfvppnnjiCbp27YqDgwMLFy7U86tbbHszqivbtGlTpk+fzuDBg/H399cHK5V5+OGHGTlyJH379iU8\nPJzHH3+8Qv6HH35IcXExPXv2xN/fnwkTJpCZmVllv4MHDyYpKQl3d/cK+w/MnDmTI0eO4Ovry9ix\nYxk6dGiV1/K73/2OkJAQOnbsyFNPPVVhgGdjY8Pq1as5duwYnTt3Jjg4mKlTp97gdnOnvPbaa/j4\n+NChQwdGjBjBlClTGDBggJ7v7e1NXFwcoM38v/POO7z44ou0bduWa9eu8fbbb+tlly1bRmhoKH5+\nfsybN4/FixfTs2fPWpX3ThB302uI2mDLli2ypotyqiP3Wgl/WhvP5WslAIxp78aLPWruN6dQKBT3\nOiUFVzj992WUFhYB4DniUVx73/nvq6J+SU9Pr+BHfzfj6urKwYMHb9v/XqG4F6nqO3ro0CHCw8Pv\nONKCmvmvAmf7RrxkYuyvO57Fmeyr1dRQKG4PFxcXXFxc6lsMheIGLmzaoxv+TR5wwSWsYz1LpFAo\nFIo7xeqM/zv1+TclPPB+OnpqK7fLJCzZk0qZlb0puRWU/6niXkQ9t7dHTTb0Urq1LEq/t+YSo1Ao\naobVGf+1iRCCV3q3opFx69//ZRXw35PZ9SyVQqFQWJ7MH7ZX2NCrWbvAepZI0RC5ePGicvlRKGqZ\nOjX+hRCDhBAJQohTQogb4j0JIcYKIY4Yj91CiA41rVvOncT5N4f3ffY83eF6PN5//ZLOpavFtdrH\nvYKKOa24F1HP7a1TcCaV3BPXdxytakMvpVvLovSrUCgsQZ0Z/0IIG+B94HEgBPiDEKJyANUzQD8p\nZUfgTWD5LdS1GH/o5IGncaOvvMJSPt6fXlddKxQKRZ1S1YZeCoVCobAO6nLmvztwWkp5VkpZDHwJ\nDDctIKWMk1JeNibjAK+a1i2nNn3+y2nSyIY/92qlpzedzuFIeu2GmLoXUP6ninsR9dzeGpcPm2zo\n1agRboP7VVlW6dayKP0qFApLUJfGvxeQapJO47pxb44I4MfbrFvrPNTKmX5+17elXrInleLSsroU\nQWGl5OTk8O2339a3GAoFZYVFZP5wfdbftV837O53rkeJFAqFQlHbNKpvAcwhhBgATABu2eExMTGR\nl19+GW9vbZfe5s2b0759e913snwm5XbSkWFebN6+k2slZaQGdGLtsSxa5Sfednv3WrpPnz53lTwq\nrdI1TZdzt8hzt6Z/+OBjLp38H509vWnk5MjJJmWc3r27yvLl5+4W+a0tXX6uttv39/dHoVDc3eze\nvZtjx45x+bLmEGMwGOjWrRvh4eF33HadbfIlhAgD/k9KOciYfg2QUsqoSuU6ADHAICll0q3Uhdrb\n5Ksq1h/P4qO4cwDY2Qo+Ht0WT+cmFutPoVAo6oKii7+R+M9PKCvVdjP3+t0Q7u/Wvp6lUliCe2mT\nr4bG2rVr+fLLL1m7dq3F+0pNTaVTp05cuHABG5vbdwTx9vZm9+7d+qRrZTp16sSSJUvo169qF0JF\nRaxpk69fgEAhhI8Qwg74PVDB10EI4Y1m+D9TbvjXtG45lvD5N2VYuwcJdG0KQFGp5P29aVjbLslV\nofxPLYfSreVQuq0ZGd9t1Q3/pq08ua9r6E3rKN1aloao306dOrFz5876FqPeGDNmTI0N/6ioKCZO\nnHhH/dXGPgoGg0E3/CdNmsRbb711x20qLEudGf9SylLgz8DPwAngSyllvBDiJSHEi8ZicwEX4EMh\nxGEhxP7q6taV7KbY2gim9GlF+dfll7Rcdpy5VB+iKBQKRa2QfzKZ3P8l6mnPEY+qzZUUCoXCSqnT\nOP9Syp+klK2llEFSyoXGc8uklMuNn1+QUrpKKbtIKTtLKbtXV9cctR3n3xytH3RkaLsH9PQHsWlc\nvlZi8X7rGxVz2nIo3VoOpdvqkaWlnP9mi56+v1t7HLxrFtpT6dayKP1WZMWKFXTr1o3AwEDGjRtH\nRkaGnjdnzhxat26Nj48Pffv2JSEhAYBNmzbRs2dPvL29CQ0N5YMPPjDbdkpKCiNGjCAwMJDg4GBe\neuklcnNz9fzFixcTEhKCt7c3PXr0YNeuXYDuhoGPjw9t27Zl7ty5ep0ff/yRXr164e/vz/Dhwzl1\n6pSed+7cOcaPH09wcDBBQUG89tprAKxevZohQ4bo5WbPnk379u3x8fEhPDycuLg4ALZs2cKiRYtY\nv3493t7e9O/fH4Dc3FwmT55Mu3btCA0NZcGCBbp3QllZGXPnziUoKIiuXbvy888/V6nrVatWMXbs\nWD3drVs3nn/+eT3dvn17Tpw4AYCrqyspKSmsWLGCtWvXEh0djbe3N3/84x/18kePHqVv3774+fkR\nERFBUVFRlX0rLI/a4fc2mdCtBQ86Ngbg8rUSPoxNq2eJFPcqLi4uuLi41LcYigZK9p5DFF7Qdi63\nbWKH+5D+9SyRQnEjO3fu5M033+Szzz4jPj6eli1bEhERAcDWrVvZt28fBw4c4OzZs3z66af6b+qU\nKVN47733MBgM7N27t0q/cykl06ZNIyEhgbi4ONLT04mK0pYVJiYm8q9//Ytt27ZhMBiIiYnR3Vxm\nz55NZGQkZ8+e5eDBg4wYMUKv8+KLL7Jw4UJOnz5NeHg4Y8eOpaSkhLKyMv7whz/g4+PD0aNHOXHi\nBCNHjtRlMX3r1rVrV3bv3k1ycjKjR49mwoQJFBUVER4ezrRp0xg5ciQGg4EdO3YAmtuNnZ0dhw4d\nYseOHWzfvp3PP/8c0AZPmzZtYufOnWzdurXaKHO9e/fWBxoZGRkUFxfzyy+/ANpA6cqVK4SEhFSQ\n99lnn2XMmDG88sorGAwGvvjiC729b775hpiYGH799VeOHz/OqlWrbn7TFRbD6ox/S/v8l+NoZ8uU\nPtdj/29L+o04w+Vqatz7NET/U8W9j3puq6Ykr4ALP1/Xz4OP9qZRM8ca11e6tSxKv9dZu3Yt48aN\nIzQ0lMaNGzN37lwOHDhAWloajRs3Jj8/n5MnTyKlJCgoCDc3NwAaN25MQkICeXl5ODs70769+UXs\nfn5+9O/fn0aNGuHi4sLEiRPZu3cvALa2thQXFxMfH09JSQktW7bEx8cHADs7O86cOUNOTg4ODg50\n7doVgA0bNvDYY4/Rr18/bG1teeWVV7h27Rr79+/n4MGDZGZmMm/ePOzt7bGzs6NHjx5m5RozZgzN\nmzfHxsaGl19+mcLCQhITE82WvXDhAps3b2bBggXY29vj6upKZGQk69evBzQDPDIyEk9PT5o3b87U\nqVOr1LePjw9OTk4cO3aMvXv3MnDgQDw8PEhMTGTv3r307NlTL1uTdY+RkZG4ubnRvHlzBg0axPHj\nx29aR2E5rM74r0u6t2pOeOD9enrJ7lQKikrrUSKFQqGoOZk/7qS0UHv93uQBF1x6Wy5SmkJxJ2Rk\nZNCq1fUJN0dHR+6//37S09Pp27cvERERzJw5k9atWzN9+nTy8/OB67PdHTt2ZNiwYfrsdWUuXLhA\nREQEISEh+Pr6EhkZSXa29kbMz8+PBQsWEBUVRevWrXnhhRd0l6MlS5aQmJhIjx49eOSRR3RXmsry\nCiFo0aIF58+f59y5c7Rq1apGEXaio6MJCwvDz88PPz8/8vLydLkqk5qaSnFxMW3btsXf3x8/Pz9m\nzJjBxYsXATh//jxeXte3SDKVzxy9e/dm165dxMbGVgj3vWfPHnr16nVT2U158MEH9c9NmzaloKDg\nluoraherM/7rwufflIlhLbnPXtsu4eKVYpbvO1en/dclyv9UcS+inlvzXDGc59KBY3raY3g4No1u\nbesXpVvLovR7HQ8PD1JTr+/1WVBQQE5Ojh4O8YUXXmDr1q3ExsaSmJhIdHQ0oNkEK1eu5PTp0wwe\nPLiC37op8+fPx8bGhtjYWFJSUli6dGmFGe3Ro0ezceNGjhw5AsDf/vY3QBsYfPzxx5w+fZrJkyfz\n3HPPcfXqVTw8PDAYDBX6OHfuHJ6ennh5eZGWlkZZWfUbhcbGxvL+++/z2WefkZycTHJyMs2aNdPl\nqrwo38vLC3t7e5KSkjhz5gzJycmkpKTob5A8PDw4d+66jWKqT3P07NmTPXv2EBcXR69evejVqxd7\n9+4lNjaW3r17m62jAgXcG1id8V/XONs34s+9WurpH09mczg9rx4lUigUiuqRUpLxzWbdiGjWNpBm\nbdTGT4q7g6KiIgoLC/WjtLSU0aNHs2rVKk6cOEFhYSHz58/noYceomXLlhw+fJiDBw9SUlKCvb09\nTZo0wcbGhuLiYtauXUtubi62trY4OTlha2trts/8/HwcHR1xcnIiPT1dHzyA5r+/a9cuioqKsLOz\nw97eXjdyv/76a30m3tnZGSEENjY2jBgxgs2bN7Nr1y5KSkqIjo7G3t6e7t2707VrV9zd3Zk3bx5X\nrlyhsLCQffv2mZWp3A2pqKiIf/zjH/obDQA3NzcMBoP+PXZ3d2fAgAHMmTOHvLw8pJSkpKTo7ksj\nRoxg+fLlpKenc+nSJZYsWVLtfSif+b927Rqenp6EhYWxZcsWcnJy6NChg9k6bm5unD17ttp2FfWP\n1Rn/deXzb0pfv/vo7dNcTy/aZeBqsfW5/yj/U8W9iHpub+TyoRNcMaQDYGNri8fQAbfVjtKtZWmo\n+v3973+Pl5cXLVq0wMvLi6ioKPr378/s2bMZP348ISEhGAwGPv74YwDy8vKYOnUq/v7+dO7cGVdX\nV1555RUA1qxZQ+fOnfH19WXFihUsX77cbJ8zZ87kyJEj+Pr6MnbsWIYOHarnFRUVMW/ePIKCgmjX\nrh3Z2dm88cYbgBZ1p1evXnh7e/P666/zySef0KRJEwIDA1m6dCkzZ84kKCiITZs2sWrVKho1aoSN\njQ2rVq3izJkzdOjQgfbt27Nhw4YbZAoPD2fgwIE89NBDdO7cmaZNm1Zw2xk+fDhSSgICAhg4cCAA\nH3zwAcXFxfTs2RN/f38mTJhAZmYmAOPHj2fgwIH069ePgQMHVrhGcwQEBNCsWTPdv79Zs2b4+fkR\nFhZWYYbf9PO4ceNISEjA39+f8ePH35CvuDuosx1+64p33nlHVvVaz5JkXynmhbXx5Bt9/keGPsjE\nsJY3qXVvYbrNvKJ2Ubq1HEq3FSm9VsjpqI8pydd8bh8cGIb74NuL8KN0a1kspV+1w69CcXdjTTv8\n1gl17fNfjqtDYyLDro/INxy/wP8yrWtBi/onbzmUbi2H0m1FLmyJ1Q3/xs5OPDiw501qVI3SrWVR\n+lUoFJbA6oz/+uTRIBe6tWwGgATe3WWgqLT6BT0KhUJRVxReyCF75/VoJ+5PPIxNE7t6lEihUCgU\ndc2thXa4B/j111/p0qV+wtUJIZjS25sX18VztbgMw6VrfHE4gwndrOP1qnrFbzmUbi2H0q2Gtsh3\nC9IYYcTBx4vmndvdUZtKt5alPvR7/C9Rtdpe6NuzarU9hUJx56iZ/1rGvZkdf3rourG/5kgmSdlX\n6lEihUKhgLzjp8g7eQbQJio8RzyiFuIpFApFA8TqjP/68vk35cm2DxDqru2SWSbhnZ0GSsru/YXV\naobPcijdWg6lWygrLOL8N1v09P09OtK0pccdt6t0a1mUfi3PsGHDWLlyJaDtIjxmzJjbaufpp59m\nzZo1tSkaADNmzOCdd97R059++ilt2rTB29ubS5cu1Xp/dUmnTp3YuXNnfYvRILE6t5+7ARshmNbX\nm8j1CRSXShKzr/L10Uz+0OnO/9kqrA8XFxcAcnJy6lkShbWS9fNuii9r+480cnS47eg+CuunIbvp\njBkzpkbGf1RUFCkpKXz00Uf6ua+++soiMpka/iUlJcydO5dNmzbRrt2NLnupqal06tSJCxcu1Gj3\nYMXNWbt2LfPnz+e3337j4YcfJjo6mubNm5stm5qayp///GcOHjxIy5Yt9RC1AJs2bWLRokXEx8fT\ntGlTHnvsMRYsWICjo2NdXo6O1T0d9RHn3xyt7rNnfBdPPf2fQxn3vPtPQ405rbi3aejP7bX0LLJ3\nHdTTHsMGYutgXyttN3TdWhql31ujtNT69tcxJTMzk8LCQlq3bm02X0qJEILqQrhbu45qk/j4eKZP\nn86yZctISEjA3t6eGTNmVFk+IiKCjh07kpSUxOuvv85zzz2nT+rl5uby6quvEh8fT1xcHOnp6fz1\nr3+tq0u5Aasz/u8mxrR3o/WDDgCUlEmitp+lqERF/1EoFHWDlJL0mP8ipfa74xjgfceLfBWKusTV\n1ZXly5fTpUsXgoODKxhMq1evZvDgwbz++usEBgYSFaUtVl65ciVhYWEEBATw1FNPkZaWptfZtm0b\nPXr0wM/Pj1mzZlUwlFevXs2QIUP0dHx8PKNGjSIgIIC2bdvy3nvvsWXLFhYtWsT69evx9vbWZ3ZN\n3YeklPzzn/+kY8eOtGnThkmTJpGbmwtos8Ourq58+eWXdOjQgeDgYN59990qr3/SpEm89dZbJCUl\nERYWBoCfnx8jR468oeyTTz6p53t7e3PgwIEKOgoKCiIqKoqoqCgiIyP1euUylRmDAeTm5jJ58mTa\ntWtHaGgoCxYsMDugyMjIwMvLi8uXL+vnjh49SlBQEKWlpaSkpDBixAgCAwMJDg7mpZde0vVQ1XWW\ns2fPHkJDQyv09eyzzxIcHEyXLl2q3KytNomJiWHw4MGEhYXh4ODAnDlz+P777ykouDGMe1JSEseO\nHWPWrFk0adKEoUOHEhISwrfffgvA6NGjGThwIPb29jg7OzN+/HizuzrXFVZn/N8NPv/l2NoIZj3s\nQxNbbVFdym/X+Ozg+XqW6vZR/qeKe5GG/Nz+tu9IhZ18W4x+vFYX+TZk3dYFSr8aGzduZPv27Wzb\nto0ff/xRN7IBDh48iL+/P6dOnWLGjBls3LiRxYsXs3LlSk6fPk3Pnj2JiIgAIDs7m2effZa5c+eS\nmJiIr6/vDQZY+fcjPz+f0aNH8+ijjxIfH8+BAwfo168f4eHhTJs2jZEjR2IwGNixY8cN8n7xxRes\nWbOG77//nkOHDpGXl8esWRXdqfbt28eBAwdYv349b7/9NqdPn65WBwEBAezduxeAs2fPsn79+hvK\n/PDDD3q+wWCgW7duFXR08uRJfea68u+AaXrSpEnY2dlx6NAhduzYwfbt2/n8889v6M/Dw4Pu3bvr\nBi5oBvPw4cOxtbVFSsm0adNISEjQZ7vLB2g1oVwmKSVjx46lQ4cOxMfHs2HDBpYtW8a2bdvM1lu8\neDF+fn74+/vj5+dX4bO/v3+N+09ISCAkJERP+/r6YmdnR1JSktmyPj4+Fdx4QkNDSUhIMNv2nj17\naNOmTY1lqW2szvi/22jZ3J4Xelzf/CvmWBZHz+fVo0QKhaIhUJJfQObG64aJ68PdafKgSz1KpFDc\nHlOmTMHZ2RkvLy8iIyOJiYnR8zw9PfnTn/6EjY0NTZo04bPPPmPq1KkEBgZiY2PD1KlTOX78OGlp\naWzevJm2bdvy5JNPYmtry8SJE3FzczPb53//+1/c3d2ZOHEidnZ2ODo61jiMeExMDC+//DKtWrXC\nwcGBN954g3Xr1ukz60IIZs2ahZ2dHSEhIYSEhHD8+PEa66M6tx5z+ZV1VB1ZWVls3ryZBQsWYG9v\nj6urK5GRkaxbt85s+VGjRlW4H+vWrdPXTfj5+dG/f38aNWqEi4sLEydO1Acwt8LBgwfJzs5mxowZ\n2Nra4u3tzTPPPFOlTFOmTCE5OZkzZ86QnJxc4fOZM2dq3G9BQQHOzs4VzjVr1oz8/Pw7Krtt2za+\n+uor5syZU2NZahurM/7vFp9/U4a2faDC5l9v7zBQUHTv+d0p/1PFvUhDfW4zvttG6dVrANi5NOfB\n8F613kdD1W1dofSr0aLF9fDZrVq1IiMjQ097eXlVKJuamsrs2bPx9/fH39+fgIAAhBCcP39ed1Mx\npXK6nHPnzuHr63tb8p4/f56WLVtWkLmkpISsrCz9nOmgw8HBwawrSW1R1TWaIy0tjeLiYtq2bavP\nls+YMYPs7Gyz5YcNG8aBAwfIyspiz5492Nra6u5JFy5cICIigpCQEHx9fYmMjKyynZvJdP78ef2e\n+vn5sWjRIi5evHjLbVVFXFwc3t7eeHt707t3bwAcHR3Jy6s4WZuXl4eTk9MN9c2Vzc3NvaHsL7/8\nwksvvcSKFSvw8/OrNflvFRXtpw4QQjCjrw8vrosnr7CUzPwiPopN49X+PvUtmuIuICcnR/2TV9Qq\n+fsAqUgAACAASURBVIlnuXTohJ72HPkYNo3Vz73i3uTcuXP6Ite0tDQ8PK5HzqvsvtKyZUteffVV\nRo8efUM7SUlJFfz/y9s2h5eXl1nXGnN9VsbT07NCP6mpqTRu3Bg3N7cq+6sNqpKr8nkHBweuXLke\ngKTyYMre3p6kpKQauQg2b96cAQMGsG7dOk6dOsWoUaP0vPnz52NjY0NsbCzOzs5s3LjxBvenchwd\nHbl69WqVMvn6+rJ///6bygOwaNEiFi1aVGW+wWC44VxYWNgN59u0acOJE9d/R5OTkykuLiYgIOCG\n+m3atOHs2bMUFBTorj/Hjx/nqaee0sscPXqUZ555hg8++KDeXfqsbub/bvL5N8XVsTGv9Gqlp38+\nncPulHsrRm99P6zWjNKt5Whoui0rKeF8zM96unnHNjRrU3M/11uhoem2rlH61YiOjuby5cukpaWx\ndOnSCgZmZZ577jneffdd3dc6NzeXb775BoDHHnuMkydP8sMPP1BaWsrSpUsrzMab8vjjj5OVlcWy\nZcsoKioiPz+fgwe1qFlubm4YDIYq3W9GjRrFRx99hMFgID8/nzfffJNRo0bp4Tdv5rZTHdXVdXV1\nxcbGhuTk5GrbaN++PbGxsaSlpZGbm8vixYv1PHd3dwYMGMCcOXPIy8tDSklKSkq17jqjRo1izZo1\nfPfddxVCpebn5+Po6IiTkxPp6elER0dX2UZoaCibNm3i0qVLZGZmsmzZMj2va9euODk5sWTJEq5d\nu0ZpaSnx8fEcPnzYbFvTpk3DYDBUedSUMWPG8NNPPxEXF0dBQQF///vfGTp0qNnwnAEBAYSGhvKP\nf/yDwsJCvvvuO+Lj4xk2bBgA//vf/3j66adZuHAhjz76aI1lsBRWZ/zfzTwccD8DAu7X04t3p5Jz\npbgeJVIoFNZG9vb9FF7UwsvZNrHDY+jAepZIobgzhgwZwoABAxgwYACDBg1i3LhxVZZ94oknmDp1\nKhEREfj6+tKnTx+2bNE2uHNxceHf//438+bNIzAwkJSUFN1FpTJOTk7ExMTw008/0aZNG7p3786e\nPXsAGD58OFJKAgICGDhQ+36ZzpKPGzeOp59+mieeeIKuXbvi4ODAwoUL9fzqFtvejOrKNm3alOnT\npzN48GD8/f31wUplHn74YUaOHEnfvn0JDw/n8ccfr5D/4YcfUlxcTM+ePfH392fChAlkZmZW2e/g\nwYNJSkrC3d29wv4DM2fO5MiRI/j6+jJ27FiGDh1a5bX87ne/IyQkhI4dO/LUU09VGODZ2NiwevVq\njh07RufOnQkODmbq1Kk3uNnUNm3atOGdd97hxRdfpG3btly7do23335bz58xYwavvvqqnv7kk084\nfPgw/v7+vPnmm6xYsULfx+fDDz8kOzubyZMn3+BeVB+IOxmB3o2888478vnnn69vMaokr7CEl2IS\nuGg0+nu0cuZv/7+9+46P6yoT//85MyNpiuqoVxfZltOdxOkhzWlOQkIILcACyf4ogWWBXZaS7y5t\nf7vA7jdAIGzYQGhLCwRCvJBeSFB6HDtxEluyXNT7qM+MNOV8/5jRSCOP7JE0d5qe9+ull3TvzB0d\nPb6eOffc5zzn8vUJrcBhlObmZhmJMojE1jirKbYzQyO03fZjgn4/ANXXbaP0/K2G/b7VFNtUMCq+\nPT09UXn06ay0tJSdO3cuO/9eiEy02P/RV155hW3btq24wygj/0lWkGfhsxc2RLZf6BznoZalT4AR\nQoj5tNb0/PHRSMffVluJ89z4qpMIIYRYPbKu85+uOf/znVZbyHXHl0e273y+m57x6RS2KD4ywmcc\nia1xVktsx/e0MtkSyvVVSlH99itQJmPf4ldLbFNF4ru0lBghRHyyrvOfKf72zBrqikL1dr3+IP/5\nVDuBYHalYIn4OJ3OSF6gEMsR8E7Td/9jke2Sc7Zgb6hOYYuESIyhoSFJ+REiwbKu85+Odf5jsVpM\nfOGitYQX/+WN/il+t2fxCTXpQMpRiky0Gs7b/geewjceWkzGku+g8soLk/J7V0NsU0niK4QwQtZ1\n/jPJpnI77zt1rl7xz3f20TroPsoRQggRbepAB67n5kreVV97CWbb0VfxFEIIsXplXec/E3L+57tx\nSxVN5XYA/EHNvz95KG1X/5X8U5GJsvm8Dfr89Nz7UGS74LgNFG45Lmm/P5tjmw6Miq/ZbI5a5EkI\nkT7cbjdms9nQ3yFLPqaY2aT44sVr+fh9+3D7gvSMz3B7cwdfvHitTHQSQhzVwMN/ZXpoBAjV9K+5\n4XJ53xDHVFFRwcDAAKOjmbXQpBCrgdlspqKiwtDfkXWd/927d3PaaZlV3q6mMI9Pnd/A1588DMBf\nDo5yaq2L7U2lqW3YAlLTW2SibD1v3R29DD/9UmS76q2XkFNUkNQ2ZGts04VR8VVKUVlZmfDXzSRy\n7hpHYpv+si7tJ1Nd3FgS1dn/r2c7OTziSWGLRLK4XC527NiR6maIDBL0++n53YPMLtKYv2ENxWee\nnOJWCSGEyARZt8Lv448/rjNt5H+W1x/kk39soX3UC8CaEit3XNdEnkWu0YQQcwYeeYaBR0OVYEw5\nOWz4x5vJLS1OcauEEEIYSVb4zUJWi4lbL1lLbrj+Z/uIlzuf70pxq4QQ6cTbN8jg489Gtiu3XyAd\nfyGEEHHLus5/ptT5X8w6p42Pn1MX2X5g3zBPHRxJYYvmSM1p40hsjZNNsdXBIN2/fRAdDAJgb6jB\neV7q7nRmU2zTkcTXOBJb40hs01/Wdf6zwfamUi5cPzeS9+2/dtA7Pp3CFgkh0sHw0y/h6ewFwGQ2\nU/Ou7SiTvI0LIYSIX1Jz/pVSVwLfIXTRcbfW+psLHm8CfgKcBtyqtf7WvMcOA2NAEPBprc+M9Tsy\nOed/vqmZAB+/bx+9EzMANJXb+dY1G8kxywe9EKvR9KCLA9/6CUG/H4DKKy+gfNs5KW6VEEKIZMm4\nnH+llAm4A7gCOAG4USm1ecHThoFPAv8Z4yWCwEVa61MX6/hnE0eumVsvWYvFFPo3bhl085OXe1Pc\nKmEEp9OJ0+lMdTNEGtNa0/O7hyIdf1tNBWUXZf3boBBCCAMkcxj5TGC/1rpda+0DfgNcN/8JWush\nrfVOwB/jeEUc7c30nP/5msod3HxGTWT73j0DvNAxlrL2SB6fyETZcN6OPLebqUOdAChlouZdV6EM\nXgEyHtkQ23Qm8TWOxNY4Etv0l8zOfy3QOW+7K7wvXhp4VCn1klLqwwltWRq74cRyzqovjGz/51Pt\nDE3NpLBFQohkmhkZp+/PT0a2yy4+E1vt6l6gSQghxPJlUgL5eVrr04CrgE8opWIuH7dly5bktspg\nSik+e+EaSu05AIxPB/i3Jw7jCwST3hZZsU9kokw+b7XW9Pz+IYIzPgDyykspv/S8FLdqTibHNhNI\nfI0jsTWOxDb9WZL4u7qBhnnbdeF9cdFa94a/Dyql7iOURnTEvaV7772XH/3oRzQ0hH5VUVERJ510\nUuRknL0dlWnbX7z4FD73QBujbbt57gDcVWrjE+fWp037ZHtl27PSpT2ynR7bD/73TxlufplTqxtQ\nStHeWEb/C8+nTftkW7ZlW7Zl27jtPXv2MDYWSvfu6Ohg69atbNu2jZVKWrUfpZQZaAG2Ab3Ai8CN\nWuu9MZ77ZWBSa31beNsOmLTWk0opB/AI8FWt9SMLj73tttv0zTffbOBfkjq/e62fH77YE9n+pwsb\nuGxjadJ+f3Nzc+SkFIkzO9nX5XKluCXZKVPP24XVfcouOIOqt16S4lZFy9TYZgqJr3EktsaR2Bon\nUdV+LIloTDy01gGl1N8R6rjPlvrcq5T6aOhhfZdSqhJ4GSgAgkqpTwHHA+XAfUopHW7zL2N1/LPd\nO06qoGXQzdOHRgG4vbmTdSU2NpTZU9wysRIulytyxS8EhBbz6vr1nyIdf2tlGRVXXpDiVgkhhMgG\nSa3znwzZUud/MR5fgL+/v5X2US8Alfm5fP9tTRRak3YdJ4Qw2MCjzzDwSOiCUJlMNH7qg1hrKlLc\nKiGEEKmUcXX+RWLYcsx8+bJ12HNC/3T9kzN8/cnDBILZdREnxGrl6exl8NFnI9sVV7xFOv5CCCES\nJus6/9lU538xdUVWPn/R2sj2zu4Jfr7T+AXAJDXFOBJb42RSbIM+P12//jNah6p52dfUpvViXpkU\n20wk8TWOxNY4Etv0l3Wd/9XinDVFvO/Uqsj2r1/tp/nwaApbJIRYqf4//4XpwWEATLk51L3napRJ\n3qaFEEIkjuT8Z7BAUPOlRw7yUtc4APYcE9+9romGYmuKWyaEWKrJ1sMc/uE9ke3ad1xJyVmnpLBF\nQggh0onk/AvMJsXnL1pDdUEuAG5fkK8+ehD3TCDFLRNL4XQ6I+U+xeoUcHvp/u0Dke2C4zZQfObJ\nKWyREEKIbJV1nf/VkPM/X6HVwpcuXUeeOXQh2Dk2zf99uh0j7uhIHp/IRJlw3vb+8TF8YxMAWOw2\nat95JUqteHDHcJkQ20wm8TWOxNY4Etv0l3Wd/9WosdTOp98yt3hy8+Ex7nmtP4UtEkLEa2z3XkZ3\nvRHZrnnHFVgKHClskRBCiGwmOf9Z5M7nurjvjUEAFPDly9Zx7pri1DZKHJOs8Lt6+cYmaLvtxwQ8\noXU7ik8/kbr3XJ3iVgkhhEhHkvMvjvDhs2o5qSofAA18/cl29g+5U9soIURMWmu6f/dgpOOfU1xI\n9XWXprhVQgghsl3Wdf5XW87/fBaT4kuXrotMAJ72B/nSIwcZmppJyOtLHp/IROl63rqadzLZcggA\npRR177kasy0vxa1amnSNbbaQ+BpHYmsciW36i7vzr5S6WCm1LvxztVLqZ0qpnyilqo51rEieIquF\nf72iEUeuGYBht48vPXIQj08qAKUrl8vFjh07Ut0MkUSezl76/vRkZLv0LVtxNDYc5QghhBAiMeLO\n+VdK7QWu0Fp3KKV+Fd7tAcq11tca1cClWs05//Pt6p7g1ofaCIT/ec9dU8SXLl2HKQMqiAiRzQLe\naQ5856fMDIcW5bPVVbHuE+/DZLGkuGVCCCHSWSpy/mvDHX8LcAXwEeAW4NyVNkIk3qm1BXzyvPrI\n9rPtY9z9Yk8KWySE0FrT8/uHIx1/c14u9e+7Vjr+QgghkmYpnf9xpVQlcCHwptZ6Mrw/J/HNWr7V\nnPO/0FWby3jHSRWR7d/tGeDBfUPLfj3J4zOOxNY46RTb0Zf2MLZ7b2S75oYryC0rSWGLViadYpuN\nJL7GkdgaR2Kb/pbS+f8e8BLwS+D74X3nAfsS3SiROH97Rg3nNBRFtr/7TCe7eiZS2CIhVidv3yC9\n9z0a2S4582SKTj0+hS0SQgixGi2pzr9SahMQ0FofmLedp7XeY1D7lkxy/o/k8QX4hz/t58CwB4D8\nXDO3X7uJ+mJrilsmxOoQnPFx8Ls/x9sfuvOWV1FK46c+iCk3rW6cCiGESGMpqfOvtW6d1/G/GKhO\np46/iM2WY+Zrl6+n1B7qaEzOBPiXRw4w5vWnuGUCQot8zS70JbJT347HIx1/k8VC/d9cJx1/IYQQ\nKbGUUp9PKaXOC//8eeA3wK+UUrca1bjlkJz/2ModuXz18vXkWUL/5D3jM3z1sYPMBIJxv4bk8YlM\nlOrzdmz3XlwvvBrZrrpuG9aq8hS2KHFSHdtsJ/E1jsTWOBLb9LeUkf8TgefDP38YuBg4G/hYohsl\njLGpzM7nL1rD7P2i1/um+I+/tBMIxp/6JYSI38zwKD33PhTZLjplMyVnnZLCFgkhhFjtllLnfwQo\nBdYBj2itG8P7J7TWBcY1cWkk5//YfvtaPz+aV/bzms1lfPK8OpSsAZASsyk/LpcrxS0RiRT0+zn0\n/V/i6eoDINdZROOnb8q4VXyFEEKkh0Tl/C+luHQzcAdQDdwHoJRqBJZfO1KkxDtPqmBoyscf3xgE\n4E/7hii2WfjA6dUpbpkQ2WPggacjHX9lMlH3vuuk4y+EECLllpL28yFgFHgN+Ep432bg9sQ2aWUk\n5//YlFJ87OxaLm6cqy/+i119kYuBxUgen8hEqThvJ/YeYOivL0W2K6++CHtD9l1cy3uCsSS+xpHY\nGkdim/7iHvnXWg8Dty7Y9+eEt0gkhUkpPntBAxPTfl7uCtX9/6/nuiiymrm4USrPJJPL5ZI3yywy\nMzRC16//FNku2NxI6Vu2prBFQgghxJyl5PznAP8M/A1QA/QA/wP8m9Z6xrAWLpHk/C+NxxfgCw+2\nsXfADYBZwdcub+SM+sIUt0yIzBOc8XHwjl/g7R0AIKeogMbPfAiLw57ilgkhhMh0qajz/x/ApYSq\n+5wS/n4J8M2VNkKkji3HzL9e3sia8IJfAQ1fe/wQewemUtwyITKL1pqeex+KdPxNZjP1H7heOv5C\nCCHSylI6/+8ErtVaP6K1btFaPwJcD7zLmKYtj+T8L12h1cK/b2+kIj+06NC0P8g/P3yA9hFP1PMk\nNcU4ElvjJCu2rmd2Mrrrzch29fWXZWWe/3xy3hpL4mscia1xJLbpbymd/8VuM0h9yCxQ7sjlG9s3\nUGQNTQOZmA7wxQcPMDCZNhldQqStqYOd9O14MrLtPOsUqecvhBAiLS0l5/87wJnAV4EOYA2hOQA7\ntdafMqyFSyQ5/yvTOujmnx7Yj8cXWvm3riiPb12zkWJbTopbJkR68o1NcOA7P8M/GUqVs9VXs+7j\n78VkWUolZSGEEOLoUpHz/zngMeD7wE7ge8CTwD+ttBEifWwqt/OVS9eTYwqdW11j09z60AHGvf4U\ntyx7OZ3OyEJfIrME/X46f/7HSMff4rDT8IG3ScdfCCFE2jpq518pdcnsF3A+8BfgI8BbgY8S6vyf\nb3Qjl0Jy/lfu1NoCPn/xmkg+V9uwhy882MbDTzyV0nYJsRxG5p/27XgCd0dotWylTNS9/1pyildP\npSzJ7TWWxNc4ElvjSGzT37GGp+5eZP9srpAK/7w+YS0SaeGCdSV4Lgjyrac70IQuAO7a18055/op\ntMqophAjL+3B9dyuyHblNReRv2FNClskhBBCHFvcOf+ZQnL+E+uhlmG+/deOyNXehlIb37xqAwV5\ncgGQKLMpPy6XK8UtEfHydPZy6Pu/JBgIAFB0ymbq3nctSkn9AyGEEMZIRc6/WIWubCrlM29piGy3\nDXv4/ANtTEzLHACxOvmn3HT8/I+Rjr+1sozad26Xjr8QQoiMkHWdf8n5T7zZC4DxA6HYzs4BkAsA\nkQkSmX+qg0G6frED3+g4AOa8XOo/eD2mvNyE/Y5MIrm9xpL4GkdiaxyJbfrLus6/MMb2plLeeXJl\nZHv/kFwAJIrL5WLHjh2pboY4Bq01vX98jMm29si+uve+lbxyqdQkhBAic0jOv1iSB/cN8e3mzsj2\nxjIb39gucwBE9hv+68v07ng8sl1x2XlUXJ5Wxc6EEEJksYzM+VdKXamU2qeUalVKfT7G401KqWeV\nUl6l1D8s5ViRHNs3l/GZ8+sj2/uHPHzxwQNyB0BktYm9B+j73yci20VbjqP8svNS2CIhhBBieZLW\n+VdKmYA7gCuAE4AblVKbFzxtGPgk8J/LOBaQnH8jzebxLbwAaB1y84UH22QhsBWQHEnjrDS23p4B\nOn9xP7N3Se0NNdS+6yqZ4Iuct0aT+BpHYmsciW36S+bI/5nAfq11u9baB/wGuG7+E7TWQ1rrncDC\nXuQxjxXJtX1zGZ9ecAfgH/60n4HJmRS2SojE8o1P0v7jewnO+ADILSmi4UNvx5QjaW5CCCEyUzI7\n/7VA57ztrvC+hB67ZcuWZTVOHNv550fnN18VvgCYHf/sGPXy6f9tpWPEm/zGZbiFsRWJs9zYBmd8\ndPzk9/jGJoBQZZ+Gm2/AUuBIZPMympy3xpL4GkdiaxyJbfqTaj9iRa7aXMatl6zFYgpdAgxN+fjM\nn1rZOzCV4pZlDqfTGVnoS6QHrTVdv/kznq4+AJQyUff+67BWlae4ZUIIIcTKJPPedTfQMG+7Lrwv\nocfefvvtOBwOGhpCTy8qKuKkk06KXInO5qLJ9tK35+fxzX/cDPz/V5zMVx49xEDLK4wDnwtovrRt\nHdPtr6VN+9N5e1a6tCebtvfs2cMtt9yypOM3TgQY39PCrt4OAK665W8p2Lw+Lf6edNq+88475f3V\nwG2Jb/I/z2Q7MZ9n82Oc6vZk8vaePXsYGxsDoKOjg61bt7Jt2zZWKmmlPpVSZqAF2Ab0Ai8CN2qt\n98Z47peBSa31bUs99rbbbtM333yzYX/Hatbc3Bw5KWNpGZzinx8+yFh44q9ZwWcvXMO2DTKqfTSz\no/4ulyvFLclOxzpvFxp5aQ/dv30gsl163ulUv+1SI5qW8ZYaW7E0El/jSGyNI7E1TqJKfSa1zr9S\n6krgdkLpRndrrb+hlPoooLXWdymlKoGXgQIgCEwCx2utJ2MdG+t3SJ3/1Ooc9XLrQwfonzfx95az\na7n+xIoUtiq9Sec/fUwd6ODwXfegg0EACprW03DzDSiTZEgKIYRIrUR1/i2JaEy8tNYPAU0L9v33\nvJ/7gfqFxy12rEg/9cVWvv3WjXzxoQO0hyf+3vl8N6MePx/aWi3lEUXamh500fHz+yIdf2tVOXXv\nv1Y6/kIIIbJK1n2qSZ1/48zP5zuaMkcut129keMr5qqi/PrVfr7T3EkgmF0rSov0F8956xuboP2H\nvyXgDl2wWvIdNNz8DszWPKObl9HifU8QyyPxNY7E1jgS2/SXdZ1/kR4KrRa+cdUGzqovjOx7sGWY\nLz1ykKmZQApbln5cLhc7duxIdTNWrYDbS/sPf8vMSGhSlclioeGmG8gtKTzGkUIIIUTmSWrOfzJI\nzn968Qc13/prB4/tn8tnbyi28tXL1lNbJKOqIrWCMz4O33UP7vZQ8TClTDTc9HYKjmtMccuEEEKI\naInK+ZeRf2Eoi0nx2QsauPGUysi+jlEvf7+jhV3dEylsmVjtdCBA58//GOn4A9S+5yrp+AshhMhq\nWdf5l5x/4yw3j8+kFDedUcMXLlpDjjl0wToxHeCLD7Wx481Bsu3u03JIjqRxYsVWa033PQ8y0XIw\nsq/6um0Un3ZCMpuW8eS8NZbE1zgSW+NIbNNf1nX+Rfq6ZIOTb12zEac9VGQqqOGOZ7v47jOd+ALB\nFLdOrBZaa/p2PMHorjci+8q3nUPp+VtT2CohhBAiOSTnXyTd8JSPrzx2kJZBd2TfyVX5/Mul6yiy\nJrX6rFiFBh9/jv6Hno5sO8/eQvXbL5cytEIIIdKa5PyLjFXqyOH/Xr2RixtLIvte65vkk/e3cMjl\nSWHLUsPpdEYW+hLGcj2/O6rjX3hSE9XXXyYdfyGEEKtG1nX+JeffOInM48uzmPjCRWu4aWs1s92u\nvokZPv2/rTzbPpqw3yPE7Hk79loLvX94JLI/f8Ma6t57jSzitQKS22ssia9xJLbGkdimP/nUEymj\nlOLGLVV85bL12HJCp6LHF+Qrjx7irhe6ZR6ASJjJ/Yfp/tX/RiaX2+qqqP/g9ZgskmYmhBBidZGc\nf5EWDrk8fOmRg/RPzkT2bSqzc+sla6kpzO71AGZTflwu1zGeKZZj6mAn7Xf/juCMD4C8MifrPvFe\nLPmOYxwphBBCpA/J+RdZZZ3Txh1va4paEbh1yM3H79vHXw6MpLBlIpMt7PjnFOaz5sPvko6/EEKI\nVSvrOv+S828co/P4iqwWvnb5ej56Vi0WU+jC1u0L8u9PHubbf+3A65c0IBG/2Y7/zvYDAFjyHaz9\n2I3kOotS3LLsIbm9xpL4GkdiaxyJbfrLus6/yGxKKW44qYLvvHUT1QW5kf0PtgzzyftbODySfdWA\nXC4XO3bsSHUzssrCEX9LvoN1H38veeVSVUkIIcTqJjn/Im1NzQS4vbmDvxycq/6TZ1bcck4d25tK\npTyjiGnqUBftP/ptdMf/lhvJqyhNccuEEEKI5ZOcf5H1HLlmvnjxWj5zfj155tC5Ph3QfKe5k39/\n8jAT0/7UNlCkHen4CyGEEEeXdZ1/yfk3Tiry+JRSbN9cxvfe1sSaEmtk/1MHR/nwvXtpPpQdawJI\njuTKLdbxf6l1b4pblr3kvDWWxNc4ElvjSGzTX9Z1/kV2Wlti43vXNXHV5rkRXJfHz9ceP8TXHjvI\nsNuXwtaJVHMflhF/IYQQIh6S8y8yzjOHR/nes5243HNpP/m5Zj56di2Xb3TKXIBVxn24i8M/jO74\nr/3Ye7BWlqW4ZUIIIUTiSM6/WLXOW1vMj244ju1Nc6O6kzMBbnu6gy88eIDe8ekUtm7pnE5nZKEv\nsTSTbe3S8RdCCCGWIOs6/5Lzb5x0yuPLz7Pwmbc08M3tG6JKgu7qmeAjf9jHH14fIBDMrrtaItr4\nnhY6fvS7Y3b80+m8zTYSW2NJfI0jsTWOxDbxtNYMTs0k7PUsCXslIVLg1NoCfvD2zfx8Zy/3vTFI\nUMO0P8gPnu/mLwdG+PT5DawvtaW6mSLBXM/vpvcPjzCbtphTmM+aj7xbRvyFEEJkvBGPj9ZBN61D\n7sj3EY+fbyQoq11y/kXW2Dcwxbf+2sHhEW9kn0nBFZtK+eDp1TjtOSls3eJmU35cLleKW5L+tNYM\nPf4c/Q//NbIvr8zJmg+/S1buFUIIkXEmpv1HdPQHp2IXMfnGaTohOf8y8i+yxuYKB99/WxP3vNrP\nr3b34w9qgjq0OvBfDo7w7pMreftJFVgtWZfttiporem7/zGGn3klss9WV8Wav30HlnxHClsmhBBC\nHJt7JkDbcKiT3zLkZv+Qm57x+NJ5bDkmIJCQdmRd53/37t3IyL8xmpubOf/881PdjKPKMZt4/2nV\nvGVdMT94vpud3RMAeHxBfrqzlz/tG+LmrTVcsqEEk1QFyhhBv5/uex5gbPdczf78jWup/8DbMFvz\njnpsJpy3mUpiayyJr3EktsaR2IZM+4McGPaERvTDo/qdo17iybfJMysaS+1sKrezqSz0va4o4/wG\ndAAAIABJREFUj927diWkbVnX+RcCYE2Jja9v38BLnePc9WI37eFUoKEpH//xVDv3vTHAR8+q5eTq\nghS3NJTuIxOkFhecnqHj5/cx2Xo4sq/olM3UvudqTBZ5CxNCCJFavkCQQyNeWgdDo/ktg24Oj3iI\np+6IxaRY57TSVOaIdPbXlFgxm4wboJScf5H1AkHNQ63D/OzlXka9/qjHzllTxIfPrKGuyLrI0SKV\n/FNu2u++F09nb2Sf89xTqb7uUpRJ0reEEEIkVyCo6Rj1RuXoHxz24Iujp29SsLbEysYyO03lDjaV\n2VnrtJJrju/zLFF1/mXYTGQ9s0lx9eYyLl5fwj2v9fP7PQPMBEL/SZ9rH+OFjjEuWl/Cu0+pZJ1T\nKgOli5mRcdp/+FumB4cj+youO5/yy86VhdyEEEIYLqg13WPTUak7bcMepv3BYx6rgLqivHBHP5S6\n01hqT4t5h1nX+Zecf+Nkeh6fPdfMTVtruHpzGT95uYfH20YACGp44sAITxwY4az6Qt5zSiUnVOUn\ntW2ZHttEc7d30/HT+/BPTgGglKL6bZfhPPfUJb+WxNY4EltjSXyNI7E1TqbGVmtN/+RMZDS/JZzC\n4/Ydu6MPUFWQS1OZnY3ldprK7Gwos+PINRvc6uXJus6/EMdSkZ/L5y9ay/UnVnD3iz3s6pmIPPZC\n5zgvdI5zYqWDd59SyZn1hTLKnGQjL++h996HCQZCVQ1MZjO1N15D0SmbU9wyIYQQ2WJ4yhfu5E/R\nOuRm/5CHsQWpwYsps+ewMZyf3xT+XmjNnC615PyLVa9lcIp7Xh3gmcOjR8zCX1di5d2nVHLh+hJD\nJ98I0MEg/Q88xdBTL0b2me1WGj5wPY7GhhS2TAghRCYb8x5ZS3/YHbuW/kJFVkuk4s7s99IUrRsk\nOf9CJEhTuYMvXbqOzlEvv32tn8fbRvCHJ+4cGvHyjb+089OdvVxzXBmXbnAmfLEwWeQLAp5pun65\ng4mWg5F91soyGm66gdzS4hS2TAghRCaZmgmERvLDtfRbB930T8ZXS9+Ra2ZTmS3cyQ9NyK3Iz8m6\nDICs6/xLzr9xMjWPL171xVb+8YI1fOD0an6/Z4AH9g3jDU/q6ZuY4Ucv9vDjl3o4q76Iyzc5Oauh\nCIvcDVix6UEXHT/9A9MDcxN7C4/fQO2N1xyzhn88sv28TSWJrbEkvsaR2BonmbH1+AJztfTDI/pd\nY9NxHWu1mNgQ7ujPpu5UF+atijWAsq7zL8RKlTty+djZdbx3SxX3vznIH98YZGI6lH8e1PBcxxjP\ndYxRbLVw6UYnl29ysrZEqgQtx+T+w3T+z/0EPN7IvvJLzqbiyguybqRFCCHE8s0EghwMd/Rna+l3\njHrjqqWfY1Y0Om1RqTv1RcbW0k9nkvMvxDF4fAH+emiUh1td7OmbjPmczeV2Lt9UykXri8nPW9o1\n9WpM+9Fa43rmFfp2PIHWobsrJouFmndup/i041PcOiGEEKnkD2raRzxRlXcOj3gjKblHY1awzmmb\nK7FZZmet05YVd+ol51+IJLHlmLl8UymXbyqle8zLI60uHt3vYmjeZKF9g272Dbr5/rOdnFiVz5n1\nhZxVX0R9cZ6MYC8Q9Pnpu/8xXC+8GtmXU5BP/Yfejr2hOoUtE0IIkWyBoKZrbHbRLA+tQ1McGPZE\n1uM5GgU0lFhDo/nhEf31Tht5aVBLP50ltfOvlLoS+A5gAu7WWn8zxnO+C2wHpoCbtNa7wvsPA2NA\nEPBprc+M9Tsk5984kiMJtUVWbjqjhg+cXs0r3RM83DrMs+1jkdGIgIZXeyd5tXeSH77YQ3VBLmfW\nF3FWQyEnV+WTu8rfkKYHXXT+z/14ewci+2z11TR88HpyigoM+Z1y3hpHYmssia9xJLbGOVpstdb0\nTsxEaui3DLppG3bjibOWfm1hXlTqzoZSG7ac9Kyln86S1vlXSpmAO4BtQA/wklLqfq31vnnP2Q40\naq03KqXOAu4Ezg4/HAQu0lqPJKvNQizGbFKcUV/IGfWFjHv9PHFghMf2u2gdckc9r3dihvvfHOT+\nNwfJs5g4raaAM+oLOaHSQUNxKN/Q5XLR3Nycor8keUZe3kPvfY8SnJm7Y1K05Thq33UVphy5CSmE\nENlEa83glO+IRbMmZwJxHV+Zn8vGMjubykOTcjeW2SlYYlqtiC1pOf9KqbOBL2utt4e3vwDo+aP/\nSqkfAE9qre8Jb+8l1OHvV0odArZqrYdjvHyE5PyLVBp2+3ipc5wXO8fY2T1x1NEMW46JTWV2Nlc4\n2Fwe+p6q2sFGCnin6b3vUUZfeSOyz2Q2U/nWS3Cee6qkRQkhRBYYcfsipTVnq++MxrloltNmiRrR\n31hmp8SWfZ+HK5WJOf+1QOe87S5gYerOwud0h/f1Axp4VCkVAO7SWv/QwLYKsSyl9hyubCrlyqZS\nZgJBXu+b5IXOcV7sGKd7PLr8mMcXjKQIzarIz2FzeehioKnCkfG3ND3d/XT94n6mh+Zu2OWVOal7\n/7XYaitT2DIhhBDLNe71R1XdaR1yMzQV36JZBXlmmsId/Nkym2WOXINbLObLpPsn52mte5VS5YQu\nAvZqrY/Ilbj99ttxOBw0NIRWBC0qKuKkk06K5J/NplfI9tK356empEN70n0712zCfeg1TgJuedf5\ndI95+dmORzk47GGy4jhcbj/jB3ZHYlrYuIW2V1+iDXi6cQsAkwd3U5Gfy3nnnU9TuZ2JA69SU5jL\nxRdekPK/72jb5513Hq5nXuHBu36KDgY5tTr0/7Gt0IzzzA1sDHf8k9GePXv2cMstt6RVfLJl+847\n75T3VwO3Jb7yeZYO26edeQ5tw252PPIXusa8eCqPp3diJvL5VRj+vFr4eTZ+YDdWi4kzzj6XTWV2\nZtpfo67YyrWXXYRSiubmZnQXlK1Nr783nbb37NnD2NgYAB0dHWzdupVt27axUslO+/mK1vrK8HY8\naT/7gAu11v0LXuvLwITW+lsLf89tt92mb775ZgP/ktWruVkmSCXKbC7kvoEp9g26efKpp5ksP47p\nOKobzJYxi9wiTbMyZv4pDz2/fYDxN9si+0y5OdTccAXFp52Q9PbIeWscia2xJL7GkdjGNu0Pzls0\na4rWIQ+do17i6SnmmRWNpXYsvW9w5SUXsqncTl3R6lg0K1kSlfaTzM6/GWghNOG3F3gRuFFrvXfe\nc64CPqG1vjp8sfAdrfXZSik7YNJaTyqlHMAjwFe11o8s/D2S8y8ylT+oOezysDd8QdA65KZziQuY\nzN5KbSq3U5eCBUwm9x+m+54H8I1NRPbZaiqoe/915JU7k9oWIYQQi/MFghwa8dI6r/LO4RFPXJ85\nFpNivdMWydHfVGZnTcnqXTQrWTIu519rHVBK/R2hjvtsqc+9SqmPhh7Wd2mtH1BKXaWUaiNc6jN8\neCVwn1JKh9v8y1gdfyEy0fxFvjaU2dlQZuet4cdmly5vmTeBauHcAQBfQEfWGpg1u3R5U+TN2UFN\nYa4hE2wDbi99f36SkRdfi9pfet7pVF5zESZL0t5qhBBCLBAIajpGvZHPkdYhNweHPfji6OmbFKwt\nsc7L0Xew1mkl17y6S1dnsqR+ImutHwKaFuz77wXbfxfjuEPAlnh+h9T5N47cJk0+W46ZE6vyObEq\nP7JvctrP/mFPVEWF/smZI471+oO83jfF631TkX35uWY2ltnYVO6ITLQqd+Ss6IJg/PVWev/wKL6J\nuYnLZpuV2ndfReEJG5f9uoki561xJLbGkvgaJ5tjG9SanvHpqEGjtmEP0/5j19JXQF1RdC39xlI7\n1iWsUZPNsc0WMhwnRIbJz7Nwak0Bp9bMLYo16vGF3uSHPKE8zUE3Lo//iGMnZwLs6plkV89cR73I\naolcCMymDDnjKDnqn5ii94+PMvZaS9T+whM3UX39ZeQU5i9ypBBCiETQWtM/OXNELX13nItmVRXk\n0lRmZ2O5nabwnWdHbuZWmBPxSVrOf7JIzr/INPPTfhJpaGom6sOgZdDNxHR8i6uU2XOiRn42ldkp\ntIbGCrTWjO58nb4dTxDweCPHWPIdVF9/GUUnNy32skIIIVZgeMpHy9BUpLO/f8jDWJy19I/2vi4y\nQ8bl/AshkqvMkUuZI5dz1xQDoU573+QM+wfn6jIvNkI05PYx1D7Gs+1jkX3VBbkclxdg86sv4uzv\no9BqwWIOvQeVbD2JymsuxuKwJeePE0KILDfm9dMSrrizf9BNy9AULnd8Hf0iq4WmBYtmZeMikmJ5\nsq7zLzn/xpE8vsymlKK6II/qgjwuWF8ChHJDu8emI3cHWofctA25jyg5qgIBcna9ht73Gq3+uQ+f\nnJIiTFdeTMMJG9k0GaAxL7ik3NBkkPPWOBJbY0l8jZNusZ2c9rN/KFxi8yhzuWIJzeUKdfJnCzys\ndC7XSqRbbMWRsq7zL0SmcblcUQvOJJNJKeqLrdQXW7l0Yyj9aLYqRMtgqM5z/6595D37AtaJ8chx\nWik612/iwHEnE/DkwPPd4dcLVYXYVOaI3FZe57SSI1UhhBACiL+KWyxWiylcdWeucINRVdxE9pKc\nfyFETJ7OXvr+90mmDnUSDGomZgKMefwMW/PZdfIZvGkuiG8NApM6YlEyqQcthFgNZvxBDrg8oTur\ng25aMnD9FpE+JOdfCGGImZFxBh58mtFdb0T2mUwKZ0k+Te84B+d5p/E3Fgtef5CDwx5aBqfCKUOx\nV4L0BXXkVvas2ZUg53+o1cpKkEKIDOYPatpHokf0D7k8xLFw+xErtzeV21lTkj4rt4vsknWdf8n5\nN47k8RknHWIb8E4z9OTzDD/9MsF5ef1KmXCeeyrll50XNaHXajFxfKWD4ysdkX1TMwHaZnNWwxOK\ne8aPzFudDmjeHJjizYG5NQjsOabIIjKbykNfVfkrv52dDrHNVhJbY0l8jbPS2AaCmq6x6EWzDgx7\nmImjp6+AhmJrdC19p43cNJsvtVxy3qa/rOv8CyGWJuj3M/rSHgYebsY/5Y56rPCEjVRefRF55c64\nXsuRa+aUmgJOmbcGwbjXH5lMPHvbe2jKd8Sxbl+QV3snebV3bg2Cwry5iWyzo2Gl9tRNZBNCrD5a\na3onZqLKJrcNu/HEWUu/tjAvUnGnqdzOhlIbthyppS9SR3L+hVilgtMzuF54leGnXsQ3Phn1mK2u\niqprLsbR2GDI73a5fZEP0dnvo3HWqnbaLEfUqi62SQk7IcTKaa0ZnPJFLZrVNhz/GikV+TmR96am\nMgcbymwU5Mk4q0gMyfkXIksYtcjXYvxTHlzP7GT4mZ0E3N6ox3KKCqi86kKKTj3e0NF1pz2HsxqK\nOKuhCDjyA3c2ZSjWB67L4+f5jnGe75irPhT6wHWwqdwWmVScLx+4QohjGHH7aAnflVzpQMTGMjsl\nMhAhMkDWfTpKzr9xJI8vs/lGxxl66iVGXniVoC867cbisFN64RmUnnc6ptzkf3gppajIz6UiP5fz\n180tStYzPhO5EJi9S+D1H3mrfWDSx8DkKM2HRyP7agrzaCq3E+zcw7WXXyy32g0g7wnGkvgm1rjX\nH3k/eeIvTzNVeXzMFMRYCvLMUQUKNpVJCuJi5LxNf1nX+RdCRJsedDH0xPOMvvIGOhjdcc51FlF2\n0VkUbz0JU056vR0opagtyqO2KI+LG0OLksWaZNc27MEXY5Jdz/g0PePTjB8Y4qmZ/Vk/yU4IMcc9\nE6Bt2B1Vead3Yq74wHj/FIX5sTv+84sPNJXb2Zig4gNCpAvJ+RcixYxI+wn6/Uy8eYDRF19jsvUQ\nC/+fW6srKL/4LApP2YwyZXbnV8rrCbG6ef1BDgxHp+50jU0fUXY4ljyzYkOZPaqzL2WHRbqSnH8h\nxBG8PQOMvPgao7veOCKfH8Cxto6yS84mf/P6rBnFsphCawY0ltq5Krxvxh/koMsTdYegI8bCOgEN\nbcMe2oY9PMAwALlmRWNpaO6ALKwjRHrxBYIcGvGG/l8PumkdmuLwSJyLZpkU60ttUR39hmL5vy1W\nn6zr/EvOv3Ekjy89+ac8jO16k9GX9+Dp7o/5nILNjZRdcjaOdXVJbl1q5FpMbK5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "\n", + "def stock_loss(true_return, yhat, alpha=100.):\n", + " if true_return * yhat < 0:\n", + " # opposite signs, not good\n", + " return alpha * yhat ** 2 - np.sign(true_return) * yhat \\\n", + " + abs(true_return)\n", + " else:\n", + " return abs(true_return - yhat)\n", + "\n", + "\n", + "true_value = .05\n", + "pred = np.linspace(-.04, .12, 75)\n", + "\n", + "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred],\n", + " label=\"Loss associated with\\n prediction if true value = 0.05\", lw=3)\n", + "plt.vlines(0, 0, .25, linestyles=\"--\")\n", + "\n", + "plt.xlabel(\"prediction\")\n", + "plt.ylabel(\"loss\")\n", + "plt.xlim(-0.04, .12)\n", + "plt.ylim(0, 0.25)\n", + "\n", + "true_value = -.02\n", + "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred], alpha=0.6,\n", + " label=\"Loss associated with\\n prediction if true value = -0.02\", lw=3)\n", + "plt.legend()\n", + "plt.title(\"Stock returns loss if true value = 0.05, -0.02\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note the change in the shape of the loss as the prediction crosses zero. This loss reflects that the user really does not want to guess the wrong sign, especially be wrong *and* a large magnitude. \n", + "\n", + "Why would the user care about the magnitude? Why is the loss not 0 for predicting the correct sign? Surely, if the return is 0.01 and we bet millions we will still be (very) happy.\n", + "\n", + "Financial institutions treat downside risk, as in predicting a lot on the wrong side, and upside risk, as in predicting a lot on the right side, similarly. Both are seen as risky behaviour and discouraged. Hence why we have an increasing loss as we move further away from the true price. (With less extreme loss in the direction of the correct sign.)\n", + "\n", + "We will perform a regression on a trading signal that we believe predicts future returns well. Our dataset is artificial, as most financial data is not even close to linear. Below, we plot the data along with the least-squares line." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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rxGEScD7iw905LsvJtgDPXlCDmZbMLBdR/wxRwi8iIiJtkk25TrolQOPuxhfn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\nbmHfXv3cEzPrDQwKn88md/8H8JcUz/fn7r7R3d8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Code to create artificial data\n", + "N = 100\n", + "X = 0.025 * np.random.randn(N)\n", + "Y = 0.5 * X + 0.01 * np.random.randn(N)\n", + "\n", + "ls_coef_ = np.cov(X, Y)[0, 1] / np.var(X)\n", + "ls_intercept = Y.mean() - ls_coef_ * X.mean()\n", + "\n", + "plt.scatter(X, Y, c=\"k\")\n", + "plt.xlabel(\"trading signal\")\n", + "plt.ylabel(\"returns\")\n", + "plt.title(\"Empirical returns vs trading signal\")\n", + "plt.plot(X, ls_coef_ * X + ls_intercept, label=\"Least-squares line\")\n", + "plt.xlim(X.min(), X.max())\n", + "plt.ylim(Y.min(), Y.max())\n", + "plt.legend(loc=\"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We perform a simple Bayesian linear regression on this dataset. We look for a model like:\n", + "\n", + "$$ R = \\alpha + \\beta x + \\epsilon$$\n", + "\n", + "where $\\alpha, \\beta$ are our unknown parameters and $\\epsilon \\sim \\text{Normal}(0, 1/\\tau)$. The most common priors on $\\beta$ and $\\alpha$ are Normal priors. We will also assign a prior on $\\tau$, so that $\\sigma = 1/\\sqrt{\\tau}$ is uniform over 0 to 100 (equivalently then $\\tau = 1/\\text{Uniform}(0, 100)^2$)." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 100000 of 100000 complete in 17.2 secPlotting prec\n", + "Plotting beta\n", + "Plotting alpha\n" + ] + }, + { + "data": { + "image/png": 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cg7VGrmHaKfexa5henArgXOM/8zbyuDch4CcntOPKY9ryxer4F/TetPsAG3bu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\nEVkuIitE5NIizw8Xkfki0i4iHSLy9WLvY6mGpJSQ5u9DySW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BRLaKSL7/35igOveIyBoRKRSRC4L254jIUr+m9Qkv/DEMo+7iZDhyGxA8ZbGr\nf18wW4E9qnoUOCoinwFDHNYFYPbs2axftJ6y7GyKDhynXpNMmnbuXfGSDixvU1vb364t4O7nl0PH\nQT4Hl39N8a5DFcdXFyykeN3eqOcLrNoWT3vy8g4xatQo3lu1t9Lx3YdKgpb7GVZRfnnmDqATAPvW\nLCYvr7jil0I0e3l5eexfu46G3U9x3L45x9dDw54hj/9x1rsx+ZuXl8fuVRugy8mOym9d/hXFOw95\ndn+E29Zhp9f4fOWqFduXz4CmDTIoWpnvqH7T/jk1tv/z11dRf/tyio+UVBz/+zsf1vj7Obx9LWVH\nfD1/E/OfZ/jw4eTm5uI2qnpMRM5R1cMiUg9YICLv+Q8/rqqVFmkUkQHA1cAAfM+oD0Wkj/p+yUwD\nblLVRSLyrohcqKpzq9p0unZkovByDT1bO9LWjgzG1o6MDSdB2CKgt4h0B3YA1wLjq5SZAzzlf+A1\nAk4HHgdWOagLQO/evenZ8yqGdGrGkh3VZ6tVnUVXG9vtWjSqyJq+tXkfspqfON536AgWlO6IWN/p\ndvG6gpDHpetJfFN0kOVBwUak8w3IyeZ9/1qCrfoMY9SoUxy3Z9SoUbRc17wiaa0Te4VRjjvZDvg+\natQo2mxpyW7/Oo7B5ZfvPFitfscBp7KpWXG186XCtlDd/+DjWqX84ZLyWm9vaedBZMVQ3sl28L5n\nbh5Gfn4+iUJVA+LCRviec+EWSACfTnWWqpYCG0VkDTBCRDYBzVV1kb/cS8A4oFoQZiQG0xelHnbN\nYiPqcKSqlgG3AfOA5fgeVoUicouI/MxfZiW+B9NS4AvgOVVdEa6u205UW5zbJbyeZX/fhxuiap9m\nFhSd2AhqcLk6W1w8mQg3HPrasuozDONNmZEURBn3nRnDsGxVoq38kCz8bXFR9EI1QEQyRGQxUAR8\nEBRI3SYiBSLygn9WN1TXrm7z7+uCr5c/QFhNq2nCvMNr+6YJS1/7buAoWauqvg/0q7Lv2SrbjwGP\nOakbiqFDhzIrn5C9YNHI356YF3JthTCRcmWFW08ywItBKRGCX7+HjpcxZnoB5/dpXdPmJRQnOdKK\nDlRfUD2VCQ7BYskRV5d46esdPJzA0TtVLQeGiUgW8LqIDASeAe5XVRWRB4EpwM2Ja4VhGEZkkipj\nfrzsOpioNerCh2HJ2MkUqk0frHE+I9CNDPuJYG0cCXC9wsltEcs1MWqGqhaLyCfAmCpasOeBt/yf\ntwHdgo49CRhrAAAgAElEQVQFtKvh9lfjySefJDMzk+xsnwS2RYsWDB48uOKXeiCfUaK2p02bVqv2\ngreDczW5ff7AkHVAb1fb9p1sb1/xNcX+Z5RTjWRgX6waS3I6VbJf9Tuobf9D2Z86dSobNmzgiiuu\n8MR+ou3l5eWxebNP9uOGrlWSJbP1lClTdFb5MK+bUYmmDTLCDu/8+NRO/OVrd2aMhdKExcOIblks\nTLFhuoDv824exg9nLXc0o7Iu4da1T0UezlFyc3Ndj/xFpC1Qoqr7RaQJPqnEw0C+qhb5y/wCOE1V\nr/P3kr2MT8vaBfgA6OPvMfsCmIRPG/sOMNXfu1+JKVOm6IQJE9x2xTF1VZifCvZvfGwWRTEI87/6\nte+lPfzR+bHbyunEDTkdK7a99j3d7efn59f4GVYnesISRSR9TXKErpVJtQAsGEvuabhIJ2CGf8WO\nDOAfqvquiLwkIkPxjdxvBG4BUNUVIvIKsAIoASbqiV+ntwJ/ARoD74YKwMA0YV7itX1bOzJ97btB\n0gRhAU1YOpKuPSFwwvfr/v4NJdHWD6qDpPO1TxSqugxf3sKq+2+MUOch4KEQ+78GBrvaQMMwDD9u\nJWtNO9IvXEgs6RiAGXUHWzsyMdjakZHx2ndbO7LmJE1PWGDtyHQknXVB6ew7mP+GEQnLOZV62DWL\nDesJi5Ny67kxDMOPacK8w2v7licsfe27QdIEYV4/xGLFzUSo6dwTks6+g/lvGIaRziRNEJZqWEeY\nYRgBTBOWGEwTFhmvfTdNWM0xTVicLI0js3840lkXlM6+g/lvGJEwfVHqYdcsNhz1hInIGBFZKSKr\nReTuEMfPFpHvRCTf/+/eoGMbRWSJiCwWkYVuNt5LVuw65HUTDMNIEryWU5gmzDtME5a+9t0gak+Y\nP+Hh00AusB1YJCJz/It2B/OZqo4NcYpyYLSqRlyJ2vKEpSfp7DuY/4ZhGOmMk56wEcAaVd2kqiXA\nLODyEOXCpe4Xh3YMwzBSEtOEJQbThEXGa99NE1ZznGjCugBbgra34gvMqnKGiBTgW+D2P1V1hX+/\nAh+ISBnwnKo+H8pIqmnC3CSddUHp7DuY/4YRCdMXpR52zWLDLWH+10C2qh4WkYuAN4C+/mMjVXWH\niLTDF4wVqmrqh6+GYRh+TBPmHV7bt7Uj09e+GzgJwrYB2UHbXf37KlDVg0Gf3xORZ0SktaruU9Ud\n/v27ReR1fL1o1YKwtWvXsn7RPBq18q0QX69JJk07967oJShe5+vur4vbWb2GJlV7bNu2E7F9ePta\nyo74JrQc+7aIgowLyM3NxTAMI10RjZJ0VETqAavwCfN3AAuB8apaGFSmg6ru9H8eAbyiqj1EpCmQ\noaoHRSQTmAfcp6rzqtqZP3++Ts4PJyszDKOu8XCOkpubWyf+6KdMmaITJkzwzH5eXp5nvQKJtB3Q\nFkUa4vLSd4AbH5tFUct+jst/9WvfD4/hj86P3VZOJ27I6Vix7bXvoew7uWaJtF+b5Ofn1/gZFrUn\nTFXLROQ2fAFUBjBdVQtF5BbfYX0OuFJEfg6UAEeAa/zVOwCvi4j6bb0cKgAD04Slqy4onX0H898w\nImH6otTDrllsONKEqer7QL8q+54N+vwn4E8h6m0A7A1jGEadxjRh3uG1fdOEpa99N0ia1BFeP8S8\nJJ17QtLZdzD/DcMw0pmkCcIMwzBSFcsTlhgsT1hkvPbd8oTVHFs7MglIZ11QOvsO5r9hRML0RamH\nXbPYsJ4wwzCMGuK1nMI0Yd5ha0emr303SJogzOuHmJekc09IOvsO5r9hGEY6kzRBmGEYRqpimrDE\nYJqwyHjtu2nCao5pwpKAdNYFpbPvYP4bRiRMX5R62DWLDesJMwzDqCFeyylME+YdpglLX/tukDRB\nmNcPMS9J556QdPYdzH/DMIx0JmmCMMMwjFTFNGGJwTRhkfHad9OE1RxHmjARGQM8wYm1Ix+pcvxs\nYA6w3r/rn6r6oJO6AUwTlp49IunsO5j/hhGJ2tQXFe48RNHB4zHVyRDYdagEWiaoUSmIacJiI2oQ\nJiIZwNNALrAdWCQic1R1ZZWin6nq2DjrGoZhpCxeyylME1ZzPlizl7dX7o29YpeTXbEfD3Xlu09V\n+27gZDhyBLBGVTepagkwC7g8RDmpQV3PH2Jeks49IensO5j/hmEY6YyTIKwLsCVoe6t/X1XOEJEC\nEXlHRAbGWNcwDCNlMU1YYkgFTVjxOu+uvde+myas5riVJ+xrIFtVD4vIRcAbQN9YTmCasPTsEUln\n38H8N4xImL4o9bBrFhtOgrBtQHbQdlf/vgpU9WDQ5/dE5BkRae2kboBPP/2U9dvn0ahVRwDqNcmk\naefeFS+owK8N265b2wGSpT3mf+K2D29fS9mRQwAc+7aIgowLyM3NpS7gtZzCNGHe4eWPKK99T3f7\nbiCqGrmASD1gFT5x/Q5gITBeVQuDynRQ1Z3+zyOAV1S1h5O6AebPn6+T80PJygzDqIs8nKPk5ubW\niT/6+fPna05OjtfNMGrA1LzN8QnzY+SrX/t+eAx/dH7MdW/M6cQNOR3dbpIRJ/n5+TV+hkXVhKlq\nGXAbMA9YDsxS1UIRuUVEfuYvdqWIfCMii/Glo7gmUt2aNNgwDCPZME1YYjBNWGS89t00YTXHkSZM\nVd8H+lXZ92zQ5z8Bf3JaNxSmCUtPXVA6+w7mfyIQkUbAZ0BDfM+42ap6n4i0Av4BdAc2Aler6n5/\nnXuACUApcIeqzvPvzwH+AjQG3lXVO2vXm/TG9EWph12z2LCM+YZh1ClU9RhwjqoOA4YCF/llEpOB\nD1W1H/ARcA+Afzb31cAA4CLgGREJDDFMA25S1b5AXxG5MJRN04R5h9f2TROWvvbdIGmCMK8fYl6S\nzj0h6ew7mP+JQlUP+z82wtcbpvhyFM7w758BjPN/HotPKlGqqhuBNcAIEekINFfVRf5yLwXVMQzD\nqDFJE4QZhmG4hYhk+DWqRcAH/kCqYgKRqhYB7f3Fq+Yz3Obf1wVfbsMAYfMcmiYsMZgmrDJHS8vY\nc+g4uw76/r31wccVnyP923c4tuWYnGKasJrjVp6wGmOasPTsEUln38H8TxSqWg4ME5Es4HURGYSv\nN6xSsdpvmRELpi+qzKtLd/H68t0V2/vXbqLF1lZR6/1iVDbn9WmdyKZVYNcsNpImCDMMw3AbVS0W\nkU+AMcDOQDod/1DjLn+xbUC3oGqBfIbh9ldj7dq1TJw4kexsX1rEFi1aMHjw4ArNSuAXe6K2A/tq\ny17w9qhRo2rVXqLsb1i2Exr0BGLLg5fVa2jMefMC++LJu1dSphG3Q9Vf9tUXNN6Z5cn1qUvbgc+b\nN28GYPjw4TXOdRg1T1htYXnCDCO9SFSeMBFpC5So6n4RaQLMBR4Gzgb2qeojInI30EpVJ/uF+S8D\np+MbbvwA6KOqKiJfAJOARcA7wFT/jO9KWJ6w1CcV8oTFy11nZXNB3za1Zi9dqJU8YYZhGG7Tp22T\nRJ6+E/CxiBQAXwJzVfVd4BHgfBEJJJB+GEBVVwCvACuAd4GJeuLX6a3AdGA1sCZUAAamCUsUpglL\nXttgmjA3SJrhSNOEpacuKJ19h/T1v54krtdbVZcB1bqlVHUfcF6YOg8BD4XY/zUw2O02Gs4wfVHq\nYdcsNqwnzDAMo4Z4nWLH8oR5h5c/orz+Aef1d++1fTdImiDM64eYl3j9h+Ql6ew7pK//yaFENQzD\n8BZHQZiIjBGRlSKy2i9oDVfuNBEpEZEfBO3bKCJLRGSxiCx0o9GGYRjJhGnCEoNpwpLXNpgmzA2i\nasJEJAN4Gp+QdTuwSETmqOrKEOUexjcTKZhyYLSqfhvJjmnCvOsR6dCsITsPJiaZXzS89t1r0t1/\nw4iE6YtSD7tmseGkJ2wEvllBm1S1BJiFb/mPqtwOzOZE7p0A4tCO4REvXj2Q1288xetmGElG1xaN\nEnbuJMmM4xpeyylME+YdpglLX/tu4CQ4qrqkR7WlO0SkMzBOVafhC7qCUeADEVkkIj8NZ8Trh1g8\nNK7vTmzp9R9S/Qwhs2E9TuualXBbj1zUu9J2bfv+m3N61IqdmeNPdlTO62sfiUTOYJw0qlv0QoZh\nGHUct3qongCCtWLBT++RqpoDXAzcKiIpE7r+6NROEY/P+VHd6j367bk9XDnP9we1C3uscQNvO0VH\n94q+xIcbeO2nG2QkMHdy37ZNE3dyDzBNWGIwTVjy2gbThLmBkzxh24DsoO1QS3cMB2aJiABtgYtE\npERV31TVHQCqultEXsc3vFntm3vyySdZv/0YjVp1BKBek0yadu4d17IObm136HUAaB72+IIFh4DM\nSsd7Dj6NA8fL2L0q37G94D8kr/w9cTNn1vh8Pz+jKzPe/CDk8f7thnLFye34+NN/sfG7o9W+g0T7\nG9AdhjreJasRB9oNcMXe5wsWULxunYP2xO//0E7NWN+0d8K+r93NG0F7d76P4nUFHN6+lrIjhwCY\nmP+8K0t+GHUb0xelHnbNYiPqskUiUg8IZJjeASwExqtqYZjyLwJvqeo/RaQpkKGqB0UkE5gH3Keq\n86rWmzJlis4qDy/Mv3NUN57I2xL2eCJ4/cZT+P5LS8Men3fzMC54YXHFdodmDfnrtYOY8tkm5q7e\n59iO1+LseTef+N6D/anJ+cKdJ2Dr7cI9TF2wJW7fsxrVY9ygdryUX+Ra2+b86BTW7zvC7+au5+Dx\nspjbFEy0eydAKP97tm7M+n1Ho9YdP6QDM5fsjLuN0ejfrikrdx+Oud7EM7ryzOdbI5aZd/MwV5b8\nSBZs2aLUx5YtMmKlVpYtUtUy4DZ8AdRyYJaqForILSLys1BVgj53APJEZDHwBb7grFoABtE1YS2b\nJE1y/6gMj1Fb5XYAdnKHTFfPF2D80A6Oy/Zo1dhRuXh9b9G4PjfkVB8unvb9fgzr3Czm83Vq3pAm\nDeoxqEMzIkmhGtRzN2YI5f9vzj0par1hnZtx9RDn1yMe2mY2jKuey1+RYRhGncWRcEVV31fVfqra\nR1UD6609q6rPhSg7QVX/6f+8QVWHquowVR0cqBsPUk3vn7yceVJLV8/3k+GRtWlVadcsvpdnNLq1\ncBZYAdwx0hvhda82TWnZpEHM9R65+MSEgRHdwgfRPzi5fVztcsrk0d3Jbhn9e/5d7klkNqwX07kH\ntK8dHZYkUNCfrJgmLDGYJix5bYNpwtwgadTDXj/E3CQjxpdQpD+k3m2a0CdGEfPP/6OLa70R3eJM\nUzCoYzNaN43ee5mIh0i0IfZQdGx+ws/bv1fzADJcGzo1rxwgB/vfu00Tzu3dusa2a5Np3+9Xbd/Q\nOHoiDSMUkyZNMo1RimHXLDaSJgirDS7p73xMvOrL0gnJ0AFww7COtGzSgF+d1d2V8/VtdyIADOVf\n9wjDjonsvYzU21LTFFRNY+xhckrvNk2Yenn1oCUeovU2tQ4xfB/L9Zh9Q/U1q0d0y6o2zNyrTeUf\nCP/3/f50jaHHtK7gdYodyxPmHZYnLH3tu0HSBGG18RC7bEA7mjdy9oKNFlCd5FDz5AQ3/5DcHoqM\n9tp+5KLeDAqjQVMH4VBV3y/ok7w9QU1jSDsRKkj6Xo+WtGhcOTj6xbUXx9WWRlFy1P3yrOyIxyPR\ntEEGWY3rUzWcVY0e4PZs0yRuu4ZhGOlG0gRh0QjOWfTk2L61YDF8v8Fjl/Tm8ctqow2x09BlVfQP\ng8Tvoc7cumkDbj6tc8i6sY4KXtq/LSN7uKCnS1A29heuHOC4L0lVefWGwUy/ckDEciK+WbUAgzo4\nH8arHyWJV8vGoXVx4QJmJygOojA/z1/RP247qYjXcgrThHmHacIqY5qw2EiaKYfBa0e2bdqAPYdL\nKh1v0uBED1a9RGaR9BPJxCmdmofcH2+r3EhRMaJbFvVEOMs/KSBUT95ZJ7Xksw3fxXTemvSsOQnC\nAr43yBDGDmrLjmJv1rB0QqTZghkC5VX8bdG4frWer6qsWryQP155IXkb93NhX/d6AcP1Qj5ycW8u\nfXFJDc7rjO6trEfMqDmmLUo97JrFRlL1hJ3TqxWTRnbjjO4tqh0b3DGTywa05a4aDLOIQJcsZ0Lz\neAKqeDRh9TOEXH8W9/bNqvdetHOYJuDi/m2474KeNKgX/pLem3sSveMYLgosz9S/fWy9KJFe2FWF\n67N/OJgerZq4oqur7WUJ62fEpn67dEDbStttMxsyblC7Sj80EoEINAxxf/zX+dFTYgSINOnheyH+\nbtMF04R5h9f2TROWvvbdIGmCsKFDh9KtZWMuHdA25ItYRLh9ZLcaJ5z7rYMcTAF7TYI0QO0yGzBp\nZDemujAU2jKod+SyAW154KbLmTq2L/ec06Nif9+2TTm3V6uQa+z5xM/xzVp84rK+vHDlAK4c7Eu1\nEElYH2DmdSfz4lUD6FwlgA0MfbaPYxJDgMBDJBCAxBqDvXBF9eE+t4Ow3m2acF2EHGl/Hz8opvP9\nMKdjxed+w0bE3a5IZIXogQv13T5xWd+wqUeq9uJF04TVsTW5DcMwEk7SBGG1RYfmDRnooEdHpLK4\nWsTXgxG5Nyh0CPHEZX35/skn1lP8+RmV1j8nQ4T+7TMr5Yfq27Ypk8/pQZum1XvHerZpQlajyMNc\nTcKIyBvWzyC7ZWN+fGon7jorm0eD8mMBTBrZrdJC3qpKZsN6dAnxon7th761M8P11sWTKiLWnrDs\nEEFkozC6uHgTrT7z/f78eHho3RtAyyYNYgpAWkYZoozEtUM68MszI/cGv3jVADo1rx6kh0oiHO4H\nD8BPhndmVA/nvVvtMmPPz1ZXME1YYjBNWPLaBtOEuUHSBGHBD7Fo7+5QL7F/XH9y1CSXscQEl1UZ\nMoqXG3M6MrBDZshgKkDgRmoeJbCKRNUBsdO7RX55NqyfwQV929CqSmLTSwe05b/H9ApbLzhAC56h\n1zFEb1ikr/vsnr4h2KoPkdYOE61GCqfC9Za++aMhlbZrQVoYkuDgftXihTHVnXBaZ8b0C98bfEn/\nNhUBc7+g9CK/yz0pbIb9cIFvVuP6/P68nlzjrzd+aMeQf0P3X9CTYZ2bM35Ix+oHDaMGWM6p1MOu\nWWwkTRAWC+2bNaykYxnUIZNWTRpwb24PV87/3BX9XQvCRvmF8lWH8uLFaS+KW5MXqr5z7zyzG9/r\n3oInqswOHTuwHVWJFPRmNa4fcmWB3m2bcsXJ1c8VC6F0T1D9O+nRqjE/HdGZ+87vWSN7EDkoDGj9\nTu1SfUJHl6zErG4AcN1QX1B0xcntOPOkllFnVIbjptM68+aPh3BKp9CzN/8juwWPXNybNlF6wjIE\n7ju/J3++KvKM0VTENGHe4bV904Slr303cPRGF5ExwBP4grbpqvpImHKnAf8GrgksXeS07tChQ1nh\n/9zbQYb473Wv/gLv4XBG1sQzunLbnFVhjzs9T1WCX3F/vmoARQeOV5xrZJBoeWjw7EqJfiMF678e\nuih8L1Vt0C6zIf8VImgJNfQYrePxtu91pWmDc7msSgB3yYC2vPbN7po0s4KB7TNZsetQ2ONXnRLb\n+otVw5jzercKWS7Y9+evGMDOg8cr3VcvXTOQ9fuO8L3u4Retj4fgHtEzurfgtR8OjtrD6qSHODA5\no6a6r1CTbgzDMNKVqD1hIpIBPA1cCAwCxotItSRA/nIPA3NjrVuVC/q05pdnZsc0aysWgrPABwjk\najq5Y2jNl5P5b8HDOl1bNK6kwRER3r9pKHN+dAqtIgxNhqJj80Y8dXlf/nbtoGoZypOF0f4Znuf0\nOhGUZEVJjNvKn9m/b5WgO1Yp2VlxrtUZ6/JSVXlmXD9+6V+ZIFKTmzSoVy2w79i8UcgfEgF+/h9d\nwh6LhXiGuCN/Kya/D4VpwhKDacKS1zaYJswNnAxHjgDWqOomVS0BZgGXhyh3OzAb2BVH3UoPsXoZ\nwph+bfhe95bcm9uDP41zvtTL/Rf05PKBoYcSI71zB3bI5B/Xncxjl/RxbKsqPx0R+cWZIVItDYHg\n7Ebq1y6T9hFydoUT4tcUp4FKu8yGvP2TIUwefWK5pPsu6MmQTs0ivtTd+CMa5U/wGhDeR2vyH847\niS5ZjfjPs2Nf2ikwMSNDfD228Q7xBQjn//cTvFB4MLHEonHMtThhJ/6qRppi+qLUw65ZbDj5mdwF\n2BK0vRVfcFWBiHQGxqnqOSIyIpa60TjrpNDDPeH4j+wWjOiWxZwVe2KqB0TsoYr2omqX2SCuoRY3\n+hUuH9iWIWH0OvFy3/k9KSvXmIKMqlqsHq2a8L+X9GHSnFWs3H3Y8Xli7aE6u2dL6tc7if4hejhD\nMbJHy7gz8/9HdhYPXtiTXq0r26ra4mQOOO49twcPfrQx7PFIX/+1Qzvyx39tdr9RKY5pwrzDa/um\nCUtf+27gVvfJE8DdNTnB0KFDXRPDZ4hw46mdohd0kWhr+UWipjfSrd/rFnVB51g5o3uLikkFNSVS\noBnK985ZDRnVoyVtMxtwRnaLqGkSRMRf3j2Re7jEoyLCiG4toorQnQbXka79r8/uXqN0FuE4q+eJ\nHzax9mxd1K9NyAkGTnCi9TQMw0gnnEQO24DgxERd/fuCGQ7MEpENwJXAMyIy1mFdAGbPns09v5zE\nww8/zMMPP8y0adMqDdXk5eVV2w6Mh6tWP16yaWml8fLidQUs+uLflbaDj2/55quI9vasXhzx+O5V\n+VHbG7wdsC9hjm9Ytihi/T7H1lG8roCL/OkKIn0/AXuxtM/t7arfd6TyIsK5jbcxsdt3FasAVK3f\nbPeKmOzF6n/V+yda+f1V7H3+7wU1/v4a71zBP64/uaL9WXsKo/srzs4f/P1IiO8rUv1fnZVN46Ll\nXJi5I2L5wPkeGtOLYbqJ7hvnVfx9T5w40XMdlZt47YtpwrzDNGGVMU1YbDj5mb0I6C0i3YEdwLXA\n+OACqloxXU5EXgTeUtU3RaRetLoBevfuzYQJE8I2omqPwahRo8hamRn2+NDTziBrz9qK7axeQxl+\nev9K28FknzycUaN6VD/fysUAtO07jFGjBoU93q5fDqNGDYzY3mCC7efl5VU730mDT2NUULb8qvVv\nveoirr24hNZN64e1F/z9ZPUayqhRwyodj9Q+N7cb18+o9n0Hjgd8d/p9TTitE43r1+PCvqdU0tdF\n+n4D27H433vICBax03H5rF5DK60decb3RlYSxYerH4v/k87tUf24/34J9/1GOl+47SGdmjFq1Clh\n67fNbMib994Q1d65Bzuy51AJQzs359SfjqMq+fn51fYZRjCmLUo97JrFRtSeMFUtA24D5gHLgVmq\nWigit4jIz0JViVbXlZbHQfCI3VWD23Nxf+dLICWjxqdNZoOIw5C/Py8xs0tj5c5R2fRr15QHL4wv\nH1ew1uvqUzrUyjqLsV7wWrk/Qhh57or+/OfZ2ZGKRKRDlckePzu9C7+IkpHfKf99YS+e/UF/13LW\nJTOmCfMOr+2bJix97buBI8GJqr4P9Kuy79kwZSdU2a5WNxS1/RD76em+mYzvrtzrqLzLkqsT56Xy\njXTL6V14ddlOro2wVqFTRvVoyYD2TSnc5VwUnwi6tGjEU5eHvgWc/BGNHdiOpg3rMbRT8xqnlagN\n6gk0dRgk1vQh0qNVE98EiE9jE8u/dM1A9h8tpU1mA46X+dravlmDijVF3cBtnaJhGEZdIyUz5ieC\nmr4v3HrdXDG4PTPHnxwxHUW6US9DuLBvGzrUYKHw2mTOj4fUeu/PdUM7UE98948TOjZvRL92vuHq\nhvUyePvHQ5hxdWwLkRsnME1YYjBNWPLaBtOEuUHSBGHxPMTa+meoDepQPcHqyR0z6d2mSaWcYQ3j\nXMDZR+JeqlVvpHTqQUjEH1FNclnFS2DZpkv6twm7bFIo3PL/x8M7886EoXEvj9WwfkZaDBsaqYXl\nnEo97JrFhvvz32uRqWP78vmm/SEXbG5QL4Nnvu8T4ndr2ZiiA8crFjYORbTXT49WkRcHT1bqZyRN\nnF2n+enpXTjzpJaVFs12m2irNqTCUG1dxTRh3uG1fdOEpa99N0iaN3Q8D7G2mQ25bGC7qDm6xg5s\nx89Or9kyMD/M6Vij+pFI5I1056huZLdszO9zk0OkX5VE/xFd5J98ES3XWE2pnyGc3LEZDWLoBYO6\n8RBJNkSkq4h8JCLLRWSZiNzu3/8HEdkqIvn+f2OC6twjImtEpFBELgjanyMiS0VktYg84YU/hmHU\nXZImCPOcML0IPVs3JkOgW5hetECertpcZiYWurVszAtXDnAt8WqqcUGf1rxwxQB+e25yBqFGQigF\nfqmqg4AzgNuC1qx9XFVz/P/eBxCRAcDVwADgInx5DgMPhGnATaraF+grIheGMmiasMRgmrDktQ2m\nCXODpBmOLCgoICcnp9bt5vZuxfy133JJmHQVT4zth6rSMExv2x2junH1KR3onBWfaFxEKucJSzMS\n7buIkJ3EQ8mx+J+qQ+K1jaoWAUX+zwdFpBDfEmoQWnlwOb70OaXARhFZA4wQkU1Ac1Vd5C/3EjAO\nmJtQB4wKTFuUetg1i42kCcK84tdnd2fiGV0rJdYMpnGUoc4MEbq0iE8MbRhOmHndyew5dJxuLS0I\nixUR6QEMBb4ERuHrFfsh8BXwK1Xdjy9A+zyo2jb/vlJ8690G2MqJYK4SpgnzDq/tmyYsfe27QdIM\nR3r1EBORsAFYbVEXbqR4SWffwZn/bZo2qEgnYThHRJoBs4E7VPUg8AzQU1WH4uspm+Jl+wzDMNK+\nJ8wwQmHzDFMbEamPLwD7q6rOAVDV3UFFngfe8n/eBnQLOhZY4zbc/mo8+eSTZGZmkp3tW22gRYsW\nDB48uNLyVEDCtqdNm1ar9oK3g3U5bp8/sLRVQKqSSPsblu2EBr5VPQJaq0BPU6TtYF2Wk/IBitcV\nOC4fbrtqG8KVX/71lzTdleX69QnsCz4+depUNmzYwBVXXJHw+y+U/UTby8vLY/NmX3Ls4cOHk5ub\nS2nS58IAACAASURBVE0Q9SKpUgimTJmikdaOrGtc8IJvzb+fDO9Et4Nr07ZHKBGasBU7D3HnW6sB\nmHfzsCilQ/OXr7bz94KdNTqHE9JZD5ifn09ubm5C4l0ReQnYo6q/DNrX0a8XQ0R+AZymqteJyEDg\nZeB0fMONHwB9VFVF5AtgEr41dN8BpgYE/cF4/fzy8j7y+h52y/7UvM287XAFlWCCgyknfPVr30t7\n+KPzY7YVr+27zsoOmcqpptSVax8vbjzDHA1HisgYEVnpn6Z9d4jjY0VkiYgsFpGFIjIy6NjG4GM1\naWxd4oELenJur1ZJO6vSMFIV//PneuBc/3MnkI7iUX+6iQLgbOAXAKq6AngFWAG8C0zUE79ObwWm\nA6uBNaECMDBNmJd4bd80Yelr3w2iDkeKSAbwNJALbAcWicgcVV0ZVOxDVX3TX34wvgfaAP+xcmC0\nqn4byY7XD7Ha5vTsFpye7ctdVRdupHhJVt+bNkzwAuF+ktX/VEZVFwChLmDIAMpf5yHgoRD7vwYG\nu9c6wzCMEzjpCRuB7xfgJlUtAWbhm9JdgaoGrxDdDF/gFUAc2jGMpGHswHac0b0Fvz23h9dNMVIA\nyxOWGCxPWPLaBssT5gZOhPldgC1B21vxBWaVEJFx+H5JtgMuCTqkwAciUgY8p6rPhzLiVZ6wZMDr\ncW0vSVbfG9fP4L7zeybcTrL6bxjJgOWcSj3smsWGaz1UqvqGqg7Al8zwwaBDI1U1B7gYuFVE7I1j\nGEadwms5hWnCvMM0Yelr3w2c9IRtA7KDtsNO0wZQ1TwR6SkirVV1n6ru8O/fLSKv4+tFq9aHuHbt\nWiZOnOjZFG8vt2tzim26bJ/oph+WFO2x7TyWLVvG/v37Adi8ebMr07sNwzBSmagpKkSkHrAKnzB/\nB7AQGK+qhUFleqnqOv/nHGCOqnYTkaZAhn/pkExgHnCfqs6ramf+/PmarsORhrvsPVzC+L9/AyQ2\nvYRRMxKZoqK2sRQVibEd0BZFGuKyFBXJlaLCyTVLpP3axI1nWNSeMFUtE5Hb8AVQGcB0VS0UkVt8\nh/U54AoRuRE4DhzBtxguQAfgdRFRv62XQwVgYJqwutCtGg+J8L1N0wY8fXk/shrXzgzHmpDO194w\nomH6otTDrllsOMqY78+N06/KvmeDPj8KPBqi3gZ867YZRq3St11Tr5tgpBGmCfMOr+2bJix97btB\n0qSO8Poh5iV14UaKl3T2Hcx/wzCMdCZpgjDDMIxUxfKEJQbLE5a8tsHyhLlB0gRhXj/EvKQu3Ejx\nks6+g/lvGJGYNGmSaYxSDLtmsZE0QZhhGEaq4rWcwjRh3mGasPS17wZJE4R5/RDzkrpwI8VLOvsO\n5r9hGEY6kzRBmGEYRqritZzCNGHeYZqwypgmLDaSJgjz+iHmJXXhRoqXdPYdzH/DiITpi1IPu2ax\nkTRBmGEYRqritZzCNGHeYZqw9LXvBkkThHn9EPOSunAjxUs6+w7mv2EYRjqTNEGYYRhGquK1nMI0\nYd5hmrDKmCYsNhwFYSIyRkRWishqEbk7xPGxIrJERBaLyEIRGem0bgCvH2JeUhdupHhJZ9/B/DeM\nSJi+KPWwaxYbUYMwEckAngYuBAYB40Wkf5ViH6rqEFUdBtwEvBBDXQDWrl0btxOpzrJly7xugmek\ns++Q3v7XpR9eXsspTBPmHaYJS1/7buCkJ2wEsEZVN6lqCTALuDy4gKoeDtpsBpQ7rRvg0KFDsba9\nzrB//36vm+AZ6ew7pLf/S5Ys8boJhmEYnuIkCOsCbAna3urfVwkRGScihcBbwIRY6hqGYaQyXvfq\nmSbMO0wTVhnThMVGfbdOpKpvAG+IyCjgQeD8WOoXFRW51ZSUY/PmzV43wTPS2Xcw/50iItcAs1W1\nzOu2GLWHaYtSD7tmseEkCNsGZAdtd/XvC4mq5olITxFpHUvdXr16cccdd1RsDxkyxHOdRW0xfPhw\n8vPzvW6GJ6Sz75Be/hcUFFQagszMzIyl+nFghr+3/TlV3e1y82qE188q04R5h2nC0te+GzgJwhYB\nvUWkO7ADuBYYH1xARHqp6jr/5xygoaruE5GodQNMmzZN4ncjtcnNzfW6CZ6Rzr5DevlfE19V9XUR\nWQZMAU4TkcWqep9rjTMMw/CAqJowf/f/bcA8YDkwS1ULReQWEfmZv9gVIvKNiOQDTwFXR6qbAD8M\nw6jDiMhfgOuAn6nqOKDY2xZVxjRhicE0YclrG0wT5gaONGGq+j7Qr8q+Z4M+Pwo86rSuYRhGjPxe\nVTcDiEhbVf2j1w0yEo/pi1IPu2ax4XnGfKfJXFMNEdkYnMDWv6+ViMwTkVUiMldEWgSVv0dE1ohI\noYhcELQ/R0SW+r+fJ7zwxQkiMl1EdorI0qB9rvkrIg1FZJa/zuciEqw19JQwvv9BRLaKSL7/35ig\nY3XJ964i8pGILBeRZSIyyb/f1WsPzAv4D9xfmz46wTRh3uG1fdOEpa99N/A0CIslmWsKUg6MVtVh\nqjrCv28yvsS2/YCPgHsARGQgviHcAcBFwDMiEtDITQNuUtW+QF8RubA2nYiBF/Fdx2Dc9PcmYJ+q\n9gGeIEzPq0eE8h3gcVXN8f97H0BEBlC3fC8Ffqmqg4AzgFv9f8NuX3sN8r8icDMMw0hlvO4Jc5zM\nNQURqn+/lwMz/J9nAOP8n8fi08uVqupGYA0wQkQ6As1VdZG/3EtBdZIKVc0Dvq2y201/g881G0ga\nRXsY38F3D1TlcuqW70WqWuD/fBAoxDcL2u1r/4yIvAZcCbRNrFexY5qwxGCasOS1DaYJcwPX8oTF\nSahkriPClE01FPhARMqAZ1X1BaCDqu4E38tLRNr7y3YBPg+qu82/rxTfdxIg1ZLdtnfR34p7RVXL\nROQ7EWmtqvsS6UANuU1Efgh8BfxKVfdTh30XkR7AUOAL3L3XuwCvAa8CjYBPktF/w31MX5R62DWL\nDa+DsLrMSFXdISLt8OlZVuELzIKpul3XcdPfZE9p8gxwv6qqiDyIL7XCzS6dO+l8F5Fm+Hrp7lDV\ngyLi9r0+BV9gVgq0iFK21jFNmHd4bd80Yelr3w28Ho6MKRFsKqGqO/z/7wbewNfDt1NEOgD4h192\n+YtvA7oFVQ98D+H2pwpu+ltxTETqAVnJ3BOiqrtVNRB4PM+JHt4657uI1McXgP1VVef4d7t97Xeq\n6n8C9wKlyeS/YRhGvHgdhFUkc/XPgLoWeNPjNtUYEWnq7xlARDLxCYmX4fPtx/5iPwICL6w3gWv9\ns+BOAnoDC1W1CNgvIiP84uUbg+okI0LlXho3/X3Tfw6Aq/CJvZOJSr77A48APwC+8X+ui77/GVih\nqk8G7XP72l8lIn8CXgf2JtSbODBNWGIwTVjy2gbThLmBp8ORfn1LIJlrBjC9jiRz7QC87h+SqQ+8\nrKrzROQr4BURmQBs4kRS2xUi8gqwAigBJgb1otwK/AVoDLwbmGWXbIjI34HRQBsR2Qz8AXgYeNUl\nf6cDfxWRNfhewtfWhl9OCOP7OSIyFN8s2Y3ALVAnfR8JXA8sE5HF+IYdfwM8gnv3+nTgYv+/b4ky\nrCsiXfEJ+zvg+/6fV9WpItIK+AfQHd81udqv00NE7gEm4BvuvENV5/n351Rp051xfVFGXJi+KPWw\naxYbcuL5ZxiGkZyIyB3Ayar6UxH5nao+EKFsR6Cjqhb4e6S/xjfD8ifAXlV9VHw5CVup6mR/2oyX\ngdPwDYN+CPTx6/m+BG5T1UUi8i7wpKrOrWpz/vz5mpOT47bbRi0yNW8zb69MfCfrV7/2TW4e/uj8\nhNsKcNdZ2VzQt02t2UsX8vPzyc3NrZFG1+vhSMMwDCf04sRM6uaRCtZS2gzDMIwaY0GYYRipgAJN\nRORkoLPTSpHSZgDBaTOCU+UE0mZ0wWGKGNOEJQbThCWvbTBNmBtYigrDMFKBKcBE4If4s+9HoxbS\nZlTw6aef8tVXX5Gd7Zvs3aJFCwYPHlwxhT7wskjU9rJlyxJ6fq+2A/qi2rC3YdlOaNATOBHcBFJA\nuL0d2FfT8wWfK1L55V9/SdNdWa5/fwGCj0+aNIm8vDzy8vISfn+Esp9oe3l5eWzevBmA4cOHk5tb\ns9zZpgkzDOP/t3fvUXKVZb7Hv0+4KaCB1hGGQAg3gWAMZsLtiHJphgRFgnMOYjzjcYhHWVwGR+UA\nnvGsOKxZiyTLjKAg90EYlQgBJShCoEcyxgFJbJo0kGC4pZNAAtIQJgQEwnP+qF2hutOX2l276n3r\nrd9nrazU3rWr3v30rrx5e+9fvTt6ZvalikV395uG2X5b4JfAr8vf2jSz5ZRuJbY+u9T4G3c/2Mwu\nyt5zdrbd3ZS+XLGqvE22/vPAMe5+Vv/2lAlrfsqESV7KhIlIq1iX/fkv4BNVbF/vaTNERGqmQZiI\nRM/d78n+3A48PdS2FdNmHG9mD5tZp5lNpTRtxl9nd69opzSFCu7+OFCeNuMutp4243rgj5Tuczvg\nFDHKhNWHMmHxtg3KhBVBmTARiZ6Z3Uopw/UOsGyobd39d8A2gzx9wiCvuQS4ZID1fwAm5NpZKYzm\nnGo+Omb5aBAmItFz99NC78NQdO/IcEK3r3tHtm77RdAgTESiZ2YPAG+QTVUBrHb3z4XdKxGR2igT\nJiLN4D53P87djwc6YhuAKRNWHyPJhD3T+zoPrX41158/rHmVZ19+fUT7qExYX8qE5aMzYSLSDPY3\ns/K3IvcNuifSMCPJFy1ZvYHrljxfh72RaigTlo8GYSLSDM4DTqd0OTK6Xl6ZsHBCt69MWOu2XwRd\njhSRZnAisLe7X0FpMCYi0vQ0CBORZnAUpYlaAcYF3I8BKRNWH5onLN62QZmwIuhypIg0g7cBzGw0\nsHvgfZEGUb6o+eiY5aNBmIg0gx8B3wCuAuaE3ZWtKRMWTuj2myET9nTv6zy2bmPu9x/93m3Zc/R7\nBn0+9M8+dPtF0CBMRKKW3bfxk+7+v0Lvi0gzuv3RF7n90Rdzv+7bx48bchAmtVMmTESilt3H8TAz\nm25mnzKzT4Xep/6UCasPZcLibRuUCStCNGfC5s6d66FP6Rehq6sr+KWJoqiW+KRSB5Rq+eY3v2nD\nbWdmpwD3AR8Etq/7jkk0lC9qPjpm+UQzCHvkkUeYMWNG6N2o2cKFC5k0aVLo3SiEaolPKnUA3Hjj\njdVuOtXdzzazH7r72fXcp5EKPTBWJiycZsiE1Uvon33o9ougy5EiEru9s0uQe8d6OVJEZCSiGYSt\nW7cu9C4UoqenJ/QuFEa1xCeVOnK6BfiLir//IuzubE2ZsPpQJizetkGZsCJEczlyv/32C70LhZgw\nYULoXSiMaolPKnUATJw4sart3L3q65aSFuWLmo+OWT5W+uJReB0dHZ5K1kVEhtfZ2Ul7e/uwwfxm\noP4rHrc8si7qG3gvvaAdgMlzOgLvyfC+ffw4PrnvrqF3I1pF9GHRXI4UERERaSU1DcLM7HozW29m\ny4bY5vtmttLMusxs0K9yhM5UFCWFa9RlqiU+qdSRmtD9lzJh4SgT1pcyYfnUmgm7AfgBcNNAT5rZ\nScB+7n6AmR1B6ZYjR9bYpoiItADli5qPjlk+NZ0Jc/fFwMtDbDKNbIDm7r8HRpvZbgNtGHqenaKk\nMG9JmWqJTyp1pCZ0/6V5wsLRPGGt234R6p0JGwOsrlhem60TERERaWnRBPNDZyqKksI16jLVEp9U\n6khN6P5LmbBwlAnrS5mwfOo9T9haYK+K5T2zdVtZtGgRS5cuZezYsQCMHj2aCRMmbDndWP5hx75c\nFsv+1LLc3d0d1f7Ustzd3R3V/rTi56u7u5sNGzYApUlnJ0+eTHt7OyKDUb6o+eiY5VPzPGFmNg64\n0923mkUyu73IOe7+aTM7ErjU3QcM5mueHZHWonnCpB40T1hxNE/Y0Irow2o6E2ZmPwWOBT5gZj3A\nTGB7wN39Gne/K7vX25PAa8AZtbQnIiIikopavx35BXffw913cPex7n6Du1/t7tdUbHOuu+/v7hPd\nvXOw9wqdqShKCteoy1RLfFKpIzWh+y9lwsJRJqwvZcLyiebekcO5+eab2bRpE1/+8per2va0005j\n222bpjwREelH+aLmo2OWTzTfjixynp2bb76ZP//5z4W933Aqc3VHH300sdyPs1YpzMFSlkotqdSR\nGs0TFk7o9jVPWOu2X4SmOlV0//33s3DhQl577TWuu+46dt99d26++WZ+/OMf88477/CP//iP7LDD\nDnR3d3P66afz6U9/moMPPpi5c+fy+uuvc8opp2w1Sv/BD37Avffey8aNG5k5cybHHHMMzzzzDN/4\nxjd45513mDhxIhdffDFXXHEFCxYsYNttt2XWrFlMmDCB4447jqOOOore3l6OOeYYOjo6eP311znj\njDM44YQTAv2UREREpBlEcyasmkzFjjvuyM9+9jO+/vWvc+mll/Lyyy9z++2386tf/YrbbruNOXPm\ncNhhh/HRj36UW2+9lbPOOosjjzySO++8k3vvvZcFCxZsdYbsK1/5CgsWLOCWW27hu9/9LgAzZ87k\n4osv5o477uDiiy/mhRde4O677+aee+7hqquuYubMmQC88sornHnmmVx11VUAbL/99px11lnJDMBS\nuN5elkotqdSRGmXC6kOZsHjbBmXCitBUZ8ImTpwIwKRJk7jmmmt45plnWLFiBdOmTcPd6e3tBUqX\nB8uXBLu6upg9ezZvv/02q1ev5sUXX2TPPffc8p7z5s1j/vz5jBo1ihdeeAGA5557jgkT3p1xo6en\nh0MOOQSAvfbai1dffRWAXXbZhb333nvLdh/72MfqWL2ISGtRvqj56JjlE82ZsGoyFeUJNzs7O9ln\nn30YN24cH/nIR7jjjjtYsGABixYtAmC77bZj8+bNQGlU/r3vfY8FCxaw++67b/We1157LXfeeSfX\nX3/9loHbmDFjWLZsGVAa0I0dO5ZHH30Ud6enp4fRo0cDMGpU3x/fqFGjkrhGXaZa4pNKHfVmZteb\n2XozW1axbqaZrTGzzuzP1IrnvmVmK81suZmdWLF+kpktM7M/mtmlg7WnTFg4odtXJqx12y9CU50J\ne/PNNznttNPYtGkT1157LW1tbXz2s5/l5JNPZptttmH8+PFccsklTJ06lRkzZvCZz3yGU045hb/9\n279l/PjxvO9979vqPY866ihOOukk/uqv/oqddtoJgO985zv8wz/8A8CWTNjUqVOZMmUK22yzDXPm\nzAHALIl5JkVSdAPwA+Cmfuv/xd3/pXKFmR0MfA44mNJdPe4zswO89FvZlcCX3X2Jmd1lZlPc/Z4G\n7L+ItICaZ8wvyty5c33GjBmhd6NmixcvTmJ0DqolRqnUAfWfMd/M9qZ0N4+PZsszgY3uPrffdhdR\nmmB6drb8a+A7wCrg3919fLb+88Ax7n5W/7ZC918hPxf1bLucLRrqElf/9hs9Y/6rT3XlOiNV5Iz5\nedvOa7gZ8wc69tUcs6KE7g+Dz5gvItJkzjWzLwJLgW+6+wZgDPBAxTZrs3VvA2sq1q/J1kuDKF/U\nfHTM8mmqTFgzSOUsBaiWGKVSRyA/BPZ190OBdcDcYbavWuj+S5mwcJQJa932i6AzYSLSEtz9xYrF\na4E7s8drgb0qntszWzfY+q3Mnz+f6667jrFjxwIwevRoJkyYsOU/ifJX6bXcmOXy1A3lQUpsy+V1\nsezPYMscPw4IfzxjWS4/7unpAWDy5Mm0t7dTC2XCChb6GnWRVEt8UqkDGpIJG0cpEzYhW97d3ddl\nj78OHObuXzCz8cBPgCMoXW68FzjA3d3MHgTOA5YAvwK+7+53928rdP+lTJgyYfWgTNjQlAkTERmA\nmf0UOBb4gJn1ADOB48zsUOAd4FngTAB3f9zMbgEeB94CzvZ3fzs9B/gR8B7groEGYFI/yhc1Hx2z\nfKI5E9bR0eGTJk0KvRsi0iD1PhPWSOq/4tHoM2F5FXkmrN6GOxPW6orow6IJ5ouIiIi0kmgGYaHv\nvVaUFO5lVaZa4pNKHakJ3X/p3pHh6N6RfenekfkoEyYiIlFSvqj56JjlU9OZMDObamYrsvuqXTjA\n8+83swVm1mVm3Wb2d4O9V+h5doqSyjfXQLXEKJU6UhO6/9I8YeFonrDWbb8IIx6Emdko4HJgCnAI\nMN3MDuq32TnAY9nkiMcBc81MZ99ERESk5dVyJuxwYKW7r3L3t4B5wLR+2zhQvmv2+4CX3P3tgd4s\ndKaiKClcoy5TLfFJpY7UhO6/lAkLR5mwvpQJy6eWs1JjgNUVy2soDcwqXQ4sMLPngJ2B02toT0RE\nWojyRc1Hxyyfen87cgrwsLvvAXwMuMLMdh5ow9CZiqKkcI26TLXEJ5U6UhO6/1ImLBxlwlq3/SLU\nciZsLTC2Ynmg+6qdAVwC4O5PmdkzwEHA0v5vpnuvaVnLaS93d3ezYcMGAHp6egq575qISDMb8Yz5\nZrYN8ATQDjwPPARMd/flFdtcAbzg7v9kZrtRGnxNdPfe/u8X+t5rRQl9L6siqZb4pFIHpDVjfuj+\nS/eO1L0j60H3jhxa0HtHuvtmMzsXWEjpsub17r7czM4sPe3XAP8M/MjMlmUvu2CgAZiIiEh/yhc1\nHx2zfGqaLiK7me2B/dZdXfH4eUq5sGGFzlQUJZWzFKBaYpRKHakJ3X8pExaOMmGt234RorltkYiI\niEgriWYQFnqenaKkMG9JmWqJTyp1pCZ0/6V5wsLRPGF9aZ6wfDR7vYiIREn5ouajY5ZPNGfCQmcq\nipLCNeoy1RKfVOpITej+S5mwcJQJa932ixDNIExERESklUQzCAudqShKCteoy1RLfFKpIzWh+y9l\nwsJRJqwvZcLyUSZMRESipHxR89ExyyeaM2GHHnoobW1ttLW1hd6VmqRwjbpMtcQnlTpSo0xYOKHb\nVyasddsvQjSDMBEREZFWEs0gLHSmoigpXKMuUy3xSaWO1ITuv5QJC0eZsL6UCctHmTAREYmS8kXN\nR8csn2jOhIXOVBQlhWvUZaolPqnUkZrQ/ZcyYeEoE9a67RchmkGYiIiISCuJZhAWOlNRlBSuUZep\nlvikUkdqQvdfyoSFo0xYX8qE5aNMmIiIREn5ouajY5ZPNGfCQmcqipLCNeoy1RKfVOpITej+S5mw\ncJQJa932i1DTIMzMpprZCjP7o5ldOMg2x5rZw2b2qJn9ppb2RERERFIx4kGYmY0CLgemAIcA083s\noH7bjAauAE52948Apw32fqEzFUVJ4Rp1mWqJTyp1pCZ0/6VMWDjKhPWlTFg+tWTCDgdWuvsqADOb\nB0wDVlRs8wXgNndfC+Duf6qhPRERaSHKFzUfHbN8arkcOQZYXbG8JltX6cNAm5n9xsyWmNkXB3uz\n0JmKoqRwjbpMtcQnlTpSE7r/UiYsHGXCWrf9ItT725HbApOA44GdgAfM7AF3f7LO7YqIiIhErZYz\nYWuBsRXLe2brKq0B7nH3N9z9JeA/gIkDvdlll1225fGsWbO48sor+1zvXbx4cVMsl9fFsj+1LF95\n5ZVR7U8ty836eeq/3MyfryuvvJJZs2Yxa9Yszj777LrmqMzsejNbb2bLKtbtamYLzewJM7sny6yW\nn/uWma00s+VmdmLF+klmtiz78tGlg7WnTFh9KBMWb9ugTFgRzN1H9kKzbYAngHbgeeAhYLq7L6/Y\n5iDgB8BUYAfg98Dp7v54//ebO3eun3/++QD09vaOaJ9isHjx4iROkYJqiVEqdQB0dnbS3t5u9Xhv\nMzsa2Ajc5O4fzdbNBl5y9znZt7l3dfeLzGw88BPgMEq/TN4HHODubma/B8519yVmdhdwmbvf07+9\nuXPn+owZM+pRSlVCfi5Cfyb7t3/LI+u4bsnzDWv/1ae6cl0WXHpBOwCT53Q0vO28vn38OD65766D\nPh/bsW+0IvqwEZ8Jc/fNwLnAQuAxYJ67LzezM83sq9k2K4B7gGXAg8A1Aw3AIHymoiip/AcJqiVG\nqdRRb+6+GHi53+ppwI3Z4xuBU7PHp1Dqv95292eBlcDhZrY78D53X5Jtd1PFa/oI3X8pExaOMmGt\n234RasqEufvdwIH91l3db/m7wHdraUdEpAAfcvf1AO6+zsw+lK0fAzxQsd3abN3blCIVZQN9+UhE\nZMSimTE/dKaiKClcoy5TLfFJpY5IjCyLMYDQ/ZcyYeEoE9aXMmH56N6RItIq1pvZbu6+PrvU+EK2\nfi2wV8V25S8ZDbZ+K4sWLWLp0qWMHVv6rtLo0aOZMGHClssl5f8s6rXc3d1d1/cPtVyecyrv68uD\nk/LlutiWy+tqfb/K96rH/nL8OGDwn3dZ5fPnnXfeli/m1PvzMVD79W5v8eLF9PT0ADB58mTa29up\nxYiD+UXr6OjwE044AWjuYL6IVKeewXwAMxsH3OnuE7Ll2UCvu88eJJh/BKXLjffybjD/QeA8YAnw\nK+D7WQyjj46ODp80aVK9SpEcGh3Mz6vIYH69DRfMb3VF9GE6EyYiyTGznwLHAh8wsx5gJjALuNXM\nZgCrgM8BuPvjZnYL8DjwFnC2v/vb6TnAj4D3AHcNNAATERkpZcIKlsI16jLVEp9U6qg3d/+Cu+/h\n7ju4+1h3v8HdX3b3E9z9QHc/0d1fqdj+Enff390PdveFFev/4O4T3P0Ad//aYO2F7r+UCQtHmbC+\nlAnLR2fCREQkSroPYfPRMcsnmjNhoefZKUoK85aUqZb4pFJHakL3X5onLBzNE9a67RchmkGYiIiI\nSCuJZhDWP1PR1tZGW1tboL0ZuRSuUZeplvikUkdqlAmrD2XC4m0blAkrgjJhIiISJeWLmo+OWT7R\nnAkLnakoSgrXqMtUS3xSqSM1ofsvZcLCUSasddsvgs6EiYhIdFa/8gZ/eu2tXK8ZZfDkS2/UaY9E\nihfNICx0pqIolbdqaHaqJT6p1JGarq4uQs6YH/JzUa+2n3hxE4//+scA/HLHTwy6XeXtf0IIrHMd\nEQAAFQdJREFU2X7o2gc69uU8WCMuS6bQH0YzCBMREak01OBL4qRMWD7KhBWs2UfllVRLfFKpIzWh\n+69WzoSFzkUpE9a67RchmkGYiIiISCuJZhCWUiYsFaolPqnUkZrQ/Veq84SdvOm3nLzpt0NuE3qu\nLM0T1pfmCcunpkyYmU0FLqU0mLve3WcPst1hwH8Cp7v77bW0KSIirUGZsOajTFg+Iz4TZmajgMuB\nKcAhwHQzO2iQ7WYB9wz1fqEzFUVJ4Rp1mWqJTyp1pCZ0/6VMWGu2H7r20Mc+dPtFqOVy5OHASndf\n5e5vAfOAaQNs9/fAfOCFGtoSERERSUotg7AxwOqK5TXZui3MbA/gVHe/ErCh3ix0pqIoKVyjLlMt\n8UmljtSE7r+UCQtHmbC+lAnLp97zhF0KXFixPOhAbNGiRVsez5o1a6vnyz/s8unHWJebbX+HWu7u\n7o5qf2pZ7u7ujmp/WvHz1d3dzYYNGwDo6elh8uTJtLe3IzIYZcKajzJh+Zi7j+yFZkcC33H3qdny\nRYBXhvPN7OnyQ+CDwGvAV919Qf/36+jo8BNOOAGA3t5e2tratjwWkfR0dnbS3t4+5BnyZtHR0eEh\nZ8xP0X0re5mzaFXo3Sjc0gtKv3hMntMReE+G9+3jx/HJfXcNvRvRKqIPq+VM2BJgfzPbG3ge+Dww\nvXIDd9+3/NjMbgDuHGgAJiIiItJqRpwJc/fNwLnAQuAxYJ67LzezM83sqwO9ZKj3C52pKEoK16jL\nVEt8UqkjNaH7L2XCwkk5E7b6lTd4dN3GQf/824J7t1qnTFg+NWXC3P1u4MB+664eZNsZtbQlIiKt\nRZmwsG7sXAed6wZ9/tWn1vD+F1b2XbnjJ/jnKfsO/ALZSjQz5g82z05bW9uWfFgzSGHekjLVEp9U\n6kiN5gkLJ/RcWa08T1jo9kN/9ooQzSBMREREpJVEMwgLnakoSgrXqMtUS3xSqSM1ofsvZcLCSTkT\nNpL2T970Wx78+Y0NaT+F/rDe84SJiIiMiDJhzeeXyoTlEs2ZsNCZiqKkcI26TLXEJ5U6UhO6/1Im\nrDXbb+XaIfxnrwjRDMJEREREWkk0g7DQmYqipHCNuky1xCeVOlITuv9SJiwcZcL6UiYsH2XCREQk\nSsqENR9lwvKJ5kxY6ExFUVK4Rl2mWuKTSh2pCd1/KRPWmu23cu0Q/rN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OA/PXMtlieTBjYP3eQ7y3chfTv9xiUboux41hS2V4p8zguTfum70m6NDu3NW7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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import pymc as pm\n", + "from pymc.Matplot import plot as mcplot\n", + "\n", + "std = pm.Uniform(\"std\", 0, 100, trace=False) # this needs to be explained.\n", + "\n", + "\n", + "@pm.deterministic\n", + "def prec(U=std):\n", + " return 1.0 / (U) ** 2\n", + "\n", + "beta = pm.Normal(\"beta\", 0, 0.0001)\n", + "alpha = pm.Normal(\"alpha\", 0, 0.0001)\n", + "\n", + "\n", + "@pm.deterministic\n", + "def mean(X=X, alpha=alpha, beta=beta):\n", + " return alpha + beta * X\n", + "\n", + "obs = pm.Normal(\"obs\", mean, prec, value=Y, observed=True)\n", + "mcmc = pm.MCMC([obs, beta, alpha, std, prec])\n", + "\n", + "mcmc.sample(100000, 80000)\n", + "mcplot(mcmc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It appears the MCMC has converged so we may continue.\n", + "\n", + "For a specific trading signal, call it $x$, the distribution of possible returns has the form:\n", + "\n", + "$$R_i(x) = \\alpha_i + \\beta_ix + \\epsilon $$\n", + "\n", + "where $\\epsilon \\sim \\text{Normal}(0, 1/\\tau_i) $ and $i$ indexes our posterior samples. We wish to find the solution to \n", + "\n", + "$$ \\arg \\min_{r} \\;\\;E_{R(x)}\\left[ \\; L(R(x), r) \\; \\right] $$\n", + "\n", + "according to the loss given above. This $r$ is our Bayes action for trading signal $x$. Below we plot the Bayes action over different trading signals. What do you notice?\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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IpNxFCCGEENmXlPSYpKRB5GQS/0IIIUTWJiU9QgghhBBC5FCS8AshcgR3r68U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\n4xhDms0XERHpmtTDL50qUFvHjpfeZNND/6T0w6VN+3tNPpy8C87kkBl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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 6)\n", + "from scipy.optimize import fmin\n", + "\n", + "\n", + "def stock_loss(price, pred, coef=500):\n", + " \"\"\"vectorized for numpy\"\"\"\n", + " sol = np.zeros_like(price)\n", + " ix = price * pred < 0\n", + " sol[ix] = coef * pred ** 2 - np.sign(price[ix]) * pred + abs(price[ix])\n", + " sol[~ix] = abs(price[~ix] - pred)\n", + " return sol\n", + "\n", + "tau_samples = mcmc.trace(\"prec\")[:]\n", + "alpha_samples = mcmc.trace(\"alpha\")[:]\n", + "beta_samples = mcmc.trace(\"beta\")[:]\n", + "\n", + "N = tau_samples.shape[0]\n", + "\n", + "noise = 1. / np.sqrt(tau_samples) * np.random.randn(N)\n", + "\n", + "possible_outcomes = lambda signal: alpha_samples + beta_samples * signal \\\n", + " + noise\n", + "\n", + "\n", + "opt_predictions = np.zeros(50)\n", + "trading_signals = np.linspace(X.min(), X.max(), 50)\n", + "for i, _signal in enumerate(trading_signals):\n", + " _possible_outcomes = possible_outcomes(_signal)\n", + " tomin = lambda pred: stock_loss(_possible_outcomes, pred).mean()\n", + " opt_predictions[i] = fmin(tomin, 0, disp=False)\n", + "\n", + "\n", + "plt.xlabel(\"trading signal\")\n", + "plt.ylabel(\"prediction\")\n", + "plt.title(\"Least-squares prediction vs. Bayes action prediction\")\n", + "plt.plot(X, ls_coef_ * X + ls_intercept, label=\"Least-squares prediction\")\n", + "plt.xlim(X.min(), X.max())\n", + "plt.plot(trading_signals, opt_predictions, label=\"Bayes action prediction\")\n", + "plt.legend(loc=\"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is interesting about the above graph is that when the signal is near 0, and many of the possible returns outcomes are possibly both positive and negative, our best (with respect to our loss) prediction is to predict close to 0, hence *take on no position*. Only when we are very confident do we enter into a position. I call this style of model a *sparse prediction*, where we feel uncomfortable with our uncertainty so choose not to act. (Compare with the least-squares prediction which will rarely, if ever, predict zero). \n", + "\n", + "A good sanity check that our model is still reasonable: as the signal becomes more and more extreme, and we feel more and more confident about the positive/negativeness of returns, our position converges with that of the least-squares line. \n", + "\n", + "The sparse-prediction model is not trying to *fit* the data the best (according to a *squared-error loss* definition of *fit*). That honor would go to the least-squares model. The sparse-prediction model is trying to find the best prediction *with respect to our `stock_loss`-defined loss*. We can turn this reasoning around: the least-squares model is not trying to *predict* the best (according to a *`stock-loss`* definition of *predict*). That honor would go the *sparse prediction* model. The least-squares model is trying to find the best fit of the data *with respect to the squared-error loss*.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Kaggle contest on *Observing Dark World*\n", + "\n", + "\n", + "A personal motivation for learning Bayesian methods was trying to piece together the winning solution to Kaggle's [*Observing Dark Worlds*](http://www.kaggle.com/c/DarkWorlds) contest. From the contest's website:\n", + "\n", + "\n", + "\n", + ">There is more to the Universe than meets the eye. Out in the cosmos exists a form of matter that outnumbers the stuff we can see by almost 7 to 1, and we don’t know what it is. What we do know is that it does not emit or absorb light, so we call it Dark Matter. Such a vast amount of aggregated matter does not go unnoticed. In fact we observe that this stuff aggregates and forms massive structures called Dark Matter Halos. Although dark, it warps and bends spacetime such that any light from a background galaxy which passes close to the Dark Matter will have its path altered and changed. This bending causes the galaxy to appear as an ellipse in the sky.\n", + "\n", + "\n", + "\n", + "\n", + "The contest required predictions about where dark matter was likely to be. The winner, [Tim Salimans](http://timsalimans.com/), used Bayesian inference to find the best locations for the halos (interestingly, the second-place winner also used Bayesian inference). With Tim's permission, we provided his solution [1] here:\n", + "\n", + "1. Construct a prior distribution for the halo positions $p(x)$, i.e. formulate our expectations about the halo positions before looking at the data.\n", + "2. Construct a probabilistic model for the data (observed ellipticities of the galaxies) given the positions of the dark matter halos: $p(e | x)$.\n", + "3. Use Bayes’ rule to get the posterior distribution of the halo positions, i.e. use to the data to guess where the dark matter halos might be.\n", + "4. Minimize the expected loss with respect to the posterior distribution over the predictions for the halo positions: $\\hat{x} = \\arg \\min_{\\text{prediction} } E_{p(x|e)}[ L( \\text{prediction}, x) ]$ , i.e. tune our predictions to be as good as possible for the given error metric.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The loss function in this problem is very complicated. For the very determined, the loss function is contained in the file DarkWorldsMetric.py in the parent folder. Though I suggest not reading it all, suffice to say the loss function is about 160 lines of code — not something that can be written down in a single mathematical line. The loss function attempts to measure the accuracy of prediction, in a Euclidean distance sense, such that no shift-bias is present. More details can be found on the metric's [main page](http://www.kaggle.com/c/DarkWorlds/details/evaluation). \n", + "\n", + "We will attempt to implement Tim's winning solution using PyMC and our knowledge of loss functions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Data\n", + "\n", + "The dataset is actually 300 separate files, each representing a sky. In each file, or sky, are between 300 and 720 galaxies. Each galaxy has an $x$ and $y$ position associated with it, ranging from 0 to 4200, and measures of ellipticity: $e_1$ and $e_2$. Information about what these measures mean can be found [here](https://www.kaggle.com/c/DarkWorlds/details/an-introduction-to-ellipticity), but for our purposes it does not matter besides for visualization purposes. Thus a typical sky might look like the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Data on galaxies in sky 3.\n", + "position_x, position_y, e_1, e_2 \n", + "[[ 1.62690000e+02 1.60006000e+03 1.14664000e-01 -1.90326000e-01]\n", + " [ 2.27228000e+03 5.40040000e+02 6.23555000e-01 2.14979000e-01]\n", + " [ 3.55364000e+03 2.69771000e+03 2.83527000e-01 -3.01870000e-01]]\n" + ] + }, + { + "data": { + "image/png": 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RJB59NInRo1O5+eZktm+vvD5Ro193EWkJjADeDFp9LvBe4P/vAecF/j8K+Fgp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\n3nKoevMrTVwugZMnCzfV9HQxZD7q1YhWW1Aj+cdngbJpvfuugzp11Gu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80LFjUoFayVyq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\nYuvs9OluHnussMaj1yMiSatORpyfD4cPlyUZ4VpUMyNDuPXWRDZ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from draw_sky2 import draw_sky\n", + "\n", + "n_sky = 3 # choose a file/sky to examine.\n", + "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", + "Training_Sky%d.csv\" % (n_sky),\n", + " dtype=None,\n", + " skip_header=1,\n", + " delimiter=\",\",\n", + " usecols=[1, 2, 3, 4])\n", + "print(\"Data on galaxies in sky %d.\" % n_sky)\n", + "print(\"position_x, position_y, e_1, e_2 \")\n", + "print(data[:3])\n", + "\n", + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Priors\n", + "\n", + "Each sky has one, two or three dark matter halos in it. Tim's solution details that his prior distribution of halo positions was uniform, i.e.\n", + "\n", + "\\begin{align}\n", + "& x_i \\sim \\text{Uniform}( 0, 4200)\\\\\\\\\n", + "& y_i \\sim \\text{Uniform}( 0, 4200), \\;\\; i=1,2,3\\\\\\\\\n", + "\\end{align}\n", + "\n", + "Tim and other competitors noted that most skies had one large halo and other halos, if present, were much smaller. Larger halos, having more mass, will influence the surrounding galaxies more. He decided that the large halos would have a mass distributed as a *log*-uniform random variable between 40 and 180 i.e.\n", + "\n", + "$$ m_{\\text{large} } = \\log \\text{Uniform}( 40, 180 ) $$\n", + "\n", + "and in PyMC, \n", + "\n", + " exp_mass_large = pm.Uniform(\"exp_mass_large\", 40, 180)\n", + " @pm.deterministic\n", + " def mass_large(u = exp_mass_large):\n", + " return np.log(u)\n", + "\n", + "(This is what we mean when we say *log*-uniform.) For smaller galaxies, Tim set the mass to be the logarithm of 20. Why did Tim not create a prior for the smaller mass, nor treat it as a unknown? I believe this decision was made to speed up convergence of the algorithm. This is not too restrictive, as by construction the smaller halos have less influence on the galaxies.\n", + "\n", + "Tim logically assumed that the ellipticity of each galaxy is dependent on the position of the halos, the distance between the galaxy and halo, and the mass of the halos. Thus the vector of ellipticity of each galaxy, $\\mathbf{e}_i$, are *children* variables of the vector of halo positions $(\\mathbf{x},\\mathbf{y})$, distance (which we will formalize), and halo masses.\n", + "\n", + "Tim conceived a relationship to connect positions and ellipticity by reading literature and forum posts. He supposed the following was a reasonable relationship:\n", + "\n", + "$$ e_i | ( \\mathbf{x}, \\mathbf{y} ) \\sim \\text{Normal}( \\sum_{j = \\text{halo positions} }d_{i,j} m_j f( r_{i,j} ), \\sigma^2 ) $$\n", + "\n", + "where $d_{i,j}$ is the *tangential direction* (the direction in which halo $j$ bends the light of galaxy $i$), $m_j$ is the mass of halo $j$, $f(r_{i,j})$ is a *decreasing function* of the Euclidean distance between halo $j$ and galaxy $i$. \n", + "\n", + "Tim's function $f$ was defined:\n", + "\n", + "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 240 ) } $$\n", + "\n", + "for large halos, and for small halos\n", + "\n", + "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 70 ) } $$\n", + "\n", + "This fully bridges our observations and unknown. This model is incredibly simple, and Tim mentions this simplicity was purposefully designed: it prevents the model from overfitting. \n", + "\n", + "\n", + "### Training & PyMC implementation\n", + "\n", + "For each sky, we run our Bayesian model to find the posteriors for the halo positions — we ignore the (known) halo position. This is slightly different than perhaps traditional approaches to Kaggle competitions, where this model uses no data from other skies nor the known halo location. That does not mean other data are not necessary — in fact, the model was created by comparing different skies. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def euclidean_distance(x, y):\n", + " return np.sqrt(((x - y) ** 2).sum(axis=1))\n", + "\n", + "\n", + "def f_distance(gxy_pos, halo_pos, c):\n", + " # foo_position should be a 2-d numpy array\n", + " return np.maximum(euclidean_distance(gxy_pos, halo_pos), c)[:, None]\n", + "\n", + "\n", + "def tangential_distance(glxy_position, halo_position):\n", + " # foo_position should be a 2-d numpy array\n", + " delta = glxy_position - halo_position\n", + " t = (2 * np.arctan(delta[:, 1] / delta[:, 0]))[:, None]\n", + " return np.concatenate([-np.cos(t), -np.sin(t)], axis=1)\n", + "\n", + "import pymc as pm\n", + "\n", + "# set the size of the halo's mass\n", + "mass_large = pm.Uniform(\"mass_large\", 40, 180, trace=False)\n", + "\n", + "# set the initial prior position of the halos, it's a 2-d Uniform dist.\n", + "halo_position = pm.Uniform(\"halo_position\", 0, 4200, size=(1, 2))\n", + "\n", + "\n", + "@pm.deterministic\n", + "def mean(mass=mass_large, h_pos=halo_position, glx_pos=data[:, :2]):\n", + " return mass / f_distance(glx_pos, h_pos, 240) *\\\n", + " tangential_distance(glx_pos, h_pos)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 200000 of 200000 complete in 141.5 sec" + ] + } + ], + "source": [ + "ellpty = pm.Normal(\"ellipcity\", mean, 1. / 0.05, observed=True,\n", + " value=data[:, 2:])\n", + "mcmc = pm.MCMC([ellpty, mean, halo_position, mass_large])\n", + "map_ = pm.MAP([ellpty, mean, halo_position, mass_large])\n", + "map_.fit()\n", + "mcmc.sample(200000, 140000, 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we plot a \"heatmap\" of the posterior distribution. (Which is just a scatter plot of the posterior, but we can visualize it as a heatmap.)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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0BgbP2dnC++87ymxda9JEcc892fzrX9lAYKdDh7RVqKx06WLy9tsZ1K9vfUCb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EsvWdm7N3/Tee3aCrfd5qNjxwD16ytlOsFm+3aZTp2SAAmDQTBypI977vEVuGPLn3/KPPxwAocO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\npDh11o4DjaWUWXmuWYH9UspaZTS+UlHS3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GAZgBCiBpB9wWdFIBYL53V1mUzQrZuPBQts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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "t = mcmc.trace(\"halo_position\")[:].reshape(20000, 2)\n", + "\n", + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\")\n", + "plt.scatter(t[:, 0], t[:, 1], alpha=0.015, c=\"r\")\n", + "plt.xlim(0, 4200)\n", + "plt.ylim(0, 4200);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The most probable position reveals itself like a lethal wound.\n", + "\n", + "Associated with each sky is another data point, located in `./data/Training_halos.csv` that holds the locations of up to three dark matter halos contained in the sky. For example, the night sky we trained on has halo locations:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.00000000e+00 1.40861000e+03 1.68586000e+03 1.40861000e+03\n", + " 1.68586000e+03 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", + " 0.00000000e+00]\n" + ] + } + ], + "source": [ + "halo_data = np.genfromtxt(\"data/Training_halos.csv\",\n", + " delimiter=\",\",\n", + " usecols=[1, 2, 3, 4, 5, 6, 7, 8, 9],\n", + " skip_header=1)\n", + "print(halo_data[n_sky])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The third and fourth column represent the true $x$ and $y$ position of the halo. It appears that the Bayesian method has located the halo within a tight vicinity. " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True halo location: 1408.61 1685.86\n" + ] + }, + { + "data": { + "image/png": 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0BgbP2dnC++87ymxda9JEcc892fzrX9lAYKdDh7RVqKx06WLy9tsZ1K9vfUCb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EsvWdm7N3/Tee3aCrfd5qNjxwD16ytlOsFm+3aZTp2SAAmDQTBypI977vEVuGPLn3/KPPxwAocO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\npDh11o4DjaWUWXmuWYH9UspaZTS+UlHS3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GAZgBCiBpB9wWdFIBYL53V1mUzQrZuPBQts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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\")\n", + "plt.scatter(t[:, 0], t[:, 1], alpha=0.015, c=\"r\")\n", + "plt.scatter(halo_data[n_sky - 1][3], halo_data[n_sky - 1][4],\n", + " label=\"True halo position\",\n", + " c=\"k\", s=70)\n", + "plt.legend(scatterpoints=1, loc=\"lower left\")\n", + "plt.xlim(0, 4200)\n", + "plt.ylim(0, 4200);\n", + "\n", + "print(\"True halo location:\", halo_data[n_sky][3], halo_data[n_sky][4])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Perfect. Our next step is to use the loss function to optimize our location. A naive strategy would be to simply choose the mean:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 2324.2292868 1123.41563759]]\n" + ] + } + ], + "source": [ + "mean_posterior = t.mean(axis=0).reshape(1, 2)\n", + "print(mean_posterior)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Using the mean:\n", + "Your average distance in pixels you are away from the true halo is 42.3177214405\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 1.04231772144\n", + "\n", + "\n", + "Using a random location: [[2712 364]]\n", + "Your average distance in pixels you are away from the true halo is 820.025908676\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 1.82002590868\n" + ] + }, + { + "data": { + "text/plain": [ + "1.8200259086760613" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from DarkWorldsMetric import main_score\n", + "\n", + "_halo_data = halo_data[n_sky - 1]\n", + "\n", + "nhalo_all = _halo_data[0].reshape(1, 1)\n", + "x_true_all = _halo_data[3].reshape(1, 1)\n", + "y_true_all = _halo_data[4].reshape(1, 1)\n", + "x_ref_all = _halo_data[1].reshape(1, 1)\n", + "y_ref_all = _halo_data[2].reshape(1, 1)\n", + "sky_prediction = mean_posterior\n", + "\n", + "print(\"Using the mean:\")\n", + "main_score(nhalo_all, x_true_all, y_true_all,\n", + " x_ref_all, y_ref_all, sky_prediction)\n", + "\n", + "print(\"\\n\")\n", + "# what's a bad score?\n", + "random_guess = np.random.randint(0, 4200, size=(1, 2))\n", + "print(\"Using a random location:\", random_guess)\n", + "main_score(nhalo_all, x_true_all, y_true_all,\n", + " x_ref_all, y_ref_all, random_guess)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a good guess, it is not very far from the true location, but it ignores the loss function that was provided to us. We also need to extend our code to allow for up to two additional, *smaller* halos: Let's create a function for automatizing our PyMC. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from pymc.Matplot import plot as mcplot\n", + "\n", + "\n", + "def halo_posteriors(n_halos_in_sky, galaxy_data,\n", + " samples=5e5, burn_in=34e4, thin=4):\n", + " # set the size of the halo's mass\n", + " \"\"\"\n", + " exp_mass_large = pm.Uniform(\"exp_mass_large\", 40, 180)\n", + " @pm.deterministic\n", + " def mass_large(exp_mass_large = exp_mass_large):\n", + " return np.log(exp_mass_large)\n", + " \"\"\"\n", + "\n", + " mass_large = pm.Uniform(\"mass_large\", 40, 180)\n", + "\n", + " mass_small_1 = 20\n", + " mass_small_2 = 20\n", + "\n", + " masses = np.array([mass_large, mass_small_1, mass_small_2], dtype=object)\n", + "\n", + " # set the initial prior positions of the halos, it's a 2-d Uniform dist.\n", + " halo_positions = pm.Uniform(\"halo_positions\", 0, 4200,\n", + " size=(n_halos_in_sky, 2)) # notice this size\n", + "\n", + " fdist_constants = np.array([240, 70, 70])\n", + "\n", + " @pm.deterministic\n", + " def mean(mass=masses, h_pos=halo_positions, glx_pos=data[:, :2],\n", + " n_halos_in_sky=n_halos_in_sky):\n", + "\n", + " _sum = 0\n", + " for i in range(n_halos_in_sky):\n", + " _sum += mass[i] / f_distance(glx_pos, h_pos[i, :], fdist_constants[i]) *\\\n", + " tangential_distance(glx_pos, h_pos[i, :])\n", + "\n", + " return _sum\n", + "\n", + " ellpty = pm.Normal(\"ellipcity\", mean, 1. / 0.05, observed=True,\n", + " value=data[:, 2:])\n", + "\n", + " map_ = pm.MAP([ellpty, mean, halo_positions, mass_large])\n", + " map_.fit(method=\"fmin_powell\")\n", + "\n", + " mcmc = pm.MCMC([ellpty, mean, halo_positions, mass_large])\n", + " mcmc.sample(samples, burn_in, thin)\n", + " return mcmc.trace(\"halo_positions\")[:]" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_sky = 215\n", + "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", + "Training_Sky%d.csv\" % (n_sky),\n", + " dtype=None,\n", + " skip_header=1,\n", + " delimiter=\",\",\n", + " usecols=[1, 2, 3, 4])" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/maxwell/anaconda3/envs/bayes/lib/python3.5/site-packages/pymc/Node.py:403: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + " self.__name__ = input['__name__']\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-----------------100%-----------------] 1050000 of 1050000 complete in 948.7 sec" + ] + } + ], + "source": [ + "# there are 3 halos in this file.\n", + "samples = 10.5e5\n", + "traces = halo_posteriors(3, data, samples=samples,\n", + " burn_in=9.5e5,\n", + " thin=10)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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m3HST4bTTlrBu3cwH/AEHON773i5PfGJgzRpht92U/feffW2aJCFpNklazWmG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GAAAg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\n8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d54wypYAvjqK40vv6y8S2WmYD2ebY1VIy9e+l5MA6eguGPVyW6tXUuf6Ywc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Ij8+/qeGrzduxJVKNWu5PWVCz/e/q90YhyNUXI0aYnHZajEcfDfP883XccksjRxyht5pXVlUl\nGTjQ8o6qquSBB+o7VKw4Wz/YnDVF1ay5xjVfpJTkkuSdyZ0NhUh3nAs8CXwLPANsAB4TQpzX4rN7\n8FBkDBhgup7UJTfd1NjtdaW6I2xyufsvX2zYILj55iDTplXx4YrUUIx7YS9EVLMlcHt+pGH9mXHd\nmvQNE6m7PEQis3HWHkZla7H99pIbbkjGQocN01t9z27aJLj8l1UceHAvDjykN4dO7ctDj/Xgu+81\np1+EqqD4Ned1qfZPW0NKqyRXa9FaA9uN7baTzJwZ5s9/DvPKK3UcdFDpFYSH5isQpFMmsgnl5otm\na4Om7CjE58CJUsoPXdvGAE9LKYfl8f3+wEPA9oAJ3Cel/IsQoifwBDAQWAOcJKXclvjONVj8OB34\nhZTytcT2PYF/AUHgJSnlZZnO6dUG7X6QEt57T+XhhwNMnx5j4kSvbFN3gx12sI0a21hRA/6UcFc2\nov4D/wxy1VXWoBk8WOelF+vo01tv1zI1ttfMeVqX1jWkTPYSEJYXyfnfSbFlCzz9tJ9HHglw220N\n7LVX6zifn36qUFvbVJn6oIPi3HFHmJ13bn7dM03LaF+/XqG+XjBwoNmkmHlXwOrVCrfcEuTLLxXO\nPDPGQQfF2XFH7+E2X+SqM2rqulOSy3lIyDFvLF26NGNt0EJmm97AJ2nbVgL55nvowBVSypHAROBi\nIcQI4GrgdSnlrsBc4BoAIcTuwEnAbsARwN1CCPsC7gHOkVIOB4b/f/bOO06uqu7/73PuvVN3N00S\nICEJoQUIATWYQEIoSYQgHUWlqI+AICVSVBDlEXlE2oPykyII0vSRooAFlCpIEiTUQCiBEAIhhSSk\n7U697fz+OHOn7exmy+zu7GY+r1de2blzy5lzzz3ne7/l8xFCHNqJ31HHAIYQMGWKx003pZg5s26o\nbY3I5x4Jne+lfB1K9LI2vuO2Co0WhyrWrhX8v/9XYGP/4AOT1Z/IvCHUkdBqNdqfD39CiWesnCqk\nPc62/oShQ+H0020efbSl24YawLbb+hxySOscp2ee4nwQSwAAIABJREFUsXjqqfZdQO+/L7n++gjT\npjVx2GFNfPnLjTz2WM/Kv/UVFi0yuO++MC+9ZHHOOXG+9a04H31Uo8mNNYgtea+LJbm6673tzJHz\ngF8KIWIAQog4cC3wfEcOVkp9opRamPs7AbwDjAKOBu7O7XY3cEzu76OA+5RSrlLqQ2AJ8AUhxLZA\nY67gAbS3LjimBPWcNY16DkYB9b7QGMj9EEyIQZiy2ONUnlMyb968km0bNkhWriydFhMJkdf+Kz++\nJ1DpvAEzen5R6IEQXi2MiYaG6pxnyBC45ppkRYPt7bcr88xt2AAPPGBx4IGv8vOfR9m8WfdpJKKY\nNq16Ybg1awSPPmpx1VURHn7YYvXqvjOOTLPUi/bSSxa//GWUdI6QqxbGRC2gvX7YUkpEtVImOuM3\nPxMdrtwshNiA9qg9D3y9sxcVQowF9gFeAEYopdaANuiEEMNzu40E/lN02MrcNhdYUbR9RW57HXXU\nUWVkMnpxe/ttg40bBbvu6jFhgsfIkbUbKslPigKMSKhAfUHrnK7g/+JQRjniMdUh7b+OYktVqkF7\niqklSqg5VG3noNUKxo1T/OY3SRYuNHjsMYvXXzeZONHl9NNby1l//LHgootiPPZYiOKyWctS/PGP\niaqpKiQScPXVEe66q8BrceCBDrfemuwTstfdd/cZOtRnw4bCWPr970N861vZbpPa9hQcB555xiSd\nFkyeXFpAls3CW28ZrFgh2W47n1139Tqs01zr6Ax1x2pgei73bHtglVJqxRYOawUhRAPwZ3QOWkII\nUT5CqzZi6zxrGnXeoALqfaHRIX4xBQ8/HOKcc2JFqhKw114uf/hDYot5P32JYkOo2DgKPgffF/eD\n8n2GDFWMGOGzZo3ed+edXUaNcvPnBB1abUtSZksI8umCNkir9XmCz77n5o2yoOoz/7sqFBR0FwPx\n2dhmG8WsWS6zZrlkMlTk/lqzRnDxxYGhBnAQoAsdbrghxaRJHqJKzq+lS2WJoQbw739bvPeeZPjw\n3jeOdtzR59Zbk3ztaw14XkE5JqBAqsUxsXix5KSTdHtPPDHLZZcVisj+8x+T449vyM9XJ52U5ZJL\n0t3Ow6uFfuhURqoQYjBwIDljTQjxqFJqUyeON9GG2u+VUn/NbV4jhBihlFqTC3GuzW1fCexQdPio\n3La2trfCn//8Z26//XZGjx4NwKBBg9hrr73yHR+4Nuuf65/rn1t/fuih+Zx/fhylAoaeZwFYtOgg\nFi0y+OijZ2uqve19FlJu8fv5z+uMjp/85GDOPbcBeIaTT04zbNhklAfz5s8H4IDpB2zxfG199h2H\n/Sfvpz/PnYcwBNMPPrhie/7z4osoXzFtqhbTnv/88wghmbr//gija9ffmj+//HLl7z/99GD++c8Q\nwfhubDyQSy9NMWzYM9i2QsrqtWfpUgEcgcazuf8PIpMRfdY/Bx44jb/+tYUzzniJlSsNhg6dzg47\n+H1+v9r67PsH5gzLZ/njH+Gggybx5S87zJs3j+uvD6PUF/P9+3//B/vssy+nnmrXTPvLPwd/L1++\nHIBJkyYxY8YMytGZatBD0JQd7wIfAaOB8cDxSqmnO3iOe4BPlVIXFG27GtiglLpaCHERMEQpdXGu\nwOD/gMnoMOeTwC5KKSWEeAGYA7wEPAr8Win1WPn1rrvuOvXtb3+7fPNWh3nzek/rbt06wXvvybxn\nYvRon4kTPTogydcr6M2+qGV0pB/WrhUceWQDS5aUv9MpHn+8hX33rc0wSWdQqR8SCVi40CQWU0yY\noMdupdBlV0h3PdsupdyQYEYibR6f52rKVYQW87xVu/pza302nn7a5NprI+y0k88Xv+iQyTzLV786\ntUeutWkTnH12PGccauy4o8tf/tL3nup16wSffCIYNEjl1SNqcUzMn29w5JFN+c877ujy2GMJttlG\ncdllEX7962jJ/jvvrMl7hwzp+jV7sx/aqgbtzNN+I/AdpdQDwQYhxFeAm9BGW7sQQkwFTgIWCSFe\nQ4c7LwGuBh4QQnwbbQSeAKCUelsI8QC6AtUBzlIFy/JsSqk7WhlqdfQ+Fi40uOCCGAsXFoaVEIr7\n7kswa5bbhy2roysYPlxx++1JfvCDGC++aAKCkSN9rrgixYQJ/d9QawsNDVCeUF6R6qML+qDSNPFV\nQWBcCKlL+41C/lzxeYolroLcu45eq46OYcYMlwMOSORfKOfNa200dcUwf/ttyXvvGYwa5TNpkn5e\nBg+Ga65JMWOGw6OPWkye7HHMMXafG2qgQ8bbbNP37dgStt9eEY0q0mltzyxbZvLRR5JttvE4/niH\n3/42QiZTsHWGDfNbkaX3BKopLVUJnfGsbQKGKaW8om0m2lM2uOotqwKefvpp9eGHk1m3TvCVr9hd\nFpWtY8t4/33JrFmN+QqqYlx6aYrzz2+d1FtH/0BzM6xaJXEcbcCNGFH7E3pPI+BAy6MTPGdaqzKj\n2SYB3/UQhsDMJVS1VTxQSaO0rVy8OqqHrnBlvfCCwZe/3EgqJYjFFE8+2czuu5cRqCqqlgu3NcFx\n4NJLo/z2t4Xcv7vvTnDkkQ5KwcsvG/z4x1Feftli5EifO+5I9HgUYEt8a51BNTxrv0d7tH5dtO27\naOqMmsVpp+la8AkTPKZOHbjegL7Gxx/LiobaoEF+3avWz9HUBE1NA48QtDvojj5oUMrv225elQC3\nQDXiey5GKFRZkaA4BJu7vu+4JW0qlp/qaLtcVxPB1kq6Qq0gKAgJuPWALRZ3fPCB5OSTG0il9Hqb\nSgmWL5etjLW+NNR62gvUk7As+NrXbO66K4xt6040DP3mJATsu6/HAw8k+PRTSUODKqkW7SlsSae3\nGujM2T4LXCeEWCGEWCCEWAFcB3xWCPFc8K+qresminnWEomt9xWmOJGxp7DLLh7HHpslcDeEQoqT\nT87yj3+01FTIrDf6oj+g3g8aXe2H7ko5BaoDWqRdgVK46Yz24Ai5RdLdShqEwd/FxkUgtdXWuT74\nQHDHHSGOPrqBGTNe4be/DfHBB1vvXAmlY6J80e3IIvzmm0YJFQa0FqvvS3RUNxdqd57Ye2+Pe+5J\nYFkKy1LssEPpbxg8WOs1V8tQ21I/dEaHd/Vqwbp1mpD4178Oc+mlEW6/PcTLLxvtyn51xrN2W+5f\nv0Q0uuV96ihFOt3xfhs1SnH99Sm+//0MjgONjTBypF9/U69jwKIzXolyT4aQWv7Kd718+NT3fJRq\nHdZs6xx5LrYKodDi/aVpVsyrW75c8JWvNLBsWbAMmFx8cZw99nD5058SregOPvxQsmCBwW67+eyz\nT+28gFUbgdRX/v7muiHYtiW89lop6W5jo2LUqNoy1so/9zfvmhA61/DZZ5tJpQR77NG3nv+OpiIs\nXGhw8skNnH9+mp/9LFbmRFKce26Go4+ufI0OG2tKqbu3vFdtIeBZa2ryGTt24E4uW0Jnq1iWL5f8\n+98mn/2sy4QJHX8IGhtp5eqvNdRaZVNfod4PGr3RD20VI2gpGgvfdnOcaxTzsbZb0BB49QJjDHL8\nb5aZNy625BVassQoMtQg4Bd7+20zRypamDPXrROce26M+fMtGhsVTz3VzC671Paz3hUo32fqfvvn\nvU6BQoRSfj5MvaWCknIVhmuuSbLjjt3rqy2FLTsT1uxMCL+W5wnD6L31piP9sKW+X71acNZZMVat\n0ilDiUSrM3DDDdE2jbUumdNCiEVdOa6vcO652Zqotql1JJPwxBMms2Y1kkgIdttt4E3GddTR26jk\nyQhghEJ57UBpaR3BSqHVts4RGBDBP2maeUOunHC3fCEZNcqnsbH1vLjPPg5jxpRe7+23DebP1/qY\nLS2C99+vLU9MJqPnr+6iLa9TpWrgcqxaJbjtthDjx7sMGeITiSiuuSbJ7NmtJa8626b2wpaVvg+8\ngxWly7oZwq+ja3j3XYPFi/XL0ZNPWpx7bjsxzwro6l0a08XjehULFy5k6FCfI4+0ezyZc8MGeOop\nk5/8JMJPfhLhmWdMNmzo2Wt2FB3JO1i+XHLZZVG+9rVGpkxxOP54G2sAahfXag5Gb6PeDxrV7Ie2\nFshKi2GxIoG0zMI/02xTR7D43JXe4otpPfLnaWdR3m03n0ceaeGMMzLsvLPH2LFPc9VVKe64I9VK\n+mju3NIgTHlOVl/irbckX/96A1/6UiN/+YtVwWPRcQgp8+THwefi/8u3B/A8uPPOMBddFOecc+Kc\nfnqWJ59s5tvftmlqoluoaJwVjbXy7z3bxsva2nBrIyctb9hvwVBr7/lozyAcaGivH1atEvztbxZX\nXhnh2msj/OtfJuvWtTY4ijWHFyww2WEHj4cfbuHgg21iMUUopDj4YLvN63SVVbHfZKD++c8Jdt21\nZweT48A994S5/PJYftvNN8OcOWl++MMMsVg7B/cxfF/nWJx5ZoylS02mTXO44op0n+jU1VFHf0V7\nvGvF+Sz6D1rt125uWo4QN/+3APyCh2RLOqPtLch77eVx5ZVpNm5M8/LLKWbNqkyx88YbpXlYllUb\n80NzM3z/+zEWLNBvlt/+dgO/+lWSb3yjay/our9EScVnPn+tnb5eu1Zwxx2azGvzZsk110TZdluf\nPfdse/HtTJvKtWtLxlrR78zz8RXp2PaENFlXeQYHGjZuhB/9KMrf/15K5DZ5ssPNN6dKwt8rVpT2\nTyQiOPBAh8mTXT79VKAUDBumWLy48rU63LtCiF8JIQKxzdkdPa4vsc8++/RKIuzatYL//d/Wmfg3\n3BDhww/7fgC3FW/fuBHuvz/El77UyNKlJlOmONxwQ7KmkmGrjVrOwehN1PtBo1r90F6oEwqejI4c\nVymkFZwjv3AXUUl0xEOyJQwZArNmtd0XgfZigO5qLVYLzc2C118v7ddLLomxbFnX++OA6dMLeYA5\n75SXtVm9SvDk0xHuvS/Mk0+Wek+yWdi4sdQ6/Pe/qxOaKA9bVtwn93053193iwfaej62NN4HGtrq\nh02bBP/4R+squgULLP71r9JxWZ5ysOOO2jaJRHSB3g47qHYdO525iwbwuBDiTWBqTtC9DmDQIMWk\nSa25xCIRajaUuHy55Mc/jnH22XFsW/CFLzj85jdJxoypjUm4jjr6A4JQUDnaWiC3FE7bUqVepc+9\ngSlTCr9x++19dt65Ngq2Bg9WjB9f2v/ptGDt2u4Hf/JSX57P8pUhTj2tka9/vZFzzmngq19t5Npr\nI/mQa1OTYvz40j7Zbrvq3ZvisGVb/HvFIfS28har2Z72Pm8t2H57xemnV/ZGl3t2J04sjI+ZM232\n3LNzz1CHe1gpNQct4H4xsA/wjhDiKSHEN4QQDe0f3Tco5lnrSTQ0wFVXpdh330IiaTyuuP32BDvv\n3PdvHOXx9sWLJaecEue++7Trdt99HW69desw1Oq5Whr1ftDoTj8EC3lAbKuUv8Wk7S0ld7e1EHe0\naKA7aK8vpk51GDfOpanJ59ZbW9N69BUaGuBHP8pQLCchhCIe73r7gn7Ih52Bp58Os+DF0jfv228P\n50NbQ4fCJZeUJozPmNG9woK20N4YCr4ThqaG6a5+bFtjYmsrUmirH8JhOO+8DLfckmCnnTyEUAwZ\n4nPeeelWhSV77eVy2WUpTjopyy9+kWZwJ3WfOnUnc1JTjwCPCCH2BP6I1ui8WQhxH/BTpdTKzjVh\nYGD8eJ/770+wbJlBNgvbbqsYO7bvDbViKAUvvWRw0kkNrF+vH67Jkx1uuWXrMNTqqKOayCd6O7li\nAV9iRtsWZQ/QXh5ZW3xNxX/3Bfv8TjspHn44geuKbtNQVBtTp7rccUeSCy+M0dIiuPLKVFUq2YPi\nD9/1eOfd1ktlJEKJ5uT06Q533pngjjtCfP3rNvvu23PKLcX5jMX8b4GXtxqh8Y62YWvH8OGKE05w\nmDnTIZEQhEJaZ9UoTfNk0CDNTOF50BUbusPaoABCiCbgK8DJwETgQeBuYDlwIXCIUmpi55vRM3j6\n6afV5z73ub5uRk0gnYZ//cvi1FPjeYmOY47Jcvnl6QGdo1ZHHT0F5fu46QzKzeWUGRIZMjHqTNB9\nglWrBK4r2G47v6rpJ8r3mTvP4rjjGvF9PXcKobj55iRf+YpDub3iebRaqHsCJUn+QWWmV1phXDem\n+h+6rQ0qhPgzcCjwHHAL8BelVLbo+wuAzVVoax1VxsaN8Mc/hrn00ihB6dBZZ6WZMydbr/qso8fh\n+/DqqwauC7vs4jNs2MAYc/kKQa9/aiwONGy/vaI4HFotCCnZbz+Pv/2thWeesTBNOPBAh89+1mtl\nqEHvGGpQmq/ouy5e1kEahg7LC3erCE9uTejMnXwB2EUp9SWl1P3FhhqA0iJ3I6raum6it3LWahmf\nfCKYM+clLr00hjbUFD//uZaF2hoNtXqulkZv9kM6DRdeGOPww5v46lfjzJ/fvgZeV5HJwBtvSP71\nL5O5cw2WLhVUyP0vQXf7oZjUVhiVKz77Gh3lw6o/GxqV+sGyYP/9PX784wwXXZRhyhSvJATaFyg3\nxKRptPt9V1AfExq10A+dkZv63w7sk+pec+qoJj7+WHDJJTEefVSHZQxD8ZvfJDn8cKemud/q6B4+\n+ECybJkkm4UhQxSjRvl9quARj8OXv2yzaJHJq69aHHmkyS9+keZrX8t2Osm2LSgFDz4Y4txzg5cS\nCIcV3/9+hq9+Nduzof6iJOtimo1aQJ0Pa+CiOIfRCIe0Ry33dmKEQ/X7PMDQqZy1/oatOWdt6VLJ\nmWfGeOUVnbzR2Kj4/e8T7LefW7N0InV0H0uWSA4/vDFfQAJaG/e7381yzDF2n0mIffih5LDDGlm7\nttCuc85Jc955GYYO7f75Uyk45pgGXn659eA+9FCbm25KVuU6xSjPGYIiItxuhqDee0+yZInBpk2C\nSESxww4+u+7qddq49V23NDJYxsNVR//CihWCd94xWLtW8tFHenyNGOEzZIhi6BCfocN8Ro1SVR/r\ndfQeup2zVkf/wVtvSU4+Oc5HH+nbO3asy113JZk4sXsL9Zo1gs2bBUOHqlYkmXXUBsJhRfn7V3Oz\n5Oqro/zud2Huuy/B5z7X+xxZY8f63HZbkuOPb8B19Tx0441RwmE455wMgwZ17/yxGHzve1lOOcWk\nXGDl8cdDfPxxmqFDq2uoFocVy4217pCRLlpkcOSRDTQ3lx4/ZYrDL3+ZYvz4jv+Ozoh29xdks9po\nWb9eYhgwcqTPttsO/Plo/XrBN78Z57XX2n/b3n13l7PPzrLffm7NVe7W0XX0/ye3HWyNOWtvvCE5\n+ujGvKF24IEOF1/8WLcMtc2b4f77LWbMaGLKlEEcdVQDb73VP4dOLeQe9CRGj1bcf3+CESNa3+9P\nP5WccUaMTz8VfdIP++/vcs89CaQsLKzXXRfNC4R3Fwcf7PCnPyUYPbo0Ue2ggxy22abyYt6dfmjF\nb1Ul/rOPP5atDDWAF16wmDMnxqZNnWtjR/mw+sOzsXSp4Gc/i7L//oM47LAmZs1q4vDDG3jnnd7h\nm+tLDBum+OUvU+y3n0N7hRTvvGNyzjlxjjmmgSVLutcvtdoXvY1a6Ie6Z20A4Y03JMcd15gXWT79\n9AznnZdh6dKuv3UqBY88EuLcc+P5bYsXm9x6a5hf/zrd7TbXUX18/vMejzzSzLx5FjfeGGHpUkng\nbdp7b6/EWOpNGAbMmOHypz8lOOWUBlIp3abzzoux554tjBnTPS9ALKbP//jjCZYvlySTOoQ4bpzf\nI8U0JV60nG6kQiENo1vG2sSJLgcf7PDMM62N2ERC5DyTnaBcGiCVqitWCE4+uYF3yzjPPvzQZP58\nk913774OZ61j77197r03wQcfGLzxhsHzz5u8/rrJypUyp6YgCIcVo0f7nHxylmik7lkbKKjnrA0Q\nvPGG5Pjjda6SZSl+9asUhx9udzuBe8UKwbRpTa3e9I87Lsvtt9frSWodGzbA6tXacIlGde5TtZL6\nu4PXX5f85CexvFft3ntbOPTQniMR7Smk0/DhMsH77xu8/IrJW28ZjBnjM2uWy5QpTpf7eu1awRtv\nGPzpTyHefNMkGlUcdJDDCSfY7Lrr1rkA//vfJsce29hquxCKRx9tYcqU2pDA6i1onr8smzcrUhkL\nxzNwXEm8QdAQ8xjUVOD/GwjG+taCes7aAMaiRQVDbaedXG69NcU++1TmAOosPE/kPSABhFB8+9uV\n9dDqqC0MHUrVc7Wqgb339rnnngSLFpksXGhUVUext/Dhh5Lf/CbM734XzpOlBrjzTnjkkWb2379r\nBsTw4YqZM11mznRpadHUEZFINVrdfzFqlMe4cS4ffFBYtrbd1ueGG5J9kofZFyjWolW+D0rRELaJ\nGWmMiEWosSG3vfSYvlS/qKM6GNB3a2vIWVu8WHLCCdpQ++Y3szz4oJ64ip/D7sTbt93W57//O40Q\n+ulvavK5664kkyb1z8mxFnIPagG10A9DhsD06S5z5mS7XfzSVXS1H1asEHzta3Fuuy3SylADXQww\nblx1flNjY+8YatUaExs2wMqVgtWrBevXC7wqTRU77aR46KEEDzzQwj33tPCXv7TwxBPNzJjhUk3R\niGo+Gx3luOvoubysjZdx8G1X/21r/clieam29GYDabTgX0faVAvzRC2gFvqh7lnrx/joI8k3vxkn\nlRLceWeCgw92aGqq7jXCYTjttCzTpzukUoLtt/cZPXrghs7rqKMjWL5c8t57rafPaFRxwQUZvv71\n7FZRoViO554zOf/8GGvX6nSMeFwLWM+cqY3XHXbQ/7pqXI0erVoVkNQqusNxV8kD5rvayEKB73go\npfQ+QiAtAyMUQvl+npql0vHF7fGFW5dG60eo56z1U7S0wM9+FiWdFpxzTobdd+9/YaQ66uivaGmB\n114zeOklixUrBLvv7jNunMe4HV122MHHCg3ooEWbWLJEcsop8YqGLEAopJg+3eGb37T53Odctttu\n4K4/XeW4KzbyoJBz5tk2vu3myW+FYSAtLS+FEEjT0JqgbVzDs+28ji2AMGXdWKtBtJWzVjfW+imW\nLZNs2CDYYw+PaLSvW1NHHVs3ggU28IiUL5rVyhXqDzlHq1cLFiwwufzyCB9+2LZxMnKkzxVXpDjw\nQKfbPHs9he70d1tG15bQlpGXD2PmwqrBuTzbQfkeRiiMNI287Fn5tYLj85yAbexXR9+iLWNtQN+l\ngZyztuOOPp//fMcMtVqIt9cK6n2hUe8HjWr1Q7CoK08nd+t8IrvV9sCg6+o1Optz1BlUqy+2205x\nzDEO//hHgr/9rZmf/zzFhAluK8qYlSsl3/pWAw89VFvenaAfunvfOsNxV35cgGD85PPecucK5KS8\nrI3TnMDZnMRubsFuTmC3pPCydqv2CimRlplvixByi7+r0pioZh5ef0EtzJf1nLU6eh3r18M//xki\nFFJMmeIxevTW89DXMXDh2bZeAP2iBVCB77lIwyxJ9O6KNyPIOdJGm4dSPmYNl4huu61i2209pk3z\nOPnkLGvXStasEaxbp3VrXVcQjyvGj6/NYqW8oR3cL1FqSDmOjnBoSpzKEapij1xbXrry7QWPmY3y\n9HbfdlHKRwhtcCnPx81ksVuSuOkMQoGTTCOkxGpqQObaWz4+8udvo1q00m9vtb2uNdsnqIdB6+h1\nzJtncNRRuhJil11c7r472SkJnTrqqCUEC5jvunhZR4dBDaOwuAsQQhY8Gkb7i3VbKM5ZAp1zZEYj\nNbFYvvmm5N13DUIh+MxnfMaO9ft9Pprvuvh2oZhBhgqh7XQa/vpXizlz4lx4YYaLLsq0e662QqLF\nocnA85W/tuMihM5VQ4FSOcJlU+K7LvaGBJ6TxXMcEOAl0yAFVmMj4aZGzIYooYZ4h9tS/H2lNuXH\nqSgab3Wt2aqjzrNWR80gnS6MwyVLTC6+OMbvfpdk2LD+PbnXsXUi8D4EeUWerb1egffCCOswn1J+\niYctOLY9T0WxISdNU1cD5ozA4Hq1YKzdd1+Ym28ueHG2287nwgvT7LOPy2OPhZg82WXyZJeGhj5s\nZBcQKFMU97Hvw6OPWpx1VhwQLF5sbPE8lTxUQspWFZqespGGWQi/qtx3vsoXEziJFF4iA0KAFBgh\nC99xMSJhPeQU+LaDkLHKv6nMw1s+ftpqE7lzK1Xoj1oYe1sLBnRPD+Sctc6gFuLtxRg6tNQoe+45\ni1df3fKEVw3UWl/0Fer9oFGNfsh7SII8HhXk9Xj5xVZIXXlXKdzU1ufynCnQhp+0TJ17VOUig+70\nxYknZvnMZwptX71a8v3vxznuuEaEgHvvDfPLX0ZYv77z506l4OmnTX74wyjz5hnYPawqFfRD0L9B\nEn7Q14sXS+bM0YYawOc/v2Uqkba4z8pRHH5Uvo/veTpHLWJpw1H5eMksdiaNnUoCYIQjhAY3Eho8\niHBTk85nC7VdFRpcvyPFBfOff75kTAqp2+B7bquw8EBGLcyXW0dP11FT2HVXj4MOckq23XprGLd/\n0CfVUUdFBOEjbVwpyPFg+W7bC1ulRTw4xi97IAIOLSMc0qGrGpIR2mMPn7/+tYXddittc3Oz5Npr\no2Sz0NIieOopi85m3ixYYPKVrzRw++0RjjmmkYULe+fFrlKBgG3DnXeGyWQK0YE99vC2mHTfVrGB\nNE0Q4Gaz2MkkbsbGSaZw0zZe1kZIgREKYYRD+J6H25LSYVFP4bakcDa3IMMm0c8MJTyoETMWxYrH\nCDXGuxyelKZZ1FZRQu8RhEGlYeZfSuroHdRz1uroE7z6qsGhhzbieXrSGzPG4+mnmxk6tI8bVkcJ\nHAfWrBFkMoJhw3yGDOnrFnUca9YIfB9iMdWKGiKTgU2bBMOHq27JsumwZ6GwwMs6BQoPz8eIhDBC\nVrucVh9/LFi1UhCNwridPGJhL39uKBh01TbOeoIGZMUKmDvX4tJLY2zYUHrOb3wjy1tvGdx4Y5Ld\nduvYIp/JwDe/GefJJwt9973vpfnpT9vPEev+TpCBAAAgAElEQVQpvPWW5KCDmvLz1qhRHk883szw\nz7ht0ra0B63vmcFJpFGupz1WihxnmoURDWFGItjJJPamFuyWJL7roBwHoQQiFiYyeBBmPJq/phGy\nKnpxi68ZvAgUhzPby6MsKbao56z1KLZK6o46ahcTJ3rcfnuSUEi/LIwZ4xMO93Gj6shDKVi40GDO\nnBhTpw7iC19o4qSTGnj//dqfMt59V/Lf/x3hoIOamDq1iUMPbeKii6IsXGjgOPDpp4KrroowbVoT\n11wTYe3a1nJRHUFe/ifr4KYz+K6HkJpNHqFzjKRp5Aw6J0/lUYw33pAcemgTsw8fxEEHN3HVVVE+\nXV+UDyToNPVDR9teDTqR8nNuP8Lly0dt5qnH1vP7e5o55BA7p02rePddgz339PjnP60On3PzZsHr\nr5caAy++aNJXDp3XXjPzhhrAZZelGb6NW9KfbjqDnUjgZjL5fm3L86YNIAUIbRR5Wu+TIiPJs23s\njS25YgeFn8miHBcZCWMYJk4iibMhgXI8pDTaDW/miwdcX0tWZXTFafkYKA+TBp/LDbNWKQB19Bhq\nf+btBuo5axq1EG8vh2nCkUc6PP54C7femuAXv0gRb124VHXUYl/0BdrrB6XgqadMZs9u5P77w7S0\naIvhhRcsliyp7SljwwY444w4N94YZc0ayaZNkvfeM7jttgizZjXyzDMmb70l+fWvo2zYILnmmgX8\n4x9tGw/FIcnyBclOJMhuaMHLZPFt/b20TO1Fi4SRIRPf8zTbPALl+iX8a83NcOGFMT75JOhTwc03\nR3n1tYIXKVggqx3urGQ0dPfZKD7n9ttkmDV9M3+4ayP33tvCj36UZuxYj3vvDfHQQyGSyY6dMxZT\njBhRSu2x++5et7yhW0J7/TB3bsFYmTDBZdo0N18o4LtevmLXz3r4Wa3fmU/Yr2AYayPIQEjwXU97\n5UIW0jLwfQ/PcbCTqbxRJIREhkIYsRhKoMeX7eL7Hm46i5NK46TSJfxsxWO3mI4jMBSDbZVeJsr7\nojiciyiXwHIrnmMgoBbWjdqeeesY0JAS9t7b4ytfcdhjj4H3gPdXvPuuJivNZks9TqGQYtSo2r5P\n4bBezCvB8wRXXRXNGZ8F/PznUVatau1dC7wlyvPzlBnBYuvZNm4yi5tJk163ESeVQkiRJxs1LKs0\nXETg1fDy52lphnffbR1Cemex0SPetGJ0NOG9K+cMcp6EIbEsmLCnFlq///4wjiNYsULS3Nwxb2Zj\nI5x6anFFgeKYY3q4wqANZLOwbJnOlxs+3OeWW5IMH64jA/q3q5xRpBBS/75iQ6nYYAoQUGMYkRBG\nLIQRDWPEwiCE1vzEQGjHG6BQnocZjxIePAjDslCup2k7MlncVEpXgSK0kei4rcZuoa1B6FO3U3l+\nh0hyC8fJgvGZo63JPx9V8tTWUQrjsssu6+s29BjS6fRl2223XV83o88xevTovm5CzaDeFxrt9cPb\nbxv84Q+lMelwWHH33QmmTPEQXYsa9gpCIdh7b5dhwxQvvlgasho+3Of665OsWiV57LHAezWWdFpw\n4olZttmmNH9XeV7J/wEXh+fYOKkMvuPgpbP4nouyXazGmObByntBRN6A01WiquBJEYJQSLH4XZPF\ni0sNtrPOyrDzLiB6sKOFEHkDIDAKu/ts5M8pcjlXuX9WSDJhgsfee3u89prB0Uc7HHGEg9HBOoER\nI3waGhTr1kmuvDLFAQe4XRaC7wja6gfTBNfVL5k33phkzz0Deguv1OOk0Dx7oDnKBNpg8n29ryHz\n32sD3tGFI6FQgSLD1wUqKJXPZdMcayZCge/6gI9hWUhDe3AFAqshposR8pXJKjeOVL6SM7jvgZZo\nMRWHHusq3762+qLwTABK6esHHIJF1+tLKEXV5qreXDdWr17NuHHjfla+vV5gUEcddZRg5UrBdddF\neOCBMIMHK770JZsTT7SZOLG2DbViuC6sWCFZt06QTmuP25gxPttuq5g3z+SooxqL9la89FIzO+1U\nma09n48kChQavuuS2diM8lyU42FEw5jRKFZjNL/gKs/XCzgFviwhCt4yYUiWfmBy6aVRHn/cwjDg\nBz/I8J3vZBg8uIc7qBdQqYBh/XqBabYu+NgSXBcSCfq8X1IpbQAUy/yVk8wqlRNaz/1uN53NhwqF\nIVAKzGhI8+QV8Zn5nqcNMkPiOy5uOotyPTzb0bmQIQs72YLbnAZDoFwPIxLGjEYAgbRMzHAYhdJF\nLcFLArSieikuhMjnsQWeN0Pm928LJfyAvp9XV+ipYpjO4s03DS6/PMLs2Q6HH+4wYkT/sXO2ygKD\nes6aRi3E22sF9b7QaK8fRo5U/OIXaRYs2MwzzzRz1VVp9t67/xhqoL0gY8f67Luvx/TpHpMne2y7\nrZ6wJ0xwOeywIJT2LIcd5jBiROuwTd5TYEhkyCwk++c408xYGOEJrMY4ViyGES4KfQrNeB8sfGYk\nghmJ5D0tCL3I7TTO5ZZbkjz/fDMvvtjM+ef3naFWzWejrQKGYcM6b6iBvp+91S/t9UMsRis95vI8\nLiElZiSCEQppI83PecccBzeRRmUdnJaUrgD1dB6jk0jhpNJ4tqY0MsIhjGgIETIwwtqo8rIOXsbR\nYxKhDTtAKJBCYoQtbUmW0MSIshy1wn0pVikoL2QJjinvi5JK0txvDsZ3MLb72lADePllg6eeCnHh\nhXHOOCPO8uXdm7xqYd2o19xWEWvXCpYskaxaJXEcTXWw225aeqWOOjoKx4F33pGsWyeJxRTbb68Y\nM6Z3x1Akoo22gYjBg+Hqq1MceqjDK69kueCCVJvM+sXUBXlNxRy/VCgex4yE8bIuwjLydAnB4hdU\nzhUvcHnkulZ5Pk2NdMmA6Ul8+qngP/8xefDBEOeem+Hzn++cfmdbjP0DFcXSUYWNRQUqnovTnEIa\nEhE3wFP4QoccvYzOL9MKFQ6252LFo1ixKNIwsFtS+LaNsrO68MDzEaaBlBIjGkEoAYbATWQwG6JY\n8WjO6yUQEqRZGJee7eRDnMXjOl+JWvR7ylGutiEMWVIdWm2S5u6gsbEwdz33nMWtt4a55JJMjxSx\nOQ588ongM59RrQz5aqIeBq0SFi2SnHZanCVLSu3f4cN9Hn64hd13rxtsdXQMjz9uctJJDfi+fhts\nbFRcckmKY47pX+78/oZ16wSrVglCIRgyROU9cQFFR0DNEUgQBdJRmmm+VKy92ENRHEotli/KL2w1\nxlX19tuSiy6KMX++rpL929+amTat88Zae/qTAw3BGAk8Zb7ng9BjxMvYuKkMrpvFMC3McCRf9amU\nj5fK6twyQxtiRthEWhYIhZfO4mayKF9hWCbKU3ieg3J9zHgEMxQBoXRFqOdihEJYDbFcpaY2BoUw\nMMKWDnkqPy8On/cIUvB+tsUTV8wnWKvjthgvvaR5PAOVCVD8858tTJ7cuXHcEbzwgsHxxzdy3HE2\n3/9+mjFjujdHb5Vh0N7Cxo3wve/FWhlqAGvXSpYs6R3G7ToGBj780MgbaqCZ33/0ozjf+16MNWv6\nUSyyHfi+rjp96CGLu+4K8eabffuMbN4Mp54a5+CDBzF16iAOOKCJG24I8/bbEifraI4rX6FcbYCY\nkYKAehD2qhQGKg5BBf8Xh5nK6RT6GgsXGhx1VGPeUBs3zmXnnUslsDrCqdUWY/9ARXBfPdvWnrKs\ng3J83ByPmZASMxQGIXUyvmVgRHQfCynwfR87lULlSHGdZJLm9z8itXotbjKtPbMKzHgEK95AbMQw\nzGgUDJXLNysk+HuOrkhFKXzbw7OzmvNN+Xk1hGIFjGLy5UrGl/J9HTX6IMK6T41WZM21iN139zjq\nqOKqYcENN0R6RKps1SpJOi34v/8Lc+KJDSxb1jNzdO32dhXQWzlrhgHbbVfZmt5zT5eJE6tvzXcG\ntRBv7y5SKZ2H8MADFg88YLFggdFhrqZi9Ie+OPBAhyFDWi+GTzwR4vXXq2PU9GU/pNPw179aHHRQ\nE6ed1sAFF8Q57rgGVq/ufUM06Id4HMaPLzyn69dLfvrTGIcc0sRNv2lk7cZCdWzeM1ZmjBQvdoFB\nUy54nd8vV4UHtEmZ0Ntko3/4w3yOO66hRHngyivTjBjuFSgoOkGk21H9yVpDV56NQvhb6OpglSO7\n9ZUOWVpankkqcp4rAy9rg6/wHEcbU66Dcj3slhbS6zbgbE6SWf0pmU8/xdnUjOfq/c2ILk4wLBMh\nTBQKz3a09ytj49lZlOehPJ0rp1yFchVOMo2b0coP5YS35b+luC/eftvg8C81MXXaEGYdNpQHHoqx\nsbm272tDA/zwhxkaGgrr8ty5FuvWdW2OaW9MDBlSuMY775jceGOERKJLl2kXtdvb/QhNTfCLX6S4\n7rokM2bYTJjgctRRNnffneDeexP1nLVuYu1aweWXR/niFxs588wGzjyzgdmzGzvFhN6fMH68zyOP\ntHDIIU7ZN6rDdAe1jBdfNDn11HgJj9vGjaJEb7G3YZpw9tlZpk0r7XPbFvzPz+P86NLBrNkQ1qLa\nOd6ISsZIeWI9UFKkkP/bbC3EXmz89ITCQHv44APJFVdE2bSp0J6zzkqz7+ez+fBekJBeqb1bOwLj\n3Qhb2nMlhA5tmgJhClSOLgNTG2q+4+Gls2Q2NWsDylNIqT2z9uYEXjKFEgp88DYlUXbOU+c4+K5W\nw/AdVxf9+No7p2xX08UogfJ83EwGL5vNGdleXrWg+D7mvboVCgyCF4WFCy2WLdMvIStXSs4+u5Fb\nb42QSvVVb3cMe+zhc889CWIxbUxlMuC61Z9jRo/2iMcLBtudd4ZZtKj6E3U9Z63K8H3tOYjFqsfx\nsrXjb3+z+Na3WmeAf/7zLn//ewuRSB80qheweTMsWWKwcqUkndbVjRMnesRifd2yrmPjRjj88MZW\nZLDf+EaGq65K9/m9/PhjwZ/+FOaaayLYdukDfPXVCU79r3S7eTpBuCqPdvJ62svr6sx5uotkEn74\nwxj33lvwHh52mM11/5tgaDyRa6PKG5l5Y3UAhTcDDdzttuveC5HvurjpjKbd8DyEoeWffM/DTaZy\n91TzmCnAsx2c5haU8pGGhRmPoZSL05zUPH4tKZTrExoxGGlaSGliDW7AsEIoNLedl8niZ21EyNT7\nhExtYNsuvvKRhqEpPiJhTclhFHLVUEVe37I8ywD/fCLCKac0lv1SxaOPtrDffn0bNeoI3nzT4MEH\nLUaP9jnpJLvqHH1Kwc03h7n00sLEPGOGzZ13JtssXGoPbeWs1WZ2YD+GlPSKbNLWhPfeqzx7nnBC\nts8X902b4MMPJZ9+Kkkm9fO17bY+48b5rUhWO4tBg2DSJI9Jk2p/QuwokknBxx+X3s9ddnGZMyfT\n5/cSYIcdFN/7XobDDrN57jmLW24Js2KFXsySyco5PcXoSFVd+XfleW1tVedV4i2rBt56y+Deewsr\n2OzZNldfneQzg9J4GQ83pTUujUgYEZN4jo0RCuWTzitpRvYnrF8Pt90W4Te/ifDQQy2dqnwtvycB\nrYvyfJRr5PjHBL5t42Zt8LUB5zsOZiyGgBzXmdLcab5HqKkRIxwms24DxKPIWBjfV/ipNIYVhuYk\ntpnEtMJo608iLF1JKoVEeQI8H2GZmEKAIdGOvqL5KFfRnP8fEErm72vx7/rs3g777uvw0kvFkQzB\nqlUSqP25acIEjwkTeq6dQsARRzjcdpvL8uX6OXj2WYu1a0VJGLa7GBivRW2gzrOm0R/ytNrDEUfY\njBpVeNhMU3HppSmOPro8TLhlVKsvlNI5dKec0sAhhwzihBMa+a//auC//quB2bObOOmkOMuW1dbj\nVRza6Ksxsc02iksvTRONKgYP9vnxj9Pcf3+SceP6xsNfqR8MQ4dQzjwzy9NPt/Dyy5tZsGAzZ5yR\n3eL5OptYXyzdUxzyLD8P0GNh0b//3ULHwZ7hvPPSXHNNiu231RQUef1I18dNJMlsbMZ3dCjNy9jg\nk9dFDdCfhL09Dx59NMQ112gZsieesDr8bFQKVQf5iMKU+Vw1N5PBa0mjbAcvq8eQDId1+NIwMGMx\nZDSMDFsIoUOYZjRCZJvPYA1uQgoTgUKGQmBJnFQS+5MNuM1JnGQaldOklZYFlqHbJAv8agL0sUKV\ncMGV0I0UUdJAQUbquWf/zYjhDjffnOKII7IE7l7L6n06ob7ElsbEmDE+t92WyodDPU+wcWN15//+\n+zpUx1aD8eN9/vnPFj7+WOI4MGKEYtw4n758mX/nHcnRRzeSTleOdb/yismmTbUTBy/nSOqrhTQc\nhlNPzTJ7to1pwvbb13YaxrBhimHDOndMZz1fbXGSFZ+nnKetmrxl22yj+PrXs+yzT4pTTtEeTuXL\nEo1P39OEroGilBmPav3TXBu84jK7Ig45qO2qwQ8/lPzoR7GSz9OmduzZKM/7CjxTQkqsWAwva2si\n26yDL0CYBkLp6s3IkMEgBMIRKE8hskKrHliGDqFuasE3VM5o8hCmiWGY+K6LvWEThhnCzWZRvqeL\nDqJRzEgEpEQaUleQquBYLW8mrYKqgRIFMtxKlaEBR5yQ2ngct6PLTTeluPDCLOvWCUaO9Nl1163H\nWOsI9t3X45FHmjn//BjLlxsMG1bdua2es1ZHHV3Ae+9Jjj22gdWrW4dohw/3+eUvk8yc2bMahp1B\nb+ZADQQUE9n2dEVjRzjJepK3zHWp+OKTF6xP26Q3bMRPZRCmgWFYyHiIyKBBhQVeFEK1Jf1V4+Ps\nscdMTjyxkI/1vTlpLv1xokP967uuruhUBY9qsUyTm8ng2y5uJoObzKB8hfAVylCY0RgyZCCkDok6\nLWldBICPm8niJlOodBYRtjCiEYxIBCHBSSRxN7SgpEDkctGshjihwU2YkTDClChP4bsOQpigtLEG\n5HINBUbYyktESdMsqG5Q8OIGvyvYVk6AW0fb2LgRUinRZVLxes5aHVsdfF9XuS1ebOB5sO++btU8\nObvu6vPIIwkWL5YsWmRiWVpwesQIn1128Rg9urZegjqTS9Vf0FM5XOVaib5y2dTSTCqdJh6PM3To\n0KpdC0pz19r6LR3Zp6toaw3O88eZJm4qjady64dSSMNEhsyCJ8YH39EkrD5uScVsLWPu3NKK8kn7\nFsK/bbU9b8irwudiz1TxvfJdT/eFAi9tI8KyoGyQVSBdUAKrIaqJc5sT+J6DcHLi6L6JEQ5rlQIk\nRiyCsj2cZIuWm7IMLd5uWdqDJiW+YyOEgTQlwjB11aih1QvMaK6IRGnKGCFkjmak1MiWlplXYwh+\nXx0dw5AhpXQe1cKAvgP1nDWN8nh7IgGPPmrx/vsD9/an0/o3HnRQE9/4hs4lW7jQqGqu1o47+sye\n7fLDH2Y4//wMJ55oM2OGW3OGGrTOpZr//PN93aRuoVrUFpXGQ3GC9ao1q/njA/fzxUMPZdKkScya\nNYs//OEPrFy5srs/oQQd4STrad6yoC/Kc86kaRIe0qiljnxN6GrFowhRCPvpe6H0/VBa0aFUo7L2\nkMnACy8ULFXLUuy8k8u8+fPbNdSCfK6A7Lbc4+S7Lp5to1w/T3kiQyZmQwTfdnASWj7Ky9p4iYwO\nZQqBDFsoI6f1GQ9hNMQxGqKYoRBWQxQjbGqyXc9DWiFMK4LVENdyUoYEVC7/TKEcD99z8T0PpRS+\n66F8D68ov7C48lMaZknOmjRNpGUy//nn8zmV/SEHsadQC3nfdc9aD2P1asGGDYJ4HLbbzicc3vIx\nPY1FiwxOOSXO+PEeDz6YaJPQt7/CcTTdx3e/G6cgN9JagHlrQbEHSlee+XoS78d6jdXWnqzkpVu9\ndg3nnn8ec+fOze+3bNky5syZw/Tp07npppsYOXJkl69Zi6iU26h8HyEkVmMclEDkktg929bkvr6P\n57hoHUodVite/Gt1jIXD0NRUGEennpph7FiXtWtFu8YalHqqi0XcA2+bm86Cr5CmgfIVXtbWxQM5\ngza7cTPSsjCiYYTr4wvtqZOGhednkVIim2IYVhgZDiHDJn7aR2gWFWQkgoyGMcNhZE7CTDn63Pgg\nTEkg4i4QBS+Z9FC+1AUQUuo8uTKuv+LPwjBaeXXr6BsM6J7fZ599+vT6b7wh+eIXGznggEFMntzE\nBRfEWLy497t82rRpJZ8//lg/yIsXm7z66sCz1195xeDss0sNte239xk/3mvVFwMd5R6ogIV+2v5T\n+7TQoLtoj3W9M5g2bVqbRLb/nj+vxFArxnPPPcezzz7bpWvWKoK+CFAcDvayDp7t6PwnpfAyTr4q\nVLm+Nhg8H89x2iT6rTUIAV/6kq4onzDB5cwzs4QjJgdMn972McVKFEVGWmD4FHtlA0Mo0JP1nZwH\nS4AUWu3AikRR+NgbmnGaEzjpFAofzwCpJNIyQAn8rIvwBTJkIRuiSCl12FlKjGiYoPJDKaXpQgwD\nI6T1QPNGpBBI08hv8z03H94sV9wIfuO0qVNb/fatEbWwbgy8lboP4fuwYoXEMBQjRyoefzzEypU6\nudNxBPfeG+aJJyz+8pcW9tyz9yYx24bFiw3eeMMgElEsXVpIir/hhjAHH+z0a6LVYmQycPPNkRJt\nzVBI8bvfDTwPYkdQvlgWizGX59j0J1Qzh6uSl25jczPXX399u8f96le/Yvbs2VXPYettlHsV8541\nv6BjqjwP3/Zy636BAsKznZzHSOtgStNAhX2UrH5uXU9g9myHsWNb2HXXynmmngdvvGGwaJHB4MGK\niRM9xox2C3lqKkd/Yeuwb74oxTDwPA/f95CmQSgSxzUyOM0OAjCa4hiWpbnVsj6YEqclkSPSNRG5\n+cvPesiIiVJKc6WR6/qQpYXgXRfXtkH5CGEgBHieh7Ak0grncthcQCCkyIdsgzkgr2BQhJLxYMiq\nPGM9hZYWHTHZGmofaq/3q4jezFmzba13OHVqE8ce28Dy5bDHHq2J+Navl1x3XRSvl7gEEwm47LIX\nOOSQRubMiXPhhXGKWQAWLjRZs2bgDIONGwXz5hWe3IYGxQMPJPjCF3SH10LuQW+iVYhD6PyTeXPn\n9VtDLUBbck+d4fiaN29eRS9dOp1mxYoV7R67YsUKkl0RqK0hFHsV5z6nvYiBx6i4slEYEjMWQoYt\njEgIaRm5saRDfE4ihXI9UErriOa8NrU+vkaOVMycWZpnWjxHLFxocOihjZx3XpxvfauBI45o4J3F\npSTAxRQevufhOXZJcYYRDuX512TIwohFCcXjSMvES2WRloFphRBhC5XLKZUhrXqAzOWhoVAKjHAY\nw7AwoxGsWExXk2Yd8IWuJnW0cSiNwjWNSAirMYoZjxQkz8oImYPnqFz/dd68eTWn77pqleDvf7c4\n9dQ4hx3WxEUXRfn4456lSaqFdaN27kA/x8KFBqedFieZFLz/vsm775pMnuxy+umZVvuuWCHIbplf\nsyp44QWTW26J5j1NLS0ir5UGWvuwq+K2tYhBgxTf/W6G3Xf3uOiiNP/4RzPTp7tbrfRXebgm4M4q\nDt8MFHS16KASkW08HmfUqFHtHjdq1Cji/VyupD2ON6BEM9KMRLDiUax4FBkyAaEZ75UCx0ea2oDz\nXa9Nr00x3n9f8sEHtf1gvvGGUaInuWqVwRVXREkkSkOigRqANIw8FYZWMyhl/TciIUINce2xcnxE\n2NRUG3iY0RihIYOQIRPDDOkcQQBTG8DClIRiMcyGGNKwdMWnlRN0lwKlm4A0LYyQNiaD+2mEQpiR\nCEYoVMhbLSs0qPSSU0zt1ddkx+k0zJtn8KUvNfDNbzbw8MMh3nnH4M47I2zYUNvjqBoY0M7D3spZ\na26Gn/40ilKFAWPb8JnPKC6+OM0hhzjccUeYt982GTPG44or0r0Sdkwm4corI8BBJduHDy9197e0\nDJyBHovBBRdkOeOMLE1Nrb+vhdyD3kSlEJeQkgOmTx9w5fidKTpIJmHDBsFOOx1AS4uisbHUCxSP\nD+Xqqx/m1VdXAIMBH8giRAu+v47331/AzJn79loItKdoSorDntOmTi2pEAyuG1R9erYDQmFY+m/l\newhpYoSsnHA5OaoKmffgtkWMm83Cz34W5YUXTB58sIWJE2snt614jqhEbPr44xaffipoGFswaIWS\nJXxrvushc4a/7wU0MAppmni2jZdMo6TAMEN4nkL4BmY8pCtIQ9rwxfMRUnOxYfo6NCoE0jBRUmkv\np6ULObyMDVLlPHkFsuKSqtWcp7ScQxBBfh8ofW4OOOCA/LbiwhPo3Rc9z4PHHtPetOJcZIDjjssy\ndmzPjp9aWDcGtLHWW1i+XLJgQWlXDh6sH/IhQ+DQQ11mzHDZuFEQj6teyw/LZmHz5tIHaocdPCZM\ncJFS5b1tmdbOv34Nw6Cioba1oXiC9Z1SKoVazUHpDjrCJbdpEzz1lMWtt4ZZtMgkHNbPxMyZDsce\n67DHHh62DbfcEuaqqybieXu3OoeUit12+xbTpqV5913NudeTntueXCgr5f6VS0cF+0nDwPfcvFao\n9l4qjHAIBLgtKUSRTmg5s38xWloEr79usH695Jxz4tx3X6Im1Sw++1mXHXd0WbasML+PGePTmOPR\nDfqspDo0ZxjloUC5uefQy+WPRUKQdfM8bMJywXZRQiF8bXwpfKQwNKWHo3CcDNLXxrEZ1sLsvuvi\nZrIIS2KGQgWh9sDb5xcViuRIcN10FiFEq3uf97QZMu8dLFdpyBtyveyVX7TI4MwzWxtqkyc7/Pd/\nZxg0qNea0mcYWLN1GXorZ23jxqBuW2PIEL+VbpppalmX3kzkHzoULrssRUPDv4jFFOeck+bBBxPs\nvrvPCScU5GEaG2tvkuwp1ELuQW+hZKL1CiFCIbvHs7ZxIyxdKvjoI9lr4fyOoFI4sxwvvmjyne80\n8MorFrYtaGn5N2+/bfLrX0eZObORJ54wkVK/bLUV7fF9wTvvhDj//EHMmNHECy+0VrGoJip5DKuJ\nIPcvGBPlYbGSvz2dQ+XbQahT4Tk2yrmEjXoAACAASURBVNPaldLMeXpsOz/eKnF0hUKKhgb995tv\nmvzrXxa1guI5YocdFPfdl+T00zMMHeozaZLDb3+bbOVxyyfjK60MUM6/FoxLpRRGyCLUEMeI5YTY\nJQgMfEA5Pj45w0gBhsTN2nieg9Spa9rbJgRuNouXsXVxgxIlhmMJMW+g5Zp1cNOZPPdbsfEVVPX6\ntovvePk547lnn8VNZ1rlsvU2li+XOE5hjR082Of665PcdVeS0aN7vj21sG70mmdNCPE74AhgjVJq\nYm7bT4HTgbW53S5RSj2W++5HwLcBF/ieUuqJ3PbPAXcBEeAfSqnzeus3tIXyt+orr0wxalRtGEBH\nHOHiuikmTdrMdtspjNy6cvrpWR54QL/tbrNNbbS1juoieNsv9o5A1xf7dBqeftri8sujvP++xDTh\nsMMcLrwwzd57V3/C7GzoryP777CDz+DBPps2tf7e8wRXXhll2rQWTjrJZtIkj3nzTH73uzAffSRL\n0hwCNDT0/LPTEY9hTyDIwwoqArVnRssjKd/DSdgYIRPl6XwpkZecUghTV4gCCGTJi4OQklhMsuOO\nHosX6wnp2msjzJrlMGJE7c1Fu+zic8UVac4/P0Msptr12uc9UkVetoBUNv8ykfvbCPjTXB9pgfI8\nPMdF2R5GJAyGgZQSO5XUVB8hAzxtHEvDwMmkwfFRQqEcFzedwozHMCNhpKl1RN1UGtC5c4GBZlja\nMPY9DyuS83iKovw0pXDTGa1u4CltxLlePv+uLzzyEye63HRTknRa85WOH++z4461EzrvDfSaNqgQ\nYhqQAO4pM9ZalFK/LNt3d+CPwL7AKOApYBellBJCLADOUUq9JIT4B/D/lFKPV7pmb2mDrlghOPbY\nBpYuNTnjjDTf/36m0+LPvQ3bhmefNdm4UXLccTZW7bzY1lFF5PNTVFEItItVegsWGMye3Uh5KKKx\nUfHUU83sskv1Js/i0B9suc2d2f+99yQPPhjij38Ms3Kl9oobhmK//VwuvzzNPvuUlmpv2ACbNgk2\nbpSkUpDNCixLv90PH656hRKmp3LWKiEYL3lJpVxhiu+5ea+Z25LGc12kYej4TG5/YZiEmmKY0Ug+\n9Aeg0F65gOdLKZ+H/xrjO2cUdDn/9rdmpk3rpTL5HkBb+rvlOWLK93EzGZSn3Y6+q8PoXtbGbkkW\nKm2lwIpGcRNpPMdBhixE7tkzoiHcdCYXLlXg+yjAiscww+HcNt3vUprIkJG/XpCnZkR00UHgffOy\nDiiV9xD6jqfvL0CO8DhP/dGR57GGKT9qGX2uDaqUmieEGFPhq0rZHkcD9ymlXOBDIcQS4AtCiI+A\nRqXUS7n97gGOASoaa72FUaMU99+fpKUFxo0r5DPUMkIh+OIX3S3vWEe/RlAJVo3JUxeitH5cW1oE\nq1fLqhtr5Z+3tDh0dP9dd/W5+OIMp52WZfNmXZkdDmvi5EppCkOHwtChCug7Q6Lai15746G4EKU4\n8TzIO/M9DyMWQXpeboEXCKEQCE1PYZh5HrLgOl7WRhqmDrO5Omy36y4uQqi8x/KVV8x+bay15QEN\nnsGSfYXEd21tbCmF5zoYpkmoMa5Dm76PZYV1TmAsDFltERvhkBZrd3T+mS8c/KyN8j1kKISbSOLn\nRNiNcBhhGZoPz/GwogX5HGHIEv1WaWljXBP3SqQ0EdJFeQohRT4XLti/oy9OfVGMMFBRCz14jhBi\noRDidiFEkCY4Evi4aJ+VuW0jgWLyoxW5bRXRmzxr48b57L13bRpqtRBvrxVsjX1RaWHuSj/stZfH\ncce1TlKbOdNm/PjqLrKVDIgAlSgE2tu/4vmFDv9/8slz7Lmnz847a0Otr+kJegNtUZwEYyII1wV8\nX8HfwfgxI+EidnyFMEBYJlZDHDMSyiWrF+TMlK9K8rfcjI2Qgh3H2Myc6eS3P/hgiFqgrevqHNGR\nnEnQHjjfdfFSGdxMRktRQZ72xMva4GteNeX7mu5jUBwjEtGcabEYSP3iJEIGvgFIgfKVziFMZ8EM\n6EQCb5pumxHWRQgB91uAQtVvLtRpSMxohBdeeREZ0jqhgWdtS89WT+dY9gVqYd3o62rQm4HLc+HN\nnwPXAaf1cZvqqBI8T4dbt1ZNzlpAvhLMLy3f7wpGjFBce22K007L8sEHBr4Po0b57LmnV/W8x0pV\nisHnSm/tbe3fUZSHiweyR6AjXsj2+lCaJr7p4md9zFg0T4zreR5WKIbyfc03litUkJYBfkHgXFr6\nvNGwz1lnpXnySQsQrF8vSSZ1xXx/RVv9Fhho+fw1IfGV0iLqlqm9XFLgp3KFGYJ8SLJEb1WAUj5m\nJIyrQPgK0WDg21rgXXvUQtqrJkWenNjMiVJrKaqCxFRwj4orRIs9aNKyWnkFO9IHfZFjOdDRp8aa\nUmpd0cfbgL/n/l4J7FD03ajctra2V8T777/PWWedxejRowEYNGgQe+21V54zJbCW65+r+/kLX5jG\na68Z/M//LGD9esEPfjCFL37RYeHC2mhfgFrpr+Dz3OeeQynFAQccgJCyKuf3HYf9J++XPz8CDjzk\nEKZNm9at80+Z4uU/b7NNz/RHUJ3Y6vdM2U9XtP7nPyBg+oEHtrl/Rz4HBuC8ufNAwdSp++vzzX0e\nYRh5rqm5c+cihMhrR/b1eOnq56n7769/7/z5ABwwXf++YJ8tHb//lCn4jseCV19GeR6T9/4c/H/2\n3jzMsqo8F3/XsPc+Q1X1xNAMMoMCEhuZBLpBo7lqvGBU1OgvcQgocp1Fr4maeHO5USRekoiZQBMn\nNEaMSsQEMQra3dCgsQUhoMzQwoWW7q6qc84e1vD749tr7aHOOTV0VXd1U9/z9NN1ztnD2muvvde3\nvu/93hcMt/zkNuqvs9eBS+mPv3btmTBK4Ufr14NzhnVnnQ1rDdZvXI9Mh3jLW16Mq65qYHLyRtxy\nSxfnnnvmouqvnf18xvOeB5MqbNi4ETpNccbpZwAw2PSzn8KoDGeeejrAGW7edAusBZ73nOfCZAob\nbt6IcFkbZ5x+BrgAbr5tE8A4Tj/1FDDOcfOPb4U1FmecdhpsEGD9xo0QUuDMM88EDwNsvOVmWG2x\n9kzSAd542y1gjGPt2rUwqcLGTTcDAE4/9TQwxrB+wwYwzrB27VrwQO70+3JveV7Wrl270+/LYZ/d\n3w8//DAA4OSTT8YLX/hC1G2XFRgAAGPsMAD/aq09If+82lr7eP73ewGcYq19PWPsOABXAzgNlOa8\nAUWBwS0A3gXgNgDXAfiUqyCt264qMFiyqv3gBxKvfvVIRZ/z2msnsHbtEkZukM0WUD9T02lKRJvu\n+DwXcw6qkjkLZfMJNPZRwpLY+s5ECp25iFoRhbSwRsMoDdmMClD1ThZoLCab631x+DNH/6DiBFYb\nSosGEkwKiCgoChRAslVue1dd6u4dlxKPPsrwp3/axMiIxWWX9faKYqdy/7pnUKcZTJrBaE1RLMHB\nhCC8mQxgjQYMoLMUupdCtEKE7REwSbxnnj/NGug4JZJiawHOqCCBuWiYKHCqmgoFGKfqXPe9FxlF\nkQKlil8L2Yx8xG1KVHupaGDBbVCBwS7rccbYlwFsBHAMY+xhxtibAVzGGLudMbYZwNkA3gsA1tq7\nAPwzgLsAfAfA/7CFV/l2AJ8F8AsAvxzkqAG7FrO2mG1X5tuffJLh/e9vVhw1AHjsscWhkrAYsAf9\nbKFwHk5eylpKrTim+R/d9EMkicGjjzI89dS8nGqKDcJG7czxyriguRJzlnFpbjw4x8JaA52lUJ0e\ndEyalzpNK23f0zE4gybdcl+oOK6Q45b39cfI03QiIu9KpxkYp+dcxXGF0wsop7Zt5dwHH2xx+eVd\nfPjD8aJw1Hb2HVHmNnPX7pwmqw1gDKkY9BKQCoQgottGg7BolkE0IzBQGtMaCzAi1LW2uHcOP8by\nBRjhCIVvgzdmYbT2RL31++/eEYRTi4o0Zq4X6wlx5/FZ3tNsNmPirrs4PvnJBj760QY2bRLo9ean\nDbssDWqtfX2fr/9xyPYfB/DxPt//BMAJ89i0JZtHGx9neOCBqSShBx/89Hq4Z2sLhfNwODUwUjFg\njKOXcNx5dwOfv3oE3/1uiBNPVPj85zt5xeP82TBs1ExX6fXtytWJczmmJwj2E2pWfHaalvnECgCW\nMeg087xVvj/3UJuuUs8oRSSrgP+/LlpeOF8MQZsAqVmnR1WKxiDr9GBVHq3RRMDGOEXYDFN9I6Kj\no4uHnNs587OJIFUIZpWq9LGFIZC+USDVKQ5mDFVqWhB3nTuf4BCNwCsPqG4C0bAwGUXirKaoLxe5\no8YYkeoyTs4yaDudpXQ/dHEtFFkv3W9W3FvCFhZi7vVr63e9S9G1qbZlC8NrXjOKX/2K+uaKKxr4\n27/t4DWvyXZa5WSXpkF3tS2lQXe97dgBvPa1I7j11mKJfMEFMT7ykd6CSECNj5M6xK5UhlgoW+g0\ng1EKv/oVw5WfaePTn27A5UEOO0zje9+bWBBnrV9qd6Yp337bueso88aBwad2pktVuonUHVdnGU14\nYBTlEJyiaT2a7EQYgTckgmazUqTh2wHMqELuiScYfv5zgZtuknjoIYFjjtE4++wMJ56oF3zslseV\nT4E5Y6hVasYkg+qMo+DiUsqnMq2xxAcmijQf48SEb7T2fGDkfIQkSYX5pyCZb5sLHKHiABsDlVAf\nekcIBiKg6sus24XqJLBWgzEB0QhyihNXMWuJD83aPLqpwbmEhQFjDLLZoJNyRqlNTQUDXEgay2AU\nRRMCJq8GNZkiUlytwIMAskHRs/q9H9YHAGbdLzOxvS21SlyU1Ymu1bK48cZxHHXUzAIWu51nbcme\nHrZsGXDFFV1861sh7r+f49xzU5xyivKOmtbAQw9xz0S9MzrYv/wlxwUXtDA2Blx8cYznPlft0Zqg\nC/3CemRLiPe/v4n/+I9qddeHP9ybd0cNGF7RWbZBq/R+23nHyBbf+e1scd5Bx3QORemoRP4pCVdF\nqTyRT4A0mYqcjsIdz2PcnO6qVUOxcw8/zHDRRW3cfHM1x/fJTzbw1a9O4rd+a+GwnFMiabUpwDvP\npdSai6gBBYlrWa6Mvhd+f4eXcv1KklPkJPCIaCJ2BT5yPmy2/H7lfXzU0TCqkE0zSk/mjqq1hpwt\nC+hEgXGACUFpzJyTjhwjA1jiNqMFCIPuJADjvnLUsty5k/n5GcghSxXdGwtwyaFjWow4beDyuB0U\nIR5WWe31Q+cBQbU38rGtWGERhhZpWjxo3S7DY48xHHXUzh17z+6ZaezpilnbsoXh4YcZXNB0V+O0\njj7a4P3vj/E3f9PFS16ivJrDQw9RLv+MM8awbt0yfPzjTaTp8GMNs8cfZ7jjjgAbNgR45StH8dd/\n3cD27cP3WayYtYW2Tge44oqo5KjdCAB4xSsSnH32wjkLZWxN+bv6NoP2deZxM6Z/GrSfI9iPL82l\nmozWAANuvu1Wnyb2EToAohmBNyMwyfs6GkTFoCvtGmS33iqnOGp5a/CLX+xaXVEAFS4wABV8EuPE\nrQYOSt3lzhpQWkzkfeUmewd6d8cUUUC/R0T7sCdNwIxzX8XqPpetjHesb+PGgSvgKfOtlccolxIi\nkuBB4Kk5nDOsk4wcskYI0YggGlQQwKQEGPP4Ncdz5xcQmqLCohnSfYtoe9EI8vvJiIYjvzfOaR/E\nKeie27qGMGPcp7dnglvr11/l38rb9MNILhab6bxxxBEGH/hAFaQmpZ0XaqM9Y7mzZDO2bduAN7yh\njXvukbj00i7OOWcnvKF5tPvvZ3jjG9u4885iyN1wQ4A//MN4iijyTG3//S2CwHqB3z//8yZWrjT4\ngz9Yks+q2513CvzDP0SV79761hjveU8PK5crWDO3qN4UTNkM0hrDVu79tvOr+XyScGBoo5SfdMop\nURdBAKau2HWaQicFEJ4LinwQYN5AoYl77mvj1h8HuP8BieOO0zjpJI3jj08hRX4ckx/fUsqqkp4t\ntd2d88ADTYWp39kzn6nw3/5bhoW0fljIKVHCkrnoZUWEvIYVZKxwwF2UkZw6S7JGxhROWl4VOluu\nrt1lDrDvilfqC4N+nIW+XywHh/Rjz6cbS8d2+/r+IGGCfKFgwQSDyTRkUyJoNaFyB80rCDBypkUY\n5hJRKVQvJlxgKU1qdQkzKAEe1MTlGWYd1RpUBDXoOZ4ucuai3H582j0fCycl8KY3JTjkEIO//Msm\nwtDgwx+OZ5wCHWZLmLW9zO67j+GUU5b7z3/yJ11cdFGCKBqy0wLbxATwwQ+28E//VG3ERRfFuOSS\nHub6bGYZ8JGPNHHVVQ3/HecW3/nOBE49dc+VrVkIu/baAG960wgAYN99DT75yS7OPivFSKvop9ni\nUOrYlrKTNJfjDbJ+motlJ8SlgeoOhHccc2kdoxSyya53PEQjrODPssziC1eP4Y8+1EY5XyiExbe+\nNY4zzjB+WwfcdtfpJJa8M8kLqoU0BX76U4Ebbwxw550CBxxg8IIXZDjhBI2DDtq9uqKzwg8OSIu5\nKIu7ZmtMQRdjCFwvG41p27LYTacpTErVmYwz7zSVzUWJgCp4v7yYqTt81hApLUkWVCOf5SpMgIEH\nwo9ZnabIJnuwGRXGMCkQjDbzNHTRnjJlh1GqcNiGYBf72Wyf90FaqfU+dc/jMBzdnmjj4wBjmLWq\n0RJm7Wli7Tawzz4GW7fSQ3PJJU2cfrrCaaftPufl3nsF/umfqi+1lSsN3vSmZM6OGgAEATl8N9wg\n8eCD+aRrGL7whQjPfW4Xe8kzPy924okKX/7yBNptiyOPNDjwQAujdOVl6hnWc5tuQq2vtI1SxLJe\n+r2eIprLJN0vOlRPi1YiHANW7CpOPEcYly41RBMbFxKPPiTwx39SddQAQGuGf/u3EM87ddI7hPUJ\nptwfZTA/4xxhCJx2mt5tz+B8RTkHYQArhR35dlqncBQdTvy9gjXcAzFK1UiRnZJyd45QXYu3HqV0\nDlp53MomSEUgj/i6tCiNUze2bMUR1CbX9DSA1RpWWR/F7Pe8uHFe5lhz6XxHvzLM6mNlJpG26Src\nuZSwbO9UO5hv/PTe0zN9bPPmzXjsMYYf/EDippsktmxZHFxfC2n77GNx3nlF6tNahg984NZpsVwL\nacQzU/T9gQdqXHPN5LwIfx92mMWXvtTBAQcUE+F11wV48sn+93pPwqwNw3vM1p7xDIuXvERh3TqN\nAw+0pJZgjD9H1u15B8ekRcXksHPXX6z1FXHFUZsjR5PHgzletdLqvcD5pH6y9A6iS4cy56iRBqNV\nJk/NaTDBKvikVlPj8MOnOlRCWLz0xYmPiAzqh0H/97smnaZT+Nvmajs7Tgbhk2a6b10P033nqkXd\nfa/333xc+0JYv3fEsHHo6E6sMlC53uew8e76uzw+CMcWwFoLl+0qnh9yesnRYti2jeHr32jgNa/f\nB2+66EB844b98MT4CGHl8sWS51YEpa3Lfe/Gn0pyXVLGYJWZkhLv1xfltpefbzf+ytft2tFPK7Uc\ngaxvM5/vvfmyxTBv7PWxh1e9agR3302XecghGl/5yiSOPXbxDIL5NimB3/3dFJ/5TASlyGH5+c8l\n7r1X4OSTd8/K/sgjDS65pIubb5Z42csynHmmwiGHzN89OO44g29+cxJf/GKIq65q4MQT9R6tLwgs\nbKUUTTyWuJmytCDuVAbapOCi4BRjlg/EG/WLyvSLoA2qsJsu2jYoRedf5raYCE2qqSrRVytKGFuk\n6IxSnjUeFlSlGIY5bQeda9/lKf7hyqfwhatH8N0bIqQpw1nrErzh97o44egJANFUsH2pbWXQfv36\ny1HGctRvukrS6Wwhx8lMrd/9cxETPyHXxsruaOdczfUxFxLGKJ+qc4uTiqMCQPVSBK2perV9j1t+\nFrQB46wS4TZK+TEFAIwzbPpJCxe+rcitffe7IdY8p4kr/24ch48pjzssRzLLkTD3vJvUVLi/KinS\nmfRJnmL111Djcau0o09/upRwWU1locdzlgH3308atIceauaMl94dttdj1l70oqrG1jnnJPjbv+3u\nFbxcg0xr4LOfjfCHf1hc5NVXT+ClL1281TbzYVlGFaKNBuZdWHxXWSW9x0ovqXnEcpSxJCqOAUvg\nE5NpWNhchJt5ZvMy8/lc0pj9nC4AfR2xQe2kjYqUqDUUUfMYtRzPI8LQ95XDw7gUkE4zT9Iqm2Fl\nktApOa2qG8OkCtvGJbJMY6zRheAW4cgIZLuJoN2cmt4Zgs2rY5Q8sNtdV15VOdd7OxNc0O4yHz2p\nceIB06fYF5OV+7iMASs7VKobF46RLCKM1hh/f+vOmcmqTpmLSBVRMeafw3JBwNe/2cZFb5+aY/vI\nhzt41/8Yh4jCigPojRUYQ8a4581z7XPVv9NZ+bhl8mCPUZRFdK/fPa5zHYLBt3khx/PWrQxf/WqI\nP/3TJpRiuOACwkzvTjx3P9vtclOLxb7//RDbtu3d6VAhgN/5nRTvfndRQvx0qI4MAkr37dGOmpvI\nbTUiNZ8TWzXiRWSwHjBvDcCo/9yq2Tk9c5Wa6Zcq6xdtq6c/6tdc3s9hf4zOwdW5jFY5iuGiH+5l\nz6UAEwxgRXrITRjlydcqhSjdglb8KBD3cg3MGFT9WYooWDPUUQOqE5NL19YjbjuT9unXRwttM20v\n4xSVLdNYuPuxpzhqQLVP3TVNSWE2QsJAhjTWsl4PKk58dEvFMbJO10tQ6SQt0sNO6qyUpiwf20ci\ncyfuhBMUxsam9v1d/yUrUdr6c+fwdMXzQO1mks/YUau3r98z2S/tWe/PYccoj6/5GidpCnzxiyH+\n+I9bPuP0j/8Y4fHH9xxfYM95YuZgmzdvhhDViXvNGoUVK+Y+mW/ZwnDTTRLf+EaAz30uxNe+FuA7\n35G45RaBe+/l6HR2ttXzY/vtZ3HxxTG++c0JvO99/4bjjluqjgQWB/ZgkE1xzvrgY+bDGOdYv3ED\nrCEBbjCWs5uLnGld5NEj29dBGzZJD5rI6zidvmmhmkM4CA/lzOF8eEBRAb9tGRvj+L8k91WhIghh\nMg2dpli//keVqJdRGmmvCzOZAYJkgNRkB0ZlsDpnlc9lu1zks4LZ6XP9dSecCU5vXhcpVMZP4LPh\nmhqGo5qLzeTZmAv+sB9GazFbP5zWIOyVMxGGCNpNWEuYT2Y5bKZzPGgXvSe2QcdUTeqwiuVxwqXM\nHZ1c4J3RAqRYRMGPuSOfMYFrv7ENZ5yewoWh9tnH4O1vj/viRuvPHQ8kPQ+SQzYbCFqtgY5avzFR\nd17LPIW+v/qkPssOWD8euoW0e+/l+LM/a1a+W7XKzjiqthjmjcURL19A+/KXJ3HxxS08+qjAiSdm\nuPTSuadAH36Y4+Uvb+OhhwYwPzOLs85SuOiiGM95jsb+++/eCM/ICHDWWQqcKxx44J4ZbXo6WT29\nttATnFvFMs58tMDhZgCAiXziQFURYFjKbxAWpd+53T6DIm3uJV6fHMq/CxFOSUmW2+IcKiY5jC1R\nemgNbUgPFKA0aDrRhUlTAohzQI9PgDEBFoWwxkInCZgWoGgkpXusLc5RFiwvOzLeYcwnTu9k5e10\nXGTF/ZidxJG77l0VVat/3im83RxT67va6m2st905IypOwRlxtVltiSomI6ko3aPCLyYFRBDAWgOd\nKshW6CtEeZDjRd2YUgo6zSCCIE8TalhjccyhE/jclV08vrWFJBPYb3/KKvRrW79rmS3v3SAsaiUF\nOgBrVkmbZgXmz/EbDjpm+fPO2v33CxhTjaK9+90xVq/ec+bFvR6z9tznPhdPPsmwfTvDqlU7J2/U\n7QJf/3qID3ygVZGT6Gdnn53hiis6OPjgvbd/l2z+bVdNYGXBbhedKadbyuBk+jL/b0i7hmFRyjbo\nxT+IN823NwdA1x3AKQD+fFvvqLnICGiy8NV71kKEATlyqYaOE3S3boWOY5gkg5roQAgJuXIUotWC\nDEIEY23SdAyJfZ7JgmNNxTGsyY9ZSsXqNCWNR1lSK7CgSJrWcMLcLrrSj7+rX1/vCqxaP6dkmJM4\n0/G7u5zN+bB62601XjPVjS2H81QZOW+u2tJai2jlKBUrZIV4e1kNAkBl0VM+n+NeczhAp73qFgF1\njOB89OtM7tVAfGkJf+uP457tQRWi89x+ALjhBonXvrYoyjjttAxXXbU45+enNc/avvvOD46p1QJe\n/3rSurztNokvfjHEXXdJdLv1frWIIpvnxhffYFiyxWu7MsrgXvw8kJWqLs8lNkvHkfGq7mY5UuRs\n0ArcbePwcU6Cx+1jUuVJbUUjRNBqVbE5vABtO/oRkxF/lC+UyJ0ZlSQAQNENbaDSFDxP/UIw6Mme\ndzzRDgAhYNMMCCOaRGFgrYVsRuCl87pzwthcdin0IG6dZdAJSAuSEU7QpCR6DmPBGqK41twpHdbn\n9SjsQoyZ6aIlfaNNM6zk80D30r1bbM7aoPFfT3HrNIMjtOVOFspaBK0GJBrQvRQaKZjmCMYalIYv\nRVLB4ItlfJpScBhdRKGytAudKgTtJngg6Zyw4LVIcrl4pd6vc10IziSaWh+P7pnw5y5VbveLmrnn\npLz9fGYWjj9e44ILYmzaJPHa16b4nd9J97hs017trG3evBnzrWAgBPCsZxk861kpzjsvxdatFLXr\ndhl6PYZm02L5cosDDjCLRlR8/fr1WLt27e5uxqKw6fpixw7g5pslkoThsMMMDj9cz9t9XExpnw0b\nN+LM088oJgwLEmc28CnM2bbTTTQ+YjAAu1L/XH55OzxYOTrnImU6JkdOaaIXKUftaNJMS2B+msxU\nbMADDekoBSw5aVoTz9QtP/4xzjj9dKhuj6pFExJy59zCCo2s26XraFEVaNbtglkGLgOIUIJxovMw\nWgNg4FIQsFxy4szSBlZpqG4PRhmwkEHICEZl4FyCcQYeFbhBk2iEo+1pnZ3yJEfdtPPjaf369Tjz\njDNmnZou/95v+37ROV9Ek1/nQVWcNgAAIABJREFUIFHx3WG+HwY4nmXHhNLhwo87otoQEIGoRoat\nQdhqeCUNlaRggJeNYpx7PjSjFWSjUZGUggGElIAhMl6RV4yZrE7tUaTgB0auZ0GJUe+LQfuVzwPA\n8xmWq1sdZKDcj24fF5msKIDMYcE4yA480OLSS3vo9Yg4fra2GObQxfOE7IHWbBJOwGEFlmzPtyxj\n+NCHWnjwQQHAYs0ahQ99KMYppygsWzb34871ZblQ5lIoHqBeMuf4AOibduxnv/41wyOPMLTbIQ47\nlIOBeNDqTsSgiNAgR83h3lSXUozUJirxdw5lGZ+msxRZp5dHF4hM1FjACIpccVHsY+I8spVrfNo4\nher1cpB4BhgL2QjBwQHOyRlUmqJjgtKbPJUe72dUBh0nAGPgCKAN/W3ilMDl1sCmBrZZ0KOwgIhM\nLTOwKo/2KQPDFTibPsLpixzmYUxNGaO1cTHdsfvd237jvu6g14tCFoMNW1SU2+4UMCw30JacKsZY\nZdHjKjCdM2dSBZ4vHKy1vrCFDgqfIndFDcZo8DCAVzewlp6B3MlzEUrfVlsU59SdqH7XM50Ni6aW\nj1d2zstjwcMXcjyeztJq9XVtex/tn+d3Judzc9TqpjVw990c998vsHUrw/LlFkccYXDMMRrN5vT7\nz9WeFpi1JVuy2dj3vy/x6lePVIS3X/ziFH/8xz0cd9zs6RWAPYAPq0TUam2BiQEwbVn/Aw9wnH9+\nC5s3BwhDi7e9LcYF5/dw4GqagGaCayrj3ayhVbhsNjwWJ+t2obopeJ7OZLIQ0i7j07JOD1mHol9a\nZxAigGhShSsECberbo/SlYzDZBnJ7QQSyfgOJE8+BZsSjgzaQi4fAZMCjAkE7SaM1hCNBkQUgUmO\nYKQFxhl0nCDrJFCdDpjgCEZHyPEyOWVHlvkJkwcBouVjRDsiBEQoYa0FA8uv34JJhnCUtFwH4YXm\ne0wNwx0Ni2zUMYPl7afTda1f02Kx2WDq3PX7fUocevVqx6zbo/tsDI1BDj9OjNLwvGr5cR0Iv1y8\nwpyjxgq1iDIm00c/Rf/I2nTXM9e+8uMgr2Z1KX1rrY8E1jFrQFUfFIB/rnWaViJxi+Wdef31Em94\nwwiyrLyasfjQh2K87W0xRkZ27vhLPGtLtmQztHXrFK68soPyLHP99SFe/OIxfOtbwZzoWfphPHaV\n+ZemMX0/e5xMXs5fj3RMRydx550CmzfTyzhNGT71qSb+7u+biJPi/GVjfCqVQ2WCEdw7akZRGkgE\nIcLRFngkwQLuIxXZZBc6yXzhAGAhowg8lLBaw2hyAlUvRjo+iWyyB9XpUdozSWBUBiQpsl4X2fg4\nbKqgrQI4oLmFNRrZZAcGClplMDCwzFI1aZog/vV2dP7fk0i3T8CoFDZTMMbApClMkoFJAdluQLab\nkO0WgmYL4bIRP5HLRggRhpCNqNIf5Qm7fi/LfVbv12F2zz0cn/lMiOuuk4jjqb/3O16/e1VvT5nK\nw7W9HoWqH7MfFUZ9XO5OG9ZGFcfIut2KOkN9MVJWNXDcagAgG8QV4aJsOk19IY6XmzJ2SnUwUWMw\nSidqF8GyFAXOj+P0V/tF0wZdz3xY3VH1UVlX9ZljQ+tqFg6nBgNfnOHk4eo8dLOhtFlI27ED+F//\nq1Vz1ACA4WMfa+Cee0Tf/ebD9mpnbfPmzbu7CYvCFgNHzGKxmfRFEAAve1mGa66ZxKpVxQuv02F4\n85vb+NrXwlzvdOa2kC/LYVZ/iboI1vr1Gyr0EoznHGT5v/KEM91qlk1ZAwJ/8zcNPPBg4I89nZUd\nNRGVqtvKWBZeEJJaY6B6CXScwaSZj8bxgKo0jdK+olLHCbLJSWTbxpHs2AGjNFSaovfrrVh/049g\nuIWe7MFqAJJDQICBVA5MkkInCfR4j9JPjIMbANzCJAqml0B3Y/S2bUPy5DboLIPJUlKD4ETEG46O\nIFyWKyAsb0M2G2BcQEZRUSVnDEn1SA7ZinwVqbuH/UhCZzOmfvELjnPOGcX//J9t/P7vj+D228UU\nx2jDxo2zHqPDnMlhbaw7gfVxujsdNveO6NdGnaQwiYLNDHSceseNNDbpXuos806HixarXoKs2wUA\nGEMFJ1wKyDDyjhyR1gZwi8QyWS49lwE5NRmRWFuroWJS3rAZFdWoXjzFKXI2neM9rC+Gmcchlj47\n8+8Xwb0D58azczKJjqS49zrOirFgXcQxTxvvpnHh+mFsDLjggj4rHZAu9/LlC5ep3KudtSVbsrla\nowH85m8qfOc7E3jjG2OUcxvve18L3//+7CUh5vKy3Fmrv9zqK9R+L79igmXTTtrWGBx3XIb9968f\nhyHNZueY9p3AjaEJyb3Y83Rt1unCJClcFZ6b0GQzAjjzBLhMCqg0gc00LGNQE5MUKdMKzDIYk0Ht\n6CDtdcBAx4IANBQAIgZmqYHuxEi37YDqdqEZTSDGKvJUGYNNU8KrwRUVKD+5puOTsNogbLcgGw2i\n67DaX59LaXEhq3x3jE/ruMxkTHUmLT72sQa2bnXbMPxqC+vrGM12jM4kujeTY07n9C0Gc06G+zvr\n9pBN9mCVLchuNWmIOkF1Fz2yiqp/VTcGkU1TBI0WGbZS+elpcnKc5RTVj7xwRccZGKsuwgBGzo8t\n0pIL3Scu9Vl2xvoVkRTYToqW03OScx7mhNAkWs8qWYAyFc7uHheMAa9+dYprrpnAeeclOPxwjWOP\n1bj44h6++c0JHHnkwrVvCbO2ZEs2jXW7wB13CFxxRQPf/W4ApRgOOsjgP/5jHPvttzDPz3xVQXk8\nmilAx2UM0Uw5k8rRtcokkG93+89DXPCWNu6/n7Z7yUtSXHFFd6BQ8rDrcwUOKk4AbQtcmhTgQuQV\ncxpWE9AaAJgUCEfbVIwQx8gme8Qkzxnip7YTBs0CqtcFYxS9A+fQcUyRkETBCga7vQcTABAMWacH\n24kpVRoGaIyNQS4bRbh8zLPLI5BAppF1J8FlQBOWBsRYC0GjAaMNhJQQUQTRILUF1YthCTJHadJG\nVKQ9HYUKK2G+UOr/WeJ2rDG44w6B579gGcoVA1/58jh+64XJlGPOZdzNx1hdSEzVfBlFc2OvA2q1\n8coZJk9/B82G7we6lzZ3xlmOBWUAo2ivL0BohBRtFQUfG2wJK5rDEnzaMNe5BcjhY4zBKAMRSk/7\nART3dFBfzva+PfQQw7ZtHEceqTE6OvWeVVO0JQ1UpcHz6liq1KYUp87o+TRaAZYqqSmyCH8NDv/m\nbDGNC6WA8XHKxIyOTr/9TO1pzbO2ZEu2M9ZqAaedprFmTQcPPsjxyCMcYQi02wvoqC1Q5Wg/EHi/\nbQaV6pfbVhZx/o1np7ju2xr3PyDBGHDUUQYrV2iiq+iD6RnG36WTXJanl8BqQ6SfAYHwdeLE2C1k\nM8zpAAThfbSBNg63Q1xXuhcDAjCphtUKjAuEy8fAuUDW7SFcvgzp9h2wMoBNMqTCwHRj2LzggKXk\nLAoDmlRgkY2Pg0cRRLsJbhgUN5AjI7BGg2kLRAIyDCk9qzQMY2B5akwlKZiFT/3IkUbF+fJO04D7\nPttxYI3BE08EKDtqnFscfHCVgNhHMuYw7uo4qbk6biRevvDKHTtjVNwiYLWFiKSv+oSl4hUAvsqa\n0vqgccG4x2ZRNafM+9yFo/KqSSHBbG1BlfelT+snGXgg6Hgyjz4F3BMr19Pl9c/uu9nc6y1bGN7w\nhhHccYfAhRcmeP/7e1jWTn07nXNaHsuOf86lMIvoH4oUvwYYWOFklnRMvdM7TwvX+TYpsVMk+7O1\nxXPlC2BLmDWyJcxaYTvTF1EEPPOZBi96kcJZZ6l5KQPvZ/OZEuqXBrXGYMPGjZXPZRuGhaqnzMqf\n99vP4vTTNZ73PI1VK3VfDJKLmpX3q//t8VmMg1kGm7n9Ka9i04yiDFqBBwFkM/IOpgN0++hcpwfd\ny2B1BtNLiSpDBhDNCMFYC5v+86eQoyPgQQCTpDDdBCaz0BMd2MxCcAZtLUyWAiC9Rz3eg1aKyGwD\nDmkI42YTBQiGoNWEbDRy/JwA05aqQa3xKSwYV/1JKbCyKHy5/3ngNCPnFlVgnEPXZIHf+tYERx6p\nvXPk0q0/vPHGKYUos7G54s7cfmW91Znss1DFCIPeEc5hCFpNquA1gIUBOKkIyEbkU5pcSu+giTAk\nnywXeneKBbLVqKT4yv87/Ga9uIExnkefmK+IFlGONY1Cf+w6trHftQz7XO+Le+4RuOMOCYDh7/++\ngZ/8mChLTFpUcReRNFV6Xqvjgj5bei64oGh5EPjornNKp+iZ7mYHfjHMoUuRtSVbskVmwyJbczEf\nCcsJNGly1hWepvp5ZhJ1805Fn+0HTQZlLFa//dyLWaUkSm0YAMZz3iULYxQsB2yioBmHbDRyxywD\nLCjC5lK/WiPr9aDjHpiQEM2AohZaA1oiGhuDaEZ5QUIK3etCKQVmLHSmAG2hhYaEhGg0wEMBazT4\naBOMC9hMIcsycBHApCkQcIgwgmw2AcYh2w3YKIRKEjDG6NoCSdg2y8A4o2hMLtJd7+fpJtyZGOMc\nhx1uMDZmMD7OccopGd72tgSNJodRvDSBFjijuRLV9rvncy1SmA7ftjs4C/2CwDuXAMDBpIMbULqP\nMe41PbkQBHTKI2+essIW11F2zExG+zHOIING32eKHJqgcIosPN9bGd821+h5P5ucrGbl/vyTDZx2\ncgcNQZXRMigKgogP0ZIzxhlcdStnNJ54IADQuAfLx35++LqjuWSFLWHWlmzJdrP1e7HONfRf38/z\nl5VwZmVMyUywUPVjTtc2D8Suafx50LE7pjU+tVM/ftbtUbpHcoggzB0qhazThY6JsFaEAVgo/Auf\nOafOkoJB8tQOJNu3Q3digBmIVhPhsjEwLiEiSQ6X1sjGJ5Fs2wH11ARUElO6Ms6Jda0Fj0IEK8cQ\nrlgGBkHVsjAQTMBGHCbWQI6pk2NtRGNjRB1iLJD3lVWWIiFSUHEDkwDo+v0ENeQeqLyWQcyRGeD2\n2wWeeorhmc/UOOCAWsQDRUrb3wsxR7HvOeDOZrvfQnIWzmRsO640gJxFY3SVmoNR2p1xRt9zRkLs\nopCSqkelPSYtLVKFTPK8crhEbZJVo4lGaTDGZjSGZnOt9d+uv17ida8rgFlCWNy8fiuesV+3kMdS\nRMNBlZ7kuIowzMc7L1K0ovi7okm8yNKcu8uWMGtLtmSL0AZFCeaE+RkUcbDFZODTEbU12qBzDWvf\nsO0ZKyRmKhWepWO4irly5M+9vGUUkSxUmsJoBSEoNSKikKrpjIWFhe1lQCAgAk7caFlGqgRawxpF\n2adAguXpIgYOcAsVJ7kTZZBOjMMaDSMAA0pRimVtBLIBCwvRjMDbTQSNFkQjoqgIA0QoYWIFSAvL\nCcskZQirNWDzYoh8QuIBaY8yxsFkiK3bGzCWYeVKixYffA/imOTPrrwywvbtHCeeqPCyl6VYs0bP\nKg3/G7+hp3xXdgJcZMbfXzH7SXMYHrI8+Ze3cX/7Csgh+5Un9fmMPFfONQRL6dohG5HXqq0uTCiC\npjOKqFkDgBNGzal5uL4upwydc+V515xIO+pA/WqKmtRFiMrDKFVRBZiJDXNIy/1gjcHBBzMIYaE1\n3SitGYyGT9cTZQ1BA6ymKlfDrE/jcyGLceY42PpE0eZz4bq32V595UuYNbLFkG9fLLbY+mIh8Wn+\nBVfGn0mJe+5r4NK/+Bk+/Xdj+NJXmrj3gWpp/DDc0nTtq0cL6pNsWSewvL2bIMqYM/rOEk2GUp4s\nVzRCotfIMsIM5RGHdKKDbLILKOK1UmlGvGnNJkSrARE1AVjYhLQZbZJh4y0bAW0oNSksRLuNxorl\naIwtQ7BqGaJVy8nRCwIEoy0Eo23wvGJNx0Sey6MQwUgLstkCkxJMCOg4p/KwyLE5dO2/erKBv/ib\nVTjrBatw5rpVeMe7xnD/g3JgNOmeezhe9aoRXH99iE2bJP7u7xo455xRXHJJE0880Yfgbpbmoqtc\nSmy4eeOcsXHl4wHI+bMKmgu3SPAEsbW/vYNSd9T6YOCmjOl5dNYAYP2GDbCGyG/ddZTbwTinyCks\njcFUw+ZyUcT1J3MqFnLOReCA/9Y7wSqOoWOSp9Jx6nnaKD1qi+t0kWxdU0cAfOrfyVDNl2xX+Rle\nv/5HMJnCUUdkuOhtBb/YvvsatEdQRMvAwLmATjLoJIErqrDaTCkWKGPQyu+bfve7PnbqeNddZYth\n3liKrC3Zku1Gm88oQf1YQJHe4lKi2zH49nUR3v3uNpKkBYBCMwceqHHddZM45Bmqb2RhNu2byfYV\nPct8nim/gAmDRhOYVSS5U66Wkw0iEhVhzhVmNHGugaIY2ljoXpJj0wArDAQLYJmhiJo1MEkGpTRh\nzSyDkBJMMdimgGy1wWS+/DdAEATgjQaYlJ7DSnd7uWZjiKDVBLek8ylbEayxNBFDg0sBHhFlx2Q3\nwIf+ZBn+/d+L9OK110ZIU4bPfraDZnNqFKHRoKqzKj0ew5VXNnDKKQqvelU29H7Mxipp8TmaS+UB\n8P/7aGsp9Vf/2203He5xIVNmfuxa4xUxdJzmShNFOtKTzjJGDgnLo5bOeSxh0nhYOCo8KDjGjNLg\nXBT9Yy1RV0QhjKZx4xzRMsmtW8hwKWFz/d35xnmVn2HiPeMIOHD++THuf4Dj+utDfOITHaze31D0\nkBH20oCoSLTR+ThiRbtKFcflVG4lgslQwW7W3wnufWHZrsMpLiZbwqwt2ZLtZpvPMH8Zm1bnU7tl\nU4CXvWwU3kMq9sKGDeN45tFpZR+Hf5lt+4ZtP0grshK9MORUmYQcEZLCouiUCIJ8wsvydItCNtmF\nCALwHHRt0gwqjqF6PdrPMoqwcQGVZjBJQufrJYAUEI0I1gI6ScC0gYgaEMvbYCCMGTU8Z5hvN6Gd\n3FBCNCGi0SCOtzCAtQCYhc1ykL4QEM0QQbuFe+6LsHZtle8MAA47TON73xvHiuVTsVvGclx7bYAL\nL2xDqep+73hHD//7f/dnU5+NDUpRzmUsqjgmSgl3bBBJrL8uVo0YAVVcY9/IWm5TtC4XIDVWLBQy\n2MxFyyxEI/SgfredyTQ8KbPNq0LDgMZMDvb3befcj1viRcv581xKNOdkY4xRup7zarFAjfKizIs3\nHZ/a448z3Hcfx6OPchx8sMXppytM12UkX0UqCw6uAADdWGDrrzlW768RBqUUbUo4Nas1tMro2QlI\nkYFJ7h3ACn6WgUhxcx+ESQYZNSrjoYzTY6xUHbtIdEIXwpYwa0u2ZIvU5nPCccfqp1Tw0EMcUx01\n4IILEjzjGWZgVGy27Ru2fb9zME5gdscATxM6IyUCxkg8XXIwxqC6CYiozAKgCJkn1lTM72eMpvSl\nFbASsNqCRQGYMVA7EsBoSmdampiEyCfIIAALZV65F8DoDNCWcHDMgmuK0DEuwKMQNlX0vQxglaE2\nawvmJmzJicKDc7SaBitWWGzbVr0HF14Yk6NmTNVxYoCQHOeem+Hwwydw9dUhrr8+QKfDcOaZCr//\n++mM78kgqxQZlMTC51plyaX0ETW3f8UJLIHLXbXpIKdrkPPoyGEZL6pZ5/P5EWGYyzblwuqBpPGV\n5tGeXJOTqhkZmGCexNhV94KhoPBw12ENuBQ+NWiM8o4MFIA8YmQtObjl58/1g4sy+/YOqMYGgMlJ\n4JZbJN773ja2bKHfTjopw7XXTqLZHNwHRilYZSjyZwDLi/4fGWUYGbUgBFUJQ2gMTEpVz0GzmVee\ns8rrxo1t5wQapWEzXRRJQMIGBJFgnOfqBkWEz4Kwq+U+mY3t6di3Pa/Fs7AlzBrZYsi3LxZ7uvRF\nv4nvpJM0TjjBTaQ3YuVKg8sv7+D9748xMjK/WKA69q3cjkEC2f730iRstQHL00MOn6NTBYs8ApIz\nxzMuCOSc0gQZNFrg4LAhReNYwGGzDLAGQgowJsDDELfevhk6TqBNCtGI6DyhzCcrKoLQuRMDwcHA\nILiEbDYQNtuIVixDODKS4/ByAt1Wg0DVUZBzYBHG7RkHZfjaP09gzZoMQWBx0EEGV3xqAq88t1Oh\nhIAlHdq77g6wcaPAww9zrFmjcdllPXz/+xPYsGEcV13VwdFH7zx2p4pPWl/BEM4FH8SlBA8lYflC\n6StKy9i4Mmap/Hc/q//uIi11XNN82vr16wmsn0uugeW0G7l6BilQ5JO+ZJCtBmEpS9Wz1uQOF+vj\nUDLAaAPZbCBotab0T2XbWj946o8SeWy//tuyheH//J8mXvOaUe+oAcCFFyYIRervbb/ntLzQ27Bx\no4/eDbpHLuolo8grLohGWPAG5tg1o1VeUEEOq5fisrpaIZtjGHWcFhxuOfWNi8jN9t00CP84U1sM\n88ZSZG3JlmwvtH5RiaOPNrjmmkls2cLws59N4kUvGsdBB9kp++3sqrMe+RiETapPwB7TolU+EeWM\n8JJDp1n+4tZEW6UsmGVgFtAqg00ysCgEDynVSRghCQsGKxg4y6kCFCDaTQhF9B4AQ9Buw8LCpAms\nMpCtJmyLJkEuIjAmoJIYJk1ho0YesWNgknn1BLoOwh053qgyQSnjVN235jdSXPOVGOOTHI3QYOWy\nLI8+RDBKQSmGO/6riY99fAQ//CHhflauNPju9eM47NAMq1bOb1SgGkUrJkRXmeskkaakJ2v3ME2B\nn/5U4PHHOQ47TOD446lSsbzPfKX5q5iqIkI3G8syYOtWhn32sQhqMr82ZxHmYZ4Czx0FX/WZlzMy\nwT0mjXasthGoirH7dKc1kM3QV0gyzqHT1PfPdOm96frx4Yc5LrywhU2bqhd23nkxnr+uSxFgACqj\nFDqXtUrgUnvc78OiUpXn23Gn8ZwzTmdwUm/W2lx2y3p8GgvZlIhrpb+Mez9Znx6ezno9IjAvbzoM\n/7in2BJmbcmWbMnmzawptP8AeGBxv5SqW03rlOSl/AsaNpfmcULXhOexObifgQOCtDmzbodA4MaC\nRRF4wCl1ozSM1jT5cQ7LGEwSew1HMEBPTII1IthMwaYaKu5BtJsIWi0EIyPgjRAyiqDTFNlT47AB\nAc1FGII3AoqcCJZHCwtdw3rF25T+SVM/YXp9Sc6RZRb/fkMbF7xlBMYU+SPGLDas345jjlI+sjCf\njO51zJrDnfn7JAvOtbIj7qKkjHP8/Occz3/+GIwhiodPfrKLV70qxcjIvDSx2tZSRI0Hclrnpp99\n5zsS73xnG298Y4K3vCXBAQdYH2Ui4fUSxi6v6nTRKLp2ATBbpcso0Y84HBdQ1fHUaZpH1CgPSXJp\n3HOTiSiYNb9d2SYmgI9+tInPfa5R+f4P3hzjXe+YxOpVvfw6c7mzRqMoZnAFDb7q0hYLkXJV5xBs\noXteffVmTMUUuZebqznkBNH5YkxnKcA4RFhEIr0D6KS7Sk7soKj/U08BN9wQ4MorG7joohjnnVcU\n3wzDPy6UTU4CP/6xRJIAz362nrIwHmRLmLUlW7IlW3CrRz4ci7vVOVYlEJCNRnXb8steG0CgqB5z\nK3AOQAifkuSSA0LAJAFYyHKaDANYwg3ZnCjUMkAImfOvGRhL1X4AINototnoKRgY8FYEHgQQQZiT\n1YbgDQmTZeDtZuE0Wkq70sRiwcB9ZaDDEA1KszBODh9Nzso7atYY3H5nc4qjBgBvelOCgw5IYZTD\nSc1vRVw9WsKlLJxJQ1x0nguslIKknWn/p55ivt1aM7z3vW0sX27x8pfPX7Wqa6s771yrIJME+Ku/\namLbNo6//MsmHn2U4xOf6GDZiKPIsLnjxWB0Bs4CMFkoOvQjdC23zzu/uaNhrYHqxp5IV3XjHBsX\neAfPp0AHsLHMFG91112i4qiNjFj83/87iRe+IMFoM0G8bQIqTiAkFUKo/NxMcATtpi/0IZ5EnS+8\naGFkA5NXq7pnsJqCdc6zj8xSF1IkTRNG1BoLHgofxTWKCHNFVMOiOS620vF9VWwf9Nb4OPDxjzf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ev3yF+PrEbbyoucep8udssy4LbbBD71qQa2bOF43etSnHtuioMP3rn5f8/pgTnY7uRZC0Pg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\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VOEcfsx6lFDd/+ya0Vjx3y+VLHh/vHNt3hOPfvGlT/7UPrwG2bduGVIqnPW0L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\n/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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\")\n", + "\n", + "colors = [\"#467821\", \"#A60628\", \"#7A68A6\"]\n", + "\n", + "for i in range(traces.shape[1]):\n", + " plt.scatter(traces[:, i, 0], traces[:, i, 1], c=colors[i], alpha=0.02)\n", + "\n", + "\n", + "for i in range(traces.shape[1]):\n", + " plt.scatter(halo_data[n_sky - 1][3 + 2 * i], halo_data[n_sky - 1][4 + 2 * i],\n", + " label=\"True halo position\",\n", + " c=\"k\", s=90)\n", + "\n", + "# plt.legend(scatterpoints = 1)\n", + "plt.xlim(0, 4200)\n", + "plt.ylim(0, 4200);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks pretty good, though it took a long time for the system to (sort of) converge. Our optimization step would look something like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(10000, 3, 2)\n", + "[[ 3819.11446472 3962.91150552 2494.95860815 1335.19792536\n", + " 933.11887832 367.979512 ]]\n", + "Using the mean:\n", + "Your average distance in pixels you are away from the true halo is 124.438987331\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 1.12443898733\n", + "\n", + "\n", + "Using a random location: [[2984 1669]]\n", + "Your average distance in pixels you are away from the true halo is 2382.06551852\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 3.38206551852\n" + ] + }, + { + "data": { + "text/plain": [ + "3.3820655185153914" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "_halo_data = halo_data[n_sky - 1]\n", + "print(traces.shape)\n", + "\n", + "mean_posterior = traces.mean(axis=0).reshape(1, 6)\n", + "print(mean_posterior)\n", + "\n", + "\n", + "nhalo_all = _halo_data[0].reshape(1, 1)\n", + "x_true_all = _halo_data[3].reshape(1, 1)\n", + "y_true_all = _halo_data[4].reshape(1, 1)\n", + "x_ref_all = _halo_data[1].reshape(1, 1)\n", + "y_ref_all = _halo_data[2].reshape(1, 1)\n", + "sky_prediction = mean_posterior\n", + "\n", + "\n", + "print(\"Using the mean:\")\n", + "main_score([1], x_true_all, y_true_all,\n", + " x_ref_all, y_ref_all, sky_prediction)\n", + "\n", + "# what's a bad score?\n", + "print(\"\\n\")\n", + "random_guess = np.random.randint(0, 4200, size=(1, 2))\n", + "print(\"Using a random location:\", random_guess)\n", + "main_score([1], x_true_all, y_true_all,\n", + " x_ref_all, y_ref_all, random_guess)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n", + "1. Antifragile: Things That Gain from Disorder. New York: Random House. 2012. ISBN 978-1-4000-6782-4.\n", + "1. [Tim Saliman's solution to the Dark World's Contest](http://www.timsalimans.com/observing-dark-worlds)\n", + "2. Silver, Nate. The Signal and the Noise: Why So Many Predictions Fail — but Some Don't. 1. Penguin Press HC, The, 2012. Print." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [conda env:bayes]", + "language": "python", + "name": "conda-env-bayes-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter5_LossFunctions/Ch5_LossFunctions_PyMC3.ipynb b/Chapter5_LossFunctions/Ch5_LossFunctions_PyMC3.ipynb new file mode 100644 index 00000000..eeebcc39 --- /dev/null +++ b/Chapter5_LossFunctions/Ch5_LossFunctions_PyMC3.ipynb @@ -0,0 +1,1537 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5\n", + "\n", + "`Original content created by Cam Davidson-Pilon`\n", + "\n", + "`Ported to Python 3 and PyMC3 by Max Margenot (@clean_utensils) and Thomas Wiecki (@twiecki) at Quantopian (@quantopian)`\n", + "____\n", + "\n", + "\n", + "### Would you rather lose an arm or a leg?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Statisticians can be a sour bunch. Instead of considering their winnings, they only measure how much they have lost. In fact, they consider their wins as *negative losses*. But what's interesting is *how they measure their losses.*\n", + "\n", + "For example, consider the following example:\n", + "\n", + "> A meteorologist is predicting the probability of a possible hurricane striking his city. He estimates, with 95% confidence, that the probability of it *not* striking is between 99% - 100%. He is very happy with his precision and advises the city that a major evacuation is unnecessary. Unfortunately, the hurricane does strike and the city is flooded. \n", + "\n", + "This stylized example shows the flaw in using a pure accuracy metric to measure outcomes. Using a measure that emphasizes estimation accuracy, while an appealing and *objective* thing to do, misses the point of why you are even performing the statistical inference in the first place: results of inference. The author Nassim Taleb of *The Black Swan* and *Antifragility* stresses the importance of the *payoffs* of decisions, *not the accuracy*. Taleb distills this quite succinctly: \"I would rather be vaguely right than very wrong.\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loss Functions\n", + "\n", + "We introduce what statisticians and decision theorists call *loss functions*. A loss function is a function of the true parameter, and an estimate of that parameter\n", + "\n", + "$$ L( \\theta, \\hat{\\theta} ) = f( \\theta, \\hat{\\theta} )$$\n", + "\n", + "The important point of loss functions is that it measures how *bad* our current estimate is: the larger the loss, the worse the estimate is according to the loss function. A simple, and very common, example of a loss function is the *squared-error loss*:\n", + "\n", + "$$ L( \\theta, \\hat{\\theta} ) = ( \\theta - \\hat{\\theta} )^2$$\n", + "\n", + "The squared-error loss function is used in estimators like linear regression, UMVUEs and many areas of machine learning. We can also consider an asymmetric squared-error loss function, something like:\n", + "\n", + "$$ L( \\theta, \\hat{\\theta} ) = \\begin{cases} ( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\lt \\theta \\\\\\\\ c( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\ge \\theta, \\;\\; 0\\lt c \\lt 1 \\end{cases}$$\n", + "\n", + "\n", + "which represents that estimating a value larger than the true estimate is preferable to estimating a value below. A situation where this might be useful is in estimating web traffic for the next month, where an over-estimated outlook is preferred so as to avoid an underallocation of server resources. \n", + "\n", + "A negative property about the squared-error loss is that it puts a disproportionate emphasis on large outliers. This is because the loss increases quadratically, and not linearly, as the estimate moves away. That is, the penalty of being three units away is much less than being five units away, but the penalty is not much greater than being one unit away, though in both cases the magnitude of difference is the same:\n", + "\n", + "$$ \\frac{1^2}{3^2} \\lt \\frac{3^2}{5^2}, \\;\\; \\text{although} \\;\\; 3-1 = 5-3 $$\n", + "\n", + "This loss function imposes that large errors are *very* bad. A more *robust* loss function that increases linearly with the difference is the *absolute-loss*\n", + "\n", + "$$ L( \\theta, \\hat{\\theta} ) = | \\theta - \\hat{\\theta} | $$\n", + "\n", + "Other popular loss functions include:\n", + "\n", + "- $ L( \\theta, \\hat{\\theta} ) = \\mathbb{1}_{ \\hat{\\theta} \\neq \\theta } $ is the zero-one loss often used in machine learning classification algorithms.\n", + "- $ L( \\theta, \\hat{\\theta} ) = -\\hat{\\theta}\\log( \\theta ) - (1-\\hat{ \\theta})\\log( 1 - \\theta ), \\; \\; \\hat{\\theta} \\in {0,1}, \\; \\theta \\in [0,1]$, called the *log-loss*, also used in machine learning. \n", + "\n", + "Historically, loss functions have been motivated from 1) mathematical convenience, and 2) they are robust to application, i.e., they are objective measures of loss. The first reason has really held back the full breadth of loss functions. With computers being agnostic to mathematical convenience, we are free to design our own loss functions, which we take full advantage of later in this Chapter.\n", + "\n", + "With respect to the second point, the above loss functions are indeed objective, in that they are most often a function of the difference between estimate and true parameter, independent of signage or payoff of choosing that estimate. This last point, its independence of payoff, causes quite pathological results though. Consider our hurricane example above: the statistician equivalently predicted that the probability of the hurricane striking was between 0% to 1%. But if he had ignored being precise and instead focused on outcomes (99% chance of no flood, 1% chance of flood), he might have advised differently. \n", + "\n", + "By shifting our focus from trying to be incredibly precise about parameter estimation to focusing on the outcomes of our parameter estimation, we can customize our estimates to be optimized for our application. This requires us to design new loss functions that reflect our goals and outcomes. Some examples of more interesting loss functions:\n", + "\n", + "\n", + "- $ L( \\theta, \\hat{\\theta} ) = \\frac{ | \\theta - \\hat{\\theta} | }{ \\theta(1-\\theta) }, \\; \\; \\hat{\\theta}, \\theta \\in [0,1] $ emphasizes an estimate closer to 0 or 1 since if the true value $\\theta$ is near 0 or 1, the loss will be *very* large unless $\\hat{\\theta}$ is similarly close to 0 or 1. \n", + "This loss function might be used by a political pundit who's job requires him or her to give confident \"Yes/No\" answers. This loss reflects that if the true parameter is close to 1 (for example, if a political outcome is very likely to occur), he or she would want to strongly agree as to not look like a skeptic. \n", + "\n", + "- $L( \\theta, \\hat{\\theta} ) = 1 - \\exp \\left( -(\\theta - \\hat{\\theta} )^2 \\right) $ is bounded between 0 and 1 and reflects that the user is indifferent to sufficiently-far-away estimates. It is similar to the zero-one loss above, but not quite as penalizing to estimates that are close to the true parameter. \n", + "- Complicated non-linear loss functions can programmed: \n", + "\n", + " def loss(true_value, estimate):\n", + " if estimate*true_value > 0:\n", + " return abs(estimate - true_value)\n", + " else:\n", + " return abs(estimate)*(estimate - true_value)**2\n", + " \n", + "\n", + "\n", + "- Another example is from the book *The Signal and The Noise*. Weather forecasters have an interesting loss function for their predictions.\n", + "\n", + "\n", + "> People notice one type of mistake — the failure to predict rain — more than other, false alarms. If it rains when it isn't supposed to, they curse the weatherman for ruining their picnic, whereas an unexpectedly sunny day is taken as a serendipitous bonus.\n", + "\n", + "> [The Weather Channel's bias] is limited to slightly exaggerating the probability of rain when it is unlikely to occur — saying there is a 20 percent change when they know it is really a 5 or 10 percent chance — covering their butts in the case of an unexpected sprinkle.\n", + "\n", + "\n", + "As you can see, loss functions can be used for good and evil: with great power, comes great — well you know.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loss functions in the real world\n", + "\n", + "So far we have been under the unrealistic assumption that we know the true parameter. Of course if we knew the true parameter, bothering to guess an estimate is pointless. Hence a loss function is really only practical when the true parameter is unknown. \n", + "\n", + "In Bayesian inference, we have a mindset that the unknown parameters are really random variables with prior and posterior distributions. Concerning the posterior distribution, a value drawn from it is a *possible* realization of what the true parameter could be. Given that realization, we can compute a loss associated with an estimate. As we have a whole distribution of what the unknown parameter could be (the posterior), we should be more interested in computing the *expected loss* given an estimate. This expected loss is a better estimate of the true loss than comparing the given loss from only a single sample from the posterior.\n", + "\n", + "First it will be useful to explain a *Bayesian point estimate*. The systems and machinery present in the modern world are not built to accept posterior distributions as input. It is also rude to hand someone over a distribution when all they asked for was an estimate. In the course of an individual's day, when faced with uncertainty we still act by distilling our uncertainty down to a single action. Similarly, we need to distill our posterior distribution down to a single value (or vector in the multivariate case). If the value is chosen intelligently, we can avoid the flaw of frequentist methodologies that mask the uncertainty and provide a more informative result.The value chosen, if from a Bayesian posterior, is a Bayesian point estimate. \n", + "\n", + "Suppose $P(\\theta | X)$ is the posterior distribution of $\\theta$ after observing data $X$, then the following function is understandable as the *expected loss of choosing estimate $\\hat{\\theta}$ to estimate $\\theta$*:\n", + "\n", + "$$ l(\\hat{\\theta} ) = E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", + "\n", + "This is also known as the *risk* of estimate $\\hat{\\theta}$. The subscript $\\theta$ under the expectation symbol is used to denote that $\\theta$ is the unknown (random) variable in the expectation, something that at first can be difficult to consider.\n", + "\n", + "We spent all of last chapter discussing how to approximate expected values. Given $N$ samples $\\theta_i,\\; i=1,...,N$ from the posterior distribution, and a loss function $L$, we can approximate the expected loss of using estimate $\\hat{\\theta}$ by the Law of Large Numbers:\n", + "\n", + "$$\\frac{1}{N} \\sum_{i=1}^N \\;L(\\theta_i, \\hat{\\theta} ) \\approx E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] = l(\\hat{\\theta} ) $$\n", + "\n", + "Notice that measuring your loss via an *expected value* uses more information from the distribution than the MAP estimate which, if you recall, will only find the maximum value of the distribution and ignore the shape of the distribution. Ignoring information can over-expose yourself to tail risks, like the unlikely hurricane, and leaves your estimate ignorant of how ignorant you really are about the parameter.\n", + "\n", + "Similarly, compare this with frequentist methods, that traditionally only aim to minimize the error, and do not consider the *loss associated with the result of that error*. Compound this with the fact that frequentist methods are almost guaranteed to never be absolutely accurate. Bayesian point estimates fix this by planning ahead: your estimate is going to be wrong, you might as well err on the right side of wrong." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Optimizing for the *Showcase* on *The Price is Right*\n", + "\n", + "Bless you if you are ever chosen as a contestant on the Price is Right, for here we will show you how to optimize your final price on the *Showcase*. For those who forget the rules:\n", + "\n", + "\n", + "1. Two contestants compete in *The Showcase*. \n", + "2. Each contestant is shown a unique suite of prizes.\n", + "3. After the viewing, the contestants are asked to bid on the price for their unique suite of prizes.\n", + "4. If a bid price is over the actual price, the bid's owner is disqualified from winning.\n", + "5. If a bid price is under the true price by less than $250, the winner is awarded both prizes.\n", + "\n", + "The difficulty in the game is balancing your uncertainty in the prices, keeping your bid low enough so as to not bid over, and trying to bid close to the price.\n", + "\n", + "Suppose we have recorded the *Showcases* from previous *The Price is Right* episodes and have *prior* beliefs about what distribution the true price follows. For simplicity, suppose it follows a Normal:\n", + "\n", + "\n", + "$$\\text{True Price} \\sim \\text{Normal}(\\mu_p, \\sigma_p )$$\n", + "\n", + "\n", + "In a later chapter, we will actually use *real Price is Right Showcase data* to form the historical prior, but this requires some advanced PyMC3 use so we will not use it here. For now, we will assume $\\mu_p = 35 000$ and $\\sigma_p = 7500$.\n", + "\n", + "We need a model of how we should be playing the *Showcase*. For each prize in the prize suite, we have an idea of what it might cost, but this guess could differ significantly from the true price. (Couple this with increased pressure being onstage and you can see why some bids are so wildly off). Let's suppose your beliefs about the prices of prizes also follow Normal distributions:\n", + "\n", + "$$ \\text{Prize}_i \\sim \\text{Normal}(\\mu_i, \\sigma_i ),\\;\\; i=1,2$$\n", + "\n", + "This is really why Bayesian analysis is great: we can specify what we think a fair price is through the $\\mu_i$ parameter, and express uncertainty of our guess in the $\\sigma_i$ parameter. \n", + "\n", + "We'll assume two prizes per suite for brevity, but this can be extended to any number. \n", + "The true price of the prize suite is then given by $\\text{Prize}_1 + \\text{Prize}_2 + \\epsilon$, \n", + "where $\\epsilon$ is some error term.\n", + "\n", + "We are interested in the updated $\\text{True Price}$ given we have observed both prizes and have belief distributions about them. We can perform this using PyMC3. \n", + "\n", + "Lets make some values concrete. Suppose there are two prizes in the observed prize suite: \n", + "\n", + "1. A trip to wonderful Toronto, Canada! \n", + "2. A lovely new snowblower!\n", + "\n", + "We have some guesses about the true prices of these objects, but we are also pretty uncertain about them. I can express this uncertainty through the parameters of the Normals:\n", + "\n", + "\n", + "\\begin{align}\n", + "& \\text{snowblower} \\sim \\text{Normal}(3 000, 500 )\\\\\\\\\n", + "& \\text{Toronto} \\sim \\text{Normal}(12 000, 3000 )\\\\\\\\\n", + "\\end{align}\n", + "\n", + "For example, I believe that the true price of the trip to Toronto is 12 000 dollars, and that there is a 68.2% chance the price falls 1 standard deviation away from this, i.e. my confidence is that there is a 68.2% chance the trip is in [9 000, 15 000].\n", + "\n", + "We can create some PyMC3 code to perform inference on the true price of the suite." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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lkz5MeyjNX/68jqZqL7n8uVw4v47Ino1A+X9ftaxlu5Y3b95MOBwGoK2tjbPP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XcDnwD2icgecpffvsTZbYr3WeBfABe5FUd+P53PRRXNt9G+ok7vb4F/ExE7cIzchpxWtL+oMYwx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\nffd1+zRMnyoX65w+Mcf46UU816dWdSkt1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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import scipy.stats as stats\n", + "from IPython.core.pylabtools import figsize\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "figsize(12.5, 9)\n", + "\n", + "norm_pdf = stats.norm.pdf\n", + "\n", + "plt.subplot(311)\n", + "x = np.linspace(0, 60000, 200)\n", + "sp1 = plt.fill_between(x , 0, norm_pdf(x, 35000, 7500), \n", + " color = \"#348ABD\", lw = 3, alpha = 0.6,\n", + " label = \"historical total prices\")\n", + "p1 = plt.Rectangle((0, 0), 1, 1, fc=sp1.get_facecolor()[0])\n", + "plt.legend([p1], [sp1.get_label()])\n", + "\n", + "plt.subplot(312)\n", + "x = np.linspace(0, 10000, 200)\n", + "sp2 = plt.fill_between(x , 0, norm_pdf(x, 3000, 500), \n", + " color = \"#A60628\", lw = 3, alpha = 0.6,\n", + " label=\"snowblower price guess\")\n", + "\n", + "p2 = plt.Rectangle((0, 0), 1, 1, fc=sp2.get_facecolor()[0])\n", + "plt.legend([p2], [sp2.get_label()])\n", + "\n", + "plt.subplot(313)\n", + "x = np.linspace(0, 25000, 200)\n", + "sp3 = plt.fill_between(x , 0, norm_pdf(x, 12000, 3000), \n", + " color = \"#7A68A6\", lw = 3, alpha = 0.6,\n", + " label = \"Trip price guess\")\n", + "plt.autoscale(tight=True)\n", + "p3 = plt.Rectangle((0, 0), 1, 1, fc=sp3.get_facecolor()[0])\n", + "plt.legend([p3], [sp3.get_label()]);" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 50000 of 50000 in 8.2 sec. | SPS: 6119.0 | ETA: 0.0" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "\n", + "data_mu = [3e3, 12e3]\n", + "\n", + "data_std = [5e2, 3e3] \n", + "\n", + "mu_prior = 35e3\n", + "std_prior = 75e2\n", + "with pm.Model() as model:\n", + " true_price = pm.Normal(\"true_price\", mu=mu_prior, sd=std_prior)\n", + " \n", + " prize_1 = pm.Normal(\"first_prize\", mu=data_mu[0], sd=data_std[0])\n", + " prize_2 = pm.Normal(\"second_prize\", mu=data_mu[1], sd=data_std[1])\n", + " price_estimate = prize_1 + prize_2\n", + " \n", + " logp = pm.Normal.dist(mu=price_estimate, sd=(3e3)).logp(true_price)\n", + " error = pm.Potential(\"error\", logp)\n", + " \n", + "\n", + " trace = pm.sample(50000, step=pm.Metropolis())\n", + " burned_trace = trace[10000:]\n", + "\n", + "price_trace = burned_trace[\"true_price\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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9cHAwBw8eJC0tjebNmxcbwCwiPPXUU1SrVo3rr7+emjVrMnz4cFeFqGfPnmzd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\nadUg0L5DZOrpSoGIiMg009raytNPP82GDRtG3EF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "import scipy.stats as stats\n", + "\n", + "x = np.linspace(5000, 40000)\n", + "plt.plot(x, stats.norm.pdf(x, 35000, 7500), c = \"k\", lw = 2, \n", + " label = \"prior dist. of suite price\")\n", + "\n", + "_hist = plt.hist(price_trace, bins = 35, normed= True, histtype= \"stepfilled\")\n", + "plt.title(\"Posterior of the true price estimate\")\n", + "plt.vlines(mu_prior, 0, 1.1*np.max(_hist[0]), label = \"prior's mean\",\n", + " linestyles=\"--\")\n", + "plt.vlines(price_trace.mean(), 0, 1.1*np.max(_hist[0]), \\\n", + " label = \"posterior's mean\", linestyles=\"-.\")\n", + "plt.legend(loc = \"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that because of our two observed prizes and subsequent guesses (including uncertainty about those guesses), we shifted our mean price estimate down about \\$15,000 dollars from the previous mean price.\n", + "\n", + "A frequentist, seeing the two prizes and having the same beliefs about their prices, would bid $\\mu_1 + \\mu_2 = 35000$, regardless of any uncertainty. Meanwhile, the *naive Bayesian* would simply pick the mean of the posterior distribution. But we have more information about our eventual outcomes; we should incorporate this into our bid. We will use the loss function above to find the *best* bid (*best* according to our loss).\n", + "\n", + "What might a contestant's loss function look like? I would think it would look something like:\n", + "\n", + " def showcase_loss(guess, true_price, risk = 80000):\n", + " if true_price < guess:\n", + " return risk\n", + " elif abs(true_price - guess) <= 250:\n", + " return -2*np.abs(true_price)\n", + " else:\n", + " return np.abs(true_price - guess - 250)\n", + "\n", + "where `risk` is a parameter that defines of how bad it is if your guess is over the true price. A lower `risk` means that you are more comfortable with the idea of going over. If we do bid under and the difference is less than $250, we receive both prizes (modeled here as receiving twice the original prize). Otherwise, when we bid under the `true_price` we want to be as close as possible, hence the `else` loss is a increasing function of the distance between the guess and true price." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For every possible bid, we calculate the *expected loss* associated with that bid. We vary the `risk` parameter to see how it affects our loss:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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8vDyGDh3KP//5T0aNGlVqmyFDhtCzZ08+/fRTbrvtNv7617+SkJBA/fr1iY+P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+HMKsYQYSZ1esOTsAPBxNM4t8xDs0SR+OBcTKmZDW7n9/WXA6d28Ju5D1JaVUjP9EH8+vb/tIhg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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 7)\n", + "#numpy friendly showdown_loss\n", + "\n", + "\n", + "def showdown_loss(guess, true_price, risk = 80000):\n", + " loss = np.zeros_like(true_price)\n", + " ix = true_price < guess\n", + " loss[~ix] = np.abs(guess - true_price[~ix])\n", + " close_mask = [abs(true_price - guess) <= 250]\n", + " loss[close_mask] = -2*true_price[close_mask]\n", + " loss[ix] = risk\n", + " return loss\n", + "\n", + "\n", + "guesses = np.linspace(5000, 50000, 70) \n", + "risks = np.linspace(30000, 150000, 6)\n", + "expected_loss = lambda guess, risk: \\\n", + " showdown_loss(guess, price_trace, risk).mean()\n", + " \n", + "for _p in risks:\n", + " results = [expected_loss(_g, _p) for _g in guesses]\n", + " plt.plot(guesses, results, label = \"%d\"%_p)\n", + " \n", + "plt.title(\"Expected loss of different guesses, \\nvarious risk-levels of \\\n", + "overestimating\")\n", + "plt.legend(loc=\"upper left\", title=\"Risk parameter\")\n", + "plt.xlabel(\"price bid\")\n", + "plt.ylabel(\"expected loss\")\n", + "plt.xlim(5000, 30000);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Minimizing our losses\n", + "\n", + "It would be wise to choose the estimate that minimizes our expected loss. This corresponds to the minimum point on each of the curves above. More formally, we would like to minimize our expected loss by finding the solution to\n", + "\n", + "$$ \\text{arg} \\min_{\\hat{\\theta}} \\;\\;E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", + "\n", + "The minimum of the expected loss is called the *Bayes action*. We can solve for the Bayes action using Scipy's optimization routines. The function in `fmin` in `scipy.optimize` module uses an intelligent search to find a minimum (not necessarily a *global* minimum) of any uni- or multivariate function. For most purposes, `fmin` will provide you with a good answer. \n", + "\n", + "We'll compute the minimum loss for the *Showcase* example above:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum at risk 30000: 14723.45\n", + "minimum at risk 54000: 13500.92\n", + "minimum at risk 78000: 11900.78\n", + "minimum at risk 102000: 11649.08\n", + "minimum at risk 126000: 11649.08\n", + "minimum at risk 150000: 11329.30\n" + ] + }, + { + "data": { + "image/png": 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UBScFKQtOyquy4MSflAUnRSkLTvy5fRnKN65tK2WrXkYX3rxWmSkMALafJ6Oy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GVRGj0rEzh9FqVg7l/BrGLHIeyHy9BHm4jp27pObZWnvwRSI3LItRgSU30T4PHnsJTy9o/PAnDp\nsNtIbe7/Imme9q38A6Us/nYzAOdc0I3W7dWHW29Ycg+x7al/cWjhbwBEd2lH95em0WRI8ExB8yV1\n7VJC0aluL11db1EoiqIo9UJqkuKq6s8JQzqgM+i9bstxYCPW9fPAYCJ69DRfhfg37//8MsXlBXRu\n2YeJg67z23lqq6LMxrxPM3E6NXoPbEXfwXUbgDVGmsPJ3v99yc6Z7+OqtKCPjKDjtJtoe8sUdGFq\nipeiBJOT/kZKKX+vz0CUhknlolb8SfWv2ivfmoejsAJDXAQxvVrWqa2yH14AIGrYTejj/ZPJZvnW\nxSzfughTWAR3jnsGnc77QU5tnK5vOZ0a8z7NpKzUSsu28Yyc0F0tfK6loj8zyXpkBuXbdwPurEhd\nn72XiJbNAxyZ/6lrlxKK1DBeURSlkZAujeLlVU8ZhnZA6D3KhXFC9t0rsWUtRpiiiRo11VchHqOo\nrID3fnoRgGvOuY/khOC4ky+lZMn8LA7uKyEmLpyJV/ZDb/D+v2VjYysoYvuzb3Lw6x8BiExtSbcX\nHiDpXP8VBFQUpe7UoEHxK3UnRfEn1b9qp2zLQZwlFsKaRBHdvYXX7UgpKVv4fwBEDb8NfXSir0I8\n5hzvpD9DhdVM3/ZnMrLPRT4/x6mcqm+tX7mfTWsOYDDomHRVP6JiTPUYWeiSLhf7P5rLjhffwWku\nR2cy0v6ea2h399XowxvXf0N17VJCkRo0KIqiNALSqVG8fBcACWd2QOjq8JRhx+/Yd2YgIuKIGnG3\nr0I8xs/rv2HD7j+JDo/jtrFPBs3Un/05Rfz6vTvb+OiLepLcKi7AEYWG0swstjw8A/PGbQAknnMG\n3V64n6h2rQIcmaIonlKDBsWvgnne5umyJlU7WdakaqGaNalaMGVNqna6rEnVgrl/BRvzxv24yqwY\nE6OJ6pLsdTvupwzPAxA98l50kb7/0JxXtI9PfnsNgJtGP0JCdJLPz3E6J+pbpcUW5n+WiaZJBp7V\nju59Q7cicX1xlJjZ8eI77P9oLkhJeEozuj43lebjhgfNQDAQ1LVLCUWnSrn6MZ6lXL3WpxEpiqIo\nPqU5XJSsyAEgYVinOn1Ys21Jx7FvHbqYZkSedYuvQvyLS3Py1g9PY3NYObPbWIZ0He3zc3jDbncy\n75N1WCodpHZO5KwxnQMdUlCTUnLwqx/Z/ux/sBeWIAx6Um+9nA4P3IAhStWxUJRQdKonDTtrfJ0I\nXAcsAPYCbYAJwGz/haY0BOpOiuJPqn95xpy5D1eFHVNyLJEdvb9rLzXtr7UM0aPuQ2eK8lWIf5m/\n8iOyD24kITqJG87zX7G406nZt6SULPpmM4fzyohvGskFl/VBp2u8d8lPp2zrLrIenUHxig0AJJzR\nh+4vTiOmW4cARxY81LVLCUWnSrn6TPXXQohFwHgp5bIa24YBT/o3PEVRFKUuNLuTklXulJZ1fcpg\nzfwOZ14WuviWRJ55vY8iPGr3oW3M+eNtAG4//2miw2N9fg5vrPo9h+2b8jGa9Ey+Oo3wiLBAhxSU\npMvFrtc+ZNdrHyJdLoyJCXR5+m5SLhnbqKciKUpD4elKuDOAFcdtWwkM8W04SkOTkZER6BCUBkz1\nr9MrXbMXzeIgvGU8EalNvW5HupyUpb8EQMyYBxEG32a7sTttvLnwKVyai9H9ptCnXWD/vFT3rV3b\nDrPsp2wQMH5KHxKbRwc0rmBlzStg1SX/YOeM95CaRpvrL+KsjM9peen5asBwAurapYQiTxdCZwIv\nCCGeklJahBARwDPAev+FpiiKotSFy2KnZPUeABLOqttTBsvqz3EV7EKf2J6IQVf4KMKjvlr2Xw4c\n2UVyQhuuHP4Pn7fvjcLD5Sz8cgNIGHZeJzp0axbokIJSwZI/2XjPcziKSjAmNaH3m0+TePbAQIel\nKIqPefqk4XrgTKBUCHEIKAWG4V7nUCtCCJ0QYp0QYn7V+wQhxGIhxHYhxCIhRFyNfR8VQmQLIbYK\nIUbX2J4mhNgohNghhHi9xnajEOKLqmP+FEK0qW18im8F87zNnOmLyJm+6LT75U1tQt7UJif9/ozH\n0pnxWLovQ6tX6clDSU8eGugwjjF6ViajZ2Wedr9g7l/BoHTNXqTdSUTbpkS0PnkfPh1pr6Qs/RUA\nYs5/FKH37fScrfvXsXD1Jwih467xzxJujPBp+94Y0H8wcz9eh93monPPZAaPaB/okIKOZnew7Z//\nZu1VD+AoKqHp8IGc+ctHasDgAXXtUkKRR4MGKeUeKeVQoAMwEegopRwqpdztxTnvBbJqvH8E+FlK\n2QX4BXgUQAjRHZgCdAPOB94SR2+T/Re4SUrZGegshKjOnXkTUCSl7AS8DrziRXyKoighz1Vho3Tt\nXgAShnWsU1tli6ajleRiaNmL8H4X+iK8v1Taynnrh6eRSCafcQOdUnr5tH1vaJrk+y83UFxYSVJy\nDGMv6amm2Byncm8uKyfdwZ63P0fo9XR+/HYGfP4apiTvB6eKogQ3j6v7CCGaAiOA4VLKfUKIFCFE\nraqyVO0/DphVY/MkjmZhmg1Mrvp6IvCFlNIppdwDZAODhBDJQIyUcnXVfh/VOKZmW3OAkbWJT/E9\nNW9T8SfVv06uZNVupMNFZIckwlPivW7HcTCLil/fBCGIm/JqnYrCncjHv7xKQelB2jXvysVDfZ/C\n1RsZP+3g91+XEhEZxuRr+mE0qpJGNeXP/4Xlo66nNDOL8JbNGTT3Ldrfc63P+0ZDpq5dSijy6Ddc\nCDEc2A5cxdGMSZ1w3/GvjdeABzm2/kNzKeUhACllPlA9abQlsL/GfrlV21oCB2psP1C17ZhjpJQu\noEQIoW57KIrSqDjLrJgz3ZfPhDO9f8ogNY3SL6eC5iRy2M0Y2/b3VYgArMn+nV83zSNMb+TO8c9i\n8PG0J2/s2naYVb/vRugEE67oS1yCqilQzWWxseWhV1h/6xM4yypodv7ZDP15NgkDA/90SFEU//P0\n9snrwGVSyiVCiOKqbSuBQZ6eSAgxHjgkpVwvhBhxil1PW1CuFtTz5ABT8zYVf1L968SK/9yFdGlE\ndUnG1Nz7tKWVf87GsXcNurgWxIx73IcRgrmymHcXuStLX372XbRODHwO/9LiSn78ehMAV98wiTYd\nvM821dCU79jD+tuepHzrLoQxjK5P30ObGy9W07a8pK5dSijydNCQKqVcUvV19Yd6ey2OB/dC6olC\niHFABBBTVXU6XwjRXEp5qGrq0eGq/XOB1jWOb1W17WTbax5zUAihB2KllEXHBzJnzhxmzZpFmzbu\nddJxcXH06tXrr1/i6seG6n3Dfp8CHu2/Kt+936ST7L83t3qJztig+vk8fZ+lVdSIPvDxZGRkYN6V\nTWyHvkETTyi9/+3Hnzn84yYGtOlOwpkdvG5vSK+OlC14hlX5EN3vWkZGxPosXiklq47Mo7SyiBhL\na2KsR3NWBOq/3xlnDGXB5xvYvnMDLdrEM3DYmIDGEyzvly1bxpFfVhD94Y+4LFZ2NY+i4wM30vba\nS4IiPvVevVfv+evrffv2ATBgwABGjvT9DH0h5elv7Ash/gCelVIuEkIUSSmbVGUzekxKOaLWJ3VP\nd3pASjlRCPEKUCilfFkI8TCQIKV8pGoh9KfAYNzTjn4COkkppRBiBfAPYDWwEHhDSpkuhLgT6Cml\nvFMIcTkwWUp5+fHnX7JkiUxLS6tt2IoXMjIy/urciuJrqn/93eGFGynPyiO6ZwrNzvd+2kjx7Juw\nZn6HqftoEm753Kd3lDOyfuQ/3z9BhDGKV274kqS4Fj5r21tL5meRuWIfsfHhXHP3UNauW9Xo+5az\nvIItD08n75vFAKRcMpbuLz2AIdr3lcAbG3XtUvxp3bp1jBw50uePAQ0e7vcA8L0QYiEQIYR4B5jA\n0ZuvdfES8JUQ4kZgL+6MSUgps4QQX+HOtOQA7pRHRzh3AR8C4cAPUsrqfJfvAR8LIbKBQuBvAwZF\nUZSGyn6knPKsPNAJEoZ29Loda9ZPWDO/Qxgjib34FZ8OGEoripi9ZDoA15xzX1AMGLZtzCNzxT50\nevc6hohIY6BDCjjzpu2sv+0pKnP2o48Ip/tL02h52bhAh6UoSgB5NGiQUq4QQvQGrgbex73YeJCU\n8oA3J5VS/g78XvV1ETDqJPu9CLx4gu1rgb/dQpNS2qgadCjBQd1JUfxJ9a9jFWVkAxDbpxVhcd7V\nOpD2SsxzHgQgeuzDGJr6ttzN7CUzKLOU0rPtIM7pPfn0B/hZ0ZEKFn+3GYAR47rSorU701Rj7VtS\nSva9N4dtz/4HaXcQ070jfd55luhOqYEOrUFprP1LCW0eDRqEENOklDM4ru6BEOJ+KeWrfolMURRF\n8Zgtv5TK7MMIg474M7xfVFy2aDquon0YUnoSNfx2H0bozpa0fNsiTGHh3DLm8YAvonU4XMz/LBO7\nzUWXXsn0O6Nx1wO1F5vZfP8LHP5xKQCtr7uQrv/8B/oIU4AjUxQlGHiaVPmpk2x/wleBKA1TzUU6\niuJrqn8dVbSs6ilDWhsM0d59yPtbTQYfpkCtsJbx3k/uB8eXnXUXzeNb+axtby2Zn8WR/HISmkYy\n+sJjC7g1tr5VvHoTy0ddx+Efl2KIjabvu8/T4+UH1YDBTxpb/1IahlM+aRBCnFv1pV4IcQ7HpjBt\nD5T5KzBFURTFM5b9RVj2FCKMBuIHtfOqDalplH5139GaDKkDfBrjp7+9TnF5AZ1SejE27TKftu2N\nzWsPsHltLgaDjolX9sMU7ukSv4ZFaho5//mEnS+/i3S5iEvrQZ//PkNk25TTH6woSqNyuqvke1Wv\n4bjXMlSTwCHgHn8EpTQcwTxvM2f6IgDaPzjmlPvlTXXXB2zx+t+y9wIw4zH3OvxpL4w94feDXXry\nUADG5i8PcCRHjZ6VCcDim/udcr9g7l/1RUpJcdVThviBbdFHeLeIt/LPj3DsWY0uNpmY8b59iLxp\n7yp+2TgXgz6M28Y+hU6n92n7tVWQX8bP892pkkdO7E5Si5i/7dMY+pbLamPTvc+TP8+dUb3dnVfR\n6dHb0IU1zgFUfWoM/UtpeE55ZZBStgMQQnwkpby2fkJSFEVRPGXZcwRrbgm6iDDi+qd61YbLfIiy\nBf8EIPaiF9FFeF8Q7nhWu4V3058H4KIhN9Mqsb3P2vaG3eZkwWfrcTo0eqS1pNeAwE+TCgR7sZnM\n6x+meOUG9NGR9H37WZJGDQ10WIqiBDFP1zS8KoSoWVANIURrIUQfP8SkNCBq3qbiT429f0kpKVq2\nE4D4Qe3Qmby7Q2z+7nGk1Yyp+3mE95noyxD5KuO/HC7NpU1SJyYOvs6nbdeWlJLF322m6EgFic2j\nGTWx+0n3bch9q3JvLisn3Erxyg2YWiRxxvy31YChnjXk/qU0XJ4OGj4Bjl8RZwQ+9m04iqIoiqcq\ndhzCfsiMPtpEbD/vMv9Yt/6MNfNbCIsg9uLpPs1olH1wEz+u+QwhdNx+/tMYfLiw2hvrV+5n28Z8\nwox6Jl7ZlzBjYKdJBUJpZhYrxt9Kxc59xHTvyJCF7xLT3fuaHoqiNB6eDhraSClzam6QUu4CUn0e\nkdKgqHmbij815v4lNUnxH+6nDAlntEcXVvsPwDVrMsSc79uaDA6nnXd+fBaJ5IKB19A+uZvP2vZG\n/oFSflu4FYAxF/WkSVL0KfdviH3r8KJlrLzoLuxHimk6fCCD5/2X8JRmgQ6rUWqI/Utp+DwdNBwQ\nQqTV3FD1/qDvQ1IURVFOpzzrII7CCgxxEcT09m5eftmiGbgK92JI6UHU8Dt8Gt93f77HgcIckhPa\ncOmZt/q07dqyWhzM/3w9Lpek7+A2dO0d+CrU9W3v+9+w7oZH0Sw2Wl4+nv6fzMQQExXosBRFCSGe\nToB9DZgnhHgF2AV0AKYB/+evwJSGISMjI2jvqJwua1K1k2VNqhaqWZOqBVPWpGqny5pULZj7lz9J\nl0bx8l0AJAztgNB7ev/nKHdNhv/4pSbD3sM7mLfyAwBuG/skxrBwn7VdW1JKfueEF/8AACAASURB\nVJyzCXOxheYtYxkxvqtHxzWUviU1je3PvcWe/34GQMcHb6bD/TcEvLBeY9dQ+pfSuHg0aJBSviuE\nKAFuAloD+4EHpJRz/BmcoiiK8ndlGw/gLLUQ1jSK6O61z6d/bE2GmzCmDvRZbC7NyTs/PotLczG6\n36V0a512+oP8aE3GHnZtPYwp3MCEK/piMNR+gBWqXFYbm+55jvwFvyAMenrOfJSWl40LdFiKooQo\nj1NtSCm/Br72YyxKA6TupCj+1Bj7l+ZwUfyne4lZwpkdEbra3zG2rKiuydCcmPFP+jS+has/JefQ\nVprGNOeKswNbyufAnmKWLtoBwPmX9ia+SaTHx4Z637IXlbLu+ocpWbURQ0wUfd97gcSzfTc4VOom\n1PuX0jh5dMtFuN0ihFgihNhYte1sIcQU/4anKIqi1GTO3IerwoaxeSxRnZvX+niX+RDmBc8Avq/J\ncLBoL1//8Q4At4x5gghT4ObMV5Tb+P6L9UhNMvCsdnTs1ngW/FbuzWXFhNsoWbURU4skBs9/Ww0Y\nFEWpM0+f0z6Le2rSu0B1eo0DwMP+CEppOFQuasWfGlv/0mxOSlbtBqDJWR29mpdunvsE0lKKqdso\nwvtM8l1sUuN/6c/hcNo4u8d4+rYPXN5/TZP88NVGys02WrZNYNjoTrVuI1T7Vsm6LFaMu4XKXTVS\nqnbrEOiwlOOEav9SGjdPBw3XAxdIKb8AZNW23UBgS3sqiqI0IqVr9qBZHIS3jCciNbHWx9u2LsG6\n7ht3TYZLfFuT4ef137DtQCZxkU245tz7fdauN1b8uou9OwuJiDJyweV90HuxUDwUHV60jFUX34W9\nsISmIwaplKqKoviUp2sa9EB51dfVg4boGtsU5YSCed5mzvRFwOmzKOVNbQKcPIvSjMfSgdDNopSe\n7L4jHExZlEbPygROn0UpmPuXr7ksdkrW7AEg4axOtf7AL+2VlM6ZBkDM2IcxNG3rs9iOmPP47Lc3\nALjhvIeJiYj3Wdu1tXfnEZb/shMEjJ/Sm5g47zI3hVrf2vv+N2x94jXQNFpePp4e0x9GF+ZdhXDF\n/0KtfykKeP6k4QfgVSGECdxrHIDngAX+CkxRFEU5qmTlbqTdRURqUyJaN6n18WWLZ7prMrToTtQI\n39VkkFIya/GLWB2VDOx0DoM7j/RZ27VVVmrl+y83goQh53QgtVPtn8aEGqlpbPvnv9n62EzQNDo+\ndAs9X3tMDRgURfE5TwcN9wMtgFIgDvcThraoNQ3Kaah5m4o/NZb+5Sy3Yc7cB0CTs2o/P9+Rl0XF\nL//2S02GZVk/sD7nD6JMMdx43sMBy//vcml8/8UGLBV22nZsypBzO9apvVDoWy6rjQ23PcWetz9H\nGPT0+tcTdFQ1GEJCKPQvRTmep3UazMCFQohmuAcL+6WU+X6NTFEURQGgZMUupFMjslMzTMlxtTrW\nXZPhfndNhjNvxNhukO/iqijkoyUzAbjm3PtJiE7yWdu1lfFTNrl7i4mONTFuSm90XqSiDSXHp1Tt\n9/6LND1rQKDDUhSlAfP4+aUQIh44D0gBDgohfpBSFvstMqVBUPM2FX9qDP3LUWrBvOEAAE2G1f4p\ng2XFRzh2r/JLTYYPf36FcmspvVIHM7znBJ+2XRvbN+WzeuluhE5wweV9iYo21bnNYO5blXsOsOaq\naVTu2kd4SjP6fzpTZUgKMcHcvxTlZDyt03AusAf4BzAQuAfYLYQI3ORVRVGURqB4+U7QJNHdW2BM\njK7Vsa6yw0drMlz4ArrI2j2lOJVVO35hxfafMYVFcMuYJwI2JWZP9hF++GoDAGeP6Uyr1ISAxFFf\nilasZ8X4W90pVXt04gyVUlVRlHri6ZOG/wC3Sim/qt4ghLgUeBPo6o/AlIYhIyMjaO+onC5rUrWT\nZU2qFqpZk6oFU9akaqfLmlQtmPuXL9gLyynfchB0goShtZ+jf0xNhr6TfRZXudXM+z+9BMAVZ99N\ns7gUn7VdGwf3lTDv00xcLknakLYMGJbqs7aDsW/t/2QeWY/ORDqcJJ4zmL7/ex5DTOAK6CneC8b+\npSin4+mgIQX45rht3+Eu9qYoiqL4QfEfO0FCTO+WhCVE1upY27ZfsK6d45eaDJ/8+holFYV0btmH\n0WlTfNZubRTkl/Ht7LU47C6690vhnPFdG+wCYM3hZNtT/2LfB+4/w21vu4wuT96FzqAyJCmKUn88\nveJ8DNwFvFFj2x3ARz6PSGlQ1J0UxZ8acv+yHTJTsf0QQq8jYUjtpp9IeyWlX1fVZBjzkE9rMmzc\ns4LfNs3HoA/jtrFPohP1XzitpKiSOR+swWpx0KFbM8Zc1BPh44XPwdK37IUlrL/lCYqWr0MYw+jx\nykO0unx8oMNS6ihY+pei1Iang4Z+wO1CiIeAXKAl0AxYKYRYWr2TlPJs34eoKIrS+BRlZAMQ2681\nhpjaFSgrWzQDV+Eed02Gc+70WUxWeyX/S38egIuH3krLpu181ranys1Wvn5vNRVlNlq3a8KEBlzx\nuWzrLtZd+xCW/XmYmjWl3wcvEt+/Z6DDUhSlkfJ00PAuaiqS4gU1b1Pxp4bav6wHirHkHEGE6Ykf\n3L5WxzoOZlHx63/cNRkue82nNRm+WPYmR8x5pDbrwoRB1/isXU9ZKu3M+WANpcUWmreM5cJr0zCE\n6f1yrkD3rUM//M7Gu5/FVWkhtk9X0j58mfAWgUtpq/hWoPuXonjD0zoNs/0diKIoiuKusFz9lCFu\nQFv0kUbPj9U0Sr+c6q7JMOwmjKkDfRbX9gPrWbT2S3RCz23nP4XBh4MRT9htTr6dvZYjh8ppkhTF\nxdcPwGhqeHP6paax67UP2Tl9FgAtLh5NzxmPoo+oexpZRVGUuvA05eosIUTkcdtaCCHS/ROW0lAE\n852UnOmLyJm+6LT75U1tQt7UJif9/ozH0pnxWOj+KqQnDyU9eWigwzjG6FmZjJ6Vedr9grl/ecuy\ntxDr/mJ04QbiB6bW6tjK5R/g2LsGXWyyT2syWO2VvJP+LBLJhMHX0q55/SbNczo15n2aSd7+UmLi\nw7n0xoFERnk+mPJGIPqWs6KS9bc84R4wCEHnJ+6k93+eVgOGBqghXruUhs/TiaDRwEYhxBAAIcTl\nwEbg9H/VFUVRFI9IKSle5n7KED+oHTqT53fzXSUHKauuyXDxS+giYn0W09s/PsPBor20atqei4fe\n4pN2PaVpkoVfbmDvzkIio4xceuNAYuJqt8YjFFTuy2PlhNs5tPA3DDFR9P94Ou3vvrrBZoRSFCX0\neDRokFJeDjwNzBNCLAOeBy6UUj7qz+CU0JeRkRHoEJQGrKH1r8qdh7Hlm9FHGont16ZWx5q/fQRp\nK8fU83zCe/uuOvP3qz5mxfafiTBGcf/k6RgN9XfXW0rJT3O3kL3lEEaTgUtuGECTxPqpS1Cffato\neSZ/jr2JsqydRHZowxk/vEvSqOB6+qf4VkO7dimNQ21STuQCVqA9sBvY6ZeIFEVRGiGpSYoy3JfV\n+CHt0Rk9n69v3fwj1o3fI0zRxF38ss/uTm/au4rPlv4bgDvHP0NK01SftOsJKSW/p29n05oDGMJ0\nXHRdf5ql+ObpSTDZN/s7Vk/5B46iEhLPGcyQH94lulNqoMNSFEX5G0/XNMwAvgDuBVKB9binK13q\nv9CUhkDN21T8qSH1r/KteTiOlGOIDSe2d2uPj9OsZZTOeRCAmHGPoU9o5ZN4CkrzeGP+I0ipceGQ\nmxjY6RyftOupVUt3s2bZHnQ6wcQr+9EqNaFez+/vvqU5nGx5eDpZD09HOl2k3n4F/T+ZQVhcjF/P\nqwSHhnTtUhoPT29ldQP6SCkPVb1/UAixAJgNfO2XyBRFURoJl8VO0W/bAUgY2hFh8PwhcNkPL6CV\nHCSsdT8iz/LNegO7w8qrc6dRZimlT7shXHrmbT5p11MbVu5j2aIdIGDcpb1p36VhpRq1Hykm8+bH\nKV6xHp3JSI/pD9NyyvmBDktRFOWUhJTS+4OFiJFSlvkwnnqxZMkSmZaWFugwGgWVi1rxp4bSvw4v\n3Eh5Vh7hrRNocdlAj6cX2fdlUvjaeSAEifcvIaxV7zrHUr3w+ffNC2gW15IXrv2Y6Ii4OrfrqW0b\n8vj+qw0gYdSk7vQdXLu1Hb7ir75l3pLNuusexnogH1PzRHfBtrQePj+PEtwayrVLCU7r1q1j5MiR\nPs+i4PHtLCHEeUKI96ueMCCEGAD4Lgm4oihKI1SZU0B5Vh7CoCNpTA+PBwzS5XTXZJAaUcNv98mA\nAeCn9XP4ffMCjAYTD1w4o14HDDnbC/jh640g4azRnQI2YPCX/O9/ZeUFt2E9kE9cv+4MWfSeGjAo\nihIyPF3TcA/wX2AHcHbVZgvuLEqKclLqToriT6HevzSbk4LFWQAkDOtEWILnmYEqlr6NM3cT+oTW\nRI99xCfxbM/dwOwlMwC4dcwTtG3W2SfteuLAnmLmf5aJpkkGnJXKoOG1q4Tta77sW1LTyJ4+i/U3\nP47LYiXlkrEM+u5NwpMb1rQrxXOhfu1SGidP1zRMBUZKKfcIIR6u2rYN6OKfsBRFURq+wt+34yqz\nYmoRR1z/th4f5yzcR/mPLwEQe+kMdKa6pyEtLi/g9bkP4dKcnN//Cob1GFfnNj11+KCZ7z5ai9Oh\n0WtAK4aP7dJg6hM4KyrZ9I/nObTwN9Dp6PLknaTefkWD+fkURWk8PJ2eFAPsr/q6ehFEGGD3eURK\ng6JyUSv+FMr9y7KviLINB0AnSBrbE6HzcFqSlJi/eRBpryS872TCu59X51icLgevz3uY4oojdGuV\nxlUj7q1zm54qPlLBnA/WYLM66dyzOedN9nyKlj/5om9Z9tco2BYbTf9PZtDujiuD4udTAiuUr11K\n4+XpoGEpcPzz738Av/o2HEVRlIZPc7goWLQZgIQh7TEmRnt8rHX9XGxZPyHCY4m96EWfxPPxr6+x\nPXcDTaKbce+klzDoPa9EXRdlpVa+fn81lRV22nZsyrgpfdB5OHgKdsUrNxwt2Na+tbtg27lnBDos\nRVEUr3k6PekeYIEQ4hYgRgixHSgDLvBbZEqDEMzzNnOmLwKg/YNjTrlf3tQmALR4veiE35/xWDoA\n014Y68Po6k96srvy7Nj85QGO5KjRszIBWHxzv1PuF8z961SKM7JxllgwJkYTP9jzuftaZQnmbx8F\nIGbCP9HHNq9zLEs3f8+idV9i0Idx3+RXiI9qWuc2PVFZYefr91djLrHSonUck67qh6EWqWb9rS59\na/+n88l6ZAbS4aTp8IH0fec5wuIbXmE6xXuheu1SGjePrtBSyjzcmZKmAFcC1wGDpJT5np5ICGES\nQqwUQmQKITYJIZ6u2p4ghFgshNguhFgkhIirccyjQohsIcRWIcToGtvThBAbhRA7hBCv19huFEJ8\nUXXMn0KIhpV6Q1GUkGc9WELp2r0gIOn8ngh9LWoyLHgGrewwYe0GEznk2jrHsjt/K+8ufgGA60c+\nRKeUXnVu0xN2m5NvPlxDUUEFic2juei6/hhNnlfADlaa08nWJ19nywMvIR1O2t56Gf0/nakGDIqi\nNAge/7WSbquklF9LKVdIKbXanEhKaQPOkVL2A/oC5wshBuGe9vSzlLIL8AvwKIAQojvuQUo34Hzg\nLXF0Iuh/gZuklJ2BzkKI6lvFNwFFUspOwOvAK7WJUfE9NW9T8adQ61/SqVGQvhkkxA1MxZTseTpT\ne84KKv+cDfow4qa8itDV7a58maWEmXMfxOG0cW7vyYzqe1Gd2vOU5tJY8MUGDuWaiUuI4JIbBhAR\naayXc9dGbfuWo8TM2qseYO+7XyHCDPR89TG6PXsvOkPoD4YU3wu1a5eiQC0GDb4gpays+tKEe2qU\nBCbhrixN1evkqq8nAl9IKZ1Syj1ANjBICJEMxEgpV1ft91GNY2q2NQcY6acfRVEUpdaKV+zCUVhB\nWEIkCUM7enycdNop/eo+AKJH/oOwFt3qFIemuXhjwWMcMefRIbkH1496qE7teUpKyZIFW9m9vYCI\nyDAuuXEA0bHh9XJufyrfuZc/x91C4e+rMTaNZ9Ccf9PqSjV7V1GUhqVeb4EIIXTAWqAD8KaUcrUQ\normU8hCAlDJfCNGsaveWwJ81Ds+t2uYEDtTYfqBqe/Ux+6vacgkhSoQQTaSUJ56Mrvidmrep+FMo\n9S/bYTMlK3cDkDimB7owvcfHlv/yBs787eiTOhB93gN1juXLZW+xac9KYiMTuG/yKxgNpjq36YnV\ny/awYdV+9AYdk69JI6Fp3VPF+ounfavg1xVsuO0pnOZyYnp0Iu3Dl4ho3cLP0SmhLpSuXUpwklLi\n1Nz/HC6JS5M4qt77S70OGqqmNPUTQsQC3wkhenA0hetfu/nwlCdMwzFnzhxmzZpFmzbuJQ9xcXH0\n6tXrr1/i6seG6n3Dfp8CHu2/qmrlzqST7L83N6vqO2OD6ufz9H2WVlEj+sDHk5GRgXlXNrEd+gZN\nPHV9LzWNdnvCQJNsDSvg4N4shrX27PjfF3xJyRfTGZQEcZfO5I+Va+oUz7ufv8HXGW+TmBrNvRNe\nZNvGncBOv//3SIrryNL07ezNzWLoyI60bJsQNP9/vHl/5plnsuedL/ju6VdAapwzYTy93niCFZnr\nYO+ugMen3qv36r1/37s0yW9Ll2F3afQbNASbU2P5H39gd0m6pw3G5tJYt3I5dpekQ++B2FwaWWtX\n4tQkbXsOwKFJstevwikhpVsaDpdkz6Y1ODWNpC7u97lZa3BqkviO/XBoGoe3rcOpQVS73rgkmHet\np1rZrg3Yit0fWB67YjQjR/p+so2Q0n8jklOeWIgngUrgZmCElPJQ1dSjX6WU3YQQj+BeSvFy1f7p\nwNPA3up9qrZfDgyXUt5RvY+UcqUQQg/kSSmbHX/uJUuWyLS0tHr5ORu7jIyMv37ZFMXXQqV/lazM\noWhpNobYcFrdcCY6o8Gj46SUFL01GXv2MiIGXkH8VW/WKY4DR3J44uPrsDoqueac+xg/8Oo6teep\n3L3FfPXealxOjbPHdmHQ2e3q5bx1caq+pdnsbHnoFXK//AGADvffSMdpN9Z5nYnSeITKtStUSCmx\nOjVsTg27S2J3adidEptLw+Fyb6v+nsN13H4uif2Y90e3WZ3u9zanhtXpbqP6n8OPd/Q9ZdCJY//p\n3a9TO9kYOXKkz/NXe/aXyweEEImAQ0pZKoSIAM4DXgLmA9cDL+POyjSv6pD5wKdCiNdwTzvqCKyS\nUkohRGnVIurVwLXAGzWOuQ5YCVyKe2G1oihKwNiLKij+YxcAiaN7eDxgALCs/gJ79jJEVBNiJz1b\npzgqbWXM/G4aVkclQ7uOYdyAq+rUnqeKj1Qw9+N1uJwafQa1ZuBZqfVyXn+xFRSReeOjlKzehC7C\nRO9/PUnyxHMDHZaiNBhWp0aZzYnZ6qTM5sJsq3qtel9mc2Kuei2zVr3aXPX+IV4AJoMOk0FHeNWr\nUS/++vqvf/rqrwVheh1hVR/uw3Tu90a9IEwvCNPp3K9693aDTri/d9x293HuwcHJCkWuW7fOLz9z\nvQ0agBbA7Kp1DTrgSynlD0KIFcBXQogbcT9FmAIgpcwSQnwFZAEO4E559LHIXcCHQDjwg5QyvWr7\ne8DHQohsoBC4vH5+NOVk1J0UxZ+CvX9JKTmSvhnp0ojukUJku0SPj9XKCzHPexKA2EnPo4v2vn6C\nJjXeWvg0ecV7aZPUkVvHPlkvVYkrK+x8M3stlkoH7bokMXJCt5CphnyivmXetJ111z+CNfcQ4SnN\n6Pfhy8T17hKA6JRQF+zXLl9xaZJSq5NSq5MSi5MSq6Pq1f3++IFBmc2J3eXdh//qD+xGvQ5j1Qd4\nk8H9gduod394N+rFX987Zj991X6Go/uF6XWEh1V/6D9uMFC1f6hcz3yl3gYNUspNwN/mBFUtUh51\nkmNeBP5W8lRKuRb4W0LxqrSuU+ocrKIoig+YM/djzS1BH2mk6Tm1+3BpnvcksqIIY+fhRAy8rE5x\nzP3zfdbs/J0oUwz3T55BuDGiTu15wulwMffjdZQUVtIsJZYJl/dBV4uaFMEm//tf2XTPc7gsVuIH\n9KTf+y9ialY/hfAUJVhoUlJuc/31ob96EHB0UOCs8d6B2eaq9TnCdIKYcD0xJgOxJgMxJv3R13D3\nq/t7Va9V+5qCqDhkQ1WfTxqURkjN21T8KZj7l6PUQtHSHQAkntcdfYTntQhsO37HsvoLMJiIu3RG\nne5mZeb8wdcZbyMQ3H3B8yQntPa6LU9JTfLjnE0c3FdCTFw4F12bFnLF26r7ltQ0ds58n10z3wcg\nZco4ek5/CJ0p+GpLKKEjmK9ddqdGXpmNXLONg6U2Dprt5JqtHDTbKaiwU5tZQAKIDTcQH24gPsJA\nXNVrfLj767hwAzHhRwcAMSY94QZdo7uDHypC6yquKIoSAqSUHFm8BelwEdW5OVGdm3t+rN1C6Vfu\ntKrRo6dhSOrgdRz5xfv5z4LHkUguHXY7/TrUz4eUpYt3sH1TPkaTgYuu6x+ytRicFRY2/eM5Di38\nDXQ6ujx5J6m3X6E+0Cghz1Y9MCi1cdDs/pdb9VpQ7jhlGssoo/6vQUB8uIG4iOpBQdhx791PCvQ6\n9fvSUKhBg+JXwXonBSBn+iIA2j845pT75U1tAkCL109c7mPGY+4lNdNeGHvC7we79OShAIzNXx7g\nSI4aPSsTgMU39zvlfsHav8q3HMSypxBdeBhNR9WuEFvZTzNxHcnBkNyV6HPv8ToGq93Cq3OnUWEr\no3/H4Vw45Cav26qN9Sv3sXrpbnQ6waSr+pKUHFMv5/W1/qkdWTnpdso2Z2OIiaLP28+SNHJIoMNS\nGoj6uHbZXRq5pUcHAwfNRwcJRypOPjDQCWgRYyQl1kTLWJP7Nc79dVK0EWMITzNU6kYNGhRFUXzI\nWW6j8JdtADQ9tyuGKM8LpznysqhY4k4GFzflVYTBuykwUkreXfQ8+wp2kpzQhrvGP4NO+P8Pfc72\nApbMd9ctOe/CHrTt6PnC72BSvGYTmdc/gv1IMZHtWpE2+xWiO6cGOixFOSGXJjlotrGn2MqeYov7\ntchCrtl20qlE7oHBsYOClFgjLWPDaR5jxKCeDignoAYNil8F87xNJfQFW/+SUnLk5yw0m5OIdolE\nd/e8MrDUNEq/uh80J5FDb8DY/gyv4/hhzWf8sTUdU1gED1w4g0iT/+/2HzpoZsHn65ESzjinA736\nt/L7Of3h8KJlrL/tSTZXFnPWiBH0eec5jAmxgQ5LaWC8uXZpUnK43M7eYusxA4R9JVYcJ8g4pBOQ\nEmuiVZzpb08NmkWrgYFSe2rQoCiK4iMVOw5RmX0YYdSTNLp7rea+V2bMwrF7FbrY5sRc8JTXMWzZ\nu5pPf/sXAHeM+yetE71fE+Epc4mFb2evxWF30b1vCmeO6uj3c/rD/k/mseWh6aBpJI0aSv+PZqIz\nqD+TSv2SUlJscdZ4auAeIOwtsWJxaCc8pll0GKkJEaQmhP/12jo+XGUUUnxKXQ0Vvwqmu8BKwxNM\n/ctlsVP481YAmg7vgiHW87Sm9t2rjtZkuPhldJFxXsVwxJzPvxY8iiZdTBx8HWd0OWE2a5+yWR18\nO3stFWU2WrdrwuiLeobcQmEpJbte/YCd02cB0OGBGxkz7aaQ+zmU0FF97ZJSctBsZ8eRCnYUVJJ9\nxMKeYstJU5XGhxtIbRJ+zAChbUI4UUZ9fYavNFJq0KAoiuIDhb9sw1VpJ7x1AjF9PJ+a4zIfoviD\n68HlIPLs24joM9Gr89udNl6d+yDmymJ6pQ7m8rPu8qqd2nC5NOZ/tp4jh8ppkhTFpKv7YQixO5vS\n5SLr0Zns/2gu6HR0f2kaba6dHOiwlAZISsnhcgc7jlS6/xVUkH3EQrn97wOEKKO+alBwdIDQNiGc\n+IiwAESuKG5q0KD4VbDNOa/pdFmTqp0sa1K1UM2aVC2YsiZVO13WpGrB0r8qcwooz8pDGHQkjenh\n8R1q6bRT/OENaOZ8jB2GEjvpWa/OL6Xk/Z9eIic/i6S4FP4x4QV0Ov/eeZRS8tPcLezdWUhklJGL\nrutPeIh9oHFZbGy482kO/7gUXbiRPv99hubnDweCp28poauw0sGOguoBgvu11OoEwLxrPbEd+gKQ\nEGGgc2IknZMi6ZwYSfumESRGhqknXUrQUYMGRVGUOtBsTgoWuzMGJQzrRFhClMfHmuc9iSNnBbq4\nFsRf/z5C792H7p/Wz+G3TfMxGkw8MHkGMRHxXrVTGyt/y2Hz2lwMYTouvDaN+CaRfj+nL9mLzay7\n7iFKVm3EEBdD/49eIWFwn0CHpYSoUquT7COVbK8aHGQXVHKk0vG3/WJMerokRSJEAuNGtqNLUiRN\n1QBBCRFq0KD4lbpTp/hTMPSvwt+34yqzYmoRR1z/th4fV7nqCyqXvQt6Iwk3zEYf08yr82/P3cDs\nJTMAuHXME6Q27+JVO7WRtf4gGT9lg4ALLutDi9b+H6T4kiX3EGuvuJ/yHbsJb9mcAZ+9SnSXdsfs\nEwx9Swleh8vtrM0tY12umW2HKzlUbv/bPpFhOjolup8edEmKpFNSJMnRxqoBQmgmC1AaNzVoUBRF\n8ZJlXxFlGw6ATpA0tifCwxSGjv0bKP36fgDiLn4JY+oAr85fXF7Aa3MfxKU5Ob//FQzrMc6rdmpj\nf04Ri77ZBMC547vSsbvn1a6DQdnWXay58n5seQVEd23PgM9eJTzFuwGb0nhYHC425Zez5kAZaw+Y\n2V9qO+b7JoOOTk0j6JR0dJCQEmtCp54gKA2IGjQofqXmBSv+FMj+pTlcFCzaDEDCkPYYE6M9O668\nkOL3rwWHlYgzriFy6PVend/pcvDavIcpqSikW+v+XDXiXq/aqY3Cw+XM/WQdLpckbWhb0oam+v2c\nvlT0Zybrrn8EZ2kZCWf0Ie3DlwmLP3ENBnXtatw0KckptLAm18zaA2Vsz7S9rgAAIABJREFUOVSB\ns0altMgwHX1TYkhrGUOv5GjaxIejr0XdA9W/lFCkBg2KoiheKPxlG84SC8bEaOIHt/foGKm5KP7o\nZlzF+wlrk0bcJa94ff6PfpnJjtwNNIlpztSJL2Hwcj2EpyrKbHwzey02q5OO3ZsxYlxXv57P1/IX\n/sbGO/+JZrPTfPwIer/5NPpwz6t1Kw1fYaWDdblm1hwoY11u2V+LlgEE0CUpkgGtYunfMoauzaJU\ncTSl0VGDBsWvgvlOSs70RcDpsyjlTW0CnDyL0ozH0oHQzaKUnjwUCK4sSqNnZQKnz6IUqP5VvjWP\nso0HEHodSeN7IfSepRktW/g89h2/o4tOJOGGDxEG7z60/rZpPoszv8agD+P+ya8QF9XEq3Y8Zam0\n8+1HazEXW0huFcf4KX3QhdAHpn0ffkvWozNBStpcfxHd/u8+hP7U2aWC+dql+IbNqbE5v5y1ue4p\nR7uLrcd8PzEqjAEtYxnQKoa+KTHEhvvuI5PqX0ooUoMGRVGUWrAXVVCwaAsATc/tiqnZiae3HM+y\nYT4VS/4FOj3x172PPsHzWg417crL4r3FLwJw43mP0LFFT6/a8VS52cqcD9Zw5FA5cQkRXHhNGmEh\nUkhKSkn2y/8j5/XZAHR65Fba33udylTTiO0rtrLqgJm1B8xsyi/H7jo65chk0NGnRTT9W8bQv1Us\nreNMqq8oSg1q0KD4lZq3qfhTffcvzeni8PwNSIeLqK7JHhdxc+Rvo/SzuwGImfgMpk7exVxaUcSr\nc6fhcNkZ1edizu3t3yJkJYWVfP3+akqLLTRJiuLSGwcSFRMaU3o0p5MtD75C7uffI/R6ekx/mFZX\nXuDx8era1TBIKckpsrBsdwkZe0rZV3Ls04SOTSPo3zKGtFax9GgehdHDp4Z1pfqXEorUoEFRFMVD\nRb9ux15QhiE+gqTRnhVx0yxmit+7BmkrJ7z/JUQNv8Orc7s0J/+a/wiFZYfolNKb60ZO86odTxXk\nlzHngzVUlNlIbhXHRdf1JzLK6Ndz+oqzwsKG256k4Ofl6CJM9P3f8zQ778xAh6XUEykl2UcsLNtd\nzLI9pRw0H810FGPSM7h1LP1bxZKWEkNCZGgVJFSUQFKDBsWv1J0UxZ/qs3+Vb8/HvH4/6AXNJ/ZF\nZzr95VNqGiWf3oGrYBeGlB7ETXnN6+kOn/32Bln71xIf1ZT7Jr1CmMF/H+Bz9xbzbdWi5zbtmzD5\nmjSMHvy8wcBeWMLaax6kdN0WwprE0f/j6cT3r/0ULnXtCi2alGw9XEFG1ROFmnUT4sINnJkax1mp\n8fRJiQmKBcyqfymhKDT+CiiKogSQo7iSgvSqdQwjumBq7tk6hvKfZmLb/CMiIo6EGz9CZ/K8WnRN\nf2Sls3DNp+h1eqZOepkmMUleteOJ3TsKmPfpepwOFx27N+OCy/pgCAuNNQyV+/JYc8V9VO7aR3ir\nZAZ88RrRHT0vuKeEFpcm2XKo/K+pR4U1KjA3iTRwVmo8w1Lj6ZkcXat0qIqinJiQUp5+rwZmyZIl\nMi0tLdBhNApq3qbiT/XRv6RTI/ezldgPmYns1Izmk/p69LTAmvUTxe9eDkDCrV8S3m2UV+ffe3gH\nT35yPXanjRtGPcyYtCleteOJbRvz+OHrjWguSY+0loy5sAe6eprjXVfmLdmsveJ+bIcLienRif6f\nziA82fvBlbp2BSenJtlwsIyMPSX8saeUkhppUZtFhzEsNZ6z2sXTrVlUUBdWU/1L8ad169YxcuRI\nn/8CqCcNiqIop1C4dDv2Q2YMcRHuqs8efBBxFuRQ8vGtICXR4x73esBQbill5nfTsDttDO85gdH9\nLvWqHU9sWLWfn+ZtAQn9h6UyYmwXjytcB9qh9KVsuuc5nGUVNDkzjX4fvERYrGfF9pTgZ3dprD9Y\nxrLdJSzfW0qZzfXX91Jije4nCu3i6ZwYqbIdKYofqUGD4lfqToriT/7uXxXZhzCv3Qc6QbMJvdGH\nn37RpGaroPj9a5GWUkw9xxE96j6vzq1pLv79/eMcLs2lffNu3DT6Ub98IJJSsmrpbpYt2gHAsNGd\nGDy8fUh8+HKWV7DtqTc48NkCAJInjqT3v59EZ6r7eg917Qosm1NjzQEzGXtKWLHPTIX96EChdZyJ\ns9q5nyi0bxIREn31eKp/KaFIDRoURVFOwFFqoeDHzQA0Obsz4S3iT3uMlJLSL+7FmZeFPqkj8Ve/\nhdB5N73nq4y32bD7T2Ii4rn/wukYvSwEdypSSn5P386aZXtAwKgJ3el7Rhufn8cfildvYuPdz2DZ\nexCdyUjnJ+6g7U2Xev3fWwk8i8PF6v1mlu0uYeV+M1an9tf32jcJ/2vqUduEiABGqSiNlxo0KH6l\n5m0q/uSv/iVdGocXbECzOYnskETcAM8W01b89hbWzG8RpmgSbvoYXbhnC6aPt2rHL8xd8T5C6Lh3\n4oskxrbwqp1T0Vwai+duYfPaXHQ6wbhLe9O1j+/P42uaw8nOme+R88bHoGnE9OxE7/88TUzX9j49\nj7p21Y8Ku4sV+0rJ2F3C6gPmY4qtdU6MZFg7d9ajlnHhAYzS91T/UkKRGjQoiqIcp2hZNra8UvQx\n4SSd79k6Blv2MsoW/BOAuCvfJCy5i1fnzi3czVsLnwbg6hH30rPtIK/aORWnU2PhlxvI3nIIQ5iO\niVf2o30X/2Vk8pXy7D1svOtZzBu3gRC0u/tqOj10CzqjyrUfSsxWJ39WDRTW5Zbh0I4OFLo3i2JY\nu3iGpcaRHCKFBBWlsVCDBsWvgvlOSs70RQC0f3DMKffLm9oEgBavF53w+zMeSwdg2gtjfRhd/UlP\nHgrA2PzlAY7kqNGzMgFYfHO/U+7nj/5VuauA0tV7QAiaT+iNPuL08+NdxQco+fBG0FxEjbqPiD4T\nvDu3rYwZ3z6A9f/ZO+/4tqq7/7/vvdqWZMl7xna2M53BziiEESDsTft72kKftk8XlJYW6POUPh08\nbaFldEBbCpQWwggtJQkkYSXEhCRkkuFsO95bsmxt6Z7fH1Kc7SzbsZPzfr0U6Z47zrnx0dX5nPMd\n0QAXjr6Cq6Z+/qSu0xORcIw3/7Ge6t1tmC0GbvziFPKL3L1eT28ihKD6+X+y/We/Rw+GsRTkMOH3\nPybt/LI+q3MgP7sGI55glBV7O1he6WVjfSf7FhRUBSbk2LuFQsYgSSB4qsj+JRmMSNEgkUgkSWK+\nIM1vbwIgbfpwLPnHHkyLaAjPc19E97dhGnUxjqseOqm6daHzh4UP0+DZy5DMEXx19v/0uoNnMBDh\njRfW0ljbgc1u4uYvTyUr9+RMqPqLUFMrm+99hNYPVwKQd+tVjPnFdzE4Ti7nhaT/aPNHKa/ysrzS\ny+amLvQDhMLkfAfTil1cVJQqszJLJIMEKRokfYq025T0Jb3Zv4Su07TgM/RQFGtJBqnnlhz7HCHo\nmHc/0Zr1aGlDcP/HX1DUE0+EJoRg7rLfsXbXMlLMDu67/lEspt519uzsCDHv+TW0NXfhdFu55a6p\nuNMH9sC7ceFSttz/K6LtHRjdTsY++kNy5lzcL3XLZ9fJ0R6I8sFuD+WVXrY2+7vLDarC1AIH00tc\nXDAkFafl7B5+yP4lGYyc3d9aiUQiSeIp30W4zotmN5N11fjjmuUPrPgbwVUvgdGC+66/o6aknXC9\nQgheXvYU81e/iKZqfPuaR8hxF57MLRwVT5uf159bg88TJD3Lzs1fnopjADuWxjr9VPz349S9+jYA\nGRefx7jHHzqlZG2SvkMXgg31nSzc1saKKm+36ZFJU5ha4GR6iYvzh6SSYhocmcUlEsmRkaJB0qfI\nmRRJX9Jb/StQ2Yp3VSUokDVnAprt2HbV4d0r8P3zhwCk3vYExoLxJ1yvEIKXlj7Jgk//jqZq3HPt\nLykbeuEJX6cnmht8zHt+DYGuCDkFqdz0pSlYj+P+TheeVRv57Fs/JVjTgGoxMep/vsWQu27q91j8\n8tl1bLzBKEt2tvP2tjbqfWEgYXp0QVEqlwxzc26hE6tRCoUjIfuXZDAiRYNEIjmriXWFuv0Y3BcN\nx1p47NWCaP1WPH+5E+JRbDO+hm3qrSdcrxCCf3z4OAvXvISmGvjudb9i6ojPnfB1eqJur4d//m0t\n4VCMIcPSuf4LkzCZB+ZjX49E2fnos1T+/h8gBM4Jo5jw+4exjyw+3U2THIAQgk2NXSzc1kZ5pbc7\n8lFmipErR2cwe2TaWePMLJGcbShCiGMfdYbx/vvvi8mTJ5/uZpwVSLtNSV9yqv1L6IKG1z4lVOPB\nWpROzs1TUNSeZ7RjbdW0PTkb3deIZeI1uL743An7MQghePGD3/LO2peTguHXTB0x86Tv40js2d7C\nWy+vJxbVGTE2m6tvm4jBMDATn3Vtr+Szb/0vvk07QFUZ+u0vMPx7d5/WUKry2XUwvlCM93a1s7Ci\nlZqOxKqCApxb6OTq0gzOKXCiHeO7I9mP7F+SvmTdunXMmjWr17+QA3PKSSKRSPoBz4rdhGo8aDYT\nmVePP6ZgiHe10v7Mzei+RkzDp+H6wp9OUjD8hnfWzkVTDdx3/aNMGT7jVG7jMLZtbODt1z9D1wXj\npxZw2XVjULWBJxiErlP93Bts//kf0EMRrEPymPD7H+M+d8LpbpqERF+taA6wYFsrH+3xdCdeS7MZ\nuHJUBleOSifLLlcVJJKzBSkaJH2KnEmR9CWn0r+Ce9vwfrIbSPgxGFJ6TiSlh7vw/Pl24i27MOSN\nw333P1CMJ+ZMLITgb+8/yqJ1r2LQjHz3ul/3umDYsKqa997aCgKmTi9m5uxR/e4PcDyEGlrY9N1f\n0LZ0NQD5d8yh9Gf3YLAPjIhOZ/Ozyx+J835yVaHSE+oun5Lv4OrSDM4fkopBriqcEmdz/5IMXqRo\nkEgkZx2xrjDNCz4DwHXBMKxF6T0eL2IRPM99kWj1OrT0ItK+9hqq9cTyGwgheP69X7Nk/WsYNCPf\nu/4xJg3rvYGDEILVy/awfMlOAKZfPoJzZw4dkIKh+d2P2fSdnxH1+DCmpTLusQfIvqp3zbMkJ86O\nlgALt7XywW4P4ZgOQKrFwOxR6Vw1Kp1cp8zQLJGczUjRIOlTpN2mpC85mf4ldEHLws+IByJYCt24\nLxx2jON1vHO/TWT7h6j2DNK+Pg8tNeeE6tSFzvPv/op3N8zDqJm474bHmDT0ohO6Ro9tFIJli7az\nZnkVKHDptWMoO29Ir12/t9BjMXY9+ix7nnwRgIyLz2fcEw9hyc44zS07nLPl2RWJ6by/q50F21rZ\n2RrsLp+Ya2dOaQYXFqViHICmbYOds6V/Sc4spGiQSCRnFd5VewhWt6PaTGTNmdCjH4MQgs5//w+h\nta+jmO2kfe01DJk9i4xD0YXOc+/+kvc2vIFRM/G9G37Tq2FVdV3w7ptb2LSmFlVVuOqWCYyemNtr\n1+8twi3tbPz6j2n/eB2oKiMf/Col3/wCiioHpKeDUEznnW2tvPpZE+2BGAAOs8blI9K4anQGha6B\nm8dDIpGcHqRokPQpA3kmZc+jiwEYev8VPR7XcG8iBGfuE+1H3P/YQ4sA+P4js3uxdf3HopzEAHZ2\n44rT3JL9XP7segCWfGVSj8edaP8K1rTj+XgXAFlXjcdg73lg5P/wd/iXPQ2aEfddL2IsLDuh+nSh\n89ySX/LexjcwGsx8/4bfMLHkghO6Rk/EYjoLX93Izi1NGIwq1945iaGjBl4CtPaVG9j4tR8TbmrF\nlJnGxGd+SvpFAzuC3UB+dp0KwWicBRWtzNvUjCeYEAvD0q3cNC6LGSUuTAM0wtaZxpnavyRnNv0m\nGhRFKQBeBLIBHfiLEOIpRVHcwKtAEVAF3CqE6Eie8yBwFxAD7hFCLEmWTwZeACzA20KIe5PlpmQd\nU4BW4DYhRHV/3aNEIhm4RNr9NM//DAS4zivBVtKzSUxg9Vw63/oJKAquzz+NedTnTqg+Xeg8u/gR\nPvjsXxgNZu6/8bdMKD7/5G/gECLhGP9+aT17d7Vhthi44T+mUFDs7rXr9wZCCKqensuOXzyNiMdx\nn1/GxD/9dECaI53pBCJx3qpo4Y1NLXSEEmJhZIaNz0/K4fwhzgHp+yKRSAYW/TmlEAPuE0KMBS4A\nvqkoymjgAeA9IcQo4APgQQBFUcYAtwKlwJXAH5X9T7WngbuFECOBkYqi7JsqvhtoF0KMAJ4Aft0/\ntyY5GuXl5ae7CZIzmOPtX6F6L/UvryLuDyf8GKYN7/n4LUvoeOU7ADhv+D+sk288oXbpQucvi37e\nLRh+cOPjvSoYgoEIrz/3KXt3tWFLMXHbV84dcIIh2tHJ+rseZPtPf4+Ixyn55uc5Z95Tg0YwnCnP\nLn8kzkvrG/l/r27huU8b6AjFKM2y8fMrhvK760ZyQVGqFAyngTOlf0nOLvptpUEI0Qg0Jj93KYpS\nARQA1wH7wmb8DVhKQkhcC7wihIgBVYqi7ATOVRRlL+AQQnyaPOdF4HpgcfJaDyfL5wG/7+v7kkgk\nA5vAnhaa3tqIiMaxlmSQfe3EHu3oI5Wr8bzwZdDjpFx2HykzvnpC9elC58+Lfs7STf/GZDBz/01P\nML7o3FO9jW66fCHmPb+G1qYuHC4Lt9x1DmkZAyNM6T58m7az/is/Iri3HoPTzvin/pvs2b0bWlbS\nM75QjDe3tPCvLS34I3EAxmWn8IXJOUzKc0ihIJFITpjT4tOgKEoxUAasBLKFEE2QEBaKomQlD8sH\nPjngtLpkWQyoPaC8Nlm+75ya5LXiiqJ4FUVJE0Ic2Rhd0udIu01JX3Ks/tW5uY6WRVtACOxj88i8\nYixKD5Fgoo3baP/L7RANYj3v8ziu+tEJtUfX4/xp0c9Ytnk+JoOZH970JGOLzjmha/SEtz3A6899\nSkd7kLTMFG656xwcqQPHYVUIQd3cBWx98Dfo4QjO8SMpe/YX2Iryj33yAGOwPrs6QjH+uamZf29t\nIRBNhE2dmGvnC5NymJBrl2JhgDBY+5fk7KbfRYOiKHYSqwD3JFccxCGHHLp9StX14rUkEskgQQiB\nd1UlnuWJnAWu80pwTx/R44Ap7qml/ZmbEQEv5nFXknrr4yc0wNL1OM8s+ikfbV6A2WjhBzc9ydgh\nU0/5XvbR0tjJvOfX4O8Mk53v5KYvTcWWMnCy8cYDIbY++Bh1r74NQMEXrqX0599Fs8jY/v2BJxBl\n3qZm5le0EkrmWJiS7+Dzk3IYl2M/za2TSCRnAv0qGhRFMZAQDH8XQvw7WdykKEq2EKJJUZQcoDlZ\nXgcUHnB6QbLsaOUHnlOvKIoGOI+0yjBv3jyeffZZhgxJxDFPTU1l/Pjx3cp/n62h3D717QPtNgdC\new7aTkZNOtbxu29+C4B9QSwP3X/+VQf/IA+Y+zvObfu8g11/Tnd7ysvL+fHok+9fy5cvx7e+mtJw\nwnZ+Z3oXKWoz05SRR72eHuqkdM1P0b31rFNKcQ67i+ma4bjbq+s6mzrfY/mWhXTWxZkz4+5uwdAb\n/x+tTV3UbjUSCkYJ6jUUlI7sFgwD4e8Vqm/C8vSbdFXspsIYpeSrtzHuf74/YNp3Mtv7ygZKe462\n/fZ7S1m6x0OFsYRwXODbvYHSrBR+8PmrKc1Koby8nPJdA6e9cntw9S+5PTi2932urk7E/pk6dSqz\nZs2it1GE6M2J/WNUpigvAq1CiPsOKPsVCeflXymK8kPALYR4IOkI/RJwHgmzo3eBEUIIoSjKSuA7\nwKfAQuApIcQiRVG+AYwTQnxDUZTbgeuFELcf2o73339fTJ48sMP9nSmUl8sENpK+49D+JWI6zW9v\nwr+9ETSFrKsmYB/dcyI2EQnQ9vSNRCtXY8gZTfp33ka1uY67Dboe549v/4TyrW9jNlp54OanKC3s\nvefL3l2tvPmP9UQjcYaVZnHN7RMxGLVeu/6p0jj/AzZ99xHiXQFsQwuZ9NdHcJSeWC6LgchAf3a1\n+CO8trGJt7e3EY0nfscvKErl82U5jMy0nebWSY7FQO9fksHNunXrmDVrVq9b2/SbaFAU5SLgI2AT\nCRMkATwErAZeI7FCsJdEyFVv8pwHSUREinJwyNUpHBxy9Z5kuRn4OzAJaANuF0JUHdoWKRokkjMP\nPRyl8V/rCdV4UEwaOTdMwjokvcdzRDyK57n/ILxlMZq7gPR7FqG58o67zrge448LH+bjikVJwfA7\nSgt7zi1xIuzY3MjCVzcSjwvGTMpj9o3jUAdIdl49EmX7z//I3j+/CkD2nIsZ//hDGBwDyyn7TKOy\nPci/t7bw7o52onri93tasYvPT8pmWLoUCxKJpO9Eg6G3L3g0hBAfA0ebHrv0KOf8H/B/RyhfC4w/\nQnmYRJhWiURyFhHrCtM4by2Rlk60FBM5N03BnO3s8RwhBB2v3kt4y2IUm5u0r887YcHwh4U/ZkXF\nYixGGw/c8hSjC3pPMGxaU8uSf21GCJh8QREXXz26x+zV/UmovpkNX/1vvGs2oxg0Rj38LYq+cqt0\nsu0jonGd8qoO5le0sLnRDyQc9mYOdXFnWQ4ladbT20CJRHJW0G+iQXJ2IpdgJX1JeXk5546ZROPr\na4j5QhjdNnJunoLRdewZ184FPyO4ei6KyUbaV1/FkD3yuOsNhv088dYDbKxcgdWUwgO3/I5R+RNP\n5VYO4tPllSx7ZzsAF84azgWXDBswA/LWZavZ+F8/IdruxZKXxcQ//wz31MPmcAY9A+HZ1eKPsLCi\nlXe2t3Vnb7YaVS4dnsZ1YzMZ4ho4kbMkJ8ZA6F8SyYkiRYNEIhm0RFq7qH95FXowijk3lZwbJ6PZ\njh1RyL/0afzvPwGqAdeXnsdUfPxRjto6m/jVvHuobtmJw+riBzc9wYi83hk0CyEof3cnq5buAeCS\nOaOZfGFxr1z7VBG6zu7HX2DXY38FIUifeQ4T//ATTBkDK6ncYEcIwfr6TuZvbeWT6g6SFkgUuS1c\nW5rBrOFp2EwDx6dFIpGcPUjRIOlTBvJMyp5HFwMw9P4rejyu4d40AHKfOHK6j8ceWgTA9x+Z3Yut\n6z8W5VwIwOzGFae5Jfu5/Nn1ACz5ytHNfQJ7WiipMqBHo91J21TTsR9pwbVv4HszkX8h9Y7fYRlz\n2XG3q7JpG79+4148XS3kuov44c1PkuMuPPaJx4HQBe/N38rGVTUoqsLsm8YxdtLAyG/g313N1gce\no235GlAUhn3vLobf92UU7cwdvPb3s6srHOPdne3Mr2iltiMMgKYkTJCuKc1kfE7KgFltkpw6A/m3\nUSI5GlI0SCSSQceJJm3bR3jbB3hf/gYAjut+iu2c2467znW7l/PkWw8SjgYpLZjM9254DLs19aTv\n4UD8nWHeeWMTVTta0Qwq19xRxvDSrGOf2MfE/AF2P/4CVX96BRGNYUxLZcIfHibz4vNPd9POGHa3\nBXhraysf7PYQTuZXyLAZuao0gytHpZNuM57mFkokEkkCKRokfYq025T0JkIIOlZX0v5RImnbNls7\nV155+TFnYIUQBFe9RMcbP4R4lJSLv4X94m8dd71L1r/G8+89ihA608Zcyddm/xijoXcSq1XuaOGd\neZsIdEWwWI1ce2cZQ4b1HPWprxFC0PDmu2z/6R8IN7QAkH/HHEY+9HXMmWmntW39RV8+uyJxneWV\nXuZvbWVrs7+7fFKenWtKM7mgKBVtgDi9S/oG+dsoGYxI0SCRSAYFQgjaPtiGb10ieU36JaNxBmuO\nKRj0QAcdr99HaP2/ALBd8EUc1/zkuOrU9TgvLX2ShWteAuCmC/+Tmy/6Wq+YicRiOsuX7GBteRUA\nBSVurr51Io7U0+vc2rl1F1sf+i2elRsASC0rpfSR+3BNHnta23Um0NgZZuG2NhZtb6MjlHBsthlV\nLh+ZzpzSDOnYLJFIBjRSNEj6FDmTIukNjpa0bRpFPZ4XqVyN9+9fJd5ejWK247z50eM2SQpHg/x+\nwf/w6c4P0VQDX53938wcd01v3A7trX4WvrKRpnofiqpw0azhnDtzKOppnF2Oen3s/PWzVL/wT9B1\njGkuRv33f5F/+9Uo6sDIDdGf9NazSxeCtbWdzK9oYVW1j32ZkYamWbl2TAYXD3NjHUDJ+iT9g/xt\nlAxGpGiQSCQDGj0cpfHNDYSq2xNJ266fhLXoGEnb9Dhd7z1B16Jfgh7HWDgJ13/8BUPm0OOq0+tv\n49E3vsvuxi3YzHa+d/1jjC0655TvRQjBlnV1vD+/gmgkjtNtZc5tE8gbcvoiEAldp3buAnb84hmi\n7V5QVYbcfTMj7v8KRlfPuS4kR8cXirFkZzsLKlqp9yUcm42qwvQSF9eMyWBMlnRslkgkg4t+ywg9\nkJAZofsPabcpORWOlbTtSP0r7q3H+9J/Edm5HICUS76N46ofoRynD0Jt6x5+Oe87tPoayEzN44Gb\nnyI/veSU7yUcivLum1vY9lkjAKMn5HLZ9WMwW06fo6t33Ra2PvgbfBu3AeA+v4wxj9yHY8zw09am\ngcLJPrt2tgZ4a2sLS3d7CMcTv69ZdiNXj85g9qh03Fbp2CyRv42SvmXQZ4SWSCSS40UIgX9HE23v\nVxD3R447aVto8yK8c7+F8LejOrJwff6PmEdfctz1btq7msffvJ9AuIthuWO5/8bHcaWculNyfbWH\nBa9+hs8TxGjSmHXtGMZOyjttM83hlnZ2/OJp6l5ZCIA5N5PRD3+LnOsulbPfJ0EkrvPRHi/zK1qo\naA50l0/Od3DtmAzOK5SOzRKJZPAjVxokEsmAItYZovW9CgK7mgGwFLjJvq6sx6RtIhrC99bDBJb/\nBQDz6Fmkfv4PaI7jD1u6dNNb/GXxz4nrcc4deQnfvPqnmI3WU7oXXResWrqHFR/sQuiC7HwnV982\nkbSMlFO67km3Jxqj+oU32PXrZ4l1+lGMBoq/fgfD7v0ihpRjZ9GWHExzV4QFyYzN+xybU0wal49M\n45rSDApOs1O7RCI5O5ErDRKJ5IxGCIFvQw3tH+1AROIoJo30GSOrQbBRAAAgAElEQVRxlBX2OPsd\nbdyG98X/JFa/BTQjjjk/JmXmfx23864QgtfKn+Zfn/wVgDnn/D/u/Nx3UJVTc/7t7Aix8LWN1FZ6\nAJg6vZjpl41EM5wep+K28rVU/Oi3dG2vBCDjkgso/fm9pAztneR0Zwu6EKyr62R+RSurDsjYLB2b\nJRLJmY4UDZI+RdptSo6HSGsXLYu3EK73AmAbnkXGpaUYHEefqRVC8P6ff8zYXc9BNIiWMRT3F5/F\nWFh23PVGYxGeeed/+bhiEYqi8uVLf8Dlk2455fvZuaWJxf/cTCgYxWY3cdUtEygekXHK1z0ZgnVN\nbP/f39P41vsAWIvyKP3ZvWRedpE0ReqBQ59dXeGEY/P8ra3UJR2bDarCzKEurpWOzZITRP42SgYj\nUjRIJJLThojpeFbtwbtyD+gCLcVE+qxSUkZm9zgA0wNeOl69F/+Hb0EOWM+5A+dNv0S1OI677s6g\nl8f+9T22127AYrRxz3W/ZNLQi07pfqKROEvf3sbG1TUAlIzKZPZN40ixm0/puidDPBSm6pm57Hny\nReLBEKrVzLB7vkjx1+9As/R/ewYrR8zYnGJkzuhExma3zNgskUjOEqRokPQpA3kmZc+jiwEYev8V\nPR7XcG8iA27uE+1H3P/YQ4sA+P4js3uxdf3HopwLAZjduKJf6w3VemhZsoVoWyIjrmNCAWkzR6JZ\njFz+7HoAlnxl0mHnRfasTORe8NRyXpGd1Ft+g3Xqia0ONHpq+OW879DoqSbNnsUPbnqC4uxRp3Q/\nLY2dLHhlI23NXWiawozZo5h8YdFpmX1uef8TKv77cQKVtQDkXHMJox7+FtaCnH5vy2AkGteJ5o7h\nu/N3sKXpwIzNDq4Zk8EFQ6Rjs+TUGMi/jRLJ0ZCiQSKR9Ct6OErbsp10bkzMxhvdNjKuGIu1MK3H\n84Qep+vd39K16FcgdIxDJidyL2ScWDjU7bUbeOxf99EZ7KAoayQ/uOkJ0h3ZJ30/Qgg2rKxm6Tvb\nicd00jJSmHP7RLLy+j/HQaC6gW0PP0nzOx8BYB9ZQukj3yV92tR+b8tgJBTTeWdbK69vaqbVHwVk\nxmaJRCLZhxQNkj5F2m1KDsS/s4nW9yqId4VBVXCdV4Lr/KGohp4dR+PeOrx//xqR3YnVkJRZ9+C4\n6iE+/mQV06Ydv2j4eOsinnnnf4nGI5QNvYh7rvk/rOaTj2QU8EdY/M/N7K5IRHoaP7WAi+eMxmTq\n30erHo5Q+fTL7H7yb+jBMFqKjeHfv4uir9yKapSP+WPhj8SZX9HCPze14E1GQbI1beUrN17BrOHS\nsVnS+8jfRslgRP6aSCSSPifWlQyjujMxuDbnppJ5xVhMmcf2QQh9thDvK99BBDyozuxE7oVRF59Q\n/dUtO3lp6ZNsrPwEgMvKbuZLl96Ppp78I3DX1ibee2srXb4wZouBy28Yx6jx/W/+0/LBSip+9Nv9\npkjXX8roh7+NJTez39sy2PCFYvxrSwv/3tJCVyQOwMgMG3eUZROv6WJG6elxXpdIJJKBiBQNkj5F\nzqSc3Qgh6PyslvZlO9DDMRSjRtqMETjLhqAcwyY8LdKE9+VvElw9FwDzmMtIveP3aI79g+Fj9a/2\nzmZeK3+GZZvnI4SO1ZTC7TO+xeWTbjlpXwOfN8gHCyrYtTUhgPKLXFx160RS3aeW0+FECdY0sO3h\np2h6exkAKSOKGfN/3yN92pR+bcdgpC0Q5Y1NzSyoaCWUdG4en2PnjrJspuQ7En2jePppbqXkTEb+\nNkoGI1I0SCSSPiHS1kXrkq2EahN5CmxDM8m4rBSDs+fBddxbx3/UP8lMz9sERQw0I85rfoJt5teP\ne6AfDPuZv/pFFnz6dyKxMJqqcdmk27jxwv/EaXOf1P3ocZ31K6spf3cn0Ugck1lj2mUjKTt/CGo/\nOsXq4QiVz8xl9xMvJEyRbFaGf/9uir5yC6pJRvLpicbOMK991sziHW1E44kEC1MLHNxZlsO4HPtp\nbp1EIpEMbGRGaEmfIu02zz5EXMe7qhLPyt0QF2g2E+mzRpMyKqfHQX+8o4Gu954gsOJvEI+AomCZ\nfBOOy+/HkD3iiOcc2r/ieowPP/s3r3/8Jzr8bQCcO/IS7pjxbXLThpz0PTXWdrDkzS001/sAGDE2\nm0vmlOLo54y/LR+upOJHjxPYk3Aiz7luVsIUKe/4M1+fjdR4Q7yysYkPdrWT1ApMK07l9rIcRmYc\nORO2fHZJ+hLZvyR9icwILZFIBjzBmnZa36sg2toFgGN8fiKMqtV01HPivqakWHgBYuGEWJh0A/Yr\n7seYM/q46hVCsG73cl5e9hR1bYmMxyPyxvOFz93LqILjT/Z2KOFQjPJ3d7BhZTVCgMNl4dJrxjCs\ntH8H6cHaxoQp0sKlAKSMKGLMI98jfbqMitQTu9sCzN3QxPJKLwJQFZg13M3tE7Mp6mdzMolEIhns\nyJUGiURyyoQbO2hfvpNgVWJ23+Cyknn5WKxF6Uc9J97Zgv+Dp/CXJzI6A1gmXot99g8w5o457ror\nGyv4x9In2FK9BoAsVz53zvg254269KT9FoQQ7NzSxAcLKujyhVFUhSkXFXHhJcMxmftvrkUPR6j8\n0yvsefwF4sFQwhTpe3dR9J+3SlOkHtja5GfuhkZW1SRWhoyqwmUj07htQja5TpnYTiKRnNnIlQaJ\nRDLgiLR20V6+szsqkmLScJ1TTOo5JahHCVOpd7XR9cHvCJQ/i4gEADBPmIPjih9gzB933HW3dDTw\n6vI/UL71HQBSLE5uuvA/uazsZoyGo69sHIsOT4D336pgz/YWAHILU7ns+rFk5fZv3oXWpavY+qPH\nCeyuBqQp0rEQQrChvouXNzSysSGx0mXWFK4qzeCW8VlkpJx8n5BIJBKJFA2SPkbabZ6ZRL0BPCt2\n07W1HgQoBhXnpCG4zis5qimS7m+n68M/EFj+F0Q4OagbOxvH7B9iLJx43HX7Q528ufJ5Fq2dS9Oe\nDrKGOpk9+Xauv+Au7JaTH9jH4zprP97Livd3EYvGMZkNTL9iJBPPLexXR+dgXVPCFGnBh4A0RToW\n7YEoK/Z2sGRHG9taEiLUZlS5bkwmN4zLxGU9uRUZ+eyS9CWyf0kGI1I0SCSS4ybWFca7cje+jbWg\nC1AVnBMLcF0wFIP9yE7BesCLf+kf8S97Zr9YGHMZ9tk/xDTk+M0EY/Eo726Yxz9X/IXOYAcAY4vO\n4cG7HyHLlX9K91Vf7eXdN7fQ0tgJwKjxOVx89Wjszv5zdI6Hwuz9y6vs/u1+U6Rh932Z4q/eJk2R\nDqG5K0J5lZfySi9bmvzsM7JNtRi4cVwm147JJMUkE7JJJBJJbyJFg6RPGcgzKXseXQzA0Puv6PG4\nhnvTAMh9ov2I+x97aBEA339kdi+2rv9YlHMhALMbVxz1mHgwgnd1Fb51exHJuPb2MXm4LxqG0XXk\n6DN60Id/2dP4lz6NCCVsy82jL8E++wFMxT3Pml/+7HoAlnxlEkIIVu/4gLnLfkejNxE1qLRgMl+4\n+F6G5Y49sZs9hFAwyvIlO9i4ugYEpLqtXHrdGEpG9l9itEh7BzUv/ou9f51HpCXRx3KuuYRRP/k2\n1vzsfmvHQKeuI8TyKi/llR3saA10lxtVhcn5DqaXuJhe4uq17M0D+dklGfzI/iUZjEjRIJFIjooe\nidGxdi/e1VWISAwA24gs0i4aftRsznrIh/+jP+P/8A+I5IqAaeRMHFc+gKnkvOOvXOhs3rua18qf\nYUfdRgDy0oq4c+Z3mDJ85kk7OUPC/n37pkY+XLgNf2cYVVWYOqOYCy4ejrGfZqgDe+uo+tOr1M1d\nQDwYAsAxbgSjfvwtMmac0y9tGMgIIajyhFhe6eXjKi+VnlD3PrNB5dxCJ9OKXZxb6JSrChKJRNIP\nnLWiIdLpw+ToX8fGsxFptzk40WNxOjfW4lm5Bz0QAcBalI57+nAsua4jnhP31hFY8Tf85X9FBBIJ\n3UwjpuOY/QCmYRccd93N3joswbcwh1fw81dbAXDa3Nx80Ve5ZMINGLT9pjon07+87QHee2srVTsS\n184b4uKy68eSmXNkEdTbeNdtofKPLycyOeuJVZuMi8+n5Jt3knbRlFMSQ4MdIQQ7WgOUV3VQXuml\nzhfu3pdi0jh/SEIoTClwYjGofdoW+eyS9CWyf0kGI2etaKh95hP0eBuReCsBvYOwESx5eQydMRNX\n0bCz+odbcvYidJ3OzfV4Vuwm3pmY2TXnppI2YwTWIYeHTxVCENn5Ef7yvxLe/A7ocQBMQy/AfuUD\nmEdMP656Q5EAq3a8z7JN89las5Z9Bk9pjmwumXA9V029E5v51DL2+jvDbFxdw+ple4jFdMwWAzNm\nj2LC1AKUPnZ0FrpO85Jyqp6ei2dVYtVEMRrIu2U2xV+/A0fpsD6tfyAT1wUVzX6WVyVWFJq7ot37\nUi0GLixK5aLiVCblOTBqfSsUJBKJRHJ0zlrRgIiiaulYtHS6XR2bwPP6btr1LcTiTYTiHoJKCFxO\n8iZNIm/K+Rgs/ZsBdrAjZ1IGD13bGvCU7yLqSdiLmzLsuKePwDYs8zARrQc6CH46F//HzxNv3pko\nVA1YJt2AbdrdmIZecEzhrQudbTXrWbZ5Piu3v0c4mavBZDDTqZYRNl/Ey1+7HVU9uunJsfpXPKaz\nZ3sLm9fWsmdHK0JPuMyWTszlc1eNJsXRtzH748Ewda+/Q9WfXukOnWpw2in84g0U3X0zlpz+850Y\nSMR1wWcNXSyv9LJir5f2YKx7X7rNyEXFqUwrdjE+x47Wj5GrDkQ+uyR9iexfksHIWSsafNOzqVm1\nDNXThAOBQ7Nj09IxatkoWipGtQijsQgHQBBiK8JUf/wheryNcLyVIF1ELBqpJcUUnT+NlLwCuToh\nGXQIXZBSMoL0aRfTPP8zAAwuG2nThpMyOuewPh2t3YS//FlC697ozrGguvKwXfglbOf/PzTnsR13\nm711fLRlIR9tXkBzR113+aj8icwcdw3nj76U6/++K3HtHgRDT7Q0drJ5bS1bNzQQ9CfMqxRVYVhp\nFlMuLGLIsKMnnesNIq0eql/4J3ufe4NouxcAS0EOxV+7jYI75mCwp/Rp/QOVBl+YJTvbWbKjjRb/\n/hWFbLuJ6SUuphW7GJ1lQ5XPUolEIhlwyIzQByCEoGZvE5s/XEy0Zjsp0SBOzUKK5sJsyELVskA5\nss4Seph4vJmQ7iWkhlFddrLGjiW37FwMTsdZKyik3ebAI9oRJFjVSrCqjWB1O3ooMXjT7GbcFw7D\nMS4f5QAzEBENEdz4FoHyvxKt+rS73DRyJinT7sY8djaK1vP8w6HmR/tIc2Qzc9wcZoydQ27akBO+\nlwP7VzAQYdvGBjavq6Opztd9THqWnXFT8hlTltfnKwv+PTVU/ekV6l5diB5KiBXnhNGUfONOsud8\nDtVw9s3ThGI65ZVeFu9o6066BpDjMHHxMDfTi10MS7cOuGekfHZJ+hLZvyR9icwI3Q8oisKQ4hyG\nfPmLh+3r9AVY/9HHtG9ehdHfjlNVcWoOrFo6Bi0LRUvFoBZipxA7gB9iq+PUrP4EoXcRjbcQ0n3E\nzDq2vGxyJk4mdXgpmkVmKZX0LfFQlFB1O8G9bQSq2oh5AwftN6RacU4agnNSIaph/8x+rK2awIoX\nCK78O7q/DQDF4sR67h2kXPRlDNkje6y3J/Ojc0dewsxx1zB2yNSTXk0A0HVB5Y4WNq+tY9fWJuLx\nxCSI2WJg9MRcxk0pICff2ecDUs+nm6h6+mWa3vkIkhMxmZddRMl/3Yn7grIBNyDua4QQVDQHWLyj\njWV7PASiCYdvs6YwvcTF5SPTmZBrlysKEolEMoiQKw2nSDSus2PTTnZ+8iF60x5SYmGcBjN2zYlF\ny0DTskE9chx7AD3uJRJvJaIEwGEkdWgxWWMmYskvRDNJTSc5cURcJ9zQQaCqjeDeNsINHd0DWQDV\nbMAyJA1bUTrW4nQMLlv3oFboOuFt7xP4+DnCW5d0n2fIH0/KtLuxTL4J1dyzac3xmB/ZzKcWqai9\n1c+WtXVsWV9H174IOwoUD09n3OQCho/JwtBL8fqPhh6N0bx4OVXPzMW7ZnOiCSYj+TfPpvhrt2Mf\nVdKn9Q9E2gJR3t/ZzuIdbdR07I98VJpl44qR6cwc6pbhUSUSiaSPkSsNAxSjpjK2bBRjy0YdVC6E\noLnFx6YVq2mtWI2pqxmnouM0pGA3uDCpGaiGbFTNhUVzJZyxQyC2QtPWHSC2oeteIno7US2MwZ2C\ne/hQ3CPHYs7JPmhGWHJ2I4Qg6gkkTI72JkyORCS+/wBVwZLnwlqcjrU4A3OOE0U9OAqN7m8nsOof\nBD5+gXhbVaJQM2GddD22i+7CWHzOUWfLhRDUtu1hzc5lrN21jF0Nm7v3pTuymXEK5kcHEgnH2L6p\nkc1ra6nb6+0ud6XZEuZHk/JwuqynVMfx0LWzirq5C6l7/Z3uZGxGl4PCL91I0V03Y87qW3+JgUY0\nrrOqxsfi7W18Wusj6WuO22rg0uFpXDEynSFuGUBCIpFIBjtSNPQRiqKQnZVK9vWXwfWXHbQvEI6y\na3MV21Z9TLShArveSapmwKnZsWluTFoWaJmoWhoWLS0hKDogtFanYe0mhNiIrnuI6l50cxRTlgt3\nyVAcw0Zjzko/yB79dCPtNvuGeCBCsLqNYFXC5GhfeNR9GNNSEiKhKB3rkDTUQ1athB4n1rSDaM0G\nIjs+IrjhTYglZoY1dyG2i76M9fwvoNkzjly/HmNbzXrW7PqItbuX0ezdv6LQbX40/tqE+ZFy8v1R\n6IKaqnY2r61jx+YmYtGEGDKaNEaNzyGo13D9zdP73Pwn1uWn8a0PqH15fveqAkDKiCKGfPFG8u+Y\ngyGl7wXLQKKyPcjiHW28v8tDRygR/UhT4MKiVK4Ymc45hU4MpynyUW8gn12SvkT2L8lgRIqG04DN\nbGTClBFMmDLioPK4Lqhv9LBt1WZqt63G0FFNqhrGZTDhMDiwqW6MWhaKlommpaNp6aADjdDZGKDz\nk3UIoaPr7UTxgVVgyXThHFJESmEJpqwMVIvxrLOvHuzo0TiR1k4iTZ2EmzoIN/qINHcedIxqNSYE\nQnE6tqJ0DM79A1ihx4k2biNavYFo7QaiNRuI1W3ujn4EgKJgLr0U27S7MZdeinIEP4NAuIuNlStY\nu+sj1u/5GH9ov7Ox0+Zm8rDpTBk+g/FF52MxndwAWuiC1uYuairbqa30UFvVTqAr0r2/oNjNuCn5\njByXg8lsoLy8o8/6sxACz6qN1M1dQONbH3RnbdZSbOReP4v8O+bgmjLurPo+dYZjLN3tYfGOdna0\n7u8/RW4LV4xMZ9ZwN26rsYcrSCQSiWSwIn0aBgkdgQh7tlazY+1neGo3kBJuxmWIkWq04NQc2NSE\nQzZaJvQwsyv0IHE6EMYIBqcZW3YmKfmFmPLyMbkdqOazR0fueXQxAEPvv6LH4xruTQMg94n2I+5/\n7KFFAHz/kdmn3CY9EiPS0km4yUe4yUekyUek1X+QTwKAoqlY8vebHJmyEhG6hB4n1ryLaM2G7ldC\nIPgPq0tLG4KxcCKVL67EW+Pgkl1rDjum1dfIut0fsWbnMrZUryGu74+nn5dWzJThM5k6fAYj8saf\nlEOzHtdpbuiktqqdmkoPdVUeQsHoQcc4Ui2MnZTH2Cn5uNP7PlRpqKGFutffoW7uAgKVtd3l7vPL\nKLhjDtlzLj5rVhWEEFR7Q2xs6GJ9XSera31Ek87mKSaNi4e5uWJkGiMzbGeVeJJIJJKBzKD3aVAU\n5a/AHKBJCDEhWeYGXgWKgCrgViFER3Lfg8BdQAy4RwixJFk+GXgBsABvCyHuTZabgBeBKUArcJsQ\norq/7q+vSbWZmDR1OJOmDgdu7C6PxnVq6j3sXreTvdu2EG55Dyde3EZBqtGCXbVjU10YtQzQMlFU\nGwasEAc8EPRAcFsdkDAv0YUfofpRrWBy27HlZGPOzceUmY7BaTnMzEVy8ujhGOHm/eIg3OQj2nb4\n4B4FjBl2zFlOzDlOTFkOzDmpKBpJgbCIzhUbiNRsIFa76cgCwV2IsXAixsJJifeCiaj2hO39qgcv\n7D5OCEFV83bW7vqINTuXUtW8fX8zFJXRBZOYMnwGU4bPJC+t6ITvOR7TaazroLaynZoqD/V7PUTC\n8YOOcaRa2B4Hj8XIb/7fRNwZKX0+INUjUZrf/Zi6uQto+WAl6MloPzkZ5N96Ffm3X03K0MI+bcNA\nQAhBvS/MhoYuNtR38llDF54DEq8pwKQ8B7NHpXFhkQuzYeCYQkokEomkb+nPEeDzwO9IDOz38QDw\nnhDi14qi/BB4EHhAUZQxwK1AKVAAvKcoygiRWBZ5GrhbCPGpoihvK4pyhRBiMXA30C6EGKEoym3A\nr4Hb++/2Tg9GTWVoYTpDC9PhuvO7y4UQtPkjVG2vYeuGPdRX7SLcuZwUpRWXKYbLZMSp2bArDixq\nOgYtA6FloqopIFIgANEAdNR1AtsOuG4ItBCqRWC0WzC5XZjS0zBkZGJMtaHZLWg2E0rSllnabSaI\nByNEmg9eQdiXefkgVAVTuh1TthNz8mVMtyA664m17iHeupLIp7sJ1G4iWrcJEe467BKauwBDYRmm\nwjKMBRMxFpZ1C4Qjtk0VNBYKnnv3V6zdtYy2zqbufWajlYklFzBl+AwmDZ2G0+Y+ofuORuI01HgT\n5kZVHhqqvcRi+kHHuNJtFBS7KShJo6DYTarbyhV/3QBAWqa9x+ufav/qrNhN7SsLqH99cXcSNsVo\nIOvKGRTcMYf0z517xudWaOwMs6G+i40NnWys76I1cPBKj9tqoCzPwcRcO1MLnGTZz44w0fLZJelL\nZP+SDEb67ddQCFGuKMqhU5PXATOTn/8GLCUhJK4FXhFCxIAqRVF2AucqirIXcAgh9mWYehG4Hlic\nvNbDyfJ5wO/76l4GA4qikGE3kzFlOFOnDAcu794XjunUtnSxd2sle7ZU0VZTQzCwC6P6EalmP26L\nSqpmJlWxkaK4MKsZKIZMhJaOolhAtyACEAlApDkMNCRfCQQ6ihZGMwtaG/fQ3KpjSHNjTE/D4LCg\n2S0Y7GYUo3ZGmDQogEWBUJ2HWGeIWGeYWGeQeGc4se0LEfeHDz9RUzBlODBnOzFlWNBMnWjxeuKe\n9cRbK4lVVRJurSTuqQE9fvj5gOrKx1hYlnwlBMKRnJejsQgtvgaavXU0d9Qd9F77jQgxE7D+NQDc\nKRlMHj6DqcNnMrboHEyG40+IFgxEaKztoLbSQ01lO411Hejxg02r0rPsFJS4KSxOI7/YjSO1fyPr\nRDs6aXjzPermLqBjQ0V3uX30UAruvIa8Gy/HlHFi4mgw0eKPsDEpEjbUd9F0gM8IQKrFwIRcOxNz\n7ZTlOih0mc+I76lEIpFITo3TPYWWJYRoAhBCNCqKkpUszwc+OeC4umRZDKg9oLw2Wb7vnJrkteKK\nongVRUkTQhzZEP0sxmxQGZbrZFjuRJg1sbtcCEFrIEp1bTt1W/ewt6IWX0M9wXALqrYLi7kdmzVC\nqgFSFQ2HYsGOA6viwqi5EaoboaWhaE6IW4kHYIJzHF07g0AQqD+kJTqKqqMYQDEoqEYN1aShmEyo\nFjOqxZJ4N2moRg3FaEjsN2qoJkOizKShGg0JAaIpiVCiqpJY6VCVUx7sCF1H19IQWjpd2xqToiBE\nPPke6wxxvSsh0upfXn3U6ygGFWO6DZNTRzN6UWO1ENiG3rqH2O49BDoajnouioLmLkDLGIqWUYwh\nvQRD3piEQHBkJv4nhY63q41mbw3Ne1cdIg7q8XQ2IziK/5IJ3C0Kn7v2LqYOn0lJTulxRTwKdEVo\nqu+gud5HY52P5nofHZ7gIW2HrDwnBcVuCkvSyC9yY+vFmerjmamLdfnxbdpBx4YKvGu30PLex93Z\nmg2OFHJvuJyCO67GWVZ6Rg6O2wNRNjbsFwn1voMFrN2kMT7XTlmunbI8B0Vui0y6xvH1LYnkZJH9\nSzIYOd2i4VB60ytb/uqdIIqikJliInNUDlNG5cAN+/cFo3HqOkLUVLXQuK2SPbvqCDW0E/d7iRu6\niFtqUW3bMFg6SNF8uNFxYSCVFBxKKlbFhUF1IbQ0hOZGaG5QTAhdRUSASMLNIvHvPpHRGzdFUkCo\nKFryfZ+oSFLz/Mf7y5L7RVxPiAN/GHL+AEDz/I1HrSYSj2BLBU0LoSh+FDpQ420QbYFQPaJtO2Jv\nM3H23echqAa0tCEYMkrQModiSC9OvGeUoLgL8MfCdAa9+AIefAEPrb4GmlY+R0tHHU3eOlp8DURj\nR1jN2Hd5RSPTmUNmah7ZrnwyU/OT73lsueirWIIKsx/9xlHP93eGaaxLCISmOh9N9T46O0KHHWcw\nqmTlOskvdlNQ7Ca/yI2lH6PpxENhOrfuomN9BR0bt+HbUEHXzqrDHMnTpk1JODVfORPNdmblEAhE\n4mxs6GJdnY/19V1Uew/+O9mMKuNzEisJE/McDE2zog3i0KgSiUQi6R9Ot2hoUhQlWwjRpChKDtCc\nLK8DDvQ6LEiWHa38wHPqFUXRAOfRVhnmzZvHs88+y5AhiWRTqampjB8/vlv5l5eXA8jtI2wPz0ih\nPFRLYXEx06Z9ASEE77y/jJauCJk5w2nesZeNSz8g1tZBiSmTmvY9xE0RwrYWsofG0Sy7aa7bjZVO\nRuer2ISgujaGGY2p+S6swkRFfQiDMHBhfhaKauHT+k7AxNTCIlDNfFrbAoqJqUNGIVQLa2qqEYqJ\nqUVjAJU11TsBlanF40HAp3u2ACT3w5q9Ww/a/mTt6h72C9ZWr0MRfs4pSEOJNvPpnk0ouo9zs2Mo\n8XY+rWtHQefcHABY3Zh4P2y70IIhvZhPvQ50ezplUyfgt6Xy0fYGOlWVwlE5+AIePlu/hcDm7aQW\nGPEFPezd1ogQOmlFiYg97XsTgurQ7aLRuWS58gnUK7jsGb6Ba3oAABs2SURBVEyfNo1MVz5VFfU4\nbS5mzvjc/r9nHC4sTfx9m/7+KPsQQvDukg/xtPgpyBlNU52PT1auIBSIUpSf+P/ZW5f4/xleMp6s\nXCctHbtIy0jhiqtmkZ6ZwopPVgAtDBs96qT7249HH/v4C887n3dfeR3/rmr8u6sZ1uSns2I3WyKJ\nULBj1ESkpQolhLU4n+kzpuOcOJrtFp1IdgZ5A+D71BvbH320nJqOMKJgHOtqfaz65GPiApzDygAI\nVX1GidvClZfOpCzXQfO2dahqJ9MmDIz2D9TtfWUDpT1y+8za3lc2UNojtwf39r7P1dWJ+D9Tp05l\n1qxZ9Db9GnJVUZRiYL4QYnxy+1cknJd/lXSEdgsh9jlCvwScR8Ls6F1ghBBCKIqyEvgO8CmwEHhK\nCLFIUZRvAOOEEN9QFOV24HohxBEdoQdjyNXBSEwXzH/3Q3JGT6GupoWWHdV07aklVtuIyefHGo1i\njAsw6AQdRoJ2lVCKQsgqiJhixBQ/KD400YERHybRhQk/ZhHBJnSsehyrrmMVOlZdxyQEJrHvPflZ\nVzEIBZOiASooBkBFKBqgwSHv3eXEUeLtKHEPyhHWBmJGCzGjlZjRQtRoIWo0EzaYiBhMhA0mQpqB\nkGogpBkIqirtCBqiIXwh70H5DY6XFLMDh82N0+bGaXWR4cw5YLUgn6zUPKzmY4cjFbogHI4RDkUJ\nB2OEQzEC/gjNDYnVg6Y6H0F/5LDzTGYDWXkOsvNTyc5zkp3nxJ2RgtpPM9RC1/HvqqZjQwUdGyvo\n2FBB55adbA54usUBAKqKfUQRqWWlOCeWklpWimPMMDTL8ftlDAYafGHW1nWyrs7Hhvouug7IAK4q\nMDozhcn5DibnOxiVacM4gBI+DhbKy6WjqqTvkP1L0pf0VcjVfhMNiqK8DHwOSAeaSDgtvwm8TmKF\nYC+JkKve5PEPkoiIFOXgkKtTODjk6j3JcjPwd2AS0AbcLoSoOlJbpGg4/fgjcRo7w9T7IjR4A7RU\nN9NR3UCwrgm9sRl7hxd7IIAtEsUU01ENRmI2B1GrnXCKlaBdI2RTCFt1YoqfqBogrgSJK0FiSij5\nHkyWhYgTwEgUoxCYk8LCeKjA2PdZ11GBgKoSVFUCikpQ1QioKgFVJaSo6Kdg862gYLemJgWAOykG\nXDitSVFgS5ZZE+UOqwtVMRCP6cTjOvGYTiQS6x70h0NRwqEYoWD0oO1w93aMUFIkRCKxYxoBWqxG\nsvKcZOc7uwWCK812kElXX6CHI4QamgnVtxCqbyJY30y4vpnO7ZX4Nm0n3nV4tClbSUFSIIxOvI8f\niSHF1qftPB10hWNsqO9ibZ2PdXWdNHQeLOzynGYm5zuYku+gLM9BiunEc2ZIJBKJ5Mxg0IuGgYQU\nDQObuC5o9kdo8IVp6Ey8N7X46NjbQKC2CXNbG46OdhxeDw6fF1sojCUeRzdZiVlTEi9LCnFrCjGr\nnZglURa1GIkroW4xsU9cHElo6EoMBQ1130sxoCoGNEVLvhtQVQOamvisqQYMqgFNNaJpBgzJd2P3\nuwUjKRiFHU3YEHoiZ4Ee14nHxX5BkBQF8bhI7EuW9+bX1GQ2YLYaMFsMWCxGzFYjGVl2svOdZOU5\nSXVbe90hWI9ECTW2EqpvIlTffMBr/3ak1dPjNSz52aSWlZJaNjqxijBhFEaXs1fbOVCI6YKKZj/r\nkqsJ21sC6Af0AbtJY1JyJWFyvoNcx5m1kiKRSCSSk2fQJ3eTnJ2czBKspirkOsyHDITygVKEEHSG\n4zQkVykSqxVhGrwhPA2tRBtasHd4cHR4cPg82Gv3Jj53eEjp6kQ3WRJC4jBxkUbMkiiPpziIm8zo\nitpjdu2eiCVfh7smB5KvE0NRQDOoaJqKqqmYzFpiwG8xYLYYu0WAeV+Z1YjFYsDULQwS+0xmQ6+a\nFOmxGNH2DsIt7URaPURa2gk3tyfEQEMLobqEKAi3tB/mjHzYPWoa5pwMLPnZWHIzseRlY8nPwlaU\nT2pZKebMtMPOOVOW+IPROFWeENtbAqyr8/FZQxeB6P58FpoC43PsTEmKhBEZNum83MecKX1LMjCR\n/UsyGJGiQTKoUBQFp8WA02JgVOahNvyjiMR0GrsSqxP1yZWKquTnJl8IU0cHjg7PfmHR4cXR0Yaj\nYRcun4eUTh/KAYNboSgINeEDITQNoe57qQdvGwxoDjuaw45iT0G1p6DaUvj/7d17cFzlecfx77O7\n2tVasmTJki1LvmDjcIeYS0yAdOjUCThtEpimSciVNpC2NCGBhtycTOm0TUobiCE0ZDpxnEmg1FB3\nJtA0MW6gzdQ1tknwJWBztfFFyFiybMmytKu9vP3jnJVWt7Vs63i1q99n5sye9z3n7L6reebVPuc9\n7zmhqjjE44Qro0QqIkSiEcLRCJFYBZFohEhllIpYlEi8wluPx6iIR6mYVklkWoyKaZVUVEbP2NwB\ngExvwksCDvtJgJ8M9HccyUsOjpDsOELqSNcJkwEAQiEvIWieRbx5NrHmRuLNs6lsnuUnCbOIzarH\nwuV9WY1zjvbjKXZ39rH7cJ/32tlHa1dyxFVj82pjXD63hstapnNJUzXTdMmRiIgUkS5Pkikj6xwd\nx1MDlz3tXL+LjnCY7uZ62o4lOZbMEMpkqDrWRdWxLir7eon19VGZ6CXW10s80UttKkF1f4Iqvy7S\n20v2SDeR1Ni3Oz1dFg4TikUJVUYJV8YIxaJYJIxZ7pkUea9mWDg85PaxWO42s/n7hQb2aV/v3X0h\nvqCZ/o6jZI6fxEiIGRV1tcQa64g21BFtrCfWWE/lnFmDCUHzLGKzZ57Uk5WvW7UVgPW3XnpSf6vJ\npD+dZe/RxIgE4Vhy5MT6sMG8GZWcPTPOkubpXNo8fco8eVlERCaWLk8SOU0hM2ZVR5lVHeXtwDlP\nHgdg0Y1XAXAsmaatu98blejpp+N4P4eOp2h7aQudFbPojoz9lGDLZIgl+piW6KXR9TM7m6Q+k6Q2\nlWB6f4J4JkVlJkU0kyaSThFOp8gm+8kkkmQT/WQTSTLJfrJJfz0xuO4yGTK9fWR6+0gF+Pfp2+s9\nfM+iFcQa64k21BFrGEwGog11g/X+a0V97UklA+Wqs3dw9OB1PznYfzQxZB5CzvRYmEX1cRbNjHN2\nfZxF9XHm11US1R2ORERkEtN/ewlUKV23OT0WYXpjhHMah959p+0/rwBg5n0dHO5N0d6TouN4P+3H\nvdeNzx0gGQkTbphBZ181ncDLJ/isSMiYURlhRjxCXbyCunjEW6Z56/UDdRVUhR0k+8km+r3EIpHE\nZbK4bBac816zWVzW4TJZcN66V+evD6nLe3VZnr/5KwD8zsbHiDbUEZleVTJPRj6T8ZXKZHmrp5/W\nriSt3Ulau5Ic6Eqyp7OPo4n0iP1D5l1itGimlxicPTPOwvo4DdMqSubvO5WVUt8lpUfxJaVISYPI\nOEXDoVEmaEPfz7yHx9312eX0Z7IjEov24/109qY52pfiSF+aI30pelNZOnpTdPSmONHTr8MGtXnJ\nxYx4BTMqK6ipDFMbi1BTFaHWn+dRWxmhOho+pUmyVYvmnXinMpfOOt46NpgUtPrzYVq7vNGn0UYO\nwHvKcv7IwaKZcRbUxamMaPRARETKg5IGCdRUO5MyVmIxXDKd5YifRBz1EwlvPZdYeHVH+9L09Gfo\n7E3T2TvybPZoDO8SmFwSUVMZoSYWHpJY1MS819rKMH3xKiLpFKlMlkjISuos+KnEVybrOHisn9bu\nBK1d3l24WrsTvNmd5OCxsRMDA2ZXR2muidFSG6PFfz2rrpLZ1dGS+rvJiU21vkvOLMWXlCIlDSJF\nEIuEaJoeo2kc99fvz2Q5Oiy56E6k6Uqk6U76r4nMQPlYMkO3vxzoGscE7a//IwAP/mg74I1sRMIh\nIiEbsoRDRkXuNWyEzd8WHrk9/5hIyLz3zC+Psk9uPZz34/u5/d0Df4P+jCPlvybTWfozWVIZN7Bt\nYJ90lmReXSrj6E/7x2WyHOlNkSmQGMyqrvASgppKmnPJQU2Mppqo5h2IiMiUpbsnSaB03eaZl8k6\nupNeYtGd9JOJXJKRSNOVzAwpdyczpDNZUlk35ln2yar79W3UnL3kpI9rrKqgpTbmjRrkjRzMmR4j\nqkuKBPVdEizFlwRJd08SkXEJh8yf/1Bx0sdmnSOTdaRHWTJZRyoz9vZ01pHO+Pu6wWMKvaazDK77\nnz18H4BoJEQ0bETDQ1/3huq58PJmomGjIn9bJLfP0LqKUIgZ8QgxJQYiIiInRUmDBEpnUkpLyIxQ\n2KgoleeILW0pdgukTKnvkiApvqQU6XSbiIiIiIgUpKRBArVhw4ZiN0HKmOJLgqLYkiApvqQUKWkQ\nEREREZGCdPckmbJ2f/spABZ96fqC+7XdUQ/AnPs7R91+74p1ANz1reUT2LozZ13T1QAsP7ixyC0Z\ndN2qrQCsv/XSIrdERESktAR19ySNNIiIiIiISEFKGiRQum5TgqT4kqAotiRIii8pRUoaRERERESk\nICUNEijdi1qCpPiSoCi2JEiKLylFShpERERERKQg3T1JArVhwwadUZHAKL4kKIotCZLiS4KkuyeJ\niIiIiEhRaKRBRERERKRMaKRBRERERESKQkmDBEr3opYgKb4kKIotCZLiS0qRkgYRERERESlIcxpk\nytr97acAWPSl6wvu13ZHPQBz7u8cdfu9K9YBcNe3lk9g686cdU1XA7D84MYit2TQdau2ArD+1kuL\n3BIREZHSojkNIiIiIiJSFEoaJFC6blOCpPiSoCi2JEiKLylFShpERERERKQgJQ0SKD3xUoKk+JKg\nKLYkSIovKUVKGkREREREpCDdPUkCtWHDBp1RkcAoviQoii0JkuJLgqS7J4mIiIiISFFopEFERERE\npExopEFERERERIpCSYMESveiliApviQoii0JkuJLSpGSBhERERERKUhzGmTK2v3tpwBY9KXrC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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import scipy.optimize as sop\n", + "\n", + "ax = plt.subplot(111)\n", + "\n", + "\n", + "for _p in risks:\n", + " _color = next(ax._get_lines.prop_cycler)\n", + " _min_results = sop.fmin(expected_loss, 15000, args=(_p,),disp = False)\n", + " _results = [expected_loss(_g, _p) for _g in guesses]\n", + " plt.plot(guesses, _results , color = _color['color'])\n", + " plt.scatter(_min_results, 0, s = 60, \\\n", + " color= _color['color'], label = \"%d\"%_p)\n", + " plt.vlines(_min_results, 0, 120000, color = _color['color'], linestyles=\"--\")\n", + " print(\"minimum at risk %d: %.2f\" % (_p, _min_results))\n", + " \n", + "plt.title(\"Expected loss & Bayes actions of different guesses, \\n \\\n", + "various risk-levels of overestimating\")\n", + "plt.legend(loc=\"upper left\", scatterpoints = 1, title = \"Bayes action at risk:\")\n", + "plt.xlabel(\"price guess\")\n", + "plt.ylabel(\"expected loss\")\n", + "plt.xlim(7000, 30000)\n", + "plt.ylim(-1000, 80000);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As intuition suggests, as we decrease the risk threshold (care about overbidding less), we increase our bid, willing to edge closer to the true price. It is interesting how far away our optimized loss is from the posterior mean, which was about 20 000. \n", + "\n", + "Suffice to say, in higher dimensions being able to eyeball the minimum expected loss is impossible. Hence why we require use of Scipy's `fmin` function.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "______\n", + "\n", + "### Shortcuts\n", + "\n", + "For some loss functions, the Bayes action is known in closed form. We list some of them below:\n", + "\n", + "- If using the mean-squared loss, the Bayes action is the mean of the posterior distribution, i.e. the value $$ E_{\\theta}\\left[ \\theta \\right] $$ minimizes $E_{\\theta}\\left[ \\; (\\theta - \\hat{\\theta})^2 \\; \\right]$. Computationally this requires us to calculate the average of the posterior samples [See chapter 4 on The Law of Large Numbers]\n", + "\n", + "- Whereas the *median* of the posterior distribution minimizes the expected absolute-loss. The sample median of the posterior samples is an appropriate and very accurate approximation to the true median.\n", + "\n", + "- In fact, it is possible to show that the MAP estimate is the solution to using a loss function that shrinks to the zero-one loss.\n", + "\n", + "\n", + "Maybe it is clear now why the first-introduced loss functions are used most often in the mathematics of Bayesian inference: no complicated optimizations are necessary. Luckily, we have machines to do the complications for us. \n", + "\n", + "## Machine Learning via Bayesian Methods\n", + "\n", + "Whereas frequentist methods strive to achieve the best precision about all possible parameters, machine learning cares to achieve the best *prediction* among all possible parameters. Of course, one way to achieve accurate predictions is to aim for accurate predictions, but often your prediction measure and what frequentist methods are optimizing for are very different. \n", + "\n", + "For example, least-squares linear regression is the most simple active machine learning algorithm. I say active as it engages in some learning, whereas predicting the sample mean is technically *simpler*, but is learning very little if anything. The loss that determines the coefficients of the regressors is a squared-error loss. On the other hand, if your prediction loss function (or score function, which is the negative loss) is not a squared-error, like AUC, ROC, precision, etc., your least-squares line will not be optimal for the prediction loss function. This can lead to prediction results that are suboptimal. \n", + "\n", + "Finding Bayes actions is equivalent to finding parameters that optimize *not parameter accuracy* but an arbitrary performance measure, however we wish to define performance (loss functions, AUC, ROC, precision/recall etc.).\n", + "\n", + "The next two examples demonstrate these ideas. The first example is a linear model where we can choose to predict using the least-squares loss or a novel, outcome-sensitive loss. \n", + "\n", + "The second example is adapted from a Kaggle data science project. The loss function associated with our predictions is incredibly complicated. \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Financial prediction\n", + "\n", + "\n", + "Suppose the future return of a stock price is very small, say 0.01 (or 1%). We have a model that predicts the stock's future price, and our profit and loss is directly tied to us acting on the prediction. How should we measure the loss associated with the model's predictions, and subsequent future predictions? A squared-error loss is agnostic to the signage and would penalize a prediction of -0.01 equally as bad a prediction of 0.03:\n", + "\n", + "$$ (0.01 - (-0.01))^2 = (0.01 - 0.03)^2 = 0.004$$\n", + "\n", + "If you had made a bet based on your model's prediction, you would have earned money with a prediction of 0.03, and lost money with a prediction of -0.01, yet our loss did not capture this. We need a better loss that takes into account the *sign* of the prediction and true value. We design a new loss that is better for financial applications below:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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qjP+a0sXLmd4+zfX0B3vTKLOytyAKhUJhKWRZGb/tP6qnXXp1ofF9zvUokUKh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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "\n", + "def stock_loss(true_return, yhat, alpha = 100.):\n", + " if true_return * yhat < 0:\n", + " #opposite signs, not good\n", + " return alpha*yhat**2 - np.sign(true_return)*yhat \\\n", + " + abs(true_return) \n", + " else:\n", + " return abs(true_return - yhat)\n", + " \n", + " \n", + "true_value = .05\n", + "pred = np.linspace(-.04, .12, 75)\n", + "\n", + "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred], \\\n", + " label = \"Loss associated with\\n prediction if true value = 0.05\", lw =3) \n", + "plt.vlines(0, 0, .25, linestyles=\"--\")\n", + "\n", + "plt.xlabel(\"prediction\")\n", + "plt.ylabel(\"loss\")\n", + "plt.xlim(-0.04, .12)\n", + "plt.ylim(0, 0.25)\n", + "\n", + "true_value = -.02\n", + "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred], alpha = 0.6, \\\n", + " label = \"Loss associated with\\n prediction if true value = -0.02\", lw =3) \n", + "plt.legend()\n", + "plt.title(\"Stock returns loss if true value = 0.05, -0.02\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note the change in the shape of the loss as the prediction crosses zero. This loss reflects that the user really does not want to guess the wrong sign, especially be wrong *and* a large magnitude. \n", + "\n", + "Why would the user care about the magnitude? Why is the loss not 0 for predicting the correct sign? Surely, if the return is 0.01 and we bet millions we will still be (very) happy.\n", + "\n", + "Financial institutions treat downside risk, as in predicting a lot on the wrong side, and upside risk, as in predicting a lot on the right side, similarly. Both are seen as risky behaviour and discouraged. Hence why we have an increasing loss as we move further away from the true price. (With less extreme loss in the direction of the correct sign.)\n", + "\n", + "We will perform a regression on a trading signal that we believe predicts future returns well. Our dataset is artificial, as most financial data is not even close to linear. Below, we plot the data along with the least-squares line." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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4+EOx8Ivi4ZfYeMSe+d24cWPT39lMpUnUyG8pxact6VOp5L5vDztOfqg26X0f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\n0uWTnZqzELTmLLkvcW1JsTeMRUSkMJl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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "## Code to create artificial data\n", + "N = 100\n", + "X = 0.025*np.random.randn(N)\n", + "Y = 0.5*X + 0.01*np.random.randn(N) \n", + "\n", + "ls_coef_ = np.cov(X, Y)[0,1]/np.var(X)\n", + "ls_intercept = Y.mean() - ls_coef_*X.mean()\n", + "\n", + "plt.scatter(X, Y, c=\"k\")\n", + "plt.xlabel(\"trading signal\")\n", + "plt.ylabel(\"returns\")\n", + "plt.title(\"Empirical returns vs trading signal\")\n", + "plt.plot(X, ls_coef_*X + ls_intercept, label = \"Least-squares line\")\n", + "plt.xlim(X.min(), X.max())\n", + "plt.ylim(Y.min(), Y.max())\n", + "plt.legend(loc=\"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We perform a simple Bayesian linear regression on this dataset. We look for a model like:\n", + "\n", + "$$ R = \\alpha + \\beta x + \\epsilon$$\n", + "\n", + "where $\\alpha, \\beta$ are our unknown parameters and $\\epsilon \\sim \\text{Normal}(0, \\sigma)$. The most common priors on $\\beta$ and $\\alpha$ are Normal priors. We will also assign a prior on $\\sigma$, so that $\\sigma$ is uniform over 0 to 100." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to std and added transformed std_interval_ to model.\n", + " [-------100%-------] 100000 of 100000 in 26.5 sec. | SPS: 3769.6 | ETA: 0.0" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "\n", + "with pm.Model() as model:\n", + " std = pm.Uniform(\"std\", 0, 100)\n", + " \n", + " beta = pm.Normal(\"beta\", mu=0, sd=100)\n", + " alpha = pm.Normal(\"alpha\", mu=0, sd=100)\n", + " \n", + " mean = pm.Deterministic(\"mean\", alpha + beta*X)\n", + " \n", + " obs = pm.Normal(\"obs\", mu=mean, sd=std, observed=Y)\n", + " \n", + " trace = pm.sample(100000, step=pm.Metropolis())\n", + " burned_trace = trace[20000:] " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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JQeXcXNXcu4uQDDOtLVUttHl9g/ZfUVFB7txzae4avG40apq72d/QwXkzCnjdDbRx8Zzi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l2bNnW1U8cXFxxKdm8/O+DLKP7aK7UzIOdroqHa+mr8dDu7Zyt0caDnYKfxw8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pm.plots.traceplot(trace=burned_trace, varnames=[\"std\", \"beta\", \"alpha\"])\n", + "pm.plot_posterior(trace=burned_trace, varnames=[\"std\", \"beta\", \"alpha\"], kde_plot=True);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It appears the MCMC has converged so we may continue.\n", + "\n", + "For a specific trading signal, call it $x$, the distribution of possible returns has the form:\n", + "\n", + "$$R_i(x) = \\alpha_i + \\beta_ix + \\epsilon $$\n", + "\n", + "where $\\epsilon \\sim \\text{Normal}(0, \\sigma_i) $ and $i$ indexes our posterior samples. We wish to find the solution to \n", + "\n", + "$$ \\arg \\min_{r} \\;\\;E_{R(x)}\\left[ \\; L(R(x), r) \\; \\right] $$\n", + "\n", + "according to the loss given above. This $r$ is our Bayes action for trading signal $x$. Below we plot the Bayes action over different trading signals. What do you notice?\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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44Rix11MAqB4RTuttGwjYvxt3m43qP82ma9euubrbJ30AhMB1LxUTxZPk1FqL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\nrkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 6)\n", + "from scipy.optimize import fmin\n", + "\n", + "\n", + "def stock_loss(price, pred, coef = 500):\n", + " \"\"\"vectorized for numpy\"\"\"\n", + " sol = np.zeros_like(price)\n", + " ix = price*pred < 0 \n", + " sol[ix] = coef*pred**2 - np.sign(price[ix])*pred + abs(price[ix])\n", + " sol[~ix] = abs(price[~ix] - pred)\n", + " return sol\n", + "\n", + "std_samples = burned_trace[\"std\"]\n", + "alpha_samples = burned_trace[\"alpha\"]\n", + "beta_samples = burned_trace[\"beta\"]\n", + "\n", + "N = std_samples.shape[0]\n", + "\n", + "noise = std_samples*np.random.randn(N) \n", + "\n", + "possible_outcomes = lambda signal: alpha_samples + beta_samples*signal + noise\n", + "\n", + "\n", + "opt_predictions = np.zeros(50)\n", + "trading_signals = np.linspace(X.min(), X.max(), 50)\n", + "for i, _signal in enumerate(trading_signals):\n", + " _possible_outcomes = possible_outcomes(_signal)\n", + " tomin = lambda pred: stock_loss(_possible_outcomes, pred).mean()\n", + " opt_predictions[i] = fmin(tomin, 0, disp = False)\n", + " \n", + " \n", + "plt.xlabel(\"trading signal\")\n", + "plt.ylabel(\"prediction\")\n", + "plt.title(\"Least-squares prediction vs. Bayes action prediction\")\n", + "plt.plot(X, ls_coef_*X + ls_intercept, label =\"Least-squares prediction\")\n", + "plt.xlim(X.min(), X.max())\n", + "plt.plot(trading_signals, opt_predictions, label =\"Bayes action prediction\")\n", + "plt.legend(loc=\"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is interesting about the above graph is that when the signal is near 0, and many of the possible returns outcomes are possibly both positive and negative, our best (with respect to our loss) prediction is to predict close to 0, hence *take on no position*. Only when we are very confident do we enter into a position. I call this style of model a *sparse prediction*, where we feel uncomfortable with our uncertainty so choose not to act. (Compare with the least-squares prediction which will rarely, if ever, predict zero). \n", + "\n", + "A good sanity check that our model is still reasonable: as the signal becomes more and more extreme, and we feel more and more confident about the positive/negativeness of returns, our position converges with that of the least-squares line. \n", + "\n", + "The sparse-prediction model is not trying to *fit* the data the best (according to a *squared-error loss* definition of *fit*). That honor would go to the least-squares model. The sparse-prediction model is trying to find the best prediction *with respect to our `stock_loss`-defined loss*. We can turn this reasoning around: the least-squares model is not trying to *predict* the best (according to a *`stock-loss`* definition of *predict*). That honor would go the *sparse prediction* model. The least-squares model is trying to find the best fit of the data *with respect to the squared-error loss*.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Kaggle contest on *Observing Dark World*\n", + "\n", + "\n", + "A personal motivation for learning Bayesian methods was trying to piece together the winning solution to Kaggle's [*Observing Dark Worlds*](http://www.kaggle.com/c/DarkWorlds) contest. From the contest's website:\n", + "\n", + "\n", + "\n", + ">There is more to the Universe than meets the eye. Out in the cosmos exists a form of matter that outnumbers the stuff we can see by almost 7 to 1, and we don’t know what it is. What we do know is that it does not emit or absorb light, so we call it Dark Matter. Such a vast amount of aggregated matter does not go unnoticed. In fact we observe that this stuff aggregates and forms massive structures called Dark Matter Halos. Although dark, it warps and bends spacetime such that any light from a background galaxy which passes close to the Dark Matter will have its path altered and changed. This bending causes the galaxy to appear as an ellipse in the sky.\n", + "\n", + "\n", + "\n", + "\n", + "The contest required predictions about where dark matter was likely to be. The winner, [Tim Salimans](http://timsalimans.com/), used Bayesian inference to find the best locations for the halos (interestingly, the second-place winner also used Bayesian inference). With Tim's permission, we provided his solution [1] here:\n", + "\n", + "1. Construct a prior distribution for the halo positions $p(x)$, i.e. formulate our expectations about the halo positions before looking at the data.\n", + "2. Construct a probabilistic model for the data (observed ellipticities of the galaxies) given the positions of the dark matter halos: $p(e | x)$.\n", + "3. Use Bayes’ rule to get the posterior distribution of the halo positions, i.e. use to the data to guess where the dark matter halos might be.\n", + "4. Minimize the expected loss with respect to the posterior distribution over the predictions for the halo positions: $ \\hat{x} = \\arg \\min_{\\text{prediction} } E_{p(x|e)}[ L( \\text{prediction}, x) ]$ , i.e. tune our predictions to be as good as possible for the given error metric.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The loss function in this problem is very complicated. For the very determined, the loss function is contained in the file DarkWorldsMetric.py in the parent folder. Though I suggest not reading it all, suffice to say the loss function is about 160 lines of code — not something that can be written down in a single mathematical line. The loss function attempts to measure the accuracy of prediction, in a Euclidean distance sense, such that no shift-bias is present. More details can be found on the metric's [main page](http://www.kaggle.com/c/DarkWorlds/details/evaluation). \n", + "\n", + "We will attempt to implement Tim's winning solution using PyMC3 and our knowledge of loss functions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Data\n", + "\n", + "The dataset is actually 300 separate files, each representing a sky. In each file, or sky, are between 300 and 720 galaxies. Each galaxy has an $x$ and $y$ position associated with it, ranging from 0 to 4200, and measures of ellipticity: $e_1$ and $e_2$. Information about what these measures mean can be found [here](https://www.kaggle.com/c/DarkWorlds/details/an-introduction-to-ellipticity), but for our purposes it does not matter besides for visualization purposes. Thus a typical sky might look like the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Data on galaxies in sky 3.\n", + "position_x, position_y, e_1, e_2 \n", + "[[ 1.62690000e+02 1.60006000e+03 1.14664000e-01 -1.90326000e-01]\n", + " [ 2.27228000e+03 5.40040000e+02 6.23555000e-01 2.14979000e-01]\n", + " [ 3.55364000e+03 2.69771000e+03 2.83527000e-01 -3.01870000e-01]]\n" + ] + }, + { + "data": { + "image/png": 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RJB59NInRo1O5+eZktm+vvD5Ro193EWkJjADeDFp9LvBe4P/vAecF/j8K+Fgp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\n3nKoevMrTVwugZMnCzfV9HQxZD7q1YhWW1Aj+cdngbJpvfuugzp11Gu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80LFjUoFayVyq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\nYuvs9OluHnussMaj1yMiSatORpyfD4cPlyUZ4VpUMyNDuPXWRDZ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from draw_sky2 import draw_sky\n", + "\n", + "n_sky = 3 #choose a file/sky to examine.\n", + "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", + "Training_Sky%d.csv\" % (n_sky),\n", + " dtype = None,\n", + " skip_header = 1,\n", + " delimiter = \",\",\n", + " usecols = [1,2,3,4])\n", + "print(\"Data on galaxies in sky %d.\"%n_sky)\n", + "print(\"position_x, position_y, e_1, e_2 \")\n", + "print(data[:3])\n", + "\n", + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Priors\n", + "\n", + "Each sky has one, two or three dark matter halos in it. Tim's solution details that his prior distribution of halo positions was uniform, i.e.\n", + "\n", + "\\begin{align}\n", + "& x_i \\sim \\text{Uniform}( 0, 4200)\\\\\\\\\n", + "& y_i \\sim \\text{Uniform}( 0, 4200), \\;\\; i=1,2,3\\\\\\\\\n", + "\\end{align}\n", + "\n", + "Tim and other competitors noted that most skies had one large halo and other halos, if present, were much smaller. Larger halos, having more mass, will influence the surrounding galaxies more. He decided that the large halos would have a mass distributed as a *log*-uniform random variable between 40 and 180 i.e.\n", + "\n", + "$$ m_{\\text{large} } = \\log \\text{Uniform}( 40, 180 ) $$\n", + "\n", + "and in PyMC3, \n", + "\n", + " exp_mass_large = pm.Uniform(\"exp_mass_large\", 40, 180)\n", + " mass_large = pm.Deterministic(\"mass_large\", np.log(exp_max_large))\n", + "\n", + "(This is what we mean when we say *log*-uniform.) For smaller galaxies, Tim set the mass to be the logarithm of 20. Why did Tim not create a prior for the smaller mass, nor treat it as a unknown? I believe this decision was made to speed up convergence of the algorithm. This is not too restrictive, as by construction the smaller halos have less influence on the galaxies.\n", + "\n", + "Tim logically assumed that the ellipticity of each galaxy is dependent on the position of the halos, the distance between the galaxy and halo, and the mass of the halos. Thus the vector of ellipticity of each galaxy, $\\mathbf{e}_i$, are *children* variables of the vector of halo positions $(\\mathbf{x},\\mathbf{y})$, distance (which we will formalize), and halo masses.\n", + "\n", + "Tim conceived a relationship to connect positions and ellipticity by reading literature and forum posts. He supposed the following was a reasonable relationship:\n", + "\n", + "$$ e_i | ( \\mathbf{x}, \\mathbf{y} ) \\sim \\text{Normal}( \\sum_{j = \\text{halo positions} }d_{i,j} m_j f( r_{i,j} ), \\sigma^2 ) $$\n", + "\n", + "where $d_{i,j}$ is the *tangential direction* (the direction in which halo $j$ bends the light of galaxy $i$), $m_j$ is the mass of halo $j$, $f(r_{i,j})$ is a *decreasing function* of the Euclidean distance between halo $j$ and galaxy $i$. \n", + "\n", + "Tim's function $f$ was defined:\n", + "\n", + "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 240 ) } $$\n", + "\n", + "for large halos, and for small halos\n", + "\n", + "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 70 ) } $$\n", + "\n", + "This fully bridges our observations and unknown. This model is incredibly simple, and Tim mentions this simplicity was purposefully designed: it prevents the model from overfitting. \n", + "\n", + "\n", + "### Training & PyMC3 implementation\n", + "\n", + "For each sky, we run our Bayesian model to find the posteriors for the halo positions — we ignore the (known) halo position. This is slightly different than perhaps traditional approaches to Kaggle competitions, where this model uses no data from other skies nor the known halo location. That does not mean other data are not necessary — in fact, the model was created by comparing different skies. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to mass_large and added transformed mass_large_interval_ to model.\n", + "Applied interval-transform to halo_position and added transformed halo_position_interval_ to model.\n" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "import theano.tensor as T\n", + "\n", + "def euclidean_distance(x, y):\n", + " return np.sqrt(((x - y)**2)).sum(axis=1)\n", + "\n", + "def f_distance(gxy_pos, halo_pos, c):\n", + " # foo_position should be a 2-d numpy array\n", + " # T.maximum() provides our element-wise maximum as in NumPy, but instead for theano tensors\n", + " return T.maximum(euclidean_distance(gxy_pos, halo_pos), c)[:, None]\n", + "\n", + "def tangential_distance(glxy_position, halo_position):\n", + " # foo_position should be a 2-d numpy array\n", + " delta = glxy_position - halo_position\n", + " t = (2*T.arctan(delta[:,1]/delta[:,0]))\n", + " return T.stack([-T.cos(t), -T.sin(t)], axis=1)\n", + "\n", + "\n", + "with pm.Model() as model:\n", + " #set the size of the halo's mass\n", + " mass_large = pm.Uniform(\"mass_large\", 40, 180)\n", + " \n", + " #set the initial prior position of the halos, it's a 2-d Uniform dist.\n", + " halo_position = pm.Uniform(\"halo_position\", 0, 4200, shape=(1,2))\n", + " \n", + " mean = pm.Deterministic(\"mean\", mass_large /\\\n", + " f_distance(T.as_tensor(data[:,:2]), halo_position, 240)*\\\n", + " tangential_distance(T.as_tensor(data[:,:2]), halo_position))\n", + " \n", + " ellpty = pm.Normal(\"ellipcity\", mu=mean, tau=1./0.05, observed=data[:,2:])" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration 0 [0%]: ELBO = 58.1\n", + "Iteration 5000 [10%]: Average ELBO = 51.72\n", + "Iteration 10000 [20%]: Average ELBO = 69.89\n", + "Iteration 15000 [30%]: Average ELBO = 82.23\n", + "Iteration 20000 [40%]: Average ELBO = 102.96\n", + "Iteration 25000 [50%]: Average ELBO = 130.65\n", + "Iteration 30000 [60%]: Average ELBO = 145.73\n", + "Iteration 35000 [70%]: Average ELBO = 149.08\n", + "Iteration 40000 [80%]: Average ELBO = 149.4\n", + "Iteration 45000 [90%]: Average ELBO = 149.36\n", + "Finished [100%]: Average ELBO = 149.36\n", + " [-------100%-------] 5000 of 5000 in 32.4 sec. | SPS: 154.4 | ETA: 0.0" + ] + } + ], + "source": [ + "with model:\n", + " mu, sds, elbo = pm.variational.advi(n=50000)\n", + " step = pm.NUTS(scaling=model.dict_to_array(sds), is_cov=True)\n", + " trace = pm.sample(5000, step=step, start=mu)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We use ADVI here to find a good starting point and scaling for our NUTS sampler. NUTS is a \"smarter\" MCMC sampling method than Metropolis, so as a result we need fewer total samples for our chains to converge. ADVI follows a completely different methodology to fit a model that we will not get into here. We may cover ADVI, as well as NUTS, in-depth in a later chapter.\n", + "\n", + "Below we plot a \"heatmap\" of the posterior distribution. (Which is just a scatter plot of the posterior, but we can visualize it as a heatmap.)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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0BgbP2dnC++87ymxda9JEcc892fzrX9lAYKdDh7RVqKx06WLy9tsZ1K9vfUCb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EsvWdm7N3/Tee3aCrfd5qNjxwD16ytlOsFm+3aZTp2SAAmDQTBypI977vEVuGPLn3/KPPxwAocO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\npDh11o4DjaWUWXmuWYH9UspaZTS+UlHS3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GAZgBCiBpB9wWdFIBYL53V1mUzQrZuPBQts\npKRk8vrrDrp189CqlY+OHb088ICL2NjyH29lQ0r4809NMenXL57XX4/GVWkiKwvi80FKiomrr45j\n8WJTAVe9TtlitWq9CdesyWT5chtDhnhy6zru2aNw992x3H13LMuXGzl1Sru+b5/C6NFWMjL8S/SN\nN7rDJr5Gp3B69/Zy112BaeROp2D27GiGDo3nwQdj2bu3cpq/Dx8O/Nz5Oy1UZorjBu0MTAU8wDgp\n5b5zyttgKWVI9gcNthu0JDidWisik6nwKtE6wcPj0ZoU33KLNVcpSUrysXRpZqVtB5WaauTaa614\nvYLrr3cxY0aW7goNEb7/3siYMf/P3nmHR1GtDfx3ZnsqSCeQ0DsoKEW6yAVEVOACXvQqRYEPFRU7\nKla8iB0VLNgAUUGwISiKiIgogkrvLaGE0MnuZrP1fH9Mks2SkLqbbDbzex4fs8PszOTNOWfe81Z/\nPNuIEU4eecTB889bWLTIlHM8JkaybJnaSkqj4mO1wq+/Gnjooag8CgpAzZpq+ZFIbw92IR99ZMxK\nxlF54QU7t99eMXp2g2o1/eknA9WqSbp185SoLMrF3KBF9pBLKTcAXS84tgBYUOynqUSYzZqSVlZI\nCb/8ouemm2IC4gZHjHAVW1GTkpCX4Ni3T0GvD22dowMHBKNHR+cUgRw82KUpauXImTOq9cBkgtq1\nfXkKti5aZMJqJaB/r6JI3n/fpilqEURsLAwc6KZ9+3S2b9fx6adGli834nSq8/TECYV580w8/3xo\nHFc2G6SlCU6eVHC71U444WC1NZsDnyE+vvyfqaicPQt33hnNli2qWpWU5GHBAnvQFO5iLdtCiN5C\niA+EECuy/n9VUJ4iRAQ7Zq2iEg7+9rJg926FUaMCFbX4eB/XXeffmRUkCzWBRM+NN0bz5JOWkNbB\nSksTjBkTzY03RpOcHBrtKTNTLeJ85ox6fYtF5lQqryxjojDKUg6HDimMHRtDz57xdOkSxy23xBAV\nJenTJzB+7bvvTNSsKYmNlRiNko8+stO7d9442GCjjQmVspRDnTqSvn09vPNOBmvXpvPtt+ksXGhl\n8WIrEycGP3bj6FHBihV6Ro6MoXPneAYOjOOGG+L48cf8a0uV9ZioWzdQOatXLzwsi0WRg80m2LHD\nH2OXnKznrruiOXkyOO+RIlvWhBC3A/8D3gPWA4nAp0KIqVLKOUF5Gg2NUrB2rR6Hwz8xzGbJp5/a\nipQ9l5GhKjaPPmoBBD/+CNdc46J69dBYM5KTFbZvV6ffr7/qSUoKvql/+3Ydl1wi6dbNzW+/GXjk\nEcdF28pohJ6dOxXWrFFfilIK1qwxMGhQDF98YefkSWjf3kft2j62b9exbJmB6dPttGvnpWVLH7rw\niLPWCBF6vVr/q3Hj0Fw/LU3wxx96Hn88iqNHAzeHSUkeevUK/WagKLRo4aVFCw+7dunp2dNNixYV\nx5pcrZqka1dPzhwH2LRJz969CjVqlP73KM6W/iHgX1LKR6WU70gpHwP6ZR0vFCFEPSHEKiHEdiHE\nViHE3VnHqwohfhBC7M6y2MXn+s4UIcReIcROIUS/XMc7CCG2CCH2CCFeu9g9Q9EbtCISDn3NyoKN\nG/17j1q1fCxdaqVLl8BJcjFZbNyoz1HUsgllG5Lcu62XXjIH3Yq3b5/CbbdF8dRTFgYOdBMf7+Oa\na9w5rt385HDunOpG3rmz8vhJy3Ju5OfSOX9ex8KFBl580cHatTpeeslMaqrCjTe66NbNQ5s2Zaeo\nVZZ1ojAiTQ7qWhDNmDExeRS1Hj3cLF5sD5veoDVrqmVt5syxMXNmRtjEGRdFDlFRcN99mVzYlfPE\nieCsp8W5SjVgxwXHdgNFLQHqAe6TUrYGrgTuFEK0AB4BVkopmwOrgCkAQohWwAigJXANMFuInCii\nt4DbpJTNgGZCiP7F+D00IpTx49Xg7HnzbKxYkc7llxdtN2OzwYwZZnIravHxvpyyLKEgd0ZmSoou\naKZyUHuWfvaZkZQUtaHzpk063nzz4gsyqIkZn3xiYsiQWB58MAqrNWiPo5FF69Ze/u//8sYgnTql\ncPCgwoEDenw+wd9/63nyySimTbNw/LiWuatRcnbtUhg8OIZ16wLdnDVq+HjnHRtvv22ncePwsrY3\naeLj3/92k5QUXs9VFDp29PDmm3Z0OlVhE0JSv37Zx6ytBV4RQkSpDyGigReBdUX5spTyuJRyU9bP\nNmAnUA+4AZibddpcYHDWz9cDn0kpPVLKQ8BeoJMQojYQm5XwADAv13cC0GLWVCpLLEqHDl4eeiiT\nQYPcFw2WzU8Wx44p/P57YETAY485qF8/dMGtFwbSnjkTvJdyaqpgzhx/VsuhQzo6dw50c1woh82b\n1VInABs26Dl3rnIoCWU5N+Lj4f77M3n7bRvNm3vR6SQdOriZPDkz68UUOCaWLDHx4Ycm3KXoFHTy\npGDXLoXTpwv/e1aWdaIwIkUOHg+8+aaZY8f8ptlWrTx88IGNH36wMny4mzp1Cl7jyloWJ04Ifv5Z\nz6xZJt5808SKFXpSU8t/LSqqHCwWGDHCzcqVVj74wBbUDO7i1Ev+P2AhcF4IcQbVorYOGFncmwoh\nGgCXAX8AtaSUaaAqdEKImlmnJQC/5/ra0axjHuBIruNHso5raJQIKdWixtluzxtvdHLddaHtpRcX\nF7hI2u3BW5BSUhSsVv/16tb1Ub36xc+XEhYvNuYkZrjdlEpB0Lg41aqpi3n//m7On1eyGkmD3Q5P\nPeXgqacCCzHOnGnm5ptdJbLybt6sY8KEKPbs0XPNNS7efNMeNm4ljdCj18Nttznp29dNdLSkVi0f\n9er5wrYd3v79gvHjY/jnn0C15NprXbz2mp1q1crpwYqJXg+XXurl0kuDG29XnNIdqUBPIUQ9oC5w\nTEp5pJCv5UEIEYPaV/QeKaVNCHGhah80c4YWs6YSaTEYpSE/WSQl+Xj6aQfffGPkv/910r+/O6B0\nQiioVi3w+sFUjk6eDDSYX2hVg0A5HD0q+PRTf02vunUlsbF5vhKRlNfciI9XXe3ZREfDqFFOEhJ8\nPPRQFGfPqn/DmjV9GI2Fj0WXC6xWQZUqEp0OduxQuP762Byl/bvvjBw4kFlgaIC2TqhEkhzat/eW\nqsVhWcrim2+MeRQ1gGXLDDz6qEK1auXnFg2HMVGsTmRCiCpAL7KUNSHEMillkZtjCCH0qIrafCnl\n11mH04QQtaSUaVkuzhNZx48C9XN9vV7WsYsdz8PixYt57733SExMBCA+Pp62bdvmCD7btKl91j5P\nnOikVaufMBigZs3Q369OHR+NG//E/v06oDdxcTJo1/d4sivqrAagZcvLCzzfbO6V9VJXz+/d+0qq\nVw/e82ifi/Z569a11KoFv/zSg4MHFf76ay0JCT5q1+5W6Pc//tjICy/8waWXepk06Uo2bVKwWn9B\npTcA27atweGQYfP7ap+1z7k/p6b+AljIHq/Z69HQoVdSv76v3J8vVJ+zf05JSQHgiiuu4Oqrr+ZC\nitPBoA/wBWpSQTJq6Y4WwL+llD8V8RrzgFNSyvtyHZsBnJFSzhDejj0cAAAgAElEQVRCPAxUlVI+\nkpVgsADojOrm/BFoKqWUQog/gLuBDcAy4HUp5fcX3u/ll1+WY8eOLdLvF8msXbs2LHYG4UA4yWLZ\nMgO33BKDoqgNups1C87Occ0aPYMHq6axpk09fPWVLU9sSm45qHWX/Ka0Tz+10r+/JyjPEu6E03go\nDU89Zeb11y05n4cPd1KnjuT1102AoEEDDytW2PIU4c1NpMiitGhy8FOWskhNFXz8sYl580ycOCFo\n0MDHpEmZXH114bF1oaYs5VDqDgbAm8B4KeWi7ANCiOHALFSlrUCEEN2Am4GtQoh/UN2djwIzgEVC\niLGoSuAIACnlDiHEItQMVDdwh/RrlncCHwFmYHl+ipqGRrjTqZOHceMyqVMnuJmnDRp4SUjwcuqU\nwsyZGYUudPpcq0CtWqHNgg1HXC5Yt07Pjh062rb10qGDJ6d3Z0XhhhvczJplxutV1/jPPzfRrp2H\nJ55wMG2amRdecBSoqGmUPd4s76RWQ0+lTh3JAw9kMnq0k8xMiI6WYRtfVx4Ux7J2DqgmpfTmOqZH\ntZRVCdHzlYpw6A2qoVEQdrva1ioqqvBzi8Pu3QpeL7Ro4Su0vdSmTTquvlq1rP3vfw4OHhQ88URm\n0J8pXNmxQ6FXr7gsRUfy6KOZjBuXSXx8oV8NG9xueP99I48+GqhltmnjZto0B506eSO+7V12D+Zw\nxW6HXbt0rF+vZ+NGPcePC8xmyQ03uOnc2VOk4t0akU8wLGvzUS1ar+c6NhG1dIaGhkYJCJUFp3nz\noi/8LVp4ef31DKxWwccfG9m5U8e4cU4aN64clpizZ0WORQoE//ufhebNvSHPCA4mBgPcdJMLIQRT\npviLO2/bZuDIERc9e1acSvDF5fhxwXffGVi0yESbNh5uvNFF+/besLJYnTsHL79sYdYs1S2dm9Wr\njVSv7mP5cqvWYaQCkZYmMBjgkkvKZp0sTp219sDLQogjQoj1QogjwMtAeyHEmuz/QvOYJUOrs6aS\nO5CxsqPJQiW3HM6dE7zyipmpUy1s364WZk1PrxxdDNauXUvt2j5MpsAF97nnzEGtfQdqb9A//9Rx\n9GjxrnvihGDVKj1ffmlg+XI9mzcrpKfnPS8uDm691cnixTaqVvW/9N95x4TdXvh9KurcWLTIyP33\nR7N+vZ733zczcGAsGzaUXFMLhRz27dMxa1Zg4e3cCEGhFvDyoKKOiWBzoRwOHVLo2zeO/v1j+fln\nPRkZoX+G4ljW5mT9p6GhEUEcPapw8KD/5aYokri4yrPDT0yU3HlnJq+84g/Q37NHdVMFY9d85Ihg\nxQoDzz5rIT1dYe5cKz6fl/h4SVxcwd91ueDJJy0sXGjKdVRy+eUepkzJpEsXT4C72mKBPn08rFxp\nZft2HT//rKdLF09YuwdLg8sFy5cbA455PIJnn7Xw+ee2sHHlN2ni5bnn7Dz/fFRADUS9XjJ6tJPR\no500alR55lxF59gxkdO669//jmH2bDvDh7tDas0tsrImpZxb+FnhhVZnTUXLbPKjyUIltxwutCB1\n6OAJeZ25cCFbDrfe6uSff/T8/LOq1URHSyyWgr5ZNHbvVpg4MZpNm7KXWkl6usIVV8TQvLmXadMc\ndO3qCUjyyI1erxY1DkTw118Ghg3T8+yzDkaPduZxpzds6KNhQx+DBhXdlVsR54bRCF27uvnzz0AB\nnjmjlLh2YSjkUKUKTJjg4tpr3aSmKvh8aheTqlUhIcEXtsp0RRwToeBCOQT2+RXcc080zZtbS1XT\nrjBKZHgVQmwN9oNoaGiUD1FRgYrZxInOSlMUN5vERMmbb9qZNcvOzTc7+fBDGw0alM7SsX27wg03\nxOZS1ODmm13Mm2fC7RZs26Zn2LAYtm+/+HZcUWD0aCfDhjnz+VfB1KkW9u8PQ/9ZGXLLLU5atMhd\naka1lIZbgoiiqOOsc2cvV17ppX17Hw0ahK+ipnFx6tTxcfnl/t2A2y147jkL54pcdbb4lHSWJwX1\nKUKEFrOmosUd+AlnWZw7p9ZIe+45M/fea2HbttC9hHPLoX59H7VqqYrJ4MFOevasHDXWIFAOdepI\nRo508cYbGfTt60GUImRt926FESNiOHHC/zds0sRD48ZeNmzwK28ej2DjxoJ9J/XrS6ZPz2DJEitD\nhjiJiclWriVXX+3Jo5Rs2aIwY4aZ777TFys+LpznRkE0bChZtMjGJ59YmTnTztKlVoYMcZX4ehVV\nDqFAk4XKhXK45BJ4+mkHuRsurVpl4NCh0K3ZxYlZy035d1bV0IggDh4UPP+8hc8/98cmtWrlpU2b\nkr90ikpiomTxYivHjyu0bu3N0wpLo3icPw/PPGMhNdWvhDVo4GHuXDtPPpnXt1qUjOBq1eCqqzz0\n6OEhNdXBuXMCs1ltR3Whsnb6tMKMGep96tTx8cILGfTq5SYmplS/VlhTr56kXr3Ks8nQKH86dPAy\nZUom06f757S6OfNb5M+ehYwMQc2astQW1OLUWXsVmCul3CSE6C6lDHuVW6uzplER2LdPYcyYaLZv\nD9w7ffmllV69tBdQRSN3BwlQY6pmzsygcWMfW7YoDBkSm9P7s149L198YQtqyYa0NMGNN8awZYt/\nPE2c6ODOO53Urasp4hoaweLECcHChUaeftqCzwfffWelc2cv58/D2rUGpk83k5KiY+5cG1ddVbS1\nPBh11nTACiHESWC+EOJQSRq5a2ho+LHZYPp0cx5FrV8/F5deqilquTlxQrB3r8Lu3Tpq15Z07+4u\nNJuyPNizR1XE4uJ8TJ3qYMAANwkJqpLUrp2PH36w5pzTunXwO0bUqiWZOdPOgAFxOJ3qmv/WWxZ2\n79bzyisZla5DhYbGhezerbBwoZFmzXx07OihceOSzYmaNSUTJjjp3dtNRoagTRsvZ8/C22+befFF\nv8Xtt9/0RVbWLkaRHaxSyrtRG7g/AlwG7BRCrBRC3CqECEsDuxazpqLFHfgJN1ns2aPjyy8DSw/0\n7+/ixRczqBLCviDhJofC2LJF4aabornuujgeeCCa//43htTU0seHhEIOPXt6+OqrdH7+2cptt7ly\nFLVsGjf2cc01Hq65xhMyxaltWx+ffWbDYgmMqRk3Lopjx/KPYqloYyJUaHLwE6myOHtW8NprFu64\nI5o+feJYsMDI+fMXP78gORiN6nzr3NmL0QhffWUMUNRALTxeWoq12kkpvVLKb6WUI4EuQA3UHp3H\nhRDvCSESSv1EGhqVCE+uzVZUlOT55zOYOTOD+vU1dxWo/RNXr9YzcGAcf//tD/po3twTtrF1zZr5\n6NnTS8OG5WfBUhTo1cvDV19ZqV7d/xwbNhiYN8+EM7/kUg2NSkKjRj5atVIXX6tVMGlSNNOmWUhN\nLV04/t69Cg89FFjcLyHBx5kzAputVJcueswagBAiDhgO/BdoBywB5gIpwP1AHyllu9I9UvDQYtY0\nwh27HbZv1+F0qll/9ev7wqpNTnnz1186rrkmFo8n9yIq+eYbK927R24LpeJw+rQgLU1w7pxAr1eV\n/ipVJDVqSEwm9QUyZUoUq1apyq4Qkp9+snLZZZr8NCov69frGDgwFin9a8uwYU6eecZB7dol2wh+\n/bWBMWP8jsaYGMkTTzh4+mkzv/xiLVLh41LHrAkhFgP9gTXA28BXUkpnrn+/DyjAkFjxkRIOH1YL\nGpa2BpOGBqiZgJ06aS/N/Dh/Hp56yhKgqOl0kvfes3PFFZrMANau1XPPPVEBHShALeo7YICL225z\n0ratl3fesbN1q46ZM838+aees2e1hH6Nyk379l7mzLEzblx0jsK2eLGJxEQfDz6YiclUyAXywZtr\nWapb18e992YyY4YZu13h1ClBo0Ylf97iuEH/AJpKKa+VUi7MragBSCl9QK2SP0rwCWbMmscDS5ca\n6NEjjl694krVe66sCWXcQWqqYO1aHd9/r2fbNoViGGrLhQtlkZYm2LZN4cABhczMcnqocqAixKKc\nOiX47Te/6zMpycO331q59lo3ZnNw7lER5HAxPB74+GNjHkUNwG4XLFliYuDAWBYuNFKliqR3bw8L\nFthYv/48HTvmDXauyLIIJpoc/ESyLIxGGDTIzbx5doxG/4vr1VfNbN0aOKeKKofOnT3MnWtj4UIr\nr79u55lnLJw+rapZdnvpNkjFaTf1UhHOKYN2puXDrl0Kt98enbPLf/hhC199ZQvLbLSyYtMmHaNH\nR5GSog4jk0myeLGNbt0qRhbjnj1q0PqBA3qMRknv3m7uvTeT9u29JdpVaQSX6tUlc+bY2L1bR6dO\nHpo392qxfLnQ6+HhhzOpUcPHnDlmXK78XgaClBRdziYqKipvxwoNjcqK0QjXXOPm22+tTJgQxcGD\neqQUfP+9oUTW+4QESUKC2tngt9902Gz+OVmaIttQzJi1ikYwY9beftvEo4/6AwdNJsmff56vtC+P\n/fsV+veP5cyZQOPs2LGZvPSSo5yeqnisW6dj0KBAbVsIycsvZzB8uKtIxUo1NMobj0et1ZeSonDy\npEJamoLVCk2b+khK8tK6tTekmcUa5cvJkwKdTnLJJeX9JBWbtDTB5s06fvjBQJ8+HgYOLGFz2SxO\nnRIMHx7D5s16QLJ2bTqtWpVBzFplZ/PmQLOo2SwrdSD4wYNKHkUNoE2bihNL1KiRj3btPAHFQ6UU\n3HdfNImJPvr0qRgWQo2Lc+4cJCcreDyCGjV8JCZG3uZKr4cWLXy0aFHx4mjdbnUtcbnU+M369X0X\nbWofLmRkqApyOHhVjh4V3HBDDIoiePppB1de6dYU8xJSq5akXz8P/foFZ92vXl3ywgsZDB0aS79+\nLurVK938jOgOwMGMWbtQ0CNGuKhZs2Is/KGIO6hSRZK7LxrAVVe5ufrq0u1GQk1uWdSurQart2+f\nd3IuWxbZ3ZUjORYlm7Q0wf33R3HVVfH8619x9OgRz/vvGzl92n9OZZBDUSkPWXzxhZFu3eLo2TOe\nrl3jePBBC3//rQtp/KjbrWbIrlqlZ+VKPevW6di3T00cg8LlsGOHjuuui+Xrrw2cPRu65ywKVqvg\nwAE9+/bpuPnmGGbMMAf1mbT5oVJSOXTs6GXlynSeecZRauU+zPcw4UPfvm5ee82M1yuoWtXH6NHO\nsN8BhpI2bbx89ZWN994zYTZL+vd3c+WVngrXzqZJEx/z59tYu1bPnDkm/vlHT7VqksGDw1vp1Cic\nlBSFL7/0Bx9arYIHH4wmJUXh4YcziYoq4Msa+ZKZCUeOKNjtahN6vV4SEyOpV0+WKM7z6FGB16t6\nfJxOwdy5ZubNM/HII5mMG5cZdCuR3Q4LFhh54omogBg/s1ny8MMORowovBfvJZdI9u/XMWZMDMOG\nOZkyxUHDhuq653CopVRiY2Wenq2hoGZNHy1aeNi1S30ZvfOOhXr1JOPGOTEaC/myRpnQvPnFLWo+\nH2zfroYu1Knjo2XLi5+rxawVEY9HrfmUkqLQtq23QrocQoGUpQ+cDBfsdrUJttEoS1xnRyN8OHBA\noU+fWNLTL3QgSH77Lb3AhVEjELdbrUv1xhtmVq0y5ChYAHq9pG9fN3fdlUmnTt5ibWL37lUYOjSG\no0fzxpTMmGHn9ttdQV1fduxQ6N49Dsj/oi+8oN6zIKSE2bNNTJ2qavtJSR4+/dROjRo+XnjBwscf\nm2ja1MuLL2Zw+eVelBD7r774wsDtt/trewkh+fZbK1deWXFCUior//yj1pF0uQRGo+TNN+00arQ+\n35i1iHaDBhO9Hjp39jJ8uDviFLVt23RMnWpm8mQLO3YUb0hEiqIGasxMYqJPU9QihEaNfMyfbycm\nJvDvaTAQ8hdopLFtm47Bg2P58UdjgKIGqoXt+++N3HBDLNu2FS+Qt2lTH4sW2fINn3jpJQsnTgR3\ngalf38e4cRdv33DhWMkPIeD6613Ur68qQ8nJev7znxj27tXx4YcmHA7Bli16rr8+li1bQh/Y3KuX\nh379/AqmlILnnrNgt4f81hql5K+/dDkWXpdLMGHCxbPaInrJ0nqDqhTkb9+zR+H662OYNcvC3Llm\nRoyI5ciRCNLALkCLwVCJdDn4fKo1qEcPDytWpDNtWgb9+7sYMsTF119badJE3XBFuhyKQ0GyqFtX\nVXKEyF+ZEUIydqyTOnWKv5Ft2dLHe+/Z+PZbK7fdlkmrVh5atPDyzDMZxMcHd+MUGwtTpjj46isr\nY8Zk0r69h5YtvVx3nYuFC60MGOAu0pioX18ye7YdnU59vpQUHZMmRTFlSibZsbxOp+Cjj4whrz1Z\nrZpk+vQMmjXzx96uW6cnOTk8e+dWREIlh5gLuqrn7qZwIZU46koDYOVKA+fO+Sf1sWMKhw8r1Kun\nmdArO263mn5evbrEUEHyLY4cEfz1l54lS4ycOSOYNCmTPn08tGzpZOJE1aJSVtZgq1UthOl2q8qj\nlGCxqFliFS2TvFYttW3OLbc4OXBAx/nzAqtVEBMjiY+XNG7spUEDX4njAOPjoWtXD126eMjIUOUV\nqmzLKlWgZ08PPXt6cDjUEBezmWKP8U6dvLzxhp077lDfuPv36/nhB8n48U7efVet2rxmjYGzZx0h\nL6vRsKFk/nw706aZWbrUBKjjrqyJpLCYsqBtWw8mk8TpLFxoWsxaJWfs2Gi++iowEnXp0nS6ddOU\ntcrM8eOCd981MXeuiTlz7BWijMnWrQqjR0dz8KB/D1qW9RAzMtT6g3v36li2zMiuXTpOnFB7dma3\noalZU9KmjYfrr3fTq5eHpKTICqmobNhs8OabZl54wZJzbMQIJ6mpCr/+amDIECezZ2eUWZHt8+fV\nbFWnU9Chg6dMy4tICZ9/bkSvlwwa5NYSHIqAzwcrVugZOzYmR2FbufInrc5aYWQnEDRp4qVVq8rR\nULtFi0ClrEYNH/XrR8YLxOVSd81a1l/xOHcOnn3Wwqefqm+Y994zhb2ytnu3wrBhsZw8Gej6adnS\nU6Q4pNKSliaYOdPE22+buVjwOsCJE4JVq4ysWmVk+vQMJky4ePyURvgTEwPjxmVit8OsWarCtmiR\nkZdfziA2tuQ9JktKfDx5EgtOnRKsWaPn/HlBz54eGjcOzfp+9KjgwQejsNvhxx+ttG+vbfgLQ1Fg\nwAAPK1ZY2bVLIS7u4muVFrOWRUqKYMSIGG67LYa+feP44Qd9uZiRQ0FB/vZBg1zUrKlOXrNZMmeO\nPSIKh+7ZozB2bDTXXRfDN98YcoJttRgMlYLksGWLLkdRqyisXGnIo6jFxEheeslB1aoX/16wxoPP\np7rRCnsxx8ZKhg1zsmiRlRtvDC9FTZsbKsWVQ7VqcM89TiZOzO7cIpg928TzzzvCIhlt8WIjt98e\nw/33R3PzzdHFikkujizOnVNd4z6fYMkSQ0BT89Jy+LBg/XpducVTh3JuCAHt2nkZMcLNgAEX3xRr\nlrUszp8XnD2rLvZut+CWW2L47jsrHTtG9u6gVSsfy5alk5Kio04dX4E1YSoK58/D/fdH5TQBHz1a\nzxdf2OjdO7ytQ+FARga8/npgl/Qrrwx/uWVkBC7izZp5mDUrgw4dymb+1qkjeeyxTEaPdnHypODM\nGTVmSFHUTPKoKEl0NFSv7iMhoeLFrEUCNhs4HIIaNYK/Ga1eXfLQQ2pf4UmTotm/X8+OHTrq1Svf\nuXPqlOCtt/w7iD179Pzzj5569YJvicg9Bz/4wMxtt7lo2LD075OzZ2Hy5GhWrTJQr56XBQtstG1b\n8d9TxUWLWcvi6FFBr15xAS2UevVys2CBTXOjVTD27xd07BhPbndU165uPv/chsVy8e9pwM6dah0q\nf1aSZOVKa5kpPfmRmir48EMTGzfqGD7cxYAB7jzWsuRkNbHAahU0bOijWTOvVoJFI4f9+xXuuCOK\nY8d03Hqrk2HDnDmFbIOJlLB1q4733jPSsaOXW24pvMhuKDl8WHD55fF4PP61cNy4TGbMCH7/5r/+\n0vGvf/mD5JYvT6dLl9KvG2ptPH+F4cREL19/bYvYeM+L9QaNaDdoNlKqBU8L0ksTEmSe+JE1a/Sk\npFQKEUUUQpDHcpGcrMNm09KUCiMjQwSkj990k4uWLcvXurx2rZ6XXrKwerWRO++M4fXXzdhsgeck\nJUmGDnUzapSLnj09mqKmEcChQwobNhg4elRh+nQLgwbFsm1b8Nf2bJfWq686GDy4fBU1UEMBGjQI\nVGoMhtDMjdjYwOueOBEc+apZuv5rp6ToWLu28jkFI1oT2bRpE8nJgv/9z8w118QyZYqFf/7R5fSA\nu5Dhw100aeI3W0spsNsr/gu+ssWi1Kkj+fe/AxfK1q09xMXJSieLi3ExOVgsEkVRF8bmzT3ce29m\nuVsj//47cGGeOdPM9u3B8SNGwng4f17NKPvgAyOrV+s5ebJka1YkyOJiVK8e2Ms4NVXtpZmSkldW\nhcnh+HHBL7/oeestE3PnGtm/P+81dDq1plt5U7UqTJ4c2Gi1c+eib76KMybi4iTVqvlfrsePB+fd\nWaOGj1atAp95yRJDmcaUh8PciGhlDeDrr428/LKFbdv0vPuuqrStX5//Qt+ggY9PPrHTs6c6Clq0\n8ERMZmRlwmKB++7LpGVLVfGuWtXHI4+UbVZWRaVxYx+zZ9uZPt3OggW2nOKx5UnTphe+XAQ7d2pB\nX9ns3Klj5MhYHnggmqFDYxkyJIbNmyN+aS8WTZt6GT8+0HNy+LCOlSuLV1xt0yYdQ4bEMGRILI89\nFsXkydG88Ya58C+WI1df7ebOOzMxGiX//a+TK64ITRxdjRqSf/3LxSOPOHj0UUfQPBlVqsBjjwUq\nnCkpOqzWwr+7c6fCqFHRbNlS8edDxMesvfdedz77LPAtnZTkZcUKKzVr5v+7nzunFoeNjZVlUp9J\nIzSkpQmOHFGoWlXSqFH5Kx0aJWPJEgP33x8V0OPzxRft3HZb+buZwoG//9bRt29gQa2YGMm336bT\nrp027rNJTlYYPz6KDRv8ClqXLm6+/tpWpIK4mzcrXH99HFZroBJy//2OPMpEuOF2Q2qqwiWX+PJU\nzQ8mP/6oZ8yYGDIy4I47MnnggUyqVCn9da1W1aL+yiuqmf/22zOZPt1RYKKOzweTJkXx6acmatXy\nsWKFlcTE8J8PlTZmLb+4geRktQL3xahSRc2S1BS1ik2tWpLLL/dqiloFxudTG1U//nhmjoslJkbS\npUv4Z6iWFU2aeBk+PNBqZLMJ7rgjmlOnKn4YR7BISvIxZ46dKVMcOXFb3bt7iqSoWa3w2GNReRS1\n6tV9eUIuwhGDQe17HEpFDeDHHw1ZWaGC2bMt/PprcFqfxMbCpEmZfPmllbfftvF//+csNKP61CnB\n6tXq/dPSlAof5xbRytqmTZvo3NnDffc5yB2v0LGjO8C3HumEg789XNBkoVJR5OByQVqajmeftXDL\nLU6eeiqD5cvTad06OPO3osihIOLi4NFHM+nYMTCIZ8cOPYcPF32JjwRZFEZiouTeezNZt+48P/98\nngkT8lrE8pODzSbYsSNQO2jc2MOSJdZyqaXmcqkZ0J4Q71mKMybOn4c2bbwMGeJXXp9+2sLp08HZ\nMMTHq03rR4xwF2kDnpkpAuI3lywx4CqhXh0OcyOilTVQ/8CTJ2fy3XdWZs608/77Nt59NyPkvdo0\nNCKB33/X8eWXBrZs0eEIfrZ/oZjN0KWLB6tV8NprFnw+aNOm8my0ikpSko8PPlBjDePjVflccokv\nT4ZeJCIl/POPjl9+0ZOaWrhiYDBA48aSSy/1Ua1a0e5Rs6bkgw/s9OnjYuhQJ/Pm2fjqq/Kr97Vn\nj0LXrvG8+aaJM2fK5REC8Hhg3jwT994bjV4v6dVL3TgcOKDj7Nnyse6aTDIrsURl40ZDmVma9+5V\nWLTIwHvvGfnxRz0nTpT+vhEfs6b1Bi0eTqca23H8uMDpFAihdjZISJAkJlaOFlwaKlLCyJHR/PCD\nESEkw4e7uP/+TJo2LdsX1E8/6Rk+PJa4OB8//GClWTNNWSuIlBTB6dMK1ar5IqIbSWHs2aNw1VVx\nOByCtm09fPCBPWQtlcKlUfm6dToGDVLjFB9/3MH48Zkhd3EWxL59Cj16xGX1t5Q8/bSDJ5+MAiTr\n16eX+ZoBqvVx5Mhofv7Z36T0zz/Phzxpav9+weDBsRw96n9Z9ujhZubMjDxlVPKj0sasaRSdAwcU\nJk2Konv3OAYPjuPGG2MZMSKW66+Po0ePOJ56ypJvqrtGZCIEjByp+g2kFCxaZGLQoFj+/FNXYM3C\nYNOpk4f5860sXaopakUhMVHSvr23UihqoCYSORzqurR1q54JE6KKZGErCeGgqAFccom/FMm0aRb+\n+KN847GSk5WcRuQgsNkEOp1k6FAXdeqUz5w1GmHAgNyhAfKiZbuCycGDugBFDeDXXw0sW1a6+L2I\nVtaK0xs0kimqv/2zz4wsXmwKqHadTUaGYNYsMytWBCdgtLwIh9iDcKCocujWzUP37v4F7+RJhcGD\nY1mzRl8mCx+owcXXXusJictJGw9+Kqos4uMDldK//zbw558lV14qghxq1pQBrZwefNDCsWPB1ySL\nKgvnBW1uPR749FMbTzzhKFeLX9euHoxGdXwkJMgsJbf4FGdM1KrlQ6fLe58L60UWl4hW1jSKx/Dh\nLvr2dZE7GcOPGodw1VVaFl5lonp1ySuvZNC8uf/vnpkpuPHGGLZt03zioeDcObV1z7Jlet5918jj\nj5t58kkz06aZmT3bxOefG/juOz2bNytatidQr56PNm0C16WPPzbmUSAiiUsukdx/vz85IjlZz/r1\n5WdduzA8RlGgb19PuVt3W7TwMWNGBkJI7rnHERDDFkzcbjh4UOB0qvd8/307JpP/XgaD5LbbSlfe\nRYtZ0wjAZlNbsxw5opCZKZBSDdSsV89HgwY+4uIKv4ZG5HHggMLdd0exbp3fstqjh5uPPrLl6dOp\nUXJOnhTce28U331nLPxkoH59L3femcm117pJSIjctbww1syySwMAACAASURBVKzRM3hwDNn9gGvU\n8PHLL+kR3XZs/36FPn38dd8aNfKwfLntovVDQ8kff+gYOND/cpgxw864ceFR0iQzUw34r1u36Akl\nxcHlgoULjTzwQBQLF9ro3duDlLBrl8L+/Qper9qvuE0bL0oRzGMXi1mr2IVHNIJOTIyabadl3Gnk\nplEjtUbVRx+ZePVVMx6P4NdfDRw6pKNq1fLtHRpJxMdL7rork7NnBevX6wP6tObH4cM6HnssisaN\nbSQkVF6rd6dOHl5/PYN77olCSkHr1t6Iz4Rt3NjHc89lcPfd0QAcOKDnwAGFmjVLPx/Pn4dTpxSM\nRjW5rDAlo3FjH02aeNi3T1UpLr00fNYEs5mQZu1u365j8uQofD7B66+bslyv0LKlj5Ytg3ffiFbW\nNm3ahGZZU/3t3bt3x25XA0FTUxVq1JC0bu2tdNmd2bKo7JREDnXqSB54IJPrr3fxxx96jhxRiIur\n2Ep9uI0HoxGuvNLLokU2jh5VOHxYIS1NnbOHDwtsNgW3Wy0/0aGDh6QkH0lJ3qDU+go3WRQHsxmG\nDXPRvLmXQ4cU2rb1Eh1dsmvllsOpU/DHHwZiYiSXXeYJSjX+YNKnj5vWrT1s366+yo8fV4CSK0pe\nL6xdq+fRRy3s3KnDbF7N+PFdGDvWWaBLs0YNycyZGYwYEcutt2bSokX4KGvBoKC5MW+eEZ9P3VRt\n3qzn9GlBnTrB3yhEtLKm4WfvXoVXXzXz2WdGQGAwSNauLZ+Uao2Ki8EArVv7aN06PFwckUpMDDRv\n7qN5c21+FsTx44LDhxWaNvVSpQp07OilY8fgKQq7dum49VY1Qv7mm508/LCDevXCx2JXt67k/fft\nDBkSQ2qqLqAIbEnYuVPhxhtjcLnU62RmCl5/3YLbLXjqKUeB3R6uvNLL2rXpVKlS8cNlnE44cUKg\nKBToVk5LE3z/fWDIQqgyhiM6weCyyy4r70cICyyWXlx7bWxWj1R1JOn16n+hZu9ehSNHwicIuqJa\nDoKNJgcVTQ5+KqIs0tIE/fvH8dBDURw+HJx1JrccMjP911ywwMScOSYyMoJym6DRrJmPJUts3HJL\nJm3alE5RTUtTchQ1ld4ALF1qKLBFYzZJST7i40v1COXO4cOCBx6IomPHeLp0iefxxy0kJPTI99yz\nZwVpaX41qn59H3FxoVHmI1pZ01ALRg4dGsupU4F/6qlTHSQlhXbXLqXafHfo0Bj27tWGmoZKaqrg\nzz91Ws0+jVJTpYraK3bxYhN33RVNcnJwx1SNGj5yZ8e/8YaZLVvCL3akRQsfL7/s4MorS6esNWvm\npUGDvLGPEyc6S1z2oqKxaJGJBQtMuFwCu10wZ46ZMWNiOH4879iy2QKP9e/vJioqNM8V0W9Qrc4a\nLF5sxGr9JeDYzTc7ueEGV5EyU0qDzwf79+vYt0/PY49FBa1HXGmoCDWUyoLykIPPp2aNXXddDAMG\nxPHqq+YyLa6bH9p48FMRZVG/vi+nJMKvvxq4777oUrf2yS2Hxo19FxRWFbz2mjnsrGsQHE9J/fqS\nRYvsTJuWQceOHjp1+pH5822MGOEM+fsiXMivoPKWLWs5cCCvACyWwAWsa9fQJflUEvGXjqNHBT/9\npGflSj27diklbgZb1khJQO0do1Hy0kt2nnrKEZIAyAvR6aBVK3XwrlxpYOVKLUSyMrNhg47Bg2M5\ncEAdB3v26HC7C/mShkYBKAoMGuQm2/r1888GFi0yBm2NjomBBx/MxGDwr5erVxvyeCoiiSZNfNxx\nh5OlS61MmaKWhQlFyYtwZcgQF0Jc+H6UmM15z61eXVK3ruqh6tvXxaWXhk5Z0+qsFcLZs3DzzTH8\n8YcaWakokokTMxk3ruDsmHBhyxYdGzfqqF5d0qSJmjVWljukBQuMTJqkpmXVru3jxx/TK3U9qPLA\n5QKHg3KNJTl4UHDNNXGcOOEffNOmZXDHHRFcuVSjTLDb4cknLXzwgfo2FUKyfLmVzp2Dk2jg9cKi\nRQbuvDMaNeZX8vvv6VryR4TidMIff+h55BELu3frqFJF8uKLGQwc6MZiyXv+unU6vv7ayPjxmTRu\nXPp3m1ZnrYQ4nYK9e/0xCj6fYNYsC1u36pk1yx72ike7dl7atSu/NOrmzf33Pn5cYcsWXaWuB1XW\nbN+uMHWqhePHdUyYkMmAAW5q1Sr7Mbt4sSlAUTOZJD16aONAo/RER8OECU6++MLIuXMKUqqFhZcs\nsVG3bunHuk4HQ4a4qV3bxlNPWWja1Evt2pqiFqmYTNCrl4fly62cPy8wGilwHHXt6qVrV0fInyty\nbbkEJ2atVi3JPffkbROxZo2hXNt7FIfyjEVp1EgtlpjNe++VbzZVRYzLKSkZGfD00xZWrzaya5eO\nyZOjmT7dQnq6Xw42m5pRF8o+nydPCubNMwUcmzEjg9aty78WU2UaD4VRkWXRtKmPN9/MINsdunu3\nnuXLS9bHOD85mM1w1VUevv3WyquvZlT4jMeiUpHHRGmpWhUaNJDUrSvDQg4RrawFAyHgP/9xcffd\nDi7smXnsmCa+wrjkEsm99/pdXb/8YuDQIU1uZYHdLti5M3BDMW+eiR07VEtxcrJgzJhorroqjuef\nNwc0gk5Ph82bFXbvVvCWUqeyWgm49vjxamHdyhKwrFE29OrlZuJE/8b6+ectQc84jo1V/9PQKGt0\nTz31VHk/Q8hwOBxP1alTp9TXiYqCK67wcPXVbqpW9eFyCQYMcDFypItq1cLbDQqQmJhYrvePivLx\nyScm3G6BlIKrrnLTrFn5uBHKWxZlicUCKSkKf/8dqLB16+Zm4MB6rFlj4NVXLdhsgnXrDOzapaN3\nbzfnzgnuuy+axx6LZv58EwkJPlq0KHm3C70e0tMFiiJ58UUHI0c6w6YSfGUaD4VR0WVhNKphF1u2\n6Dh8WIfDIejZ002TJsVbayq6HIKJJguVspRDamoqjRo1evrC4xXDj1cKkpPVBq4FVV4uCjEx2b5p\nLw5HJmZz6CoVRxqNGkkefdTBY4+pBWg0i2TZoCgwapSThQuNpKf7ZZ5dL+nCjLlVqwxs3KjDZhMs\nW2bMOkdw991RXHaZh9atS6Zgx8bCs8868PkIWQ0iDQ2AevUks2fbmTw5mlWrDCxfbmDAAC02UqPi\nE9FvzU2bNtGlSxwvvmgOao0vi6ViKWr5+dvT0gQ7dyrs3Klw7lxo7y+Emg59+eVqnYZ9+8qvqGQ4\nxB6UJa1a+Vi+3MqQIS6SkrxMmpTJpZd6Wbt2LQ0a5FW+/vxTz7ffGomJkdx3n4POnT1IKUhOLt1S\nYTaHp6JW2cZDQUSKLOrXl7zxhlorLCam+N+PFDkEA00WKuEgh4i3rDmdgpdestCunTerHk/l5vRp\ntebZtGlRHD2qAJK+fd288IIj35d3sKhdW/LGGxnccks0TZqUf2B5ZaJVKx9vv23HahVUqSJRFNi7\nV3UZ3XyzkwUL/MH/KSk6GjXy0qGDh9mzzfznPy68Xkr00tPQKC/q1JHccYcTq7W8n0RDIzhEfJ21\nvn2vBmDKFAcPPpg3q7MyYbfD88+bmTUrb7GYjz6ycf31oVdmjx4VSElYNUOuzBw9Knj5ZTMffaQq\nbB9/bKNOHR9Llxp57TULQvhrDNWurf3NNDQ0NEJJJa+zJrnySs2qlpysMGtWPmWYkWVWN6gkdel2\n7lTYvVuHxSJp2tRHo0ZajaNgkZAgefZZB2PGOBGCnGDsZ55RXdVSCk6eVDRFTUOjkuLzwalTAodD\n1R9q1fLlW81fI7REfMxa7do+PvrITvv2ldf1lu1vNxrzpp0bDGpAbnkWzi2If/7R0a9fHGPHxjBy\nZCz9+sXy99+Fx7ydOCE4dChva7BwiD0IB3LLIToa2rb10aaNugi7XJCa6pfxqlX6CtNirbiE+3jw\neODcOThzhlKXUCmMcJdFWaHJQcXhgDlz1jF+fDS9e8fRoUMcnTrFcdNN0WzYEH7N7ENJOIyJMrOs\nCSHeBwYBaVLKdlnHngTGASeyTntUSvl91r9NAcYCHuAeKeUPWcc7AB8BZmC5lPLegu67alV6uVsF\nPB51ZyIlxMfLcgu0btLEx7ffWvnuOwOnTgmaNfPSqZOXNm28YVvzauNGHXa73yJ85ozCqFExrFiR\nftGq0ikpav2wHTv0PPSQg9GjnVStWlZPXPExGAIbFB88qOPMGVHu8yiSkVJN+jl+XHD8uMKZMwo7\ndihs2aInLU2tdTd8uIs778zU4gc1Qo7PB4sXG3n44SjAmHPc7YbVq438+aeB335LJykpOF6OkycF\nGRmCGjV8YZmIFA6UpRv0Q+ANYN4Fx1+RUr6S+4AQoiUwAmgJ1ANWCiGaSjXA7i3gNinlBiHEciFE\nfynlivxueNlll5XrC8Zuhw0b9Lz/vok//9TjdkPLll5uvdVJjx6eoLRCyb7Pjh06Tp4UNGrko0WL\nwAnUvXv3nJ/btvXStm14WtHyIy4u77GjRxVOnBAXld+WLXr++Uet1fLss1EkJfkYOlR1g+eWRWWm\nIDlYLJCU5GPzZvWzzSbwRGj1g/IcD8ePC44cUTh0SGHlSgM//2zg5Mm8u6Zq1Xw8/riDAQPcIVXU\ntLmhoslBVZ6ee84CXJXvvw8Z4qJ69eAoahs36hg/PoqjR3Vcd52Lxx7LpGHD8Ap1CYcxUWbKmpRy\nrRAiKZ9/yq8Ixg3AZ1JKD3BICLEX6CSESAZipZQbss6bBwwG8lXWyps//9Tz73/HkPtX/P13hd9/\nN/Dvfzt5+eWMfJWR4nDsmOCtt0xZsWiChAS1WXqkWEG6dPHQqpWHHTv8QzU+3ldgu5cLM8AefzyK\nrl0jRyZlQceOHr75Rt1RS6n+p1E63G44eFDhwAGF1asNfPmlMV/lDNRm5Fdf7ea225y0bOklMVH7\nA2iUHTVqSObMsXPPPVEcOpTt8pQ0auTjoYcc9OrlITq69PdJSRHcdFMMp06p8+CLL0xUqSJ57jkH\nJlMhX65khIPz6y4hxCYhxHtCiOxXcAJwONc5R7OOJQBHch0/knUsX4LRG7Q0nD8vyF8XhZ9+MmCz\nla5YW0YGWYqaJec+R48qeWrKhYO/vaQkJfmYN8/G1KkZXHaZh/79XXz5pa3AndeF1ofjxxWOH1dl\nUpFlEUwKk8MVV/hNaZde6qF69chUFspiPBw/LlizRs9990XRo0ccN90Uy7vvmvMoagaDpHdvF2++\naWf16nQ++shO//6eMlPUtLmhoslBLajdo4eHadO+Y82a86xadZ7169P54Yd0RoxwU6tWcMZkWpqS\no6hl8/HHJo4fDwfVxE84jInyzgadDTwjpZRCiGnAy8Dt5fxMQaNrVw9Tpjh49VUzmZl+BSohwce7\n79pK7Qbds0fH7NmBaTkJCb6Ie7E2aiSZPNnJhAlOjEa1fVFBNG3qxWiUuFx+mef+WaNwWrTw0qeP\nm1WrDNx8swtL3movGoWQmipYvdrA//5nyappGIiiSFq39nD99R7at/eQlOQlIUFqmXYViPR0NUGn\npK3Ywp24OEmbNqFzSaqxsZLcRg2TCfT6yHqHBYNyVdaklCdzfZwDLM36+ShQP9e/1cs6drHj+bJv\n3z7uuOOOnL5e8fHxtG3bNsf/nK0th+rznj2/0qkTrFvXk2PHBH//vZboaMnAgd2oVUuW+vrLlv2G\nlBagd9ZvvJqRIx3UqtWlTH6/sv78999FO79r1+5Mn57B/fer3vLo6F5Ury7z7I7K+/cpz8/du3cv\n8N/j4+E//1lBhw46+vW7styfN5Sfswnm9fftU/jPfzZy4IAO6EXVqj6qVfuZRo28DBjQjYYNfaSm\n/sIll0j69fN/PzW1/OSRfay8/x4V5fNXX/3GjBlmunbtzl13ZXL06K9h9XwFfU5NFcyd+zuHDyuM\nHn0lHTt6y3R+ZH/OzIQ77ujL7NkWYDUAd9/dOSjvx7JcL0vzOfvnlJQUAK644gquvvpqLqRMi+IK\nIRoAS6WUbbM+15ZSHs/6eTLQUUp5kxCiFbAA6Izq5vwRaJplgfsDuBvYACwDXs/OIL2Qn376SXbo\n0CHEv1X58f33em66KbsWh+S++zK5885MLfMRtdxBdlzQhAlOunaN0Ah5jbAkPR1On1ZwOMBkUjPA\nq1SRmoUygvjjDx0DB6pBx23aePjwQxuNG4e/RejAAYWJE6PYsEFNwqpd21euVRPS0gTr1un5/Xc9\n3bp56N7dTbVq5fIoYcHFiuKWmWNYCPEJsA5oJoRIEUKMAV4QQmwRQmwCegGTAaSUO4BFwA5gOXCH\n9GuVdwLvA3uAvRdT1KD8Y9ZCzWWXeXn5ZTt33ungm2+sTJ6cv6IWDv72sqZKFRg82M3cufYARa0y\nyiI/NDmohEoOcXHQsKGPVq18NG4sqVMn/BU1bUyoFFUOZrNfudm2Tc/bb5vJyAjVUwWHs2fh4Yf9\nihqoNSmdzvzDRMpiTNSqJRkyRG15eMMN4amohcPc0JfVjaSUN+Vz+MMCzp8OTM/n+F9A2yA+WoWl\ndm3JmDERWq1UQ0NDI4ypVk0SH+/j/HnV5vH++yZuvNHFFVcUrTSS263WNCxLdu3S8dNPgTft188d\ntDIcGqEj4nuDRrIbVENDQ0Oj/HjjDRNPPumv4jpqVCYzZjgwGi/+HZcLfvxRzzvvmGnZ0suIES7a\ntPEWWqoiOVmwZYseo1HSsKGPBg18Bd4nPz75xMhdd/lrbiiKZPlyK506VZzamxdy8KBCRgY0aOAL\nSjmR8qbc3aAaGhoaZU1KiuC77/Rs3Bih6XplgM8Hv/+u45df9Jw+Xd5PE14MGOAmLs5vlVqyxMTJ\nkwVnnqelCcaNi2HtWgNz5pjp1y+Wjz82YrMVfK8dO3SMGqW23evePY4XXzSTnFy8V3jVqv5nNZkk\nH35YsVsxbt+uY8CAWHr0iOOll8ycPVveTxQ6IlpZi/SYtaISDv72cEGThUplkMPWrQrDhsVw882x\njB8fnaf+IFQOORSVi8nixAnBLbfEMGRILHffHc2BAxH92ijWmGja1Merr2aglp9Qu31YrQUrawaD\nWhIjGykFDz4Yzbp1BUclJSb6MJnU73k8gpdftnDddTH8/beuyEWrr7jCy4cf2njtNTs//GBl0CB3\nga7YcJ8f8+dnF5YWzJxpYdOm0ER2hYMcInvWaWhoVEr271cYMSKWffvUxdvpFCFvhB6p6HTkJEd8\n952R22+P5uhRrW5hNv36uXnzTTs6naRKFR/R0QVrTrVrS554wkHt2j4aNfIPygceiCrQKteqlY/X\nXrMHHDtyRMd118UW2XJco4bkhhvc3Hqri7ZtvYgK/GfMzFTbOeZm3jwTvggNv9Ni1jQ0NCIKhwMe\neSSK+fP9QUBDh7p49107SiXYnu7cqfD333qioyWJiT7q1/dRo0bp1vmpUy1ZLe1U7r7bwSOPZGoF\nfLNwu2HPHgW3W3DZZYXvCnbuVFi40IjVquBywYIFJkCyceN5GjW6+N8qPR2++srIffdF4fP5Na3E\nRC/ffGOtVG3JPB4YMSKa1av9gXstW3r5/vt0YmML+GKYo8WsaWhoBI1z52DDBh3794ffErJtm475\n83NHXkvGjs2sFIoaqJawxx+3MHZsDH37xnH11bHMnm1i1y6lxNbFoUNdKIpfEXjjDTNbt2pxgNkY\nDNC6ta9IilpyssKtt0bz+usWPvzQRMuWXkwmycSJzkK7z8TFwciRLr791krTpv6SRCkpOnbsqFx/\nD70eRoxwBxyrW9cbEUkG+RHRy1c4xqy5XPDbbzrWri27iRUO/vZwQZOFSmnkkJIieOCBKPr3j2P9\n+jKr/lNkNm3Skbt9zciRqssnPyJxPDRr5mPxYhu1aqn+oCNHdDz+eBRXXRXH9Olmdu5U8o1xKkgW\nbdp4efDBzJzPUgreeceEJwJrTYdyTLjd8OGHRvbv98+bKlV8rF9/jqlTHcTFFX4NgwG6dPHyxRc2\nPv3UyujRmQwa5KJu3eD7/8J9fnTr5qZ16+xBKBk3zhmSTVk4yCH8VtoIZ/16PYMHx1CrluTnn9OD\n1hBXQ6MsOHBAMGpUDNu3q0tHYfE55cHGjf5lLTHRw/33Oyq0W6QkXH65l6VLrTzySBSrVqkR5E6n\n4JVXLLz1lpnHHnNw7bVukpKK9oI3GKBfPxfff69n82b1eitWGElNdVC/fviNgXDl4EGFt98O9B1f\ncokkqyNisUhIkCQkeOjf34OUVOj4s5JSv75k/nw7W7boqFJF0rFjaHYP6ekixzJdo4akZs2yH/Na\nzFoZcuiQwrXXxpKaqiCE5J9/0klMjNBoSI2I4/RpwX33WVi6VI0FUxTJmjXptGoVXmN4wQIDd98d\nzbBhLh5+2FFgDFCkc/Kk2srnkUeiSEsLNDkkJXl4//0M2rcvWqD5woV6jh3Ts3Klnt9/NyCE5I8/\nztO0aeWVb3FZs0bH4MF+85leL/nll3RatgyvOaShkpys8NtvembONLF3r7oJbNLEw6efhq612MVi\n1jTLWhmyfr2e1FR1wTQaCYgB0bg4e/cqbNmi48wZwRVXeLn0Um9ExB8dPSpyAsH79Alff9KuXQpb\nt+qw2USOogYweLCLBg3C7yUzaJCbLl3OU7u2jNj4laKSnf3Xvr2Vn37S89xzFs6cUSdPcrKea6+N\nZc4cO//6l7vQoqwNG0omTjRz000u+vXLwGCAEycUmjbV0myLSkZG4Dv47rszadIk/OaQhlpbcNSo\nGE6dCnzZHDigw+0WZJdrKS0nTwq2b1fjf+vX91G9ev7nRcAr7+KEU8za+fPw1lv+1bBJE29ArZ1Q\nEg7+9pKyfr2Ovn3jGDcuhocfjmbgwFh27Cj5sA0HWfh8alzVsGExjBoVUy51q4oiB69Xja+85ppY\n0tIUpk71V2o3myWTJ2cSFVXABcqJ+Hho3Lhoilo4jIeyIDHRx5gxLlatsvLuuzbatPEAEqdTMGpU\nNH/9pStUFs2be+nTx8Mnn5h4+ukonnzSwogRsWzeHFmvkVCOibp1fej16rrfpYub0aOdZd5yqjhU\nlvlxIZs26Rg+PDaXorY66/+SV17JoHHj4CjYyckKEyZEM3RoLA8+GM1//nPxeA3NslZGpKQobNni\nF/ewYa4iBZNWZpKTFcaMiQkoMul0Co4dU2jTpmLuRt1utdXMbbfF4HQKdDpJx47haZn45x8dQ4fG\nUqeOj4MHdQFWgZdeyggb9+fp04K0NEHz5j50lSshrtgkJvpITPTRr5+blBSF5GSF06cVzGYKbUIe\nHw/Tp2cweHAMqak6vF6BwwGvvmrmrbcywr5RfTjQqpWPL76wYrMJ2rXzUreu5l0JR1auNOSxgtao\n4eOllzLo06fgQsJFxeWC994zsnp10S6mxayVEcuW6bnlFr/WvHRpOt26hedLOlxYtUrPsGGBOw1F\nkaxaZaVdu4onO69XVdT++9+YnBpJ99/v4KGHMsNud52SIhgyJIaDB/XceWcmn31m5PRpdZd5881O\nnn02gypVyvkhUV3kkyZFkZKi45df0ktdT0yjcLZtU7jxRlVhAxBC8uuv4Re7qKFRUrZuVfjf/yyk\npirUq+dj5Ei1f2tRE3KKQnKyQufOcbhcgUrhypU/aTFr5cmRI/4tf0KCT4tTKAIWS94X79SpDlq2\nrHiKGsDatXpuvdWvqNWu7WPkyPBzg3i98PXXRg4eVJeHuDiZo6iNGuXkgQccYaGo7dun8N//RrN3\nr57ExMiIY6wItGnj44svbMyaZebjj41IidYdQiOiaNvWx7x5djweMJkIydpiMEiio2WAsqaGJ+RP\nRC9v4RSzltuk+vTTGWVasqOixh20aOFl2jQ7der4aNfOzdy5NkaNKp1yU16y2LpV4dZbY/B41HFg\nNkvmz7eFLFMxPV21gBw7ln+aX0Fy2LtX4bnncvu0JH37unj/fRtTp2aQkFD+1qsTJwT33BOVk6E1\nbJiLatWK/1wFyeHUKcGSJQb27o3oZTKH4syN5s19zJiRwZo16fz0k5WmTSNn81lR18tQUJllYTCo\nbdYUJTRyqFtX8tFHdlq18pCY6OWJJzKYP99+0fM1y1oZUaOGupj17++id293IWdrAFStCnfc4WLY\nMDdms6ywMX6HDwvGjo3Oib1TFMmHH9ro0CE05oj9+xWefdbMN9+YGD8+k+nTHcWqwbR3ry5gt9eo\nkZfJk53ow2S1kBK+/97A77/7tfaePYOfTbtihYFJk6IZNMjFO+/YtZisC7BYqLCxoxoa4UCPHh6+\n/daK1ytyNpunT+d/rhazVkbs+X/2zjs+ijr//8+ZrcluEpLQQ0ITROmIWEBAURAbWE4s6NlR9Kyn\ngnd2v/ZyePbyQzxF1ONAESsoIiqCUqULJoQeEkg2yfb5/P74sNlsGiHJZmc383w88kh2szuZvPcz\nM695180qCxdaOOssH507J67No4EQ8isew1xCwOuv27jvPlk2qSiCN98s49xzmyZJtSp5eSoXXuhg\n2zaprI4/PsC777po167+23jwQTv//rdUJn//ezm33OLVlVDesEFl1KhUPB4pKIcM8fP++2UN8qzV\nxr59CmeckUJ+vgmzWfYTa8n92gwMDJoHo89ajOnZU6NnT2+sdyPuyM9XeO892fLklls8cdeJftMm\nlUcekcLHYhG88koZZ53VOKG2davK1q0q3bsHIxozlpfDSy/ZKoQawLHHBtm61US7dvX34vXoEeS6\n6zyMHOmnqEjl4YeTKChQ6dxZ47LLvDFt4OnzwcyZ1gqhBoIHHnA3qVADWb2dny/zTAMBhT17VLp1\nMxKz9MLGjSovvmjntNP8DB8eiElHeQOD5iQOfRX1R085a7EkXvMOiorg0UeTeOYZ+bVpU+P7MjS3\nLTZsMOHxKHTrFuDzz12MH+/Hbj/8+2rfnso556RwySUpXH+9k4KC8A3Y77+bePvtyp1NBT17Bpk9\n21ptO7XZYedOBatVFkNMnJjCrbc6mD7dzmefWXn5tK78tgAAIABJREFUZTu5ubHtjbFli8qrr4YN\nePXVXvr3b7iIqs0OxcWRN7aJOAOzKvF0nsjNVZk1y8YNNzi57joHW7c23aUsnuwQbQxbSPRgB8Oz\nZqBbVqww89//hsVH5X5r8UJOjsa775YyYECATp0ad/dfXAyPPJJUMTZo1Soz+fkqbdpIsTJnjpXK\nA8zPPNPPt99a2L9f9sM6XM7VmjUqN9/sqJj7GYngnns8DBkS23zLjRtNFdW0mZkakyd7ozKloKws\ncq0Z/dv0ReUWLUuWWLj11mTeeKNMF8UvBgbRIKE9awMGDIj1LuiCYcOGxXoXjhivF955J3L+Tajz\nd2Noblscd1yQc87xN1qogRxz8tVXkV4y7VBEsqSEiOaKbdtqnHBCgIULLezcqVbzFFW1w4YNKuee\nm1qjUOvdO8CcOaXcequHzMxG/xsNRtPg00/l/5+SIg7N52tcSLa29aBV2aweB9Y3NfF0nujaNUiv\nXmF3588/W5g+3YbH0/htx5Mdoo1hC4ke7JDQYs0gftm1S2XBgrD4MJkEHTok/gWzLnbvrurtEaSl\nSZuYzdCqlVQYxx4b4Pnny3j2WelK83qVauKjKi6XUkkMC7p0CfLPf7r5/PMSPv3UxYgRgZiPlhIC\niooUWrfWmD3bxeDB0cshs1pFxM9paVH7UwYNICMDnnmmnMrzGV94wc6aNYYL1CAxSWixZuSsSfQQ\nbz9SCgqUiPYRo0f7ycpqfGJ7PNoiRDAYKdbGj/eRnS1tkpwsL17//a+Ljz4qpaREiQjlVS36rmqH\nIUOCLF5cwi+/FLNiRQkLFri4804PJ54YJD098r1+v0z0b25MJjnuaMGCphNqta2Hymvt/PN9dOqU\n+C0q4u3YOO64IPfdF3alCaEwe7b1sDcmhyPe7BBNDFtI9GAHI2fNQJdE5ggJbrjB2+L7XHXsqKEo\nAiEUUlIEt9/uiShWkD2v5JWqcniwd+9AvaolZb5P3a9bt07loYeSKClROPnkAIMHB+nVK0i3btoR\n9XJrKM3V1ys7W+O44/ysXGludCNmg+hgt8uJGps3qxW5rf/7n5U77vDQvn3L9sIbJB5GnzUDXfLn\nnyojR6bicinccYebO+/0RCWRPJ7wemHBAjO//WZm/Hh/nfNRDxyAiy5ysnKlhaeeKuP665vGFbZt\nm8KoUakUF4ed8g6H4KabPIwf70uoYeqbN6sUFSkMGhTEWr2g1kAn7N+vMH++hX/8I5mOHTW+/NJF\nRkbiXtcMEpva+qwZYs1AtyxbZuLAAYXBgwNHnNheUgKbN5twuRS6dtXo0iXxw1hV+f13lWeeSeLh\nh8vp0qXpjvMVK0xcdpmTffsisyisVsHdd3u49FIvHTsm7nml2dA0Gb9WlPjsCI3sV7dhg4qqQqdO\nciZyNLyUQsi/JQQt8lg3SBxqE2vxeQaoJ0bOmkQP8faGMGRIkDFjjlyobd+u8Le/JTN6dAoXXpjC\n6NEpbNwol3q82qIh9OmjMX16WY1CrTF2GDQoyLx5Ls46y0flsKnPp/B//5fE9dc3bd+raKK79aBp\ncip6IBAWa4GATBQMBOTvQklZodc2NknrEE1tiz17FC66yMGll6YwYUIKw4en8sQT9lrn1TYGRYHO\nnZvmpkx3ayKGGLaQ6MEO8XFGNTCoJ14vvPaanXnzbIR6ju3fr7J+fYLE5o6QaDlkevTQeO21MubP\nd3H66ZGi7eefLVx7rYN9++KvL15M0bSwQPP7wwJN0+R3nw9KS2XDveJicLvlc4FAdSGnA9xu2W4m\nRDCo8K9/JTFlSlJEM2cDA4PDY4RBDRKKrVsVTjghraJxaogZM0o599zYNnRNVMrLZch52TIzX39t\nZv16M+npgrfeKo3paKq4IiTIQoTEVzAYDoN6vVQ0EtM0mWEfqjBRVbBa5ffQV4zDqF4vPPBAEm++\nWX1kx8cfuxg1qgWMhTAwOEKM2aAGLQJFUTCbI1tLtG2r1ZmMb9A4kpNhwIAgAwYEueYaL0VFCjab\n0Zus3oQ8aqGfhZAL2OuV34WQX8FgOCwa8rLZ7WCzyQ9BUWQZtcUSuc3QDXkzCzabDW67zUNxscJH\nH0U2uHa7Dc+agcGRkNBhUCNnTVJXvL28XFYOJgqdOmk8+GA5qiovUP37B/joIxedO8sLlx5yD/RA\ntOxgNkPbtvEj1HSxHkJiStPkAVlUBGVlskomPx927oQ9e+T3/HzYvRt27YJ9++TX/v1SuPn9YUFX\nNWJSjwhKNGzRsaPgySfLmTPHxc03uzn5ZD+PPlrOoEH69arpYk3ECE2D334zMW2aje++M/Pddy3X\nFpU5kjVRWKjwyCN2Jk9OZtEiM4WFTbMPhmetheJ2y4Py8ceTKChQueceNxkZgmOOCcZ1JZ/VCldd\n5WPkyAAej0w6zsiI9V4ZGNSBokihVVoaDnWWl0shduCAfD4YlK9RFOlVM5nA4YC2bcPPBQLyAFAU\n+VVZoDVHE7xaaNUKRowIMGJEAE2L28LWFsHy5SbOOy8Fv19BUQRPPqly6qmx3qv4oqhI5mYCzJpl\nY9w4L4884iY7u3HXVSNnrQWiaTB3roXrrnMQSsJPSRFcfbWXvXsVnn22vMX3NDMwaDY0TXrSiovl\n98JC6S3bv1/+fPCgFHGaJkWXpkkXZnIytG8POTmQlQUdOkBKihRsZnPMc9YM4ovCQoVzznGyaVPY\nh/Pyy6VceqmR63skFBUpnHWWk82bw3Y89VQ/L71UVq+RiS2ydYdBzfzxh8ott4SFGkhPm90u+PBD\nKzt2GMvCwKBZCOWWBQJSlO3eLb+vXw8bNsiw565dkJcHf/4JmzfLn/Pzpddt+3bYulW+ZscO6ZEL\nbdeg2Tl4MNZ70HC2b1cjhBoYGr8hZGQI/vEPT8Rz331n4aWX7BX1QQ0hoT8KI2dNUjXevmmTCY8n\nUrifeaafRYssgFJxvk9EWnI+SmUMO0hiaofKLTlCX3v3wpo10su2fz/k5kohduAAFBTIr5C3bfdu\n+Xj3bingcnPlY58v3MZDiMhigzow1oSkIXYIBuHLL82cfXYq69fH52W1pvP+gQPfH/Z9xcVS6AX0\nm4bYaI50TZxyip8bbohUZq+/bmPLloavjfhcVQaNomrkOz1d4+STAyxbZkJVBU5nbPbLwKDFULnR\nrdstw5/l5fLKV1mIFRRIARd6vGdP+HFxsRRx+/ZJQVdQIAWe11v97yVwuoseWLfOxJVXOtmwwcRn\nn8XnbLK0NIGihNfJmWf6yMmpW+Tn5alMnuzg+ONTefVVGy5XtPcyPmjVCu64w8M114QFm6Yp/PFH\nw/t9JrRYGzBgQKx3QRcMGzYs4nGfPkGOP96PxSIYM8bHPfd4eOKJJEDhggt8ZGUlbgilqi1aKoYd\nJDGxg6ZJoebxhNtzuFxSaIXEWmGhrAbds0eGPPfskb93uaQo27FDCrXy8rCnzeWS7w8EqhcU1KPA\nwFgTkiO1g6bBjBlWAgFp40WLzBGtg+KF7t01nnqqHKdTMG6cj8ceK+ess+q2xfz5Fr74worfr/Dg\ng8msXJmYNYsNOTbatRNMnerm3XdLOfroAFarIDOz4TdNiWlZgzrp1k3jww9LcbkUNE1wwQVOXC6F\nzEyN227zkJwc6z3UN9u3K8ybZ6VTJ40zzvAb9jKoP5oW2UMtEJAiy+WSoivUtsPjCRcdhKhc4ako\n8rUWC7RuLb1zLpf8Hpp6oKrhylAj+Shq7N2r8MknYW9aSYmCzyfrPOKJpCT46199jB3rJyNDkJRU\n9+tLS+HDDyP/yS++sDB8eALHQ4+QzEw45xw/J5/sp6xMoV27hou1hD6CjZw1SU3x9latIDtb0Lkz\nfPRRGR984OKLL1z07p24XjVofF5OSQn83/8lcf/9yVx9tYPff4/PMVZGfpKkWe0Qyh0LTSbQNCnK\n3G555fP5pMctlL9WUFB9GyHxBdKr5nbLRXnggNxWIBDuuRZqkltPoWasCcmR2qGgQKGoKGzjbt20\nuE0lsVggKyss1OqyhezLHOmx3bw5PiVFXp7CzJkWVq0y1Zgx0NhjIyNDXm8bI+Dj07IGTUr37oIx\nYwIcdVRiC7WmYO1aMx9/HOrGrrB1a3yKNYMYUHmSgMkkv8xmKbJCbTv8fvm9tFR+r2kboe34fDJX\nrbg4XFQQCIS3U8/CAoPGUVISKViGD28ZrS7S0mDo0Egv2oknxuekmDVrzNxyi5OxY1P4/nuzLg+b\nhBZrRs6axMhFCdNYW6xeHSnO4jWh1lgTkmaxQ8ibFhJZJpOMkVmt0pUR6p1WVCRFWigPDcKetKpN\nbkOEvGxCyO2FCheOsBIUjDUR4kjtUPVj6dlTh1f6BlKXLUwmmDjRi8kkDaCqglNPjU+hGqrJ8XoV\nLrnEybp14fP8/v0KgwfH/tgwctYMDI6An36KPGQak4Ng0AKoSSyFQpNmsxRxJlO4QGD3bllIUFIi\nX1tXYYAQUpjZbNLNERrm7vdLwRfqbB0SbUaD3KjQurUABKAwaJCfY4+NH+/Spk0qq1aZMJmgX7/g\nEQvNgQODfPqpi6++snDGGX7694+f/70y6enh87jPpzBtmo3HHivns8+svPiineHDA1x6qZeUFMGx\nx2qYY6CcEvqoNXLWJEYuSpjG2MLnk3dZlYnXylljTUiiboeqbpfKnrJQsUGo9UZJiRRvtbXeqM3L\nZrFIgWYySeHm98scNpdLetoqi7U6PG3GmpAcqR2ysjQuvNBHRobGs8+6D4k3/bNmjcpZZ6Vw001O\nbrjBybnnpvDHH5GS4HC2sFjgpJOCPPSQh6FDg1gs0dzj6NG9u0ZaWvi4+PxzC0uWWLjnHgc7dpiY\nOfNnZs2yceONDn77LTapLwkt1gwMmhKrFU47LZyjMWyYn27dqt9JahqsWmVi3jxLXHc0N2gCqnrG\nhJACyuORIc+dO6U3rXLeWk2x9ZBAC31V3m6oVYeiyG0UF4eLF0LFCpUFmtFzrUlJTYWHH3bzzTcu\nBgyID8+SEPDaa3YOHAhLgIIClV9+aZnBti5dNO68M9wTbcSIAG+9ZYt4zYIFFk4+OVAtFaa5SGix\nZuSsSYxclDCNtcWYMX6cTkHHjhpPPllebUi83w9ffmlhzJgU/vpXB0VFsRugXRfNtSZ8Pli82Mz7\n71vZuVN/toi6HVQ13EJDVcNiLSTYQsPaDx4MN8f1eiOrPmtDUWSo02KRIdXQ36mcB1e50CAk2GrZ\nrnGekDTEDh07Crp2jR8ve1kZrF1bXXT4q6ScRXtNlJfD1q0Ka9ao7N0b2/PDuef6ad1afoaZmYI9\neyrLo5F4PPKGPSsrNjc7CS3WDAyamv79gyxYUMJXX5Vw7LHVT84LF5q58koHfr9Cq1YCuz0GO6kj\nfv/dxPnnO/nb3xy88oq9xghfwhOq/oRw2w4hwtWbBw6EG9weOBBZ8VmZmkRWRgbY7TL8aTJBerr8\nqiwOQ0IutC9GzlqLx+mEceMilZmqCvr2bR7PoKbBb7+ZuOoqByeemMbIkWmMG+ds1DimxtKli8aM\nGaUkJws2bjQxaFBkpevIkQF27VKqPd9cJPRRa+SsSYxclDBNYYuePbUa7642blSZNMmJpsmL6rhx\nPjp00GfIqbnWxA8/mBFC2uP1121s2hT9U05urkpubv3u0pvt2Ah5tkLeL02TIsrplD/bbPL5UGFB\niMqhT4j0uFks0rNms8nt2GyyQW5GBqSkyN/b7WGxVlm01YBxnpC0FDtMmODliiu8JCUJsrI0Zs0q\nrSbWomWL7783c/bZKSxYYCUYlOt582YzeXmxlSQnnRRk3jwX3boFuPpqWVAAkJr6LWPG+PnHPzzV\nzunr1qncf38SV17pYNo0G8uWmaIyX7tlBqgNDJoYlwueftqOyxUWCRdc4K/PlJ+EZu3a8ClG0xR2\n7VLp1y964aLSUnj8cTtOp+Dxx9368WxW7rFmtUqvGsi4U6tWsm1HyDsWrMO7UdnjlpwsxVpamhRo\nrVuH+7c5HFKwWa1GFahBjWRnC556qpy773Zjs0GbNs1zY7ltm8rVVzvw+SJPjg6HoFOn2IeSBw4M\n8sorbsxm+PTTEnJzVQoK3Iwd6yMtLfK1hYUKV17p5M8/pedczoUV3HWXh+uv99K2bdPZNKHF2pHm\nrBUWKigKZGTo0xvSUIxclDDRssXatSbmzg23pz7jDB/9+ul37EpzrYnk5MiTb2UxGw3y8lT++18r\nZjNMnuw9bKPnZjs2aqrgdLvDY6dCkwtCr60PrVrJGUGh75mZ8rvNJj1qIXFmql9CtHGekBzODqFI\nddV81XjEbodOnWq/3kVjTRQVKZSURN44JCUJ3nuvlF69Yi/WgIrWHP37a/TvrwEn1/g6q1WQnq5V\niDWJwnPPJdG6tcakSU03JNa41ULejc+caeHUU1MYPTqFX34xutLriVB+w7x5FlauNEWMS9QDbjc8\n95wdkBdZi0Uwdaqn2l1YS6Rfv0gvUbQ9jTt2qIBCIKCwe7eO3JqVCw0UJTypIBAI55aBFF6Vqdyu\no+rzDge0bSvf06qV9LTZbFIIhjx0oTmhBo0mGITvvjNz1lkpnHVWCkuWmI3C2gbQubPGrbe6cToF\nHTpo3Hijh6++cjFihH5vbmsjJQWefNJdES6tzKxZtiYNhya0WKtvztrixRZuucXJjh0mtm0zMXGi\nkx07dHSibyTxnoORn69y9tkp/PWvTkaNSuHuu5PrnZNUlWjYIj9fZfHicIOh//u/8mZL1G0ozbUm\nBg4MoijhE1nnztEVDps3h2+09u07/OmtWY+NUKGBooTHQ4Xme4b6oFks1fPUoHrOWrt28kphs0lv\nWkaG/F5Z2IXeU88pBs1pC78fdu5UKCqK3t8oL5dNX4+0yrA2O6xfrzJhgpNNm8xs3mzm4oud1XIw\n8/IUFi40xzRRvimJxppo00Zw330efv65mO++K+Hxx9306RO/58vBg4N8/nkJF14YnuZgtQpuu81D\ncnLT7UNirKhGUFwsc1wqU1ioUliYOGIt1pSXw549Cvv2KQ26E1UUga2i5Y3Cf/9r49JLnWzdqo/l\nu3OnWpEke8MNHsaN89c38pTwHHtskClTPIDg/PO9HHVUdE/KlROUox1ybTCVKzVBCji7XXrGQpWd\nlancVy0k4kIFCWazzEsLvS/UygMiCwp04gJyu+HXX03cdVcyJ52UxssvRy+p8OuvLZx0Uipnnuls\nkkama9eaCQTCa8rjUaqdg1auNPOXv6Rw+umpzJ9vqXG8q0G4BUZT5nTFkt69NV56qZxffinh22+L\n+fHHYs47r2lHb+njahcl6pOzVl6uVOmnAiaTaFJFHGtilYuSm6vy7rtWzjvPyfDhqYwcmcrTT9uP\nODyVnS244w53xHObNpm5667kIw6JRsMWNpsgKUnw4IMyWbe5EnUbQ3OtiaQkuOkmD99+6+KJJ9yk\np0f37xUVhY9lj+fw6ywmx4aiSIFmscjigPR0KbSs1vBw96pUFluZmfJ9drvcRkaGfE+rVpFh0MoF\nBfWIP0fbFvv2Kbz8sp3Ro1N47z0bpaVK1I4VIWDGDCugkJdn5oILUli7tn6Xu9rs4PFUfy5U+R3C\nZpP/j8ulcMUVTubPtxBoouheIAArV5qYNs3Gt982T7q5kccoqY8dbDbo1k1jwACN7t1Fk9fzJHSB\nQX1o1UoweHCAr78OJ4ffdJOHnBwjz6Mx/Pqricsvd1JQELlin3oqieOPD9ChQ/3PYIoCF1zg49tv\n5QiQEIsXW1i/3sRJJ8XWhd6/f5CffiohKys2M+OaE58Pli0z8cEHNmw2wdixfoYMCdSZn+d00myd\n3SuL96oNPmNOKNQphBRToeKA9u3lJAOHQ36lpsrCg1BVaMiD5nRK75vTKUOgqany58xMuQ2nUwq+\nkEct5L3TQSXojh0KU6Yk8/nn4fNserrGqFHR+ZAUhYgWCy6Xwj//mcyMGaXV0gLrS69ekWvYbBZ0\n7x75XLduGmazqPDA3Xyzg86dXZxwQuPWf3k5fPSRlbvvTiYYVOjRI8hXX5U0+H8xiD8S2rNWn5y1\npCQ5KmTgQD+tWmlMnuzmxhu91SIR8Uxz56zt3atw9dXVhRpAq1Zag4RwTo7gpZfKmDAhsqvqkU4I\niIYtHA6ZixVPQq2hdli+3MS4cSl88IGNd96xM2FCCm+/bcPtPvx7m4PKrTpSUw/vtWn2PmuhZrgm\nU7j1RjAoRZbFIp/LyJA5aU6nFFkh71nr1rKgoG1b6NJFfh1zDHTvDjk58r2hEGjIs1bVw1YH0bLF\nzp0Kt97qiBBqqip4/fUyevSI3k3x2LGRQvCHHyxVqvZqpjY79O0b5NFHyzGbBampGm+/XVZt8HnX\nrhq33x52wQWDCjffnMz27fU7T+3Zo7Bpk0purhrRQPq77yzceWdyRbpFZqbWLNeoeM93bir0YIc4\nurxEj6OP1pg9uxS3W6F1axG3w2j1gtdb8yzqIUP8PP10+WHbKdRGTo7g8cfLueQSH4sXm7HZqHGK\ngEH02LDBVNHkNsRjjyVxxhl++vaN/WfhcIQFWlKSjsLRVYsF/P7q+WYhr1hycriVRygPzWqVP9ts\nYW/cgAHQsSO0aRMOoYYKGHSC3y+r4hYtCp9UTSbBjBllUa/+GzAgQMeOGrt2hcXqjh0qAwc2zMuV\nkgKTJnk580wfFos8H1XFaoWJE33Mnm3hzz/l5XXbNjO//momJ6d2L6LPJ4eH33tvMgUFKmaz4LLL\nvNx0kzyR3nijg1C1OcCECT6Skhr0bxjEKQkt1o6kz5qsfq/95L57t8LGjSa2blXxehVOOCFA//7B\nuBB2jck7+OMPlTlzrGzbptKli8bw4X569QrWmXuUkyP49FMXP/9sZs8elXbtNHr2DHLMMRqZmY27\ngKanyyG7DT3RGzkYkobaoWavqILbrQ+BUNlTk5Z2+LXW7H3WQlWZqhoeOxUIyO9JSeHwaOg5oOKq\nHJoB2qEDdO4sPW9paZGzQUOVLQ0oKIiGLTZsUHniibC7MzNTjvQZMiQYdU90drbgnXdKGT8+hfLy\ncFudw1GXHcxm6N697m3k5GhMn17GOeekUloq/+7771s5+2x/rd6wtWtNXHuto+JGKBBQePddO3l5\nsol0WVn4+GrfXmPkyOZpc2GcLyV6sEOziTVFUd4GzgH2CiH6HXouHfgQ6AzkAhcLIYoP/W4qcA0Q\nAG4TQnx96PlBwDuAHfhcCHF7NPdbCJnUef31yRV3SiDvDhctKqF379h7E6LJf/9r5emnw7dwTz2V\nxCmn+Hn00fI6O9H36qXRq1fTNQQ00AfHHRdg8mQ3r7wSXhMjRvij3pKjvhxzTPgi1rGjPvYJCIci\nQyOnKt/l2e3SbXPggAx1FheH889UVbqnQp63zEzpaQuFSlNTpRAMBCKrSHXiXdu1S0XTFGw2weTJ\nHi6+2MfRRzff5zJ4cJDPPnPx73/b0TTo3bt5cif79dOYO9dVcd3IyzNRVla90DeETGWs/pl16yaY\nPTscPjaZBG+8Uaqb482g+WjOnLXpwJgqz00BFgghjga+BaYCKIpyLHAxcAwwFnhFUSrOPq8C1woh\negI9FUWpus0KmmI26Jo1Js49NyVCqIWIlxylxsTbjz+++h3cDz9YOP/8FNavj7+URz3kHuiBhtoh\nMxPuucfD/PklvPVWKR984OLll8to104fIceOHeV+5OQE69UWoNn7rIU8YIoixVdIgGVlye+tWkkh\nVtlrFnocKi7o0SMcGjWbw+FPszlcTNCAgoJo2KJfvyBffFHCDz+UcN99nmYVaiEGDAjy1ltlvPFG\nGdnZzbcmBg0KMmdOKe++W8oLL5TXGY3o2TPIbbe5AVHl+UBFXq7NJnjzzbJGFyscCcb5UqIHOzSb\n3BBCLFEUpXOVp8cBIw79PANYhBRw5wGzhBABIFdRlC3AEEVR8oAUIcTyQ+95FxgPfBWt/f70U0sN\nIR7Bk0+W061b7O9u1q1TSUsTdY4MaQwnnBDggQfKeeSRJCrnTBw4oPL66zamTdNJZrlBs5GayqEK\n3MNfNLZtU9m+XSUrS4tqMnmIDh2CjB3rY9CgAAUFim5EZAWV+56FctMCATnNoHNnyMuTv7fZ5PM+\nnxRsqanycahNR8jzZrGEhZ8OZ3927Cjo2DH2DU8VhZikrOTkiDpz1UKkpsKdd3oYO9bPb7+ZKS5W\nOPbYIAMH+snIEOzcqTJqVIDevYN6/JgNmoFY+4baCiH2Aggh9iiK0vbQ81nAz5Vet/PQcwFgR6Xn\ndxx6vkaOdDZoTWRna8i7HSlU2rfXeO65ckaM8Mc8X03T4LnnksjNVZkxo7TWu8bGxNudTrjuOi9D\nhgR49tkkFi0yE7JFmzaiIqoTL+gh90APNIcdCgoUrr3WwerVZlJSBDNnuhg6NLoX7pQU6N07wMKF\n8ibr2GM9da7PmKyHyqOnUlLClaIpKfL3e/aAyxX2koX6sjkcMmkzVOFZuUFuE7j5jWNDEis7pKTA\nkCFBhgyJPEays2PXg8ZYExI92CHWYq0qOrsNhosu8tGrV5CiIoX0dEHnzlpFqCXWCCFLvVetMjNz\npo077/RERUA6nXDyyUH+859S/vxTpbhYwWaTrns9CLX161V+/NFMx46Ck07yJ8SA5URg926F1avl\nKcblUrjkkhS+/DK6eZ4OB/z2m5mlSy2sXm1mwgRfs3j0jphQoYHdHq4KtdnkoGKTSX63WMLtPIJB\neSBCuPIzdLDr4SA0MGgivF7YskWlY0fNOJdXItZiba+iKO2EEHsVRWkP7Dv0/E4gu9LrOh16rrbn\na2TatGk4HA5ycnIASEtLo2/fvhUqORSHPpLH27ZBx44Nf39TPv755yWkpdmA0Tz7rJ22bb+lRw+t\n2utD72ns31u2bAk7dyqceOIpHHWUFvP/f8mSJeTnK9x//1mHOtcv4sYb3Tz++Im1vn7t2rXcdNNN\nUdsfjwcGDRpGRkbs10ddj6uujWj8vQ0bfkCu/eZiAAAgAElEQVRRHAhxKgBlZd/zwgte3nprSFT/\nv27dzuC778Dt/p5PPinn738/qdbXR3s91PpYCJb8+KN8fNJJ4HSyZPlycLsZ1qsXFBWxZOVKSE1l\nWO/e8v2rVoEQDBs0CJKSWLJsGdhsDDv1VDCbWfLTT43av1dffbXR58dEeBx6Ti/7E8vHsTg+9u49\nlRtucDBu3DdcdpmX00+PvT2ieb4M/bx9+3YABg8ezKhRo6iKIppxZpyiKF2AeUKIvocePwUUCSGe\nUhTlXiBdCDHlUIHB+8AJyDDnN0APIYRQFGUpcCuwHJgPvCiE+LKmv/fcc8+Ja665Jtr/Vkx55x0r\nd97pAODyy708/3x5Ne/akiVLGu3GFQLmz7dw9dUOunQJMnduKVlZsfcwvvCCjUcfDc8Gy8kJsnCh\nq9YWIU1hi9rYtk3l4YftbNli4vXXy3TRd6w2ommHEKWlcPnlTn74IbwgD/f5NAUff2xh0iTphbr8\nci/TppXX6nxqDjvUSOXh6sGgDHVqmmxVX1wsh2i63dLrlpISbvURas8RKk6wWKRHLhRabYSXLWa2\n0BmGHcI0ty3+/FPl1FNTKClRAcH335fo4jzanHZYsWIFo0aNqlYa3Gz+c0VRZgI/ISs4tyuKcjXw\nJHCGoiibgFGHHiOEWA98BKwHPgcmi7CqvBl4G9gMbKlNqEHT5KzpnS5dwgv5o49kP7SqNMUi+/13\nlUmTHASDClu3mtm+PfahF6+XiK7oAHv2qJSX1/6eaB1wgQC8+qqNefNsbNxo5p57jnxuaXPSHCce\npxPuu8+NyRQWZsXFCr4od3TJygofE/PmWdi1q/Y2FjG7KFfOWwvloIUqO83mcPgzOTk86D00wSBU\nHRp6XRMNazcEisSwQ5jmtsUff6iHhBqAwrZth5840RzoYU00WxhUCHFZLb86vZbXPwE8UcPzvwF9\nm3DX4pquXTVSUgQul4LfL/PXjj666a+GixZFVsW6XLHv42Q2Q0ZG5F1X796BejVDbWry8lTef99G\np05BzjgjQGqqRkGBSlpa7O8KY8lxxwWZMaOU66934nYrXHWVl9ato/v5dOggsFoFPp9CSYnKrl0q\nnTrFviKxGpW9YKFRVKGmuKoqPWuBQOTvLJawh02IIx7WbmCgZ0pKItewx1PLC1sgsXePRJGm6LOm\nd7KzNS68MDzbacYMK2Vlka+pHBtvCAcPwnvvRXZzrM/cxWhjMsGFF0YK03vv9ZCaWvt7GmuL2igs\nhOuv93LuuX6+/NLCG2/YufHGZFat0sedYVWiZYeqmM0wdmyA774r4fPPS7jpJm/Uq6g7dNAYOjRc\nQbdzZ+2nueayw2EJedkqf4dw7zSQIi00V7RyX7VG9FarjG5sEWMMO4Rpblv4qxS++nwKixebYz57\nWA9rIqHFWktAVeH888Mr/Jdfmj5EWVio8Mcf4W0mJQnd9K867bQATzxRxtChft59t5ShQwMx2Q+z\nGZYsMfPqq3Z271ZxuxVWrLBw661J7Nmj4HJJJ0lLRFGgZ0+NE0+sX6PaxmK3w1/+Ej4mfvyx2QII\nDSeUwxYKbZrNYQ9b5SHwECnKQsLNqAg1SADs9sjHe/eqjB/v5Ndf4+AYjjIJbYGWkLMGcPTRQbKz\ng+TnyyHbeXkqxxwTDr81Nt4eDCoRo1DOP993qP9c7GndWjBpko+rr/ZhtR7+9dHKPdi/X2XlysjD\nqU+fAJdc4mfCBCeBgEK/fgEuushHnz7BmItdPeRgRJOePcNhz59/tuByuSvamFVGN3aoLMTs9rC3\nrHIhQuUJCEJEeuCaAN3YIsYYdgjT3LaQOdiyr6nDIQgGARS++srMKafE7m5XD2vCuB3TIWVlch7p\njz+a6kyODtG2reCBB8J+4v37m/ZjTU0VtGkjLxjJyYIbb/TobtRWSKht3KgyZ46FWbMsrFhhOnSw\nRx+ZJxcpwE48McBLL9lZu9bMhg0mPvzQxl/+ksJ55zlZtkyf4dFEoXv3IMcfL71rhYVKxSBv3VI5\n30xVpVfNZpMFBna7/ApVglb+bmDQhKxbp/LFF2by82NzvHTvHmTCBB8gZ8nOmiVP7KEWgy2ZhD7a\n4zFnrbgYpk2zM2pUCueem8pllznJyzv8xzR8eIDjjpMXpy1bIl/f2Hh7+/aCZ54pp18/Px9+WEqf\nPvrwqlVl2TITo0encu21TiZPdjJ2bApLl0aqymjlHvTvH+T990vp189P585Bxo/3cdllXv7+9+rJ\nFlu2mDn//BSWL4+dYNNDDkY0SUuT43sAiopqr0DVjR0qV4eGPGhWqxRpDof8HuWRUrqxRYxpqXbY\nvFnlnHNSuPzyFG64wcHu3Uqz2yIlBa691ssDD7j58UczeXnyHNm/f2xzSPSwJnTmHzH49Vczzz6b\nVPF4zRozy5eb6Ny5boHUpo3gmWfcnHWWOSoJ3Oec42fkSH9E8v7u3Qq//mrm119N5ORonHhiIKrd\n6euioEDhxhuTKS0N3xH6/QrTp1ubJY/NbpeJ9KecUorPJ2f9mc3QrZsPvx8eeCAZvz+8b263wjPP\n2HnvvbJ6hW8NJJs3q2zdqnLUUYefNdqvX5AuXQLk5poqIom6pqoQC4mz0Ew3vbmzo0xpqTwfLlli\n5i9/8cVkCHxLYt06E8XFcg3+8ouFtWtNJCcf5k1RwGYTEbOoe/cO0K+fDqu5m5mEPvrjMWftp5+q\nfyQ1tcnYuFHll1/MfP+9Bb8fzj7bx6hRAebPd1U7pzdFvF1ViRBqBw7AHXck8/XXYaWRnCyYN8/F\nwIHhA2vDBpW8PJVWrQTHHhuss1KzMZSVQW5udU9Vp06RJ/ho5x5UddenpsK11/oYNizAN99YePNN\nO7t3KyQlwbhx/phdf2OZg6FpckTY5s0muncP0r9//S7CBQUK11/vYO1aM61ba8yZU0rv3rWfxDt0\nELz8cjl//7uj1uplPeSi1EkzLhA92WL/foVXX7XxwgvyxrVbNy0qLYlqQk92aE7++CPy/PnZZxZe\nfLH5bdG1q8att3p48cUk+vQJ8PrrZTFvwK6HNZHQYi2abNyo8uWXFvr0CTJ4cIBWrZpmuzZb9ecq\nN74VAhYuNHPttc4IETd/vpVnninj2mub54S2ebMpQqgBlJcrvPeelYEDZehvzRqVc85JrfB23X23\nm5tvrru1RkNp3VowbpyPTz4JG7BdO+1Q/kNsMZuhd2+N3r29XHqpD49Hit+sLNHi0o68XvjkEwu3\n3urA51Po1UveYKSnH/69e/YorF0rT1n796vcfXcS//lPWZ3TEE44Ici775bWa/sG+iAYlNNSQkIN\nZAW6QXRJTo608ZYtZgKB5nfoOp0yheHyy31kZIioTjuJJxL6UtHQnLUNG1SmTbPx9ttWfvzRXK0T\nvRDw73/beeSRZC6+OIV//cvOwYNNsMPAmDF+HI7w4vzrX7306xcO4/3xh8oVVziPqCltNOLtDodA\nVasfRJXd5u++a4sISz7zTBJr1kTnyHc64bHH3Dz/fBkTJ3p4/PFyPvnEFVEVC7HPPWjXTtC5syA7\nO7ZCLVZ2WLrUzE03SaEGcOCAWvHz4TBVcZwuXWph48a6jaiq0L177Z67WK8HPaEXW2zYoHLPPZHx\nt8pTKaKNXuzQ3PTqFeml7to1yNKlsbFFair06KHpRqjpYU0YnrUamD3byvPPh+/qzjzTxwMPuOnV\nS54w/P5Il7F01wa56CJ/tW0dKf37B5k/38Uff8jQYb9+QTIzw793uRS83uoXt379Apx2WvMlYR51\nlMZTT5Vz773JaJrcn5ycABMnhhv0yuHqkeTnR0+hZGUJrrrKx1VXRe1PGDSC/HyFyZMdEW1gjj8+\nUO+JBunpgtattYhq57w8E0OHGvksiYLfD9On2yLyO0eP9lUTEofj4EHpfU1P1yLOnwa106tXkE6d\nguzYIa9tY8Y0/npm0HQktGetoTlrlXOuAL780srZZ6fw229yEVutcPrpkQt56tRkduxomnLnfv2C\nXHCBn9NOq34hO/roIG++WUq3bkFat9bo18/PSy+V8cEHpXTtWvPdZzTi7XY7TJzoY9GiEt57z8Xs\n2S4++6w0Igl49OjqB3tlr2Es0EPugR6IhR3WrjWxe3flU47g5ps91TxmtdGhg+C22yLnzxQWNu6Y\nM9ZDGD3YYs8ehY8/DqcyWK2CKVPqnzrh8cCSJSYmTHAyZEgaM2fWkFdyGPRgh1iQlSWYObOUM87w\ncccdbk46KdBibVEVPdjB8KzVwIknBhg1ys/CheGyygMHVK66ysG8eaV06aIxfLifJ56wE6pYKSxU\nyc2N/gxChwMuvNDPaaf58XoVnE4Rsx40Nhv06aPV2spjxAg/EyZ4+fBDecI8/ng/Awe20Db+BmzZ\nEqnK7rzTQ9++R3a8nHeej//8x8rmzfLUddRRRoVgInHwoFIpdULwr3+V1bsSsKwM5syxcuutyYTO\ny3v2JLQ/osnp00djxowyzOYWV3ysexJ6JTc0Zy0zUxzKffJGPL9zp4m1a+UFp0+fINddF/n7Awea\nr5Fgerrsf1YfoRareHuHDoLHHy/niy9K+PTTEqZPLyM7O7aeNT3kHuiBWNihTZvQZy+YNMnDtdd6\nj7g1QHa2vPu///5ypk51M3hw48S/sR7C6MEWrVrJUHdGhsYHH5Qybpy/XrmdmgZff22JEGrQsFCe\nHuwQDYJB+PxzM3fdlcTnn1vYs6fm65XdHhZqiWqLI0UPdjC0cy1kZwsefbSc887z8fDDSaxfb0JV\nISVFXnAcDrjjDg979yrMm2cDBB066CMZUk+kp8uKPAODESP8vP++i4wMQd++wQb3cOrWTXDHHd7D\nv9Ag7sjOFnzzjQuLRdCxY/3Pp2vWmLjxRgeVhdrIkX6OOcY494TYv1/hrrsc7N2rMn26jHS89loZ\nXbsa1614QBEicT+ohQsXikGDBjV6O8XFsG+fvL3LztYihs0WFcGGDSYURWHgwABJSbVsxMDAwMCg\nydE0eOghOy+9FD75ZmcH+d//SuusBG5puFwwfryTlSvD6T1DhviZPr3McDToiBUrVjBq1Khqbs+E\nDoM2FWlpsoy4R49IoQaQkQFDhwY5+WRDqBkYGBg0N0VFCnPmhAsJjjoqwMcfN06oCQH79in8+adC\nfr6CNwEcuSkpMGlS5D+ybJmFjz4yRqjEAwkt1uJxNmg00EO8XS8YtpAYdpAYdggTr7ZIThaMH++j\nT58A06aVMXt2KT17NlyoffDBjzz7rJ2RI1M57rg0hgxJY/LkZLZti//L5ciRAU47LTKP79//trNz\nZ835a/G6JpoaPdjByFkzMDAwMIg6Pp+s9szIEE1aaZicDP/8p5spU2QucWNYt05lypRkXK5wmMTr\nhTlzbHTsKHj0UXcj9za2tG0rePbZMiZNcrB8uQyHFhWpHDyoxHykk0HdGDlrBgYGBgZRZeNGlWef\ntbN0qYXhw/3cdZeb7t31d+159VUb//hHzZUv06fL6tREID9f4fvvLbz+uo1evYI8/ri7UrW2QSyp\nLWfN8KwZGBgYGESN3FyVv/zFyc6dsu3RrFk2LBZ4+unyGmchx5ITTgjgcAjKysLXylatNB55xM2I\nEYkh1EBW3U6c6GPcOB9Wa80zqQ30RfwH4evAyFmT6CHerhcMW0gMO0gMO4SJli02blQrhFqIzz6z\nUFTUfH0p68ugQUGefno+H37oYsYMF3PmuPj2WxcTJ/po1SrWe9f0pKTULdSack1s26ayaJGZ5ctN\nlJU12WabBT2cJwzPmoGBgYFB1PB4qouyY44Jkpamz7BbdrZg2DBj0kpTUVCgMG+ehYcfTsblUgDB\nJ5+Ucsopho2PBCNnzcDAwMAgamzapHLGGakVY6QsFsGcOS5OPtloWJvo7N+vcP/9SRUjB0N88IGL\nMWMMsVYTRs6agYGBgUGzc/TRGvPmufjmGwt+P4wd6z/imbAG8clnn1mqCbW2bTWOPtpoVnykGDlr\nLQA9xNv1gmELiWEHyQcf/FjrjMSWRjTXRP/+Qf7+dw9Tp3oYMCCIyXT498QK49gI0xhb7Nyp8Mgj\nkZ3irVbB9OmldOkSX2JND2vC8KwZGBi0SAoKFB56KImnnnLy7rtl9OtX8wXk4EEoKVERQqBpsru9\nxQJWK9jtAqeTRokPIeS+lJXJ/C6fTw7TTk4Gm02Qni6wWA6/HQMDPaFpCm53+EaoS5cAr75azvHH\nG17VhmDkrBkYGLRIdu9WGDYslQMHVNLTNebMcdUo2PLzFdatM/HJJ1Y++8xKWZmC1Spo1Up+tWmj\n0bVrkK5dBe3bazidGsnJ4HAInE5Baio4nRrp6aBUceLt2qXw7rs2ZsywsXevQuVB5GazoE0bQffu\nQQYPDtC3b5Du3YPk5GgJWZlokFhoGvz6q4ktW0y0b6/Ru3eQ9u0TV280FbXlrBlizcAgjigrg6VL\nzSxaZOHqq7106xZf4QQ9EQjA1Vc7mD9fzkbs1SvA7NmltQ61DgZhxw6V7dsV8vNNLFhg4ccfzRQU\n1J1NYrEIOnXSOOqoIAMGSMEVEnpJSYJ9+1RmzrSxbp2J3FwVn6+usKygV68gd9zhYeTIgNHItJ64\nXHDwoEqrVhopKbHeGwOD2mmRBQarVq2iqcVaQYHCgQMKZjN06qRhjYMZuEuWLGHYsGGx3g1dEO+2\n+OEHM5dd5gQUSkrg+efdDQrBxbsdmgKzGY45ZiHz548FYONGM/PnW7juOl+NrzeZoHNnjc6dAYJc\ncomPffsUCgsV9u1T2b1bZckSMz//bCYvTyXkJfP7Ff7808Sff5r45pvq201N1ejaVeOEE/xceqmG\nEHI0k6Io7N2rsHWriT/+MLFrl4IQChs3mpk0ycG0aeVccUXN+9oQEnFNCAGrV5u4//4kli41c9VV\nXh56yF3nWKpEtENDMWwh0YMdElqsNSVlZfD99xamTk0iP9+E2Sx46CE3V17pxemM9d41DJ9PfsXr\n/rc0du1SuPtuByERsGCBlcJCD23b6te7UlYmO9i3bSt06QU6+uggmZkahYXSO/bII8mMGBGgR4/D\neyxVFdq3F7RvL+jdW77+sst8FBWFBJxCQYHKn3+qLF9uZsMGE/n5KpoWedNcUqKyerXK6tVVT8fS\nZj16BDn3XB9HHRUkPV2QkaHRqpWge3fDq3o4fv7ZxIUXpuD1SptPn27jpps8dOumv7VoYFAXRhi0\nHggB//mPldtvT6ZyTgkIfvihpOJEHS+43bBsmZlp02wUFKicc46fiy/20bWrvv+PPXsU8vNVTCbo\n0SOou3DG+vUqK1eaURRo3VqWp3fu3HQ2XbLExHnnpVY8bt1aY/HiEl3ngXz6qYWrrnLQv3+Qt94q\n06XAmDXLwuTJ4TuWp58uq9W71lCEgKIihZIS6ZkvKpJfGzaY+O03M1u3mtizR3rO6rE1OnYUDBkS\nYPhwP506abRtq9GmjaBtW6HrSsvmJDdXZfToFPbvD4epMzM1fvhB38eMQcumRYZBm4odOxTuu6+q\nUJMVW3Z7bPapMfz8s5mLLpKhNIB168ysWWPilVfKSEuL7b7VxurVKldd5SAvTy7Zyy7z8uCDdQ8f\ndrth/361Irk7mgQCcP/9SXz3XTgunpqqMWWKh7Fj/U0i2vbti8yN6tIlSGqqfi86xcXwxBNJgMLq\n1WZefNHOU0+V6+6YOe20AMcd5+e332TJ5fvvW7nkEl+TepwVBTIzBZmZgq5dK//Gj98PBw7IatDi\nYoWDB1UOHlTYtUtl7VoT69aZyMszHer+DqCwa5fC3LlW5s4Nr7f0dI2TTw5wxhn+ikKErCyBmtAN\nmmpn9WpThFADuPtujyHUDOKShD6Mm6rPmhBKtSouRRFMm1ame28URPaI0TR4+20bVYXnF19Y2LtX\nn8thxw6FK65wVgg1gJkzbWzYULcL4cMPrQwalMqFFzr57Tf52mj1yzGbZQisMiUlKvfdl8y4cU42\nbWq8bas6wa+4wkdycsO21Rx9g8rLFQoKwuvsvfesbN6srzW2ZMkS2rYVvPBCORkZ8lheu9bMvn3N\n13vNYoG2bQVduwoGDNAYOTLA+PF+Jk/28uqr5XzxhYuffy7ml1+K+fbbYubNK2HWLBf/7/+V8q9/\nlfH3v7u54AIfPXtqbN1q4sknk7j8cifjx6fwxBN2fvvNRHn54fdDD72kmpLVqyPPD/37Bxg79vAe\n00SzQ2MwbCHRgx0Mz1o9yM7WeP/9UqZOTaawUKF//wB/+5uH448Pxt1dq6rK/6cqnTtrpKfr845z\n+3aVHTuqCzOvt/b37Nun8OyzSQSDCqtWWTjvPDNz57qiuJdw+ul+7rvPzeOPRzaC3L7dxOWXO5g7\nt5ROnRpu48pexMxMjaFD9T2uxWYDp1NQVCQfCyET7WvrZxZL+vTR+N//XFx+uZN9+1RUVc4w1AMO\nh2wDcrj9CQSgvFz2agsEpDdPVWVhRENFfTwT7ucluOgiH1OnusnO1sdnamBwpBg5a0dAcbE8EbZq\nJbDZDv96vbJ5s8qVVzrYvFlq9awsjXfeKeW44/TZrHDtWpWRI1Mj8nmysoJ89llpreHF4mI488xU\nNm0Ki7yuXQPMn18a1TBIaSmsWmXioYeSWLEispPp/PklnHRSw21cWCjDiqtXm3jqKTeDBunz86rM\nlClJvPFGOO75yiulXHKJP4Z7VDc7dijs3avSt28wLiq9DWqntBQ2bjRhNkO3bkFSUw//HgODWGP0\nWTOIYM8ehbw8lUBAetUa4/GJNh4PzJ1r4c47HXg8cPzxAZ59tpy+fev20Lz9tvVQ9WSYOXNcjBgR\nfY/UwYOwZYuJrVtVCgpUunTROPHExvfFKi8Hvx/d5hZW5bffTJxxRgqhsPtbb5VywQX6FWsGBgYG\nsaQ2sRZnQbwjw5gNKqkp3t6+veCEE4IMHRrUtVADWcQxYYKfn34qYenSEj78sPSwQg1g1KgAWVmR\n3qfFi5sn96BVKxmGueQSP3/7m5dzz/U3SeuK5OSmEWrNlYNx7LFBHnjADchQ3tFH68sbqIdcFL1g\n2EJi2CGMYQuJHuxg5KwZxAWKwhEP/+3SRePDD0uZONFBbq5c6q1a6VuYJhpJSXDttV5OOimAzUbc\ntbkxiA0ejyy8MNqQGBhIjDCoQcKzfbvC+vUmrFYYNChgzFU0qJHCQtkeJTkZOnSIj+kkiUZ+vsJP\nP1l45x0rbdoIHn7YHRcV9wYGTYXRZ82gxZKTI8jJ0XflpEHs+fhjK/fd58BuFwwb5ufGG70MHBiI\neo8+A8nmzSo33uhg1arwZem66zxV+tIZGLRMjJy1FoAe4u16wbCFxLCDpLIdevWSHhyPR2HBAisX\nXZTCVVc5WbtWrdbjLhGJ5ZrYtk3hyisjhZrFEpsRZcaxEcawhUQPdkhosWZgUBtBfeW5G+iAwYMD\n3HOPO+K5H36wMHp0Kp98YsHXtBOoDA6hafDee7aKVkIhbrzRw1FHGSFQAwMwctZaHPv3K+zcqZCS\nIlt2tKQEXq9XdjX/9lsLS5eaSE6G0aP9HH98gGOP1apNqTBoeRQWwn/+Y+Oxx5IiBq4riuD990s5\n80wjnN7U5OWpDB2aSnl52N5jxvh4/vlyOnRI3OuTQXxQUKAghJwy0hwYOWsGrFmjcuutDtasMWO3\nC159tYxx41pOz6tffzVx3nkpEc11v/zSSlKSYPZsFyeeaLjbWjqZmXDzzV5OPjnAffeFGxsLoXD9\n9U4WLSrR5TD6eEZRpHcNQFUFkyd7uOkmryHUDGLOnj0K48c7cblU7r3Xzemn++nYMTbrMqHDoEbO\nmmTJkiVs365w8cUprFkj9bnHo3D77cnk57ccd9LWrSaE+L7a8263wvPP2ysuGC0BPeRg6IGa7GCx\nwJAhQWbNKuOjj1xMnOihfXuN1q01PJ4Y7GQzEas1kZ2t8dlnLt5/38X335dw332emAo149gI09Jt\nUV4um5vv3r2Y2293MHmyI2bXTMOz1kLYuNHEvn2R2ry4WMHr1c8MxGgzfHiAfv0CrFkT+bzJJLjm\nGm/czXk1iC6tWwtOPz3AqFEBCgo8mM2QkdEyjpXmRFGIi9FpBi2Pdu0Ep5wSYPFi+XjxYgv33JPM\niy+WN3vxi5Gz1kL4+mszl1ySEvHc2LE+3nijDIejljclIIWFCps3q2zdauLAAYVOnTSOOipIr14a\nFsvh359o7N6tsHq1Cbudisa1LY3ycigoUAGB1QrJySJuxnkZGBhEl0WLzFxwgZPQyDyAJ54o44Yb\nfFHJczZy1lo4vXoF6dEjwJYt8iPv2TPAgw+6W5RQA8jMFJx0UrBRA9UThc2bVW65JZlff7VgMgl+\n/LGEnj1bUCwYKCuDKVOSmTXLiqZBaqqgXTvByJF+hg0LkJMTJCdHMxopHwHFxbBtm4kNG0yUlcHp\npweMxrYGccuQIQHuusvDc88lVTz3+OPJjBkTOOKpOo0hoQM/Rs6aZMmSJeTkCD7+uJSPP3Yxe7aL\nuXNLW9yFGYwcjBDz5v3IbbdJoQYQDCr4W06tSQUrVy7hhhs8dO4cRAiF4mKVzZtNvPGGnSuvdDJy\nZCpnnZXCG29YWb3ahNcbfm9hocK2bQqrVqksXWrixx9N/P67yq5dSlz2ZWvsseH3w4oVJq64wsmo\nUSnccouDKVOS4y7PzzhHhDFsIecx9+u3kIkTwwe/y6Xw55/NK58Mz1oLwujkbxBixQoTv/wSjvum\npWmkp8ehwmgC+vbV+OSTUpYuNfPgg8ns2lX5JKywcaOZKVPMqKpg6lQ3Q4YEWbrUzPvvW9mxQ41o\n8QGQkaHxz3+6uegiH05n8/4vsWLvXoVZs6w89lgSwWDYHv/8p5tu3RLnprCoCHJzTbhcMoXCqAxu\nGaSnC/7xDzcnnhjgn/9M4uBBheRkI2etyTBy1gwMqrN9u8Lpp6eyf39YlPzf/5Vz003eOt7VMti5\nU2HLFhOLFpmZOdMWYaPjjgtw0kkBXm5a5FkAACAASURBVHrJRuX8lZoYO9bHiy+WkZkZ5R3WAVu3\nqtx1VzKLF0cmfV50kZfHH3fTunViXGP++EPl9tuT+ekn+X+mp2v897+lDBzY8JSKsjLYvl1l/36F\njAxBz54tM3c2nsjPVygrU+jSRcNub/rtGzlrBgYGAOzerUaIkI4dg5x5ZguMgdZAVpYgKyvAyJEB\nJk3ysmuXyo4dKkuXmklN1cjLM1GXUBswwM+tt3o54YRAixBq+fkKN9zgYOXKypcSwT33ePjrX70J\nI9QKCxVuuSWZZcvCSurAAZV58ywNFmvr1qn86192Zs+2AgqqKliwwMWAAUY+rZ7JzhbEooNCQou1\nVatWYXjWZN7BsGHDYr0busCwBYc6xS8CRmK3C958s6zFJoDXtR46dBB06BDkuOOCFc2j9++HG27w\nUFiocuCAgtkMNpsgLU2QkSHIytLitpL0SI8NtxtefNEeIdTat9d46aUyTjwxQHJyNPYy+tRkh+3b\n1QihFiIz88gv2sEgLFxo5tprnZSVhYW/psmmwHrCOF9K9GCHhBZrBvGF2y1PWC2tQrW56dxZo1On\nIN26+XnoITf9+xt38vWldWto3VoDWqa4rcyuXSrvvCN7vXTsqHHLLR7GjvXTuXPi2SYpSWA2CwKB\nsLjKygoyevSRe6TXrDExcaIzYlsAN91kzEI1qB0jZ81AN7z2mo1Zs6zcfbeHU07xk5oa6z1KXIqK\nFOx2Ebfej+akpAT27pVhY6tVFhCkpBzmTY3E64UDBxSCQSoqS61WaNNG6GaGrcsF69ebUBTIydFo\n3z5xryWBgOy3NXVqMuXlCmPG+Jg0ycvRRx+ZuAoG4dprHXz6qTXi+QkTvEyd6iYnJ3FtaFA/jJw1\nA10TCMCnn1pYs8bMFVc4ue46D/fe62lQmMHg8Bid+OtHUZHCpEnJLFxoARQURdCnT4CLL/YzaFCA\no47SGtXJPBiEffsU9u9X2LtXZc8elbVrTaxaZeLPP02Ul0vBBrIi7aKLfPztb55m755eEykpcMIJ\nLcMrazbLfnGDBpUQCCi0bi0aNPEkECCi/UvbthpPPVXO8OF+0tObbn8NEg+jz1oLIB565ZjNRIQU\n3nrLzsyZ1ibv0RQPtmgODDtIDmeHtDTB+PHhdSmEwtq1Fu6/P5mzz07ljDNS+OADK3v31t/dJQTk\n5qosXGjmzjuTOOWUVEaMSOPii1O49VYHb75pZ/lyC/v3q5SXy5FwXi/07Bnkggu8UbuBMdaEpC47\nZGRA27YNE2oANhs880w5c+eW8OWXJSxcWMK4cfoVarFcE+vWyZ6FekAPx4bhWTPQDSefHEBW2cgD\n9KGHkhgyJNBi7t4N9IfJBBdc4CM7W+P225PIzY08ZW7fbuLmmx306xfg5ZfL6N277rBYXp7KrFlW\nXn7ZTmnp4S5Egr59g1x3nZd+/YJ07x5sMX3bEplOnQSdOhnntLr4/XeVsWNTOeGEAK+9VpYwVcWN\nQRc5a4qi5ALFyKxdvxBiiKIo6cCHQGcgF7hYCFF86PVTgWuAAHCbEOLrmrZr5KzFF243PPaYnVdf\nDY/16NMnwNy5pUbYziDm7Nyp8PvvJt5918bXX1simr8CZGcH+fxzF1lZNa/VQABmz7awdasJi0UW\n0wAoisBikUnsbdoIMjM1nE45n7Rt2/itLjUwaCivvWbjvvtkQu2cOS5GjGg5zdz1nrOmASOFEAcq\nPTcFWCCEeFpRlHuBqcAURVGOBS4GjgE6AQsURekh9KA6WwBChJsCtmunkZHRdNtOSoLrr/excKGF\nzZvl0vz9dzO5uSoZGcadqEFsCfVgGz48wI4dKvn5Krm5KgUFKj4fDBwYrLWreUkJLFtmZvZsKz/9\nZDnUPqUmBFlZggsv9HLZZT5DqBm0OMrL4X//C7dJmTvX0qLEWm3oJWdNofq+jANmHPp5BjD+0M/n\nAbOEEAEhRC6wBRhS00aNnDVJU8Xbi4vh7betDB+eytChaZx9dgrLlpmaZNshunTRePvtMrKywuJs\n9+6my1vQQ+6BHjDsIGmIHZKSoEcPjdNOC3DNNT7uvdfD/fd7OOec2nOPcnNV/vpXJwsWWOsQajJp\n/+ST/SQny47527fLvJ3mmK9prAlJItphzx6FTZtUtm5VKC2VRQ5btqgsX25i587a12MsbOHzwcGD\nYTmwYoWZ8vJm340I9LAm9OJZE8A3iqIEgdeFEG8B7YQQewGEEHsURWl76LVZwM+V3rvz0HMGUWbl\nSjP33BNugrZpk5nLLnOycKGrSXsr9e6t8emnLmbMsDF/vpWOHQ2nqUF807evxjfflLB6tZkFCyz8\n8ouZ4mIpwjRNDot2OAQPP1zOv/9t5+OPZVd7RRE4ndCrl5yq0LdvkKwsjQ4dErtVhkHTkJenMHOm\njenT5eg0VRX07x/guut8vPSSjQ0bzHTsqPG//7no2VMfPd5UVeaKhti7V8Xlav5ZnHpDL2JtqBBi\nt6IobYCvFUXZRPV5Dkf8Sf3xxx9MnjyZnJwcANLS0ujbt29FJ+KQWjYe1+/xZ5/9CNiBkYcsvIii\nItizZxCdOzft3+vaVXDaaQsYMgQGDmza/ydErO0Zy8fDhg3T1f7E8nGIaP49RYGiosVkZ8Nbbw2j\nsFBhyZIlaBoMHnwKJpNgxYolJCUJHn10JLfc4mD37u8RAlyukSxfbmH58h8P7elI2rXTGDx4AUOH\n+rn44qFkZIhG72/ouVh/Hsbjpnn87bdLeP11G998MxrJIjQNVq4cyd/+Zuaqq77i/7d33vFRVNsD\n/95t2WSzSShSJXTpiAgoUgR5Ij46IojlgYodfOqzYMXesGB5iILyBH34QBHlhyCKIB0E6U2ahI4E\nSLKbbLLl/v6YDZtNgbTNTnbv9/PJJ7uzM7t3zpy5c+65556zc6eVo0d7cPSogZMnlxX6fblUVPuv\nuqordet62b17OQBeb3ekjNz+Mvd1SkoKAB06dKBXr17kRxcLDPIihBgPOIDRaHFsJ4QQtYAlUsoW\nQohxgJRSvuHffyEwXkq5Nv93qQUG5cuyZSYGDQrOBlqtmo/Fi9NVMkeFohzJXczwwQdWVq0ycb56\npM2be3juORedO7t1G+PmcIDTqSVittspdeoLRfFxOuHmm+NZvrywyvCSF1/M4rnn4rBYJEuXptO8\nuT48awBvvmnl9de1hWYNG3r56af0co2P1jNFLTAI+y0jhIgTQsT7X9uA3sBW4HtglH+3kcB3/tff\nAzcJISxCiIZAE2BdYd+tYtY0ymu+/bLLPEyc6KRqVe2mbtPGw8yZjkplqOkh9kAPKDlo6FUOdetK\nrrtOu7+WL0/nv//N4MEHs2je3IvRGHy/7dqlhSP85z8xlGXsXZ6yOHZMsGyZienTLYwebeP66+10\n757AddclMGqUjV9+MZGVVW4/V67oVSdKis0Gr7+eSadObvJOTNntkieecLFggRmQTJ7sLHIKNFyy\nuPrqQG7DgQNzwm6o6UEnTOFuAFAT+FYIIdHa86WUcpEQYj0wSwhxB3AQbQUoUsodQohZwA7ADdwf\nTStB3W4tMHT3biNnzwpq1/Zx+eXeCslo7nRqv/faa06cTi2z+rZtBtLTBfXq+WjUyBcUa6Co3Hg8\nsH27kaNHBbVqSVq39mIubJCuCBl2uxbD2aqVjz59PDzyiItTpwz89ZcgI0PgdmvXKTZWW5wT7lJU\np04Jfv3VxPPPx3HkSEFfwF9/wR9/GNm3z8C33zqIjY2arjsstGjh46uvHBw+bOD0aa1KxvbtRr74\nIoaYGMns2Q6uusqjO09n8+Zehg3L5rvvLPTvX/L6q5GI7qZBy5NImwbdv18wfXoMkyZZg4oAz56d\nQa9eoV/aPGeOmdGjC8/KabFI/vUvF0OHZtOwYeTqVDSxapWRgQPteL0Cg0Hy6quZ3HJLDjbbhY9V\nRB9eL0yYYOXNN2OL3MdgkNx0Uw4PPujSTUB7NOFwwP79Bnw+qFdP6rqc38mTghMnBK1bh38QUpHo\nPc+a4gLs2WNgyJB4jhwJdl0ZjbLCsju3b++lc2c3q1cXdK/k5Aheey2Wr7828/XXDurV028noLgw\nUsKkSdZziV99PsG4cXG0aeOlc2eV805REKMROnXy0LKlh337jGRnC8xmSZ06Pjp08HDNNR5atfLS\nrJmXmJhwtzY6iY+Htm0rj5GcmSlYsMCEyyVo0MBHu3Ze3XkBK4qIPu1IiVlzOrXSS/kNNYD333fS\nsuX5H57lNd/eoIGPzz93MnNmBt26uYmJKWiQSQnZ2fodBukh9iCUSAmnT2u5is5HceRQ8IEqWLs2\nssZ3ka4PJaE8ZHHNNR5++CGDdevSWLs2jd9+0+pffvJJJiNG5NC2rf4NNaUTAc4ni/37DcybZ+aB\nB+K45RYb778fw8GDZe/79+83MH26hd697Vx/fQK33mpn9Oh47rjDRmpqeJ4tetCJyOp5KyleLwhR\n9Aqp06cFS5cGe7Pq1fMycWImnTp5KjSOqHp1LfD56qsdHDtm4NQpQVqadgPZ7ZLkZB+1ayuvWjjw\neODDD2OYPj2G5GQf113n5sorPTRr5iUurmTfJQSMGJHNt99agrZbreXYYEVEkpAACQmSUmRbUlQC\nzp6FefMsPPtsLOnpgYfWggUWGjb0Ub9+6WLMnE5YtMjMI4/EkZaW/2EoeeGFrAqJzdYrKmYtjHg8\nsG6dkcmTrdSs6ePBB12FTh96PLB2rZHFi81UqSJp2dJLy5ZeZRSVksxM2LLFSNOmvnMxG14vpKYK\n4uNliQ0bPfHhhzE891zeE5AMGpTDgw9m06pVyRYIpKXBF1/EMH58LD6foEYNH3PnZuhqib9Coag4\nnE4tPOK11wrGJdpskoUL02nVquT9g8MBU6fG8OKLseRPUxMTI/nsMwc9eniILTocMmIoKmZNGWth\nZMMGI9dfbz+3WOCxx7J48skKqCsT5Rw/LujePYEOHTxMmJBJQoJk2rQYPvnEStOmXl54IbNSxXXk\n5cgRLbZs/vxgj5jRKBk3zsU//pFdotGp2w27dxtISxPUrStp0KByykWhUJSdzZsN9OyZQH6DKjFR\nW3V6xRWli2ddvdpI374JQdusVsmYMS4GD86hefPoWWSg2zxroUTPMWuZmfDqq8GrOhcuNIekBpoe\n5tv1wooVK7DbJfXqeVm40MIrr8Ty229aqoGjRw38+quZQYPs7N5dOW+NunUlb76Zyf33u9Cy4Wh4\nvYJXXonlxRdjOXFCFFsnzGZo3dpHly7eiDTU1L0RQMlCQ8khQH5Z2GzQtGnAIEtO9jJhgpOff04v\ntaEGULWqZORIFz175vDAA1l8/rmD5cvTeOIJFy1ahN9Q04NOqJi1MJGaaiiQWTo+XmJSVyTk2Gxw\nyy05bNxo5quvYrj88uC0J2fPGli61EyzZtkV2q49ewx88kkMw4bl0KGDt9QdVO3akmeeyWLgwBxe\neSWWZcsCevbllzF07OihUaNyarRCoYgamjTx8f33Dv76S2AwQI0a5ZONoFkzH+++W/wsyVlZ2gKo\naFoZGtGn2q5du3A3oUTcdFMOFsuF9yspeWv/RTu5smjXLjAKPHu2oFW0bl3FW80zZ1r49FMrAwbY\n2bKlbNmFrVbo2NHLjBkOFixI54knsmjXzk3Nmj5SUwVduiidAHVv5EXJQkPJIUBhsqhZU9K6tY+W\nLX0VljYql+xsmD3bTN++dp5+OpZ9+yrGhOnatSspKYK1a43s3Gng9OnSfU9mppY/7kKr9Qsjoo01\nPXPRRT5uuCFwxdq29dCrl8rUXFE0buylWzdN3sePG2jdOti71r596JMM5yUnB1as0Dxg2dmC55+P\nxeEo+/fa7XDFFV6eeMLFvHkOli5NZ+zY7LBPKygqFq9KjaeIALZtM3LvvTY2bTLx8cdW7rjDRkrK\nhTuzkycFx4+XvtOTEl58MZbrr0+gSxetbNrs2WYOHy7edx49KvjySwsDBtjp2TOBBx6IY+/ekplf\nEW2s6TlmzWqFJ5/M4s03nUya5ODzz53UqROaUYoe5ttDgdOpTR26S2Dj5soiMRHGjdPc7tOmxTB4\nsJuBA3NISPBx3XU5FV7ixO0GV561JcuWmUhJKd/b02bTRsUm04V1wuWCLVsMrFxpZMMGI6dORaZ1\nF6n3BmheiHXrjDz1VCz9+tl57LFY1qwxFjmqj2RZlAQlhwB6k8WJEwIpA33R1q0m1qwpehbk6FHB\nzJkWevVKoE8fe6kNtpUrVzB4cO4zQbBvn5F77onn73+38+uvJpzOoo9NSRHce6+NsWNt/P67iWPH\nDHzzTQyff16yhIMRbazpiY0bjcyfb2LnTsO5YsvJyZLRo3O46SY39etHXvB2KHE64f33rXTunMAP\nP5Qu0Vzr1l769MnB5xO89JIVg8HHTz9lMGWKk+Tkir0eNht07hzw5kkpOHgwfLfn0qUmevZMoH//\nBK69NoFrr7Uzc6al2CNJRfhZtMjM9dfbmTzZytq1Jj791Eq/fnY2bVIFfCsbUmrJYletMnLgQPQ+\nthMTCzo08sd+57J3r4Gbb47ngQdsHDliwOsVZapd3a2bm8cfD46rO3zYyODB8UyaZCUtrfDjFiyw\nnJs1yUu1aiV7xkT0VddLzNrhw4KhQ+O57TY711yjGRdZxY+lLDORGIOxY4eRCROs+HyChx+O49Ch\n4hkReWVht8Pjj7swmSQg+PZbK9u3G4kvvPxpyLn66mBv3qFDoXuoXkgnfL7gEezBg0YeeMDGoEHx\n/PFH5HQbkXhvgJYzcPz42KBrCNp1/eOPwvUqUmVRUvQmh0OHBG+9ZeXqqxPo1y+BL78MQWBzEehN\nFk2b+mjZMjhEJS6uoAG3Z4+B4cNtbNkS8Lo98kjpk+p27dqVhAS4+24X773nxGrN+z1aqcVZsyyF\nzvJs3VrwfqtXz0vfviWbvYmcXlfHZGYKzpzRRJ2dLbjtNhsrVlR8APvevQY8FRuKFTJWrzaRm+vn\n7FkDf/5ZOlVu3doblNvugw9iSE8vjxaWnKZNfUEdT3CHULF06OBh+PCCq2H37zcxapSNY8eKZxxL\nqendL7+YWLDAxOrV5TOlKqWKwzofMTGS5s0LCig2VtKmjRJcWUhPhx07DMWKlSoru3cbuO22eF57\nLRanU/u9hg2jdxamRg3J1KlOGjXSHmSxsZKbbgqe109JEdxzj40DBwLP2Hr1vFxzTdkfflWrwq23\n5rBoUTqjRgWnR3rqqbhCvZ533+0iOTnQ3rvucvHNNw6aNlWetXPoJWbtoot8+QLYBffdV7zAyPJg\nxYoVpKXBqFE2Vq6MjNwgO3cGj1ZcruLJMn8MhskEN9yQTatW2vXZuNFUasOvrDRt6uPddwPBD3Xq\nhK5TvlAsSo0akvHjtZhKuz3YaNy1y8Tx4xeW0dmzMHWqhZ49Exg61M4tt9jp2zeBO+6wlWk6df16\nIzfdZOPmm22sXGksUcxifvQWk1NexMfDSy9lcfvtLmrU8JGY6GPo0Gz+7/8yaNu2cGMtUmVRUoqS\ng88HmzcbuftuG127JvD++6GtvbZ7t4GhQ+ODvEMXXeSjS5eKG3HrUSeaN/cxb56DhQu1urN5V/Z7\nvfC//8WwaVNAZna7ZMYMR5lCjfLKQQgt9+Rrr2Xxyy8ZTJ3q4O67XTzzTBaxsQUH2G3b+vjxRwer\nV6exZk0ar7ySRZMmJW9LZDy5dU6VKvDkky5uuSUwv3b6tIGdO43nLO5Qk55uYNcubSXNokXphZa1\nqkzkN87KEouQnCz55BMn/fvbOX3awN69xiIrGPz5p4GFC0306uUp8cioOPTp4+azzxzs3m3kssvC\n6wGpVUuLqezZ08POnUbWrTOSlSXo2tVDgwYXbtvq1SaeeMJWYPuKFWZ27zZy8cUl1/29ew3ceGP8\nudqBixeb+fprrRSNIpjGjX288UYWjz/uwuuFatWk7ouo6xWfT1v0c9NN8eTkaH1PUlLo+tCTJzXv\n0JEjgY7NbJZMmeKMyOTUPp9WAzsrS0vEnZQkg+oQO50QF8e5Vey1a0tq1y7YB+3ZY+CddwIHJiX5\nmDXLEZKKNDExcOmlXi691MuQIecfMdasKalZs2z6EtHGml5i1gA6d3Zz++0upk0LKNKRIxWXI+bw\nYYnFAidOGNiwwUS9epU7TUh+r1NxO86iYjBatNBu6mHD4jl5svDr4nDA+PFW5s2LYciQbD76KLNE\ntTaLg90Ogwa5gdBen5LEojRu7KNxYx/9+pWsTYcPFy7HKlV8pX7gHDliCCrynLs45PLLHdjtJf8+\nvcXklDcmE8V+SOSVhdOprbxLTJRUqxaq1umTwnRizRpjkKEGkj59QneP/vabKcijFhsr+eILB127\nVuygpCLuj337BJMnW1m0yMyxYwYSEiSNGnnp3dtD+/Yeqlf3MX58LM884+Lyy88/SDx82EB2tnaN\nrrzSzRtvZNKmTdkNNT30ExE9DaonkpI079oLL2RisUiEkDRrVnGek5gYzhUtf/VVKydPVu5VfX/7\nW6Cj7NjRTaNGZZdl+/Zefvwxne7dC++Et283Mm+eFtz7008WTpwouQxz41327RNlmr6rDFx3nYcB\nA3IATe8MBsmwYdl8/30GjRuXrgPNPyULsGePifT0yq3PemLbNiMPPBBHhw6JvPNOLOVVPtrhgJ9/\nNrFkialSpYLZtUuLGwsYalrcUmExgeXFTz8FDLWmTT3Mn59Bz56eiMzYf+CAkU8/tXLokBGPR3D6\ntIH16828+mosQ4fauesuG9df7ylWnGz9+j7eecfJnDkZfPGFo1wMNb0QgZc+gF5i1nKpXl1y//3Z\nrFyZzsqV6XTqVDHG2ooVK4iPl9SooSnu3r2mEifk0xtt2ni56aZsqlf38frrWSQlFe+4C8VgNG4s\nadmy8Bv8998DixoyMkSJDQTNMxdL164JXHVVIk8/HcuePeG5DhURi5Kc7OPf/3aybl06S5aksXZt\nGhMnZtKqVek70MaNtXQreenQwVPqKSk9xuSEixUrVrBli4F+/eL5/vsYQLBkiZmMjPL5/sOHDQwb\nZueGG+yMHGlj+3Z99kF5dSI7Gz76yHpugRhAq1YeHn00K6Srxm++OYeXX87km28ymDfPERSXVZFU\nxP3Rvr2H115zFhrvBdpg7LnnYomNvfB3NW3qY9SoHHr08FC1avm1UQ/9RERPg+oRo5FSexXKQmys\nlhpi40btkm/dauKqqyrvqrDq1SWvvprJ008L6tYNffyd16vlHstLTEzJfvfsWcGsWdpD0O2GqVOt\nzJtn4dtvM2jePHJGgHmx2ShVMG1RJCbCG29k0qCBjzlzLDRp4uXVVzOxFQyNU5SQEycEY8faSE8P\nGCY9e7pJSCif74+J0VY4u1yC1avN3HCDnblz9a37+/YZglJlNG3q4bPPnCQnh7bP6dTJW2GD+XBT\ntSrcdVcOV1/tYcMGE/PmmVm/3sTp0wIQxMVJrrvOHdbV8XpAyPLyceuQxYsXy/bt24e7Gbrhhx9M\n3HqrFtjTqpWH//u/DBITw9yoSkJaGvTpk8Du3VrAb1KSj5Ur06ldu/j3T2YmjBxpY/Hi4DxJ3bq5\n+c9/HFSpUrq2HToksNtlsb2LkYDHo+USs9lk2PLiRRrvvBPDyy/HnXsvhOSHHzK44oryMRo8Hnj0\n0VimTw/E7bZu7WHmTEeFDLhKw6+/Ghk8OAGQDB+ew7/+5SrXwYeiIG43HDsmWLrUxPHjRjIzBb//\nbmTixEwaNYp82f/+++/06tWrwLSNPv3QipBQt25A0bdvN3LsWNGX//BhwbJlJnbtUioCkJMjcDgC\n989ll3lKXMQ4Lg6eey6rQBLH5cvNpS4tdfCggSFD4nnrLWu5TVdVBnID55WhVj6cOCH49NPgVBTj\nxrnKdfrNZILRo3OC9H/bNhOzZlnKLS6uvGnY0Me0aQ7mz89gwoRMZahVAGYzOByChx+28frrsbz/\nvpVGjbwVXlVGb0T0k1hvMWvhIne+vXZtmcdgE0WuRt2718DgwfEMGmSnd+8ENmyo+PI0hw8L9u41\nlHuC2tLGHiQlSS65JLASa8SInFKtBG3TxsfcuRnUrx/4LrM5eJl6SdAWK5iYNMnKjh3Fv04lkUNK\nimDhQhNffGFh3jxz2PLQhQI9xKLoAYdDcOzYr+feDx2azciR2eWe6qN1ay8ffeQkd9EJwHvvWYtd\ngaQiyKsTycmSgQPddO7sjcqBQbjujz/+MAZV3xgxIgdTGIO29NBPqJi1KKJGDcmIEdm89ZYWqbln\nj5FevYKXgvt88NVXFvbt01TD4RC8956VadOcZcplVlycTvjpJzMPPxxHWppg4MAcXnsti1q1wjv0\nNpth8GA3S5ZYqFfPy5VXln4JfYcOXhYscLBjh5HUVEGjRr5S52zTFj0ACP7v/yxccUX51jHbvFlb\nCXf4cODit2jh4b//dVC/vk7dIYoCZGfDypUm5s41c+KEAYNBWznXoYOH2rV91Kol6d3bzalTbsaM\nyaZr15J7jovL3/7mZsKETB57LA4QpKcbOHTIQHJydMRoKS5MbrgJaGEioVx5W1lQMWtRxpIlJm64\nQYtb69s3hxkznEGf//WX4JprEoK8bsnJXhYvzjiX+iOU/PyziWHD4slddQnw1VcZ9O4d/qSnx44J\nfvjBTJcuHt0ERd9xh425c7UYuObNvSxYkF5ucYhpaTBwYDxbthR0Ic6dm0H37uG/Jori4XTCK69Y\nmTy58CV1cXGS++5zce21OTRu7At5brXMTNi0ycizz8ayf7+RefMyaN1aH/eUIvzcc08cs2fHEB8v\n+eGH9KjSDRWzpgCgWTPvuYSyR48acLkK7uPLd1/UqOErtFhueeN0wrvvWslrqIGWJkMP1K4tufPO\nHN0YagB2e6AtBw4YyjXfWEaGYO/egs53m01Sq5Z+ZKC4MDYbPPRQNpMnO86l8MlLZqbg7bdj6dMn\nkQED7KxZYwxpHFlcHFx1lZdv96VsNAAAIABJREFUvnGwcmV6mdK5KCKP1q29xMVJPv/cEVWG2vmI\naGNNxaxp5J1vr1NH8tRT2lRZaqogMzP44V61qqR37+A8VmPHZhcrx01ZcToFBw7kn2uV5boCSA+x\nB+XJxRcHnqjZ2YKcnPPsnIfiyKFWLckbbziDihXXretl9uwMLrkkMjrQSNOH81GjhmTYMDc//ZTO\njBkOhg3LzpdkeCkAO3eaGDTIztatoY97SErS+iShj/EYEF06cSHCJYsBA3L45Zd03ZSR04NOqJi1\nKKRzZw9Vq/rwekUBL5rRCPffn83+/UY2bjTx8MNZXHVVxaTar1ZNcvPN2bzzTq5lKHnppSxatFDx\nCkWRv3KD1yvIG7xdFrQi927atk3n5EkDMTGShg19uk2zoCge9epJ6tVz06ePm2PHsjh+3MDJk4JV\nq7Jo0MCJ2awlNK5dOzIMckXlQ4uHVf1MXlTMWpSydKm2um/y5MxCV9mcPastLqhTR1ZoiZOjRwWr\nV5v4808jV17p5rLLvMTFXfi4aGX9eiO9e9sBQVKSjxUr0qlTJ3LvaYWiNEipxZyeOiUwmbSyZTVr\navWSFQo9UVTMmvKsRSldu3po2tRb5HLopKTiF0cvT+rUkdxwQ+gLmUcKTZt66dzZw+rVZnr08FCj\nhjLUFIq8nD4NM2fG8NZbVtLStJFnbKykQwcP99/vomPH8i1NpFCEAhWzFgUUNt9uMhGV01l6iD0o\nTxIT4fXXM2nRwsvYsa5i5yKqLHLw+bTEv9u2GUKSi6uyyKEiqIyycLk0/Th8WBS5IOLwYQPPPht7\nzlADyMoSLF9uZsQIO889F8fZs4H9K6McQoWShYYe5BDRxppCEQ20aeNj3rz0sBV7DhWpqTBlioWu\nXRPo3j2Rq69OYPlyNRmg0FJ/rFxp5Kab4rniigS6dk1g/frCF0Q0buxj3DgXRcVA/fe/llJXEFEo\nKgoVs6ZQKHTJJ59YGDcuuEJ79eo+li1LD3uSZEX4OHlS8NlnMbz5ZnCany+/zOD66wtfPZiZCdu2\nGZkzx8LPP5s5fNiA1wstWnh57DEX11zjxmYr9FCFokJRMWsKhaLScPo0TJ5csAaXx4Nu60gqQk9m\nJkycaC2gGxdd5Dtv/sO4OOjUyUunTlmcOZOFwyHwegXVq/uisoyUovIR0b5fFbOmoYf5dr2gZKGh\nFzm4XNoDOD9mM9SsWfDhO25c+ZYe04sc9EBlkMWWLUYmTw4uWGq1SqZOddKwYfFSjVSpoqUvadCg\ncEOtMsiholCy0CiJHM6ehRMnyj++NqKNNYVCoU9SU+F//zNzww3x/P3vdqZMsZCSEujg7HZ4991M\nOnd2Y7FIkpO9TJ7sYPjwHF0lUFVULH/+aSDv1GeTJh7mzcuga1d9JE9VlC9ZWfD770bWrjUWyAmq\nR3Jy4Jln4ujZM4GPP47hyJHy66xUzJpCoahw/vMfC488Ehwk1Lt3DpMnO0lKCmxzOODMGUFcHBVS\nm1ahb3buNDBpkjYF+re/uenQwROVq9qjgaNHBZ9+GsO771q59FIv8+dn6D7n5unT0Lt3Avv3a4td\n2rXzMG2aw5/kt3iomDWFQid4/E6A4qbZiDRcLvjii5gC2xctspCSkkVSUmAIHR8P8fHqYazQaNHC\nxwcfFDJvrogoUlIM3H13HOvWmQGt6k5FlDwsK1WraqWyJk7UGrtpk4lHHrExaZKTmjXL1o9F9DSo\nilnTUHEHAcIti61bjQweHM9998WxfLkJhyM87QinHKxW6Nu3YBHT+HhZ4SPncOuDnlCy0DifHByO\nwmMsI5Vw6MSJE4Knn449Z6iBZNCgosMfcnLAG+KsRSWRQ9++bozGgGG2ZImZb76xnBukl5aINtYU\nivLC4dA6kbJ2Crt2GVi50sw338QwcKCdSZOsnD5dPm2sTNx4Yw633+7CYNA6taQkH9OmOWjSpBIE\npiiiklWrjPTrF8+AAfHMnm3m2LGKCZ7MzITt2w1s2mQkPb1CfjJsuFwwY0YM8+cH6oD1759D8+Ze\n/vpLsGVLIHYtJweWLTMxfLiN996LwekMU6Pz0batl5deygra9vLLsRw8WDZ9UTFrCsUF2LDByJNP\nxnLokJHevXMYOza71EbFsmUmBg2yB217/vlM7roru1K4+cuT7Gw4cMBAVpbgoot8XHxx5PZFisrP\nyJE25s0LGBEdOrj56KNMGjcO3QAjLQ0+/NDK229rOeUeeiiLhx5ykZAQsp8MK8uXGxk0yI6UmmFT\ntaqPBQsySE728frrViZNsjJ/fgYdOnjz7StZtEjbrgdSUwUvvRTL9OmBcI+vvsqgd+8Lu9eKillT\nnjWF4jzs22dgyBA769ebOXHCwIwZVu6/P67US7ObNfPSvHnwDfv887Fs2lR49vVIJiYGmjf3cdll\nXmWoKXRJZibnPDmXXhpsCKxfb2bcuDhOnQqdh+2330y8/XYsuStgJ06MZffuyOwrUlMF48bFnTPU\njEbJtGlOmjb1ceCAgQ8+sOJ2C2bOtHD8ONxzT/y5fUHgcOhnmXi1apJx47J44YVMTCatbyvrrExE\nG2sliVk7fRrduFHLGxWLEqCksjh+XJCREdwJrF9vZv/+0t06NWtKpkxxkpiYdzQu+O47S5HHhILy\n0AmnE9atMzJrlplZs8z8/ruRrKwLH6cn1L0RQMkCTp0SfPLJKj74IIZ//MPG3/9u55FHtCmsfv1y\nqFIl2Iu2eLGZLVtCZzzNmVOwX0hLqzijpCJ1YudOIzt35q66knz8sZPOnbWB7d69Rnw+7bznzrVw\n8KCR48eD++C8C5PKm9LIoVYtyf33Z7NkSTrffpvBZZeVzVqL0vVowZw6pQU09unjZvBgd7ibo9AR\nSUkSk0ni8QR3kGZzEQcUg1atfHz3XQa33BLPkSNaR793r1b+xliJBs3z5pm5/34bgbxXkn/9y8UD\nD7iC0m8oFHrn0CHB+vUmXnnFyv79NiCw0iUtDR5/HOrX9/HVVw6GD4/n7NmAoRBKz1ph3piqVSPT\nC51r9MbHS6ZMcdCtm+fcivmjRwMyPnPGUGAAfcklHurV059cjEatv4eyG5IRbay1a9euWPtt22Zk\n9uwYNmwwcfXVbqpWDXHDKpiuXbuG/DeOHBH89puJ334zMXx4Nm3b6jNQvKSyaNbMx9tvZ/LPf8aR\na5QMGZJNo0ZlGyW1betj/vwMNm82sX27kWuvdVeooVZWnUhNFbzxRmB6RkPw9tux9OjhpksXfcSO\nXIiKuDcqC9EoC48H1q83Mnp0PEeP5hpgPc593qyZh6lTndSpoxkCHTt6WbAgg++/t/DVVxZq1vTR\nunXodH3AADezZwfinkaNctG0acXdWxWpEy1bennuuUx693bTsmXw8+PkyWAvWrARK3nttayQ5mHU\nw70R0cZacfD54LvvNDfJ/v0GUlMNVK2qT0NDr2zebGTkyDhSUjR1atPGo1tjraSYTNrKxRYtvKSk\nGEhMlFx2madcDPrkZElyspv+/SufNzcxUdK9u5sZMwpamOnp+okdUSjOx48/mhg1Kh6vN1hnLRbJ\n2LEu/vGP7AIem2bNfDz2mIs773RhtRLSdDPdu7uZOtXB3LkWevZ006ePG7v9wsdVRnr08NCjR+EB\n+MEDWclFF/kwGiVSwoQJmVx5pX4rWJw5A6dPC0wmQbVqpa9FG/Uxa8eOCebMyR25CE6frtwPGqdT\ny/K9Y4fhXAxeKOMONm0yMmhQ/DlDDdB1sHhpZGG1QocOXoYMcdOrV/kYauGmrDphMsFDD7no3z8b\nCFzv667LoV27yuFVAxWnlZdok8XBgwbuvz/YUKtXz8tddy1g6dJ0xo1znXdqrWrV0BpqoJVdGzLE\nzfTpTm6/PYfatSu2b9WLTiQlBc67ShVJzZqSX35JZ/nydG69NSfkK+lLI4f0dJg/30z//nY6dkyk\nY8cEbr45nm3bSmd2Rb1nLS0tOIC8Mmcy2bfPwIsvxjJvnhkh4K67shk3LnQR33v3GrjtNhtpaQHl\na9nSQ4sWledhXVk4exbWrzexaZOJjAxo395L06ZeGjf2EVOwGECF0LCh5MMPM3nooWzOnBEkJEga\nN/ZSpUp42qNQlIRq1Xz8978OTpwQ2GySqlUl9ev7+OMPD82bV8zMgMul5QuryFQcZ85Q6e7RSy4J\nPFP698+hVi2p+zJjP/9sZvTogBvN44EVK8yMGmVjwQIHF11UsvZHtLFWnJi1/IGKlSXAOzVVcOyY\noHZtH9WqaUGu990Xx/r12pSulPDJJ1aGD88JyXy7xwPTpsWcC5AHsNkk//yni927BW3bylK7e0OJ\nHmIPSsPKlWZuuy1YoEajZPTobMaMcZW44yovOdjtlHmVUziprPoQCqJNFvHx0KVLwemzGjUqRg6b\nNhl5/XUrhw4ZefHFTHr1Cu1U3tmz8M03FqZMsTJ5srNYHnC96ETjxj4SEnykpxsYMqRi43uh5HLw\nerX6x0VRVDWG8xHR06DFweUKfh8bq29rHTQP2siRNrp3T2TuXE0htm83njPU8uIL0QDxzz8NfPZZ\nwKVjtUqefTaLp5+Oo1+/BB59NI4jRyr3lLKeSEyU5J1uBPB6BR9/bGXcuFjS0sLTLoVCUXI2bTIy\nYICdRYss7Nxp5I474jl4MHSP49zKAI89ZuOPP4wsWVK5/DQNGvj43/8cTJ3qoH17/can5WI0wpgx\n2UFlp0BL8jtpUibVq5fczohoY604MWt5UzIYjVL3wZuHDwtGjLCxapVmmH37rQWfT3Ol56drVzeN\nGnlDEneQni7IztZk17ixh5deymLiRCunThkAwaxZMTz6aOmTx4YKvcRglJTLLvPw4YfOc+WZ8jJ/\nviXPSrbiUVnlUN4oOQRQstAItRycTnjppdigJK4ZGSKkNUd37TLy/POBwK7cvvtC6EknrrhCixsO\nx4xNaeTQs6eHn3/OYOpUB++842TmzAwWL86gU6fSzURULvM6BOR1pyYn+7Db9b2KcdEiM3v3Bi5b\njRoSgwGaNvXRoIGHP//UPrv8cjdvvZUZstiE+vW9fPmlA7NZ0qiRl02bjAUMxh9/tLB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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "t = trace[\"halo_position\"].reshape(5000,2)\n", + "\n", + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\")\n", + "plt.scatter(t[:,0], t[:,1], alpha = 0.015, c = \"r\")\n", + "plt.xlim(0, 4200)\n", + "plt.ylim(0, 4200);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The most probable position reveals itself like a lethal wound.\n", + "\n", + "Associated with each sky is another data point, located in `./data/Training_halos.csv` that holds the locations of up to three dark matter halos contained in the sky. For example, the night sky we trained on has halo locations:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.00000000e+00 1.40861000e+03 1.68586000e+03 1.40861000e+03\n", + " 1.68586000e+03 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", + " 0.00000000e+00]\n" + ] + } + ], + "source": [ + "halo_data = np.genfromtxt(\"data/Training_halos.csv\", \n", + " delimiter = \",\",\n", + " usecols = [1, 2,3, 4,5,6,7,8,9],\n", + " skip_header = 1)\n", + "print(halo_data[n_sky])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The third and fourth column represent the true $x$ and $y$ position of the halo. It appears that the Bayesian method has located the halo within a tight vicinity. " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True halo location: 1408.61 1685.86\n" + ] + }, + { + "data": { + "image/png": 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0BgbP2dnC++87ymxda9JEcc892fzrX9lAYKdDh7RVqKx06WLy9tsZ1K9vfUCb\nNzeZOjVLK2pRiscDjz4ay7XXJnDBBfGsWROe4oNFfaf37zdYsMBR+A/FUN2vySeAfxL8JoGmSqkD\nAEqp/UAT//qWwJ9B2+3xr2sJ7A5av9u/rhDljVlLTAw0yzSFO++M4+mnXRw/Xq7DhI3kZMUzz2Th\ncFjtbNKkbJlcdTHuIDcX5s1zkJdeDZbr+IMPvue88xL59de6rSFUZ59wu+GZZ1z8+muo295mU9x/\nfw6JicXsWA1E0rPRq5ePV1/NQCTwHvroo5hyKVtNmypuuSWHhQvTmTo1iwceyCpzSYFIkkVNIQI2\n2zKWLUtj2bJUFixIq9PT70V7n3A44LTTLN/377/bGTMmkXXrCn8bKiuHoUM9+QOAYIItuKVRbUFP\nInIecEAptVZEhpSwaZX5Zb/++mtWrVpFmzZtAKhXrx49e/bMn5A17wbkLaemfkOHDrFs3z7Mf4Rl\nPP009OjRj4su8hTaviaWTRM+/HAIjzzi4uyzF/L992ap++cRCe2vrmWXC849dyHffRdHbu5QvwSW\nAWtJSxvC8uUOjh9fHDHtjeblVq0G8dVXTiz5AwwhPl7xf/83D5/PB9Rc+9avX1/j8slb/u675cTF\nwQcfDOGOO+L4889vSUz0Ehvbt9zH69vXR3b21wC0a1e2869fv75Grz9SlgHatFHs2vUtaWnQsmVk\nta+uPh/hWh42bDBPPBELLCMzEyZMGMSnn6azZ8+3VXa+bt1MHnxwLp984uTHH8/G7YaTT15Iu3a5\nLF+uWL58Obt27QKgX79+DBuWp4MEqLaYNRGZClwOeIFYIBH4GOgHDFFKHfC7OJcqpU4UkTsBpZR6\nxL//fOA+4I+8bfzrLwEGK6VuLHjOipTu2LjR4PzzEzl8OKBdt2hhsmhRWoWL44aDnBz0fH9l4Ndf\nDV5+OYb33ovB7bZGMc2ambzzTga9euk4nnCyf78wb56DL790MHSolzffjMHlMvnrXz2ccYaHrl3r\nrsWiNPbuFXbvNkhOVrRvr+WkKZnUVDh+3Kqj16iRngu2PBw/DrfdFsfnnwfcVBMn5vDAA9nEx1ft\nubxeK7bU57M8ZUWV3oqoOmsiMhj4uz/BYDpWgsEjxSQYnILl5lxIIMHgB+BW4CfgS+BppdT8guep\naJ21DRsMrr02ni1bAobH779PLfd0U5rIwOOBPXuMfHd2kyaKFi0iR/GORtLS4IEHYnntNeur0aiR\nydChHiYDZynOAAAgAElEQVRNyqF/f/0caTSVxeOBX36xsWSJgw8/dLJjh4HLBQMGeHjggWw9GCoH\nW7YYjBiRSGpqnpFGMXduOqeeWv0D+ohIMCiGh4GzRWQLMMy/jFJqI/A+sBGYC9ykAprlzcArwFZg\nW1GKGlS8zlr37ibvv5/B669nMG6cm2nTMmnSpPZ2/GiPOygNh8MqbZCSYpKR8U21KmqpqbB8uZ1P\nPnHw8882zAjpRuHuExs22PIVNbCSYebMiQmxWEcCdf3ZCEbLwqI2yCEzE95808mIEYlMmxbL1q02\nvF6r1tfChU7eeadqSgTUBllUBV26mMyenYHNlvdtEH/Ms0UkyKHaYtaCUUp9DXzt//9R4KxitpsG\nTCti/WqgZzjb2Lq1onVrD6NHF1F4J6QtVtXrRo2UnrZFE0J6Osyc6eLRRy1bt9Op+OKLdPr1K3q0\n5nbDsWNCgwa1vy+lphYOnG3a1NTWaY2mCti0ycbf/x5HcAJVHnFxijFjSv5uaQpz6qk+3nwzg2uu\nSSArS/jiCye33ZYTMdPXRdYwt4pJSUkJ+zmWL7czaFASjz7q4siRsJ+uQuQFPGqqVxYbNtjyFTWA\n3FzhlVeK1sK2bTO44YZ4Bg1K4uab41i/Pjwp5HmEWw7t25skJwcUs5Ytfbz1VkbExV/pZyOAloVF\nbZBDQoKiZcvQZ8luV4wcmcv8+en06VM17rvaIIuqwm6H4cO9zJ+fzmWX5TBsmCc/piwS5FAjlrVo\n4cAB4aab4jl2zODxx2NJSfExapQe0Wgsdu8uPBYqKlXb64WnnnLx6aeW6+Kjj2JYvNjB/PmFCybW\nFjp3Npk/P52tWw1iY6FDBx+tWuk4QY2mKuja1eTLL9PZtcsgNVVISlI0a6Zo3drUyQWVpEcPH888\nk43bTUR5OKLashbuuUEPHRL27AmI8H//iyEjI6ynrBCR4G+PFKpTFgkJhZWTUaMKT/iYkQE//hg6\nbkpNNVi8uOwFE8tLdcihfXuTESO8DB7sjVhFTT8bAbQsLGqLHNq0UQwc6OO887wMGmTNuFPVilpt\nkUU4CFbUIkEOUa2shZucnFAryapV9ogLoNbUHCed5OOMMwKW1quuymHwYG+h7ZKSYPTowkrcH3/o\nvqTRaDSaGirdUV1UtHRHWdmyRXj+eRctWiiefz6GY8cMfvwxlU6daqfrSlP17N8v7Nhh4HBA586+\nYufA/O03g0svjee33/IsbIpPPsngjDMKK3cajUajCZCRYSVoNWpU0y2pPMWV7tAxaxUkKwt277bx\nzTd2QBg50sNnnzmJi4te5VcTyvbtws6dNnJzoUULRZcuvkJFDps1UzRrVnqwb8eOJnPmZLB2rZ3d\nuw169/aSkqKL9mo0murnyBGrwkFtQCn46CMnixbZeeyxbJo0qR3tLi9R7WcJV8zawYPC9OkuLr44\ngZ077TRvbrJ/v8H48W6aNo28jhIJ/vZIoapksXatjWHDkhg3LpHLL0/kzDMTuf/+WPbtq/ik2W3a\nKP7yFw833eRmwIDCil9VUpoc9u0TXnvNybPPxkS1O1Y/GwG0LCzquhzWrLExfHgib77pZOHCyJfF\nnj3CfffF8sUXMWHLoo+EPhG9b+EwceQIzJjh4umnY8mrcXPttW769fNw881u7NpWWSd47TUnaWnB\nj4/w0ksuvv669ncAnw/eeCOGv/89nnvvjePee12kp9d0qzQaTXWwYIGDHTts3HprPCtX2iOmkHdx\nHDhg5M888MknTnxR6pCIamWtquusZWXBa6+5eOmlQMpNv34ezjjDy+TJbtq2jcxeHQk1YiKFqpJF\n795FvxF+/rl2KGslyWHvXmHmzEAf//xzZ9Ra1/SzEUDLwqKuy+HIkYB3YObMEezYEdnPfnB7v/zS\nwcGDFfduFEck9InIvgsRxrJlDqZODXzEkpJMnnwyi4YNI8/1qQkv55zj4bLL3EDg3iclmVx6qbvm\nGlVFHD0qpKcHv/CE/fv1q0KjqQu0aBEwOmRnC2vXhrdAd2UJtqQdPy5kZdVcW8JJVL+BqzJm7bff\nDG68MZ4816fdrnjjjUy6dYtMa1owkeBvjxSqShYtWigefjiLhQvTeeONdN57L51Fi9Lp1av6+sNv\nvxm88oqTxx5zsW1b+R7lkuTgdEKwEgrW/KrRiH42AmhZWNR1OYR6DZbx3ntO3BE8BjVCXn1CZmbV\nW9YioU/UDp9NBLBggSPf2mAYijfeyOD003VZhbpMfDz07VszARI7dxqMHx/Pzp3WI/zllw4++CCD\n5OTKW3lbtDDp1s3Hxo3WsR2OwlPbaDSa6KRjRx+NG5scOmRpQd995+DQIalUYesjR4QtWwycTujV\ny1elg7/Y2NB26Zi1WkhVxawdOiQ895zl/kxONvnggwyGDfNiq2HrsGlamaneUnTGSPC3RwrRIou5\ncx35ihrAunX2cmWiliSHevXg4YeziYlRgOLBB7M44YToVNYitT+YJvz8s4158+zs3Fk9r+lIlUV1\nUxfkUJKrsFUrxd13Z/uXhlDZUqwHDwr/+Ecso0YlMWJEYpUnYcXHhy4rFZ0xa9qyVgaUgm7dvFx+\nuY+xY3Mjouhtejq8/76TJ56I5Yor3Fx9tZvGjXXsXDC5uVaxxPj4yJrjrbK43eTPIxqMUYFvus9n\nzXGbmSk0aKDyLXOnneZl0aI0srOFbt18Osu5mvnpJxtjxiSSmyu0auXjww8zIuK9UxvJyYHDh4XU\nVME0reekfn1Fy5Z17325fbvBSy/F8MMPdjp0MBk3zk2/ft5CxWRHjvSwfLmbOXNi6NHDS1JSxWW1\nYoWdTz+1XsCmKUyb5mLAgIxCSlZFadzYJCnJJC3NwDAU9epF53MS1Za1tWvXcuiQkJpaueM0aaKY\nPTuTyZNzIuaF+fPPdv75z3j27jV4+OFYli4t/msaCf726mTHDmHWLCcXXJDA2WcnMX58AitXWmbQ\naJCFUpYrPpiePb00b172vrl8+XJ+/dXg7rtjGTQoiVNOqcfo0Qls2mS9EgwDunc36dfPR1xclTY/\noojU/jBrVgy5uZaFYPduG599Vlg5r2oiVRYVYedOg2XL7DzzTAznn5/AaafVY9CgegwebP17xhlJ\n+e+EgkSTHAoyY4aLF1908csvdj7+2Mlf/5rIlClx7NkTao1KTlb85z/Z/Pvfc3nyySySkip2vpwc\neOWV0JHyvn22Ko0ra91aMX68NV1f585mlYSCFCQS+kTUj5dHjUrg7LM93HlnDgkJFT+OM/zvynLx\n/feht27mzBjOPddDYmINNShC+O47G1demcCRI4FxyM6dNn7/3WDRougoFuZywU03uVm50gr8iItT\n/qzksh9j/Xob06YlkZEReGlu2WJn61YbJ54YGQOSukpmJmzYEKpIvPeek4kTc2jQoIYaVUvYts3g\nq68cPPpobIGM5lB69fLRrFnd6+eJiYUVmTlzYujf38ukSaHzEzdrpujf31epJDrLqhlqE2rXzkdC\nQtUpVCIwfnwur78ew8035xQ7pV9tJ6qVtZSUFLZts7Ntm41LLsmlR4/oeTj//DP0AfjjDxsZGVLk\nwxgJ/vbqYPt24ZJLEkMUkDyGDPFQv76KGlmceaaHDz5I59gx4cQTfXTvXva+vWWLwcMPn1tITk6n\non37KI3OLYZI7A+xsXDCCSa//hpY5/FQ6dih0ohEWZSHH3+0MX58QoFi1aH07eth8uQcevf2FTud\nUm2XQ0lccYWbDz90cvRoqIy+/dZRSFmDyssiIQFOPNHH1q2BwcfNN7ur3Frfu7eP+fPTadUqPN/4\nSOgTUa2sBRAOHDCiSlnr08fL228HzMsnnOArUlGrSxw9ahSpqI0a5eb22yNvdolt2wy8XipkyUpI\ngGHDKpaNvHu3Ucjq4HIpZs/OKJfSpwkPhgFXXunmiy8C5vxBgzzaqlYK27bZMM1Av7bZFB06mAwY\n4GHoUC9t2/po08as03Ls3t3kiy/SeeIJFx995MTnE+rXN7npppywnM9uhzvuyObrr+2kpQm3357D\nqad6qvw8IkT9XMoR9vmqWqw6a8MAIn7KjPJy8sleYmMV2dnWy+m663KLdfMuX748IkYG4aZrVx+v\nvZbBCy/E4PUKvXp5GTXKQ69eXurXt7aJFFn8/LON889PxDAU8+al07Vr9XXQdu1M+vRZxM8/DyM5\nWXH++blcfnkuPXr4kKpPpIpoIqU/FKRvXy9TpmTz2GMu2rb1cdNN7rDfm0iVRVm59NJchgzxkJMj\nKGUpCg0bmuV2i9V2OZRG164mTz+dxeTJOWRkWMkWbdoUPdCvClmcdJLJkiXpuN3QurVZK2NgI6FP\nRLWyFky0WZ26dzf59NN0nnvOxaBBHs4+u+pHK7WNxEQYM8bDued6UKrqMkCzsuDYMcFms+I4Ksuh\nQ8K//pUXUyNs2GCrVmWtfXuTf/4zmy5d0nC5FE2bqjqnpNUke/cKmzbZqF9f0bWrr8isuPr14fbb\ncxg71k18fNX0u2jHMPDXAiufrA4eFPbtE+rXJ2KnDKxqYmKs90B1Ea2lf6oTUeEOhKhBFi9erM46\naxh2u+KHH1Jp3z56r1VT9bjdsHKljenTY1m71k5cnFVzbPRoDy5X6fsXx48/2jj33EB61S23ZPPA\nA+FxQ2iqDtO0FG2Apk0r/i559VUn//hHPKAYNy6Xu+/OpnVr/W6qCbZtM7jxxjjWrHEQH6945ZUM\nzjlHFzvX1Bxr1qxh2LBhhYbPUV26I48hQzx6ZKopF0pZswKcf34iK1Y4yMwUDh0yuOGGeNavt7Fj\nhzUazy0ck1sqe/eGPnbFBTprIod9+4RHH3UxeHASZ5yRxKuvOjl+vGLHyqsMD8L778dwxx3x5Spo\nrKk6Zs2KYc0aK6s6M1OYODGBzZvrxGdRU8uI6l65du1aDEPxr3/l1Eo/eVURCTViIoWyyuLPPw1u\nuy2+UDVsux2WLrXTr199Bg5M4uqr4/nuO1u5Jg/evTv0sasJ10tRctiwwcb997t45pkYtm6N6ldD\nPmXpD243PPusi0ceieXgQYNDhwz+8Y94fvqpYlEk/fqFWm6WLHHw3ntOPDUcyVDX3hOZmfDtt6H3\nMCtLmDt3RQ21KPKoa32iOCJBDlH/Rn7zzQxOOim6s0TqKkeOwP794bFIuN2QnV1wreLWW3P46CMr\nGO7YMYN585yMGpXIl1+WfbK7gsku4Uo3Lw979wqXXRbP00/Hct99cVx8cUK5J4ePVvbvt6q+F2Tb\ntorNN9ejh4/TTgvVzB55JLZQOR5NeHG5rLISBYmm2U400UNUvx1SUlIYMcIbcQVtq5uazmIJB0eO\nCHffHcfVV5fPhVRWWbRta/LCC5nUr29isyl69PAydWo2K1bYQ2oGWQiffOIs8wTCXbsGNrzgAjed\nO1f/YKKgHPbtM9i1K3Bdf/5p4623nGGv7VXTlKU/2O2K2NjC6ytak65pU8WMGVm0aBHY3+2WQlXk\nq5tofE+UhM0GN92UEzIReM+eXsaOPa0GWxVZ1LU+URyRIIc6kw2qqV7WrbNx7JjQv7+3yuaAC+aX\nX2y8/741BN682Ubz5lUbFOx0wtixHgYMSMPjsWoRHTkiuN1WPbcdOwy8Xmv9JZfkMnGiG1sZDS3d\nu1uWFY8H7rwzJyJmnUhMNHn44Ux8PmHJEgeLFzv44gsnt96aU66ZEaKRFi0Uzz6bycSJ8fh8Aihu\nvDGH/v0r3ue6dDF5//0M7rsvjsWLHdjtigYNolwzjkB69TKZPz+d1attOJ0wcKCX5s31fdCUTk4O\nbNxoY+NGGzExir59vWFNYoxqZW3t2rX06dOnpptR41R3jZicHPj3v2NZvtzBSy9lMHasp0pLQ3g8\nMHt2wFy6YYONoUPL9uEsjyxErA91XimAevUUt93m5qqr3KSmGvh8ipgYaN68fKUvWrVSzJqViWGo\nGlOECsohN1f473/jyMwUpkzJZtUqW9Rb1aBs/UEEzj3Xw+LFaRw8aFC/vqJLF1+llexu3UxeeSWD\nHTsMHA6qtXxLUURCLamaoGdPHz17BqycdVUORZEnC6WsEkZut+ByqToXA16wT+TkwJtvOpk8OS4/\nrrlzZy+ffppRqUzxkohqZU1TM+TkWHE+ALfcEk/nzukhL8PKcvSo8N13gRix336rXm9+vXpQr17l\nPqzhmGy4Mvzyiz1/cuU33ohh3Lhcevf21nmrWh52u1XcE6pWoUpKgpSUmo9ZjHb27xd++snOokV2\nDANGjPDQu7ePJk0i6zmMFHw+K8nql19sbNwYw4IFdg4csGY+adnSZNq07GJjwbOyIC1NqFev6PCB\naGDdOluIogawdaudQ4dEK2sVISUlpaabEBFU9yjR6YT4eKvD5uQIs2c7mTo1u8qme8rMtApZ5lGe\ngGA9YrbIk0NuLhw9CsuWBW7Onj0GI0fm0qdP9Cfm5MkhPR2OHxfq11cR4ZauCaL12cjMhMcfd/Hy\ny4HiiK+/7mLsWDfTp2cVGpBEqxzKwuHDwvr1Nj791MGcOTFkZY0stE1cnCIpqegBxpYtBvffH8vq\n1XaGDPFwzz05tGlT+wcjBfvEqlX2QpUCGjQwqVdPu0E1EYRS1kg1Pl6RlFT473FxcMopXtats7rX\n7NkxTJrkplOnqnloPR6r8n8eLVpU3ctg506DmBjld39GJ4cPCzt3GmzebOOTTxx4vVJI4T140CAx\nMfqVNbAKo06ZEsc339gZOzaXBx/MjjjLp6biHDwovPJK4RHdRx/FcP31bho2rBv9vCSysqwp8O65\nJy7/vV0Ql0tx7bU5OJ2Qmlr477t2CRddlMiePZanY86cGNq2Nbn77ugr+F3wmyOimDkzM6zFraM6\nG9SaG1RTlTVijh2D5593MnBgEhMmBApI+nywebPB3Ll2Jk92hWQ4ut1Spa7KgrFUrVuXXVkrSRZr\n19oYOjSR4cOT+PXX6Hs0Dh4U5s51MHJkAsOHr+G22+JZutTJ/v0GSUmhQm3YsPaPhsvCRx+tYMKE\neJYssZTW99+PYd26ipXkqO1EQi2pcNC4sWLw4MIxrQ6HCskEzSNa5VAcmZnwyisxjB6dWISitoyu\nXb08/ngmH32UzmefOXn88Vj++9/4QkWhN2+25StqeSxc6ChXDcpIpWCfOOUUL3femU379j5Gjcrl\n88/Tyxw3XVG0ZU1TLn74wcHdd1vpnd9+a/Cvf8Xx+ONZfPihk8cfd/mtXjBlSjZxcYqsLGt5wQIH\nI0Z4qyTRoH59RdOmJgcOGICiXbvKKxa5ufDEEy7S0gzS0mDy5DjeeSejSMthbWTbNoObbopj9erC\n9eD27jUYPTp4KgZVZyxL27bZ2Lo19DWYF7uniQw8HsuS73YLpglJSVb/LGtYRUICPPpoFk8+6eLd\nd534fELTpiZPPpnJiSfWjUFJSWzdamPRIjuJieBymTRqpOjVy8s553g4fjyTMWPSadgQli+35Zf3\nWbLEwebNNk49NTAoz3vXB9O9uy8qkxFatFD84x85TJqUQ3w81VIeLKqVNR2zZlFVMRg+nzWvYTAr\nVtj5/HMHjzwSiCQ1DMUpp3i46iph5kwrTmTlSgcZGdlVEg/UtKni/PNzeeEFF0OHeunYsexujOJk\ncfy4sHJl4HH4/ns7O3bYSEmJDhfJ/PkOVq8OftyH0Ly5yRlneBgxwkPTpiZPPeXC5xN69/bWmYmX\ns7KGFFrXpEnduPaCRGKs1rFjMHOmi5kzXWRnW8pA48Ymfft6GTPGQ9euPrp29ZUat9qhg8ljj2Vx\n++3ZuN1Cw4aq2CkII1EO4eTLL+3Y7cKECW6Sk00uuiiXFi0UhgEQqDmXmKi4665sTNPKkN61ywhR\n1tq39xETo3C7rfsUG6u45hp3NV9NeCiqTxgGNGhQfW2IamVNU7V4PJCaGjp6Ugq83sA6p1Px8suZ\nDBjgo1EjN7NmxZCVJWRkWOUh8spgVAYRmDjRzfHjwu23V02dMq+34MhQQpIYajtXX+3mzDM9ZGUJ\ndrvC5bLmJG3c2Co74vHAc89lMm1aLI89lk29ejXd4uohISF0+cwzPXTpEh0KejQgYgWt5ylqYM2t\nOn++k/nznRiGYtIkN9dc46Zjx5KV7JgY6NAhUIpHY7F/v42lSx0sXWpZ3bt399GqVahLb98+Yfr0\nWObNswbrMTGKv/89m9RU8t8VPXuafPRROi+84CIuzrovvXvrZ6mqiL7AnCB0zJpFVcVguFwwZkzo\nNDknn+xj/XrLND5ggIevvkpn5EgPDgd0727yzDOZgOW2dLmq7iXZqZPJc89l0aVL+awgxcmiXj1F\n586hL6iarjNWledPSLDuR//+Pnr3Njly5BuaNAnUh3M44IILPCxYkF6nXrDNmy+mQQOrDw0e7OHR\nRzOrdbQcSURirFb9+vDQQ9ncc082TmfhB8I0hRdecDFuXDx//FE1n7NIlEM4KViC47XXYsj1R0Xk\nyWLlSnu+ogZWHPLUqXEh1noRGDDAx6xZmcycmRVV75FI6BPasqYpFyNH5vLZZw5++slBq1Y+Lroo\nl5kzncyencHJJ3tp3Dj0hXrOOR4+/jiDpCQVlpkMqor4eLjmmtyQmK5GjWpGW/v9d4MPPnCyerWN\nu+7K9tf3Cj82W81dc01xwgmKxYvTycyEli1N6tev6RZpCtK6teK223IYMSKXjRttfPyxkx9/tHP0\naJ5yZmVve711q+9WFSkpoYPUJUsc7N1rhIRCFDdw3LUroCDv2GHw228GCQmKlBQfIlbB8tRUoXlz\nkxNOMKMyfq26EFXT5oMwsnjxYqVnMKh6vv3Wxm+/2WjYUNGggUnHjmZUlLrYvVuYMCGBdevsnHNO\nLs89l8n+/QbvveckLs6qYl+VxX2LYs8e4dpr4/nxR0tpPPVUDx98kBHRiq5GU514vXDokHDsmJVw\n4HJBcrJWtCtKaipcemkC338fGKiuWnU8ZOqknTsNLroonp07A/Ydp1Px+edWwfOvv7Zz443xHD9u\nJX0tWJCOUjB8eCJWmSXFtde6ueGGnLBOyRQNrFmzhmHDhhWKwdGWNU25GTTIx6BB0WPizqNVK8Vb\nb2WwbZuNjh19pKUJF16YmD8bw3PPxfDll+l06xY+S9f8+Y58RQ1gxw4bGRmSX2RYo6nr2O3WFG/F\nzeG5erWNRx910aePjwsvzKVDh7qZMFJW6tWD6dOzGDMmkaNHDVq2NAvFcrZrZ/Lhh5ksW2Zn4UIH\nDRuanHOOl969fXz2mYNrr40nUPtSyMnJK1YeWPfyyy6WLLEze7bOwq0IOmatDhAJ/vZIoTRZtGhh\n1WRq2VKxc6ctX1EDSE01eP/98OVoHzkiPPOMK2Rdhw6+Yif4/vNPYeVKW4Vq2Ok+YaHlECAaZJGV\nZc1LvGCBk4cfjuWii+Lza0GWlWiQQ3np3t3k00/T+e9/s5g1KyN/Gq5gWZxwgslVV+Xy+uuZ3Hxz\nDn36eNiyxeDmm4MVNWje3KRdO5POnX2MGJEbcp4dO+xcf308Bw5YhbnXrbPlx8dFMpHQJ6JaWdNo\nKkNRNeFWrrTjC5NR8fjx0BgQsLI4C9bwcbth0SI7Z5+dxIgRSQwZksTatXWzkKtGE4zPZw2q8vjj\nDzv/+EccR45ET2Z3uOje3eTmm9307VvyC85uh65dFS1bwty5zvxSHRaKJ5/MpGVLRb168MAD2Zx0\nUmhM3K+/2vnlFxvffmvnrLMS+eorB6Y2tJVKVCtrus6aRV2rG1QS5ZHFCSeYJCeHvkV69PBhC5Ne\nFBNDSBmSQYM8nH564arY331nZ/z4BA4etB7frCzh11/L1yjdJyy0HAJEgywSE2HcuNDaXt9952DL\nlrJ/6qJBDlVFSbJQClauDLx3RBQzZmSFvLM6dTJ5440Mbrklm+CSKVbcoYHPJ1x3XXzEzxoSCX0i\nqpU1jaYytG1r8uabGflTL7Vs6WPixPAVeWzVSjFzZgbt2vm45pocnnwyq1BczsGDwj//GVtoEuFG\njfTQNNL47TeDd95xMmlSHPPn6/Dg6uLssz3ExYU+Nzt3RrYyUBvJq3fZtq2Ps8/OZe7cdC69NLdQ\nxmebNoopU3L4+us03n47nTlz0unXz0fr1pYFz+0Wbr9dWz9LI6qVNR2zZhEJ/vZIobyyOPlkH4sX\np7NwYRpz56bTtWt4laKRI70sXJjOtGnZRU6jdfCgsGNH6Ie/ZUtfubNUdZ+wCIccPB5YvtzO2Wcn\ncvPN8Xz4YQzPPusKm/u8qoiWPtGtm8ns2RnExAQUtoSEsifoRIscqoLSZDF8uJfFi9N4/fVMTjml\n+JkkXC6raO6IEV7OPNMq8ZQXFwewfr293N6BypCaCr//LmzebLBrl5QaNxcJfUIP9+oQBw4IcXGq\nSir+1yXatjVp27Z6ziUCDRsW/2GpV88ql3LsmDXOat7c5K23MmjVSmeLRgKmCUuW2Ln88gR8voCl\nYMyY3LC5zzWFGTLEy7x56Xz2mQOnE3r3Du8k23UVw4CGDSu2b/v2PurVM/NjDJ9/PoaTT/YSG1vK\njpXkp59sTJ4cy7p1dpQSYmIUo0blcu21bvr08eEoPH1yRKDrrNURvv3WysLp39/DAw/k1Jm5H6OR\ndetsrFplo1EjRZ8+Xtq0id5nuLaxerWNkSMT8XgCilqDBiYLFqTrEhIRhFKWdcXrtaZf0zXaqh+l\n4MEHXTzxhKWdGYbi22/TwlrWY88eYeDApJAklDwMQzFnTgZDhtSsYl9cnbWodoNqLHbuNJgwIZ79\n+w0+/zyGd94JX/kJTfjp1cvHNdfkcv75Hq2oRRCZmfDUU64QRS0hQfHeexlaUYsQdu0SPvzQwaWX\nxjN8eBJDhyYxfHgSjzzi4pdftOmzOhGB0aM9iFjvMNMUtm4N7z2oX18xZkzRPk/TFObNi1CzGlGu\nrOmYNYsvv1xBWlrgVr/+egz799fNYM5IiD2IBLQcLKpSDocPC19+GXjZt2zp47PPrGDq2kC094lt\n20NaENwAACAASURBVAzOOy+JSZMS+OorJ9u22dizx2DbNhuPPBLLqFGJbNhgRLwcjh6FFStsfP65\ng40bw/sJD7csunTxcfHFAeVp27bwKmvx8TB5cg5PPZVJmzbWc2kYijZtvFx+uZsbb8wpcr9I6BM6\nZq0OkJUVunzwoEFmZs20RaOJVhITFVdd5WbzZhuXX57LgAFeHW4QQezZY7BnT/HKTf361tyVx45V\nY6PKyYYNBpMnx/Hdd9agoF07HwsWpNfaOX1jY+Hvf89hyRIHhw8bbNoUfutm8+aKCRNyOfdcD4cO\nwe+/21i+3EFWFrz0kou+fb20bm3Stq0ZkgRR0+iYtTrA11/bueCCQFZBYqJixYpUHZSu0VQxSlnZ\noAULGWtqnowMWLbMwbPPxvDTT1ZwudOpaN3a5LrrcjjzTA8dOihyc6240DVr7GRlCV27eunc2Uf7\n9qrIQtnVxcaNBqNHJ+YnFwE0a2aydGkaTZvW7nf5jz/aGDcukZtuymHy5KKtW+Fg/37h7LMT2bOn\nsJLYsqXJ9dfncO65nlLDGP74w2DLFoNevXyVvhd6btA6TNu2JklJZr4rdNSoXJo1q90Pt0YTiYho\nRS1SSUiAUaM8DBni4dAhaxJ4h8OKKwzOaNyxw+DccxMxzcD3Mj5eMXlyNhdfnFsjitHRozB5clyI\nogZwyy05tV5RAzjlFB+LFqVVe8Z0s2aK2bMzmTgxjt9/D1WH9uwxuPfeOJ54wmTmzEzOPNNbZKZo\nRgbcdVcs8+Y5mTDBzdSpWcTHV31bdcxaHWD37m947bVMkpJMunb1cuutOdjrqJoeCbEHkYCWg4WW\nQ4C6IouEBGjXTtGhg6JNG1Wo9MTmzd+SnByqAGVmCvfeG8dDD8Vy5Eg1NtbPb7/ZWLEiVFPo399T\nbLB8VVGdfaJTJ5P27as/bCAlxcdnn2UwY0Ygji2YY8cMLr10VbF14P74w8hPTJg92xk2V24d/WTX\nPYYO9fLNN2m4XESUH16j0WgiieRkxdtvZzB2bEJIYhbAm2/GcMklbk47rXqTRkKjlRTjxuUyZUoO\nLVrod3lV0KqV4uqrcxk92sPOnQZ//GGwbJmD3bsFhwPatHHToEHRiuSBAwaBieyFjRttYUkq0jFr\nGo1Go9EUYPNmg88+c/L88zEcP24pbc2amXzwQTrdu1evBSgtDVautHPggEHHjj569PCFxdWmKT9L\nl9q58MJATPjVV+cwY0Z2hY+nY9bKgGlaD+imTTZ27rSRnGzStauP7t19uup/NZKeDtu329i40cam\nTQZHjhiMGZPL0KFeHQ+k0Wiqha5dTbp0yeHSS93s22cgAk2bmrRuXf0GjqQkOOssPQtDJFJwHtoj\nR8ITXaZj1oJYvtzOsGFWHZ6pU2P5v/+LZ+TIJP73P1eh8he1idoSi3LsmDXTwmWXJXDmmYn87W/x\n/O9/sbz7rjW3Ymnzt5WF2iKLcKPlYKHlEEDLwiJYDiKWi6x/f59/8vHo9UQVhe4TFsXJweu1skY7\ndw4o0sW5SyuLtqz5yciAf/87Fre7cG729OkuxozJDes0GHWdXbsMHnjAxccfF54JuGFDkwcfzCIh\noQYaptFoNDXE/v3Cpk02TNOa37Si83BWB2lpkJMjNG5csyVOqgO3GxYudPD88zGYJgwa5OWvf81l\n+3Yb55zjyd9u715h716DuDhFp05mpeYd1TFrfnw+ePbZGB54IK7Q3wYN8vDqq5m1tvBgpLN7t3DV\nVfGsWVO4J/fv7+Gpp7Lo2rXqFOX0dNi71+DoUeHoUSE11eDQIWHfPoPEREWrVibJySZduph07KgV\ndE3Z2LfPmi7HMBQnnmgWyijUaMrD1q0GN90Ul/9efP/99Ih0hebkWB6RadNcHDpk46qr3FxyiZuW\nLaO3/+/fLwwZksTBg6HOyW7dvEyblsXpp/tYu9bG5ZcnsH+/gWEo/vOfbK680l1qrGGNx6yJSAzw\nDeD0n3eOUuoBEbkPmAQc9G96l1Jqvn+fKcBEwAvcppRa4F/fB5gFuIC5SqnbK9s+mw0uv9xN+/Ym\nb73lZPNmG02amFx+eS5Dhni0ohZGNm60hShqIophwzzcfLObnj2rbjS5ebPBmjV2XnvNyerVdgIZ\nPEXTurWPL79M18WDqwCPx5L/99/b+eEHB4MGeRg92hM1Cs2OHcKkSQn8/LP1Sr3ttmz+9a8cYmMr\nfkyPxypoPW+egy5dfPTs6aNlS5PMTKs+VIMGVdR4TcSxc6cwfnw8f/wR+ESnpkamuWrdOhvjxyeQ\n9z596KFYv6cqByNKA62aNVPcdVc2t98eqnlt3GjnoosS+eSTdK67zpqPG6x5R++5J5ZTT/XSp0/F\nMkWrTVlTSrlFZKhSKktEbMAKEZnn//PjSqnHg7cXkROBccCJQCtgkYh0UpYp8DngGqXUTyIyV0SG\nK6W+KnjOtWvXUp5s0EaNrIllhw/3kJEBLhfEFTa01TqWL1/OwIEDa7oZxXLiif/P3nmGR1GuDfie\n2Z7sJvRO6IRuBEREEJAmCIqCIqKIigqKYle+o+I5KlZEQUWwHbEgSFWkWhBQUeSI9A7SkWaS7WXe\n78ck2SwJkLLJTjZzX5eX2WV3Z/bZtzzvU0N89lkmbreE3S6oXVuttxNN2f/8s5EbbrDj8fwIdDvv\na5OSFIYP9zF0qD9uFbXSHBOnT8OsWRaeecZGKKQu6AsWmGnZMoMqVWLbNzMacvB44JVXbDmKGsCU\nKVaGDfMXyzJ75ozE2LGJHD0a3vG6dfPTu3eQVauMPP+8m4YNozc+tb5OlBaxloOiwBdfWCIUNRDU\nq1f6Vv6CyGLt2rwH3w8/tHLXXb64KS2Snxyuv14Non7iiYSI8KlAQOLXX435dEWQ+OefoivcpRqz\nJoTIDtO3ZF07+5fM7xtcC3whhAgC+yVJ2gV0kCTpL8AhhFiX9boZwEAgj7JWVMxmNB0bEG/UrSuo\nW7dkzfuVKimMHu1lwYIQLpfCyZMSCQlqMGi1aoKLLw7Spk2IunUV6tdXA4njPe6iNHC54OOPrTz3\nXKSJyWoVVKgQHwv50aMyc+dGpikLoVqIi0OlSoJbbvHx6qth2a1caWb9ehPPPONhyhQrzz/v0Us4\nxBn798u8/bY14rnevQOkpsb2YHMuatbMq0TWrh3Cao2P+X0u7HYYNszPJZcE+f57E+++a83pPVux\nosBkEgQC4U0kOVkhJaXoCnepxqxJkiQD64FGwNtCiHFZbtARQDrwO/CIECJdkqQpwC9CiM+z3vs+\nsBj4C3hRCNE76/nOwONCiGvOvp5eZ03nbFwucDol/H7V9W2xqK1krNYLv1en8KxbZ6BPHwdnn8fe\nftvJkCGBuHCTbN8u06lTErm/Y9euAWbMcBa75M/hwxK33ZY3nrNCBYUHHvDSp09AT3yKM9avN9Cr\nV1LO42rVFBYuzCQ1VZu/8/79MsOHJ7J5s2r7MZsFs2c7ueIK7cXXlSR//y2Rnq62MateXeHHH03c\ne28iHo9ElSoK//2vs0DFlGMeswYghFCAiyVJSgLmS5LUAngH+I8QQkiS9DwwERhZmvelU35ITFSV\nM53S4eDB3NW9wWgUvPKKm2uuiQ9FDdRCqX37BliyRLWuVa2q8NxznqjUZqxdW/DRRy7ee08tX5Mt\ny3/+kfF4JDxFr72po1GqVlWoVk3h779lrrgiwKuvumnSRJuKGkD9+gpffOFkyxYDbrdEo0YhWrTQ\n7v2WFNWqiYjuQNdcE6BVq3TS02WqV1eKnXARk9IdQogMSZJWAledFav2HvB11t+Hgbq5/q1O1nPn\nej4Pb775JomJiaSkpACQnJxM69atc3zP2bVT4v1x9nNauZ9YPt60aROjR4/WzP3E6vHZY6Okrufz\nSfTv35v9+2XatPmOSy4JMmxYJ4xGbcgjWuNhwgQPLVt+h6LAjTd2omlTpVifFwrBDz+swWpVH48b\n56V69e9ZtszEX3/1QFEkMjNXsnt3kLZtoyOPqVOnanZ9DIVgwYKfEAKuu+5yDIa8r1+1ag2HDknI\ncnf+9z8DTZp8R/PmSplcL5csyWTNmtVUqyZo0qT0rr9vn0RCQjcOH5ZxOn8kM3MDjzwymipVxHnf\nX6uWYO/eldhs0KpV7MdLtB8XZb386aeCj7c1a9Zw4MABANq3b0+PHj04m1Jzg0qSVAUIZLk4bagx\nZi8B/xNCHMt6zUPAJUKIm7Osbp8BlwK1gRVAkywL3FrgAWAd8A0wOTuDNDcTJ04Ud9xxR2l8PU0T\n64BZLaHLQqU05eDzqcUjYxFblZEBu3YZ8HqhZk2Rp1G01sbDiRMS335r4osvzJw+LdGlS5AbbvDT\nurXqPlmzxsiiRapL9MorA1x1VTBqFkqtySIbpxNmzTLz9NMJCAFTpri48spARFzx6dPwzTdmHn00\nISdO6Nln3TzwgK/Q19OqHEqaDRsM9O/vwO3O7YFbSevWnZkyxUWbNuG5c+KEhMcjIYRqCYyHRLzz\nUZpj4lxu0NJU1loDH6N2TZCBWUKIFyRJmgGkAQqwH7hHCHE86z3jgDuBAJGlO9oRWbpjbH7X1GPW\ndHTKLwcPSjz9tI2vvlILLTscgpkzMy8YN7J6tYFFi8y0bx+kZcsQDRooxSrBURimTTMzblykVmsw\nCL780km3bmoM0KFDEn6/REqKgjEmvpHS5ZtvTNx6a7gitsWilk0wGKBfvwAWi8KECQl89lm4oLYk\nCZYtyyyRhtrxyu+/G+jdO298KahzZ/HiDNLTJVauNDFzpoVjx9T4rMGD/bz4oltPyosSMY9ZE0Js\nAvJoTkKI4ed5z4vAi/k8vx5oHdUbLIesX2/giy/M3HGHTw9S1ok7li415ShqAJmZEiNH2vn++wxq\n1Dj3IfXYMZn33rPy3nsgy4IRI3zcdZevVAK8//e/vEtyKCQxYYKVDh2cJCSQVU6mfMRdZmbCa69F\ndjXx+SS8XokXX7QxbVqIp5/2MHNmZDbuI494c6yROgWjefMQU6a4eOihRILBSF0hM1NizRoT48bl\nNaGlp0t6z+ZSIE5CfPOnsL1B45XcvvFs/vxT5pprHHzwgTXiRBrv5CeL8kh5kMPKlXk7Ypw+LUXU\nRMpPDpddFuTii1UrlqJIfPihld69k1i0yITTWXL3CzBypA+LJa8ilpYWKvENUYtjwuWSOHQosl5V\nYqLAl+XdPHjQwIcfWiJa/Iwa5cmSY9GuqUU5lAaJiTBkSIDlyzN56SUXXboEqFLlOzp3DvDss26W\nLcs7n7p2DTBhgifuWwFqYUzEtbKmkz+nT8MDD6gpxaCWHtDRiTcGDfLneW7YMB81apzfQlanjuDd\nd13UqRO2zGRmSgwfnsgrr1g5frxwBfj27JFYutTIqlVGjh07/3vbtw+xbFkmY8Z4aN48RLt2QZ5/\n3s3993vLhcvzbCpUELRrF4x47q67vMybF9Zc9+0zULeugtEomDTJxaOPeiOy8nQKjtGoHgzuvtvP\nnDlOnnrKg8EgeO01W8Thp3ZthbfecjF1qitPHKiO2n3E643uZ+q9Qcshv/5qoG/fcB2fvn39fPaZ\nK4Z3pKMTfU6fhq+/NjNtmhWPB+64w8f11/sLnEK/Z4/MM8/YckpyZDNqlNpKqkKFC3/G339L9Olj\nz6lGX6dOiLffdnPppcELWsoyMtQC3dGoAXjqlMSZMxJuNwSDEhUrClJSFAxnF1nXIDt2yDz4YALH\njsmMGuWlZcsQn3xiYds2A1WrKvTvH+DkSYmePdXC1mXhO5U0TqfqUq9YUaF166IrU3v3yrz/voW1\na40kJgouuyxI585BmjQJUbNm/OoOxcHvhy+/NLNli4GHH/YWuqVezBMMYoGurOXPO+9YeOqpcOzB\nW2+5uPnmvFYIHZ14ICNDVVAqVSr8WnfypMTy5SaeeCIBlyu8fk6b5uSGGwLneafKgQMyHTok4feH\n3yvLasJA9+7B87yzeCiKeu3du2V+/tnI/Plm/vorrMXY7YIVKzI0W2j1bDIzwe+XIno0u1xqprHf\nD9Wro3ccycW8eSZGjrRTt65qqT1fjOaFEEK1ElksxE1txJJk+3aZK65IIhiUmDMnkyuvLNw8P5ey\nFtei12PWVHL7271e+Oqr3LEHgubNy08grhZiD7RAeZJDUhLnVNQuJIcqVQQ33+xn+fIMnnjCQ+XK\nqnIzebKVjIwLX7tmTYU77ogsH6EoEiNHJvLXX9Fffv1++OMPA088YaNLlyRuvNHBG2/YIhQ1k0l1\nF+ZXxkSrOBxEKGqgxlhVqgQ1akRXUdOyHArCnj0SjzyiHsYPHjQU2m2fmzVr1iBJYLOVb0WtMGNi\n/345J0FjwQIzoShtr+UwCqJ8oyjg9eZui6OatEsDp1MdyPv3G9i7VyY5WdCokcLFFwf1/oY6mqZ5\nc4Xmzb0MG+bjyBGZhARRoA4FJhOMGuXj55+NbNwYXm7PnJE5fFiiXr3o3eNff8n8979mpkyxoij5\nbdCCG27wM2aMjxYtdHdhaRAKUepy3r7dSHp6WLPKzCw5k+OxYxJbtxrYvNnA0aMylSoJLr88QLt2\noSIneJR1duwI/+Dffmvi1CkpKjGUca2spaWlxfoWNEHuYn5WKzRqpLBxo1o754UX3KWSybN3r8wL\nL1iZP99MZB0fwaefOunXLzouoVAIPB7O+Z3KY7HL/NDloFJYOdSpIyISDwpCSorCjBlOZs5UW0a5\nXBLVqytRDYI/elRi1KgEfv317Iw9QdOmIe66y0e7diGaNAnlezDy+SA5+QrmzTOwb58Bq1XQqVP5\njAEr7tzYvl1m/XojS5eaOHlSpkmTIL16BWnbNljslkMFYc2ayG29OAVrzyeL3383cM89Cezbd7Ya\nYWXBgvjqDVqYMZE7XELNPo/OPcS1sqaTF1mGsWM9OBwKI0b4S6WH26FDEkOGJLJnT37DTYraZnDq\nFEydamXZMhO33OLj+usDVK0avzGZOmWHlBTBY495ufFGP2fOSFSrpmTVS4set9ziJzU1hMMhqF1b\nUK9eiLp1FWrVUs5bsPTQIYlPPrHw2mtWhAhvNCaT4McfM2jWrGzEtWmBTZvULgC5rVm//mrk00+h\nbdsAM2a4qFWr5NYkt1u9XjZGo6BChehfb98+mRtusEdY8MJIevxgFn6/FDU3aFx7ofWYNZWz/e1t\n2ii88YaHtLTScX8ePiznq6hJkuD559XMuGiwfr2R11+3sWWLkXHjEvnwQ0ue9OmyHo8SLXQ5qJSm\nHGQZGjRQaNs2FHVFrWZNwbBhft54w8Nzz3kZNcpH375BWrU6v6L2zz/wzDM2Xn3VhhA/RvybzSZK\nrXODlijOmNizRz6n2/F//zNy/HjJbrlOp8SxY+FrtG8fvGCpmvNxLll4veS09cqNxSKYONFFWlr8\nWNWgcGOiWrWwvA0GETVjhG5Z0ylxUlNDTJ/u5L33LBw+bKBBgxADBgRo3z5Iq1bRK/Z59GjkQvjK\nK1b69vVH9LTT0dEJc+iQzIIFeYOLHA7BjBku6tXT505huOSSIIMG+Zg7NzLcw2IRvPSSm2bNSvaA\nbLcLqlVTchS222/3lUjfzubNFRYtymT5chO7d6sxnJddFiItLUjjxmWjJExJkTvztkaN6B14yl3p\njr/+UoP9yuOJMdb4fJCRIZGcLEqkGvtXX5kYMSIyWO2TTzK5+ur4OuXp6ESL48clJkyw8emnZoSQ\nqFhR4bbbfAwZ4i8zZT20htOpxugePSrj80k4HIK6dRUaNlRKJaNywgQrr71mo3nzIHPnOotVtkOn\n8GzbJtO5cxJCSDzwgIdnny1cddyY9wbVAjt3ytx0UyILFrhISdEXotLGYqFEY8hSU0MkJAjc7vA4\nD4XKVvCEopTvFHmd0qV6dcGECWqHBEWBpCRB9epCjzkqBna7GmoSK4v+TTf5cDgEV10V0BW1GNCg\ngcLIkT4++shC//4XrsVYUOJ6W8gds5Ydm7F/vzFq2RllhfISn5SaqvDBB04MBnWBcjhEnrIkWpbF\nokUmBg1K5PHHbcyfb2LzZrnExqqW5VCa6HJQ65U1bqzw99+rqFFDV9TK+pho2FBw//0+mjQpvrJY\n1mURLQojB6sVHnzQy9KlmVx8cfTc3uXGsrZxo4Hly83Y7YKEBP20Ea/06BFk+fJMDhyQqV9foXnz\nsmNBzcyU+PFHMz/+CO+/rwan3nyznxEj1LpY5bVukY6Ojk5ZomZNQc2a0Y1PLBcxa6dOSdx0UyLr\n15vo0CHAggXOqPTb09GJJidPSkycaGXatMjBKcuCUaO83H67n0aNyo7yqaOjE3+cOiWxe7dMKKTW\n7KxePX51iFhQLttNZbN5s4H169VikVdcEdQVNR1NUqWK4IknPLzyiguTKbwAKorEO+/YGDTIzubN\n5WLK6ujoaAxFgd9+M3D99Xb69k2if/8k3njDShzbezRFXK/8GzZsIBCAmTPDqYcXXVRyqdOHDkn8\n8YeBYK7kQ68XNm2S+f57I9u2xUbcetxBGK3LokIFuP12P999l8GwYT4kKbwSHjhgYOBAB9u3h8eR\nywVr1xoK3WdS63IoLXQ5hNFloaLLIUxuWaxda+Caaxxs2hSOnvrtNyMeTyzurHTRwpiIa2UN1BRq\ntcWR6k5q1KhklLXDhyVuvdVO794O1q83ZF1b4rHHEujWLYnBgx306pXEjh1xL3KdYmIwQKtWCq+8\n4ub77zN57DEPdeuGAMHp0zK//x5eLNetM9Kvn4Orr7azc6c+tgqDEGopmfT0WN+Jjk4YrxeWLTMy\nenQCkydb2Lcv9vP6wAGJkSPt+P2R3rmbby6ZOm46eYn7mLW//rqUO+9Ua29ddlmAL790lsjgmj3b\nxKhR6nVuv93L/fd7ufFGO7t3R+ZwLF+eQfv2pdM5QKfonDkDPp+kmdT3U6ck/v5b7TNXq5bI6Sv5\n6KM2PvxQ9etfdZWfqVNdJCfH8k61j9sNW7YY+OADC2vXGrHbBVOmuKOauVXSbN8us3u3jN0OrVqF\nqFJFG+NUp/j89puBvn0dOa2/mjUL8vnnLurXL1q86uHDEhs3Gjh2TMZqhaZNQ7RoESpUrdGVK41c\nf70j4rm0tCCffuos0fZZ5ZFyW2ftk0/CKXS33uovEUXN5YJ33gkHwh05IvPOO9Y8ilpqalCv71YG\nOH5cYvx4Gw6HYMIED6aze2PHgMqVBZUrRy6KoRBs3x4uFb50qYn9+w0l6uov6xw+LPHBBxbeeMNK\n7grzO3bIZUZZ++MPAwMGOHLqCXbpEuCtt1zUratvmvHArl2GiB6t27cbWbXKSP36/kJ/1okTEg88\nkMgPP+RexASjRvkYO9Zb4OQAu10AAnXOCAYP9jNunKfIilowqFq2tbC2lhVib18tQTZs2MDq1arC\nJEmC1q1LppL96dMSO3eGN82OHYPMmBFZZyEhQfDOO+4ci0hpogV/u1YoiCxWrDAxe7aFOXPMnDyp\n3aJTBgO0bp1bwZDYu7dgU7o8jokzZ9Rai2+8YSOsqK3EbBa0aFF2DlEff2yOKPy8erWJ1auLv+uV\nxzGRH7GWQ4UKecfit98W7fc9c0Zi5cqzbTIS775r5aefLmyryZZFq1YhFi/O5KOPnKxYkcmkSW4a\nNCj8Xub3w+rVRm65JYE5c0xMmWJh2jQLGzYY8BdeFy01Yj0mIM6VNQhXsO/VK0DDhiWzIHs8El5v\nePEMBCKbuaalBfj66+gWyItHfD7Ys0fi998NbN4s43KV/j3s2SPx1FO2rPuRCGX9ZC4XrF9v0Fx8\nU8eOkQeQDRvKcVO+C/C//xmZPz/yECVJgnfecdGqVdmZm2fO5F22v/++eMra6dNq6ZhQ2RFDvrhc\ncOCAHJHkVdZo3lyhSpXIvaqosda1ayvcfHP+WlBhkpKsVujYMcS11wZo1y5EYmKRbodVq4xcd52d\n2rXhlVdsjB+fwLhxCfTo4eDzz83lIlmhqMS1spaWlpbz94gRvhLrB6qcpQOePi0xd66TmTMz+eab\nDObMccZUUevcuXPMrl1Qtm6VGTs2gY4dk+ndO4krrkhi0iQrbnd0r3MhWWzZYiQjQ50WBgM51dwX\nLTLRq5eDjz+2aGojaNo0hCwX/oRbFsZEtDl8OHK5a9w4yKJF7RgwIFCmWnwNG5a3rcXllxe9rc3R\noxJDh9oZO/ZqXnnFytGj2rUmn4+//pIZNSqRDh2SWLWq6BE+sZ4bDRsqzJmTSdOm6kLToEGQoUOL\nZnZKTIT/+z8PEye6cimAgt69/QwceOHPjKYsDh+WGDMmEUWRqFFDiVAWhZB4+OEENm7U5mEz1mMC\nykHMGkD16kqJnpwrVhTUrKlw9Kg6+K68MkiTJkpU2n1oBSFg926ZzZsNbNpkIBCAG27wR6X/3fr1\nBq6/3kFmZu5NQuKjjyzceaev1DpOBAIwd264zEuzZkEqVhQcPSoxfnwCIPHiizb69QvQuLE2ftvG\njRX+8x8PTz2lBmNGukV1ctO5c5BJk1z4fOqG2KpViPR0yMyESpVifXcFp2NH9Xs8/XQCbjcMHOin\nR4+iK2t79sisW6da5l591ca2bTITJ3pKtI9vtPH7Ydo0C998o87fceMSWLo0g4oVY3xjWRw4ILFl\niwGjEdq1C15wvLVpo7BokZOTJyUqVBDFSnSqWVNw++1+rroqwD//SJjNav9Xu73IH1kkjhyR+ftv\ndY/cssVAhw4hfvsttwoiMXeumUsv1c1r+VGGzpOFJ7s36HPPualTp+QWnurVBSNHegG45JJAkQO8\nt2yR+eEHIydORPdkW1x/+6FDEu+8Y6F79yTuvNPOG2/YePttG0uWmC/85guQmQmPP247S1FTGTXK\nF/UN43yyOHZM4rvvwu6k3r2DJCSoJ/bsRcbnk9izRzvTxmRSleYJE1z07++nQ4eCmf20EINR2jRs\nqHDbbX7uvttPz55BzpyR6N37f+zYoc3T/LlISoLbbvOzZk06a9dmMHmym5SUos8Tc840XgnACqfY\nsAAAIABJREFUokUWfvihbJ3jd+6UmT497OLev1/G6SzaOhrtubF7t8z119sZNszBkCEOVqwomMu6\nShVBs2ZK1DLSa9YUNG+u0KhRwRW1aMoit4v9669NDBqkNpzPjdmszQOCFtZL7ew6JURKSpDLLit5\nv9XQoX5mzHAyfbq7yArG7NlmBg1yMHp0Ivv3a8MVsWuXzHXX2bNO8eF7MpsFPXsW/TSfjc8n5YnB\nkSTB//2fh+HDfRhLcc84flyO+I7t2qnjJvdzQJE3gZKialXBqFF+3n/fVaxNuzzh98N771nIzJQ5\ndqxsLoMpKYLGjZViZ7inpCjUrBlpKZ40ycqZM8X73NLkwAEZRQnPS4sFTbi2MzPh6adt7N0bXsg+\n/9xc5mMDi0LDhgodOqh7hiSpGaYLF2YyfLiXSpUULrsscM74Op04d4OmpaUxebKH2rVLfgOrUUPQ\nv3/xlJfsTNHvvzdx8812vvjCFZVSH0X1tx8+LHHXXYns2RM5TEwmwUcfRScOr0oVweefO1m82Myx\nYxJt2oRo1SpEs2ahEmkLdj5ZnDoVXuytVpFT1+jsmMRAMX7mf/6BkydlnE6w2aBmTYWkpKJ/Xm7M\nhTB0aiEGI5bs3i3z6acWoBtCOGN9OzGlRg3Byy+7GT68W85zO3YYOXlSpmJFbbj7L8TZB6qOHQNF\nPjRHc27s2yezbFmkJa1OHYGhjBhzoymLatUE06e72LfPQMWKCs2aKZjN8MorHp54wovDUfqu2YKi\nhfUyrpU1yJstp2XatAnf6/btRt56y8Izz3hiNoB37TKwcWPuIaJa0556ykvLlqGonVybNVNo1swb\nnQ8rBrlPu3fe6aVuXXWjslrPNtUX7fPXrzfw2GM2Nmwwkl2vqFWrEE8+6aVLlwAOx4U+QSda/Pyz\nkWBQ3eDLysZZklxxRYDnnnPz9NNqWZMqVZRSixWNBjZb5L2OHu0r8jyNJqdOyeSu5wfQt2/xPRJl\nlZQUQUpK5J5sNqsu2nORnq66tStWFOXac6ABQ3HJsWHDBk1M2ILSpImSkwEE8P77VtavL74+XVR/\ne926CmPGeLjmGj///rebJUsy+eADF23ahMrsBnc+WWQXaLTZBMOG+XMeV6kiMBjCi0RRqsUfPixx\n4412NmwwEV68JTZvNnLLLXbWri3dc5MWYjBihcuVu1/wyjwbfXkkKQlSU79j8eJMJk1y8dlnzlLx\nSESLZs1CVK2qHq5uv91LWlrRD+nRnBsVK4qI/r69evm55JKyY0CI9Trx998S//d/CXTvnsx119nZ\nvbv89teOe8taWSLbHXHddWG/2OOP21iwwHnek0dJ0aiRwn/+E3uLV2mRkqKQnKzw7rsuUlPD7p8G\nDRT69/ezcKGFKlWUItU8SkwUtG0b4rvv8l9s0tO1FQdXGIRQOwDs3GnAaBSkpYU03YLmyBGZP/8M\nL31lKeuxJMmupdWxY9kLqGrUSI1/OnNGolmzkGayQJs1C/Hmm24++MDCVVcFGDrUV+CuATrwyy9G\nZs5UE0f27TPy889GGjcun3Ftcd8btG3btrG+jULhdMJzz9l4771wwNbChZl06VJ2TmMlQUaGWifL\n7ZZIShLUqqUUuTDjuVAUNfO1bl2RU18tmx07ZB5/PIFHH/UW+bc4cEDiq6/MTJ9u4dAhAyCoVUtw\n331eBg/2l0mlIT0d5s83869/JeDxqEJ7910nN96oXVdP7j6HVqtg7dr0cu1e0Sl53G70hueFRC1L\nY+f338Mxf3fd5eXll+O7tEe57Q1a1rDb4b77fKxebWT7dvXnWb/eUK6VtQ0bDDzxhI1169RYL1kW\n9OkTYPx4D02bRi8AWpY556admqowa5azWEkPKSmCMWN8DBni559/1LlYoYIok0oaqIkWn39u4V//\nityF8ivDoiVyF8dt2zZYIPkfPaqWbMk+LDRooOgWknLK339LLFtm4scfTVSooNCrV4CWLUPnLQ9V\nFhS1QEBNiDh1SqJaNXWMxzKjNiNDYu/eyHibChXK75yL+5i1skhKisKnnzrp3l21Thw6VLyfSQv+\n9qJy6JDEzTfbs4p2qkqAokgsWWLmmWdshe5wUBxZRCs7tWpVkVM0OVaKWjTGxKZNhqyA9DAmk6B9\ne2270X7+OXxGbdPm2wt2Ntm3T2boUDvXXJPETTc56NcviWuvtfPbbwUL3HS74eBBiRMnpDyZxVqi\nLK8TxUVR1C4qCxaYmDBhLb//bsB7jgiQHTtkxo5NZN48Mx9+aGXoUAdXX+1g5UpjsTLFY4nbDTNm\nmOnSJYmrr06ia9ck5s41sXJl7MaE1SqoVClyfYxVwqAW5kZcK2tlmYYNBVOnuvjyy0xuuy1ve5ny\nQjAo4XLlb6nx+7W9+cU769YZI2pbAbz6qlvTfTadTvjzz7CSlZ3xez527JDPyoqGnTtVV+r27edf\nQo8cUcvftG+fzJVXJvH881Y2b5bLZZ0traIo8M03Jnr2TOKOO+y89pqN3r0dfP21ifyihGrUEHmK\nuR48aGDwYDtr1pRNZ9X27QYeeyyBQECdz263xL33JnLoUOys5BUqwO23h/e+K64IlOsOLXGtrOXu\nDVoWqVZN0KNHkNati6eRaKFGTFGpX1/hs8+c1KiRWwaCDh0CvPCCu9BlTcqyLKJJNORQqVL4N0lO\nVnjvPSfXX+/XdKZwIABer7oB1aihcO21l1/wPfXrKyQm5t213W7pglZvl0tiyRITgYDE4cMyb7xh\no2fPJD74wMypU0X7DiVFeZ0b2T1Fs8cFdAMknnkmgb//zqusNGmiej7OrravKBIPPpjAyZPaDgPI\nD/V7Rt53KCRRu3bX2NxQFoMH+3nnHSdvvuli8mRXkTLxo4EW5kbZPAbolCs6dw7y/fcZHDok4/FA\ncrIgJUWhQoVY31n55oorgsyenUkopPYobdRI+2bOUEjCn5VM9thjngJlrTZrprBgQSaPP27jjz/C\nwc5XXhkgNfX8J/06dRQeeMDL5MlhX6vfL/Hkk4kEAhIjR/qwWM7zAToljstFTnJMburVC2G35z8+\nLr88yLffZjB9upUvvjDn1Oyz20W+1jitU7++gsUi8PnCcnA4BCkpsbVkVa0quOmmMupbjjJxbVkr\nqzFr0UYL/vbiUqOGGgvVpUuINm2KrqjFgyyiQTTkUL26oGfPIH36BMuEogZgsQiSklQ3VufOwQLL\noV27ELNnu/j22wzmzctk6dIMpk1zUbfu+Xdmmw3uucfH4MF5QxmeecbGzp3aWYLL69yoX1+tJxlm\nJdWqKbz4ouecGeeyDK1aKbz2mptVqzJYsED9b/ZsZ5lMGEpNVZg7N5OWLYOA4KKLAsyalcnRo6tj\nfWuaQAtzI+4ta1u2yHi9EjVrKpqu/aSjo1PyOBwwcqSPlBQ1weP48YK/t3JlQeXKhbc01KwpePVV\nN4MH+xk/3saOHeFl1+8vey6zeMNuh4ce8tKnT4Bjx2T273czeHAm9epd+ABiNmd3YCmFGy1BMjOh\nadMQCxdmkpEhUbGiIDkZNKCj6GQR93XWevW6EiEkKldWePNNFz17BstUV4OyyO7davp3/fp6eQOd\nwhEMqqU1jhyRsNkgNTV0wWzNwuJ2q42+YxFbd/KkxP79MpmZakun1FRFX49KgZMnJf75R90HtFIw\nVyvs3Clzzz0JnDolc/fdPgYO9J+3DIlOyXKuOmvascGXEEKo3/nUKZlbb7Xzyy9xb0yMGYEALFli\npHv3JPr2TWLqVEuZTWXXKX0OHJB5/XUrnTur5QOuvNLBjh3R16gSEmLXD7RKFdWd3727mjikK2ol\nz6lTEjffnEiHDkn06+dg1ixTmUwCKCn27JH5808Thw4ZeOaZBIYOtbNnT9yrBmWOuP5Fzo5ZE0Li\ntdes56yfE6+Ulr993ToDt95qzym1MXOmhdOntbUoaiH2QAtoTQ5//GFgwAA7L71kyxk/Fgsl3kxc\na3KIJfEqC78fdu82ABI7dhgZPdrOvfcmsH9//mtTaclBK2WHKlaMnGNbthh5/PEEzpyJ3zFRWLQg\nh7hW1vJDCGJalTleOX1a4vHHEyLqblWtquhNsnUuyB9/GOjf38HBg5HmrgkT3DRurJEdTafMUqOG\n4MEHI0/o335rZsQIOwcPxuYwuWmTgREjEhk1KoH5803s3Ru7Q23z5iF69Ih0gfzwgymif65O7Ilr\ntSUtLY0ZM5w0aBACBCkpQf7zH0+5cz2URo2Ygwcltm6NnNy33uonKekcb4gRWqiXU1qcPCnx008G\nVq40smWLjC9XQqJW5HD8uMTYsQl5Sic89JCHAQMCJX6w0ooctEC8ykKSYOBAP+3bRyokGzcaWbIk\n72ZwLjns2yfhdEbnno4dk1i0yMzs2RbuvNNO795JLFxo4p9/ovP5hSE5GZ57zk316pEHow0bDHE7\nJgqLFuQQ18oaQP/+AVasyOS33zJYvtxJ27bltwJySZKREbnZVqum0LOnP0Z3owOwZImJAQOSuP56\nB127JjF+vI1du7Q15Q8ckNm8OazkV6yo8MknTh56yBuzApg68UdKiuD9990MHBhZQmXaNAunTxfs\nM/7+W2bWLHOhW9zlR8uWoawyGSqnT8vcfrud8eMTYmLty64l2L9/WD7R7LusU3y0tXJHmeyYtUqV\nBI0bK1SrVj4X/9Lwt9eqpeS0YKlZU2H27EwaNdKevLUQe1BaWCxh+SuKxPTpVq6+2sH69YYIORw7\nJjFvnolNm0p/OaheXeGhhzzcdJOPDz5wsmxZJldfHSh0Z4qiUp7Gw4WId1mkpChMnOjm00+ddOsW\nIClJoU+fQJ6ixOeSQ506Ci+8YGPZsvzbUBWEo0clFi0ysWWLgXfecVGnTqTx4JNPLLz0ko0zZ4r2\n+cUhNVXhrbfc/PBDOitWZNC5cyDux0RB0YIcdKe0TlRo1EiwaFEGJ0/KNGoUIiVFe4paeaNjxxD1\n6wfZvz88zU+elLnttkTGj1dP704nvPGGlenTrbRtG2D+fCcOR+ndY0qK4Omny1nGj07MqFgR+vUL\n0L17gDNn1HpiNhukp6tJCLt3y6xebebrr23Islo6pkWLEKmpIWrVEtx6q497702kYcMMLrqo8Jan\nDRsMDB+unkRSUoJMm+Zi6lQrixaF3bEzZ1oYONBPr16l37Q8KYkifS+dkifu66y1bds21rehac6c\ngXnzzKSlhWjXTvsu4lOn1DpV+/fLHD+u1qu65JIgl10WjHo9rnhg61a172FuVyPAxx87GTAgwKpV\nRgYOtAMSNpvgt9/SqV27bK8Jbjds3mxg3jwzGRkSo0d7i91fVyd+2btX4tFHE1m50nTO14we7eHJ\nJ73s3GmgVy8HrVuHmDnTed5C6zt2yKSnSzRpEsqp7bZkiZFhw8KnoaQkhXnznBw9KvH00wns368m\n2Tz7rJsHHsjb9UIn/jlXnTXdslbO+eEHE489lsi993pp185z4TfEiF27ZH791cjrr1tzFrRsUlOD\nLFrk1DNP86FFC4WZM518952JCRNs/P23TGKioHJlBZ8P3n/fQnYDZ59P7Z0JZVeOp07BtGlWXnvN\nSvb3qlRJoXVr3Xqnkz/r1hnPq6gBHDsmoyhqlf8rrwzy/fcm5s41M2qUD1M+b920ycA119hJT5cZ\nNszHs8+6qVwZGjVSMJkEgYA6NjMyZMaMSeDLL52sWJHJoUMSLpdESop+uNCJpFzErJV3zuVvP3BA\n5sknE3L+1iLp6TB/vokrr0zigQcS8yhqNWooTJ3qpnLlgikYWog9KG1q1xYMH+7nxx8z+OWXdFav\nziAY/JFDhySWLg3vNE2bKlSoUHY3iUAAPv3Uwmuv2chW1IB8LYXHjkkcPCixalX5Gw/nojzODYCu\nXYO8/LKLJk3UqgGwEgCzWdChQ4CPPnLy3HMekpPVdmUPPKAq/v/5j42NG/Ovrjxvnon0dHVN/ewz\nS45lu1EjhVdfjcxQ2L7dyJYtBipXFlx0kUKnTiFq1xbs3y+ze7dMZmaJfO0CUV7HxNloQQ7a3KF1\nSoXffzdw8qQ6BLRYe87lgrfesnLnneFCu9nIsmD4cC+LFmWQlqZ9921psG+fzNdfm1i1yphv4efq\n1QWpqQr16yvIMhw9KhMMhuXar5/2Sq0Uhq1bDTz/fKQv3G4XdO0aLtmwb5/Em29a6No1iY4dk/nq\nK1NESROd8keNGoK77vKzdGkGa9dmMHmyk59/TmfdunTmzHFy7bWBCHdnq1YhWrcOEgpJPPBAAkeO\nRK5Nfj95OuV8/bV6KDIYoH9/P/fdF+nFWLcu8vXLlxvp0iWJDh2SGDzYzooVxpgqbTqxR4NbdPRI\nS0uL9S1ogvxqxPh8MHNmOKi1dm3tWVT275eZONEa8VyDBiFeeMHNypUZvPyyh4YNC+ey00K9nJJg\nxw6ZAQMc3Habneuus7N16/n7KXXu3JkzZyKnf7dupR/QHE127pSz3LgqsiyYNs1Jixbq2N6xQ+b6\n6+38+98JnDgh4/FIzJ/fW3NdNmJFvM6NglKxompdvuWWy2nWTKFuXZFvVnKlSoInn1SVrW3bjMyf\nb47oRmAwqIeE3OzaJedkkFaqBA8+6GXyZBeVKqlvbNky8sC5eLEp64AqsW6diSFDHEyebCU9PWpf\nt0CU9zGRjRbkoMeslVMOHZJZtSrsAmvfXnsbdf36Ct9+m8mJExIWC1SoIKhbVymwy7O8cPy4xF13\nJXLkiKp8CSFx7NiFFRCTKSzHtLRglhuo7FKpUvj7NGkSZNIkN5dcon6nEyckHnwwgb/+ilzyLr44\nSHKyPp50CkdaWoiUlCAHDhh5/nkb3boFaNlSVbwMBrjuugDffx8+DLdsqSBJaoup48clMjMlWrcO\nMmtWJqGQOhdPn1YVuVAIBg/2s3GjkY0bDTn9rSdOtNGsWYhBg/SGy+WRuLasaTVmzetVT/mlVUsn\nt799926Z6dPNrF5tzAlyBbVOmtZITIS2bUP06ROkW7cgaWmhYitqWog9iDZ//mnIk+1ZocL55bRm\nzRpq1hTIsiAhQTBpkovq1cu20nLppUGWLctg8eIMvvrKSadOoZzg7927ZX79NTIS3GYTDBiwnISE\nGNysBonHuVEUCiKHmjUFEyaosQY+n8SUKVZcrvC/d+oUpHbt7MOPoF8/H/v2SYwbZ6NzZ9UF3717\nEnfcYWf6dBtr15qZPNnCt98aGT06gSefTKRhwxAvvuihWbPwIertt61RKcpbUPQxoaIFOcS1sqZF\nXC6YOtVCp05JvP126TaV//13Az17OvjXvxI4fjz801esqFCnjvaUNZ2CsXp1pBJSvbpCvXoX/j2b\nNw8xZ46TpUuLVjNKa9jtcMklITp2DOVRPA1neYWrV1eYOzez0G50nfLL7t0y8+eb+O03A14vdOgQ\nJC1N9UjMnm1mw4bwIGvQQGHOHCevveZiwQIn7dopzJlj4b33rLnCDyQOHlRLzDz1lI169QQPPZTA\nnDkWtm0zMH++hXHjbIwY4UWS1HHarFkoz1jWKR/oddZKmZ9+MjBggAOQkGXBTz9lkJpa8hvltm0y\n/fo5SE+XqVZNoX9/Px9+qMaD3XGHl1df9SDpoTua5uhRiYMHZTwesNnIqd80fHhirqKagk8/ddKv\nn/bc2rHE5YJffzWyfbuBhg1DtGwZom7d+F37dKLL3r0yQ4bY6d49QLVqCg0aKNSsqZbhuOqqJISQ\naNEiyJw5TmrUyH9cbdokM2iQIyep62xSU0OkpQWZNSuypcJTT7np1ClAKCTRuLFS5i3gOudHr7Om\nAYRQSwtklxVQFInjxyVSU0v2umfOwLhxCTmp5LKsxkVk3RU33ujXFTWNEgqpwcnLl5uYOtUaYRGd\nONHF7bf7ueYaP4sWmZFlwSuvuMt8okBJkJgIV14Z5MorddnEI8EgrF9v4M8/DdStq9C+fYiqVaOn\n1OzfLzF8uI/337dw8GDYtJWWFuTVV108+qidrVuNrFpl5MYb848pa91aYdmyTFauNDJvnpmtWw2k\np0skJQm6dAkwZIif0aPPzmgQdOwYpGPHsm/51ikece0G1VrM2okTUkRQP5BvQcVoM3/+zxHX9fnI\nWciuu86fJxMpntFC7EFBcblg7lwT3bsn8eyzka5rEDRsqC7gPXoE+OabDH74IYNbb/UXKAarLMmh\nJNHlEKYsy2LbNpn+/R08+WQiw4Y5GDMmgUOHinYCzU8Oe/YYspqsR/ogN2wwUr++yHFTjhuXwN69\n595WGzRQuP12P3PnOlmzJoP16zNYvDiTJ57wUqNGiKeectOgQQirVa3xNneuk7ZtY7c+l+UxEU20\nIAfdslaKeDyqJS2MoGLFkjdpnzkTuWjdeKOPyy4L0qRJkCee8JKYWOK3oFMEvv7axL33JpK7wCuA\nJAmmTHFzySWqlahiRbjssvKjcOcmI0OtL7d3r4EtWwwcP662+KldO0SHDiG+/dZErVoKV1/t56KL\nFN2CHKccPBhZtmXFCjMLFgQZM6b4RfROn4Z337Xm+289ewZo3jzEPfd4efddG2fOyHzzjYn77vOd\nt3al2awmKZzdLaRtWz+DBgVwuyE5WZRqn95Yoyjw119qh5Vq1XRX79mUWsyaJEkWYBVgRlUS5wgh\n/i1JUkVgFlAP2A/cKIRIz3rPOOAOIAiMFUIsz3q+LfBfwAosFkI8mN81tRazduSIRJcuSTkBpq1a\nBfnqq0wqVCjZ627eLDN0qAOzWfDUUx66dAliswkyM6VzxlfoxJYTJyR69HBw6FDuk7xgwAA/Y8b4\nSEsLlYpVVsv89ZfE+PE2vvrKzNkK7bhxHl5/3YrPpz5vtQq++MLJFVfobtB45NdfDfTtG1nRuUYN\nhR9+yCh2jFcgoLZl+9e/wp0xHA7BY495uO46P7VrC3bskOnVKwmnU8JqFXz3XQbNm+uuy4ISDJKl\n5CZy880+/vMfD9b89WNNcPSoxJYtBoJB1VrapIkStcLyMY9ZE0L4JEnqLoRwS5JkAH6SJGkJMAj4\nVgjxiiRJTwDjgCclSWoB3Ag0B+oA30qS1ESo2uVU4E4hxDpJkhZLktRHCLGstL5LUalRQ3DttX7+\n+18rIJgwwV3iihpAq1YK332XgcFAROmLxMTYKWrBoJpddfSo2nOvVi2Fxo2Vcq+AZFOpkmDaNBc/\n/mjCZIKUlBDNmoVo2FDRLaFZ+HwSmzYZOFtRAzU+NFtRA/B6Je65J5EVKzKoU0c/oMQbTZqE6Nw5\nwJo14QUkPV0iEIWSZCYTjBjho02bIBs3GlAU6NgxRNu2oRxLbWqqwvPPu3nwwUS8XonPPjPzzDNe\nzObzf7YWOXVKwmwuGaveoUMSf/6pdmOoV0+hWTM1Seq33wyMHJlIKCTx2WcWHnjAq9l5evKkupZk\njzWLRfDWWy6uuSZQovtXqcasCSGyK8RYUBVFAVwLfJz1/MfAwKy/rwG+EEIEhRD7gV1AB0mSagAO\nIcS6rNfNyPWeCLQWsybLMGaMl7vv9vLll07aty8d19WaNWuoVk1opphsKAQLFpjo2jWJQYMc3HCD\ng65dk3jpJetZbuLoo4XYg4JgMKiuzSef9PLII15uuCFA69bRU9TKihzOR9OmCgsXOpkzJ5N//9vN\nVVf5ufzyAJdeGqRqVYXKlSMtG8ePy+zZExlzFA9yiBZlWRaVKsHrr7vp0iWsnT34oDfL1Vg48pOD\nzQaXXx7illv8DBvmp127UB6Xes+eARo1Ui23775rZcuWslVjw+OBr74y0aOHgxEjEjl4UIr6mJg8\n2cqtt9q59147V1+dxOjRiezZo1rIs93YXq+afKclcsvh2DEp4lDg86nKW+7SLSVBqcasSZIkA+uB\nRsDbWZax6kKI4wBCiGOSJFXLenlt4Jdcbz+c9VwQOJTr+UNZz5cJGjYUvPSS58IvjGMOHpS5777E\niKK8waDEpElqhe4bbtArdOsUjDp1BHXqqFme99/vQwg19iXbijxiRGTMn9GojQOLTvRp3Fjhgw9c\n7NolI0lqKYxo1yQ7n7WpVi3Bq696uP56B4oiMXWqhTffdGOznfs9WmL9ekPOfDlwwMBvv/mpXj16\nnx8MqsXgc7N8uZmrrgqwfn1Y+WnQQMFu164L2W5XvVK5+1UrisSKFaacjiklQakqa0IIBbhYkqQk\nYL4kSS05O8Iy7+Mis3v3bu69915SUlIASE5OpnXr1jl9vrK1Zf1x6T5u0aIzqakhNm/OPq10y/r/\nStas8XLDDZeW6PWz0Yo8YvG4c+fOmrqfknicmPgD48cb+PTT3hw8aKB79xX8848fuDzi9dnE+n6z\nH6emduHMGYnffltNpUrQr9/lUf38cz3Ofi7W378sP/b54Npre7NwoYU5c36mUyc3I0Z00sz9nevx\nP//A2LHrAAPZ6/GaNWsYNIgcinu9tWvX0KmTkdWr+2Z94kqsVsGBAx1zHgMMG9aBSpW0JZ/c6+Xl\nl3dm0iQXd9+9DvUgqMorI2Mla9YEi7QfrVmzhgMHDgDQvn17evTowdnErCiuJElPA25gJNBNCHE8\ny8X5gxCiuSRJTwJCCPFy1uuXAuOBv7Jfk/X8TUBXIcTos6+htQQDnTDbtsk8+WQCq1cbybZ8tG0b\nYPp0d05JCh2daHDqlITbDVWqCE1bOY4ckVi2zMSkSdacxJJLLgnwzjtuGjXS50RZYft2mT59ksjM\nlBg1ysu//+2JeizTkSMS69cbMZsF7dqFqFKlePv4tm0yl1+eRG4r9Ntvuxg61F/MO40kPR2mTLHy\n+uvqRGzaNESrViHmzQsX9f7uu0wuvljb2e0uF/zyi5FJk6xs3WrgqqsCPPaYNyp717kSDEotZk2S\npCqSJCVn/W0DegHbgK+AEVkvuw1YmPX3V8BNkiSZJUlqADQGfhNCHAPSJUnqIEmSBAzP9Z4ItBaz\nFiuiHXcQDZo3V/j0Uyc//JDBggUZfPttBrNmuUpcUdOiLGJBeZJD5cqCunXzV9S0Ioe5A5e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EsvWdm7N3/Tee3aCrfd5qNjxwD16ytlOsFm+3aZTp2SAAmDQTBypI977vEVuGPLn3/KPPxwAocO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\npDh11o4DjaWUWXmuWYH9UspaZTS+UlHS3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GAZgBCiBpB9wWdFIBYL53V1mUzQrZuPBQts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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\")\n", + "plt.scatter(t[:,0], t[:,1], alpha = 0.015, c = \"r\")\n", + "plt.scatter(halo_data[n_sky-1][3], halo_data[n_sky-1][4], \n", + " label = \"True halo position\",\n", + " c = \"k\", s = 70)\n", + "plt.legend(scatterpoints = 1, loc = \"lower left\")\n", + "plt.xlim(0, 4200)\n", + "plt.ylim(0, 4200);\n", + "\n", + "print(\"True halo location:\", halo_data[n_sky][3], halo_data[n_sky][4])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Perfect. Our next step is to use the loss function to optimize our location. A naive strategy would be to simply choose the mean:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 2312.96009501 1127.87170923]]\n" + ] + } + ], + "source": [ + "mean_posterior = t.mean(axis=0).reshape(1,2)\n", + "print(mean_posterior)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Using the mean:\n", + "Your average distance in pixels you are away from the true halo is 46.0082084242\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 1.04600820842\n", + "Using a random location: [[ 288 3167]]\n", + "Your average distance in pixels you are away from the true halo is 2908.49191694\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 3.90849191694\n" + ] + }, + { + "data": { + "text/plain": [ + "3.9084919169390866" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from DarkWorldsMetric import main_score\n", + "\n", + "_halo_data = halo_data[n_sky-1]\n", + "\n", + "nhalo_all = _halo_data[0].reshape(1,1)\n", + "x_true_all = _halo_data[3].reshape(1,1)\n", + "y_true_all = _halo_data[4].reshape(1,1)\n", + "x_ref_all = _halo_data[1].reshape(1,1)\n", + "y_ref_all = _halo_data[2].reshape(1,1)\n", + "sky_prediction = mean_posterior\n", + "\n", + "print(\"Using the mean:\")\n", + "main_score(nhalo_all, x_true_all, y_true_all, \\\n", + " x_ref_all, y_ref_all, sky_prediction)\n", + "\n", + "#what's a bad score?\n", + "random_guess = np.random.randint(0, 4200, size=(1,2))\n", + "print(\"Using a random location:\", random_guess)\n", + "main_score(nhalo_all, x_true_all, y_true_all, \\\n", + " x_ref_all, y_ref_all, random_guess)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a good guess, it is not very far from the true location, but it ignores the loss function that was provided to us. We also need to extend our code to allow for up to two additional, *smaller* halos: Let's create a function for automatizing our PyMC3. " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def halo_posteriors(n_halos_in_sky, galaxy_data,samples = 5e5, burn_in = 500):\n", + " #set the size of the halo's mass\n", + " with pm.Model() as model:\n", + " mass_large = pm.Uniform(\"mass_large\", 40, 180)\n", + " \n", + " mass_small_1 = 20\n", + " mass_small_2 = 20\n", + " \n", + " masses = np.array([mass_large,mass_small_1, mass_small_2], dtype=object)\n", + " \n", + " #set the initial prior positions of the halos, it's a 2-d Uniform dist.\n", + " halo_positions = pm.Uniform(\"halo_positions\", 0, 4200, shape=(n_halos_in_sky,2)) #notice this size\n", + " \n", + " fdist_constants = np.array([240, 70, 70])\n", + " \n", + " _sum = 0\n", + " for i in range(n_halos_in_sky):\n", + " _sum += masses[i]/f_distance(data[:,:2], halo_positions[i, :], fdist_constants[i])*\\\n", + " tangential_distance(data[:,:2], halo_positions[i, :])\n", + " \n", + " mean = pm.Deterministic(\"mean\", _sum)\n", + " \n", + " ellpty = pm.Normal(\"ellipcity\", mu=mean, tau=1./0.05, observed=data[:,2:])\n", + " \n", + " mu, sds, elbo = pm.variational.advi(n=50000)\n", + " step = pm.NUTS(scaling=model.dict_to_array(sds), is_cov=True)\n", + " trace = pm.sample(samples, step=step, start=mu)\n", + " \n", + " burned_trace = trace[burn_in:]\n", + " return burned_trace[\"halo_positions\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_sky = 215\n", + "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", + "Training_Sky%d.csv\" % (n_sky),\n", + " dtype = None,\n", + " skip_header = 1,\n", + " delimiter = \",\",\n", + " usecols = [1,2,3,4])" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied interval-transform to mass_large and added transformed mass_large_interval_ to model.\n", + "Applied interval-transform to halo_positions and added transformed halo_positions_interval_ to model.\n", + "Iteration 0 [0%]: ELBO = 102.73\n", + "Iteration 5000 [10%]: Average ELBO = 113.4\n", + "Iteration 10000 [20%]: Average ELBO = 128.11\n", + "Iteration 15000 [30%]: Average ELBO = 131.97\n", + "Iteration 20000 [40%]: Average ELBO = 132.94\n", + "Iteration 25000 [50%]: Average ELBO = 133.52\n", + "Iteration 30000 [60%]: Average ELBO = 133.95\n", + "Iteration 35000 [70%]: Average ELBO = 134.24\n", + "Iteration 40000 [80%]: Average ELBO = 134.31\n", + "Iteration 45000 [90%]: Average ELBO = 134.43\n", + "Finished [100%]: Average ELBO = 134.31\n", + " [-------100%-------] 5000 of 5000 in 621.1 sec. | SPS: 8.1 | ETA: -0.0" + ] + } + ], + "source": [ + "#there are 3 halos in this file. \n", + "samples = 5000\n", + "traces = halo_posteriors(3, data, samples = samples, burn_in=500)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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CjEhJMmYMuZzhnvsynHNOM6+95vCLX3Ry9NF9ywJQeZ/eSJzRmiefcjjhhHG8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UAAAg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\n4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HNBhw4aH33kZOxYD2ef7ee664pYssTZYB216kjqFbh582aGDPHx0UdWiopCT3K/Hw4e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7dbBWLKxbJ1myJHooe/RwAqKePWH6dIvDD7fYvl1QU6OLZsTd2go7d0afVLvtZjNm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\n1Gd2Is5aJEfGubFrBg2yGTPWYtRIu+iBWrq2Qbkg03p7Jr6TxUb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1xxxWscc0wjixebhJI7K/VpdHY6HZQvvpj8nGhpIU76YvVqkzfeiA5i3n1XsnBhPSec0MQZ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\nJgruhhtMLoilS7s4+mijb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RUfBxHD7YdkEmbNyravpUWz667BoN8uMz5F0GgkcpdAMila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\n1rf6OOigACd84E+fPnom7fZ2uOSSPvr64I47T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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\")\n", + "\n", + "colors = [\"#467821\", \"#A60628\", \"#7A68A6\"]\n", + "\n", + "for i in range(traces.shape[1]):\n", + " plt.scatter(traces[:, i, 0], traces[:, i, 1], c = colors[i], alpha = 0.02)\n", + " \n", + " \n", + "for i in range(traces.shape[1]):\n", + " plt.scatter(halo_data[n_sky-1][3 + 2*i], halo_data[n_sky-1][4 + 2*i], \n", + " label = \"True halo position\", c = \"k\", s = 90)\n", + " \n", + "#plt.legend(scatterpoints = 1)\n", + "plt.xlim(0, 4200)\n", + "plt.ylim(0, 4200);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks pretty good, though it took a long time for the system to (sort of) converge. Our optimization step would look something like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(4500, 3, 2)\n", + "[[ 3790.95827012 3794.60133909 3170.00252772 3142.31644835\n", + " 2265.01634741 3623.32277728]]\n", + "Using the mean:\n", + "Your average distance in pixels you are away from the true halo is 175.125422038\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 1.17512542204\n", + "Using a random location: [[1199 3589]]\n", + "Your average distance in pixels you are away from the true halo is 2522.2681726\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 3.5222681726\n" + ] + }, + { + "data": { + "text/plain": [ + "3.5222681725978306" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "_halo_data = halo_data[n_sky-1]\n", + "print(traces.shape)\n", + "\n", + "mean_posterior = traces.mean(axis=0).reshape(1,6)\n", + "print(mean_posterior)\n", + "\n", + "\n", + "nhalo_all = _halo_data[0].reshape(1,1)\n", + "x_true_all = _halo_data[3].reshape(1,1)\n", + "y_true_all = _halo_data[4].reshape(1,1)\n", + "x_ref_all = _halo_data[1].reshape(1,1)\n", + "y_ref_all = _halo_data[2].reshape(1,1)\n", + "sky_prediction = mean_posterior\n", + "\n", + "\n", + "print(\"Using the mean:\")\n", + "main_score([1], x_true_all, y_true_all, \\\n", + " x_ref_all, y_ref_all, sky_prediction)\n", + "\n", + "#what's a bad score?\n", + "random_guess = np.random.randint(0, 4200, size=(1,2))\n", + "print(\"Using a random location:\", random_guess)\n", + "main_score([1], x_true_all, y_true_all, \\\n", + " x_ref_all, y_ref_all, random_guess)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n", + "1. Antifragile: Things That Gain from Disorder. New York: Random House. 2012. ISBN 978-1-4000-6782-4.\n", + "1. [Tim Saliman's solution to the Dark World's Contest](http://www.timsalimans.com/observing-dark-worlds)\n", + "2. Silver, Nate. The Signal and the Noise: Why So Many Predictions Fail — but Some Don't. 1. Penguin Press HC, The, 2012. Print." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.core.display import HTML\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter5_LossFunctions/Chapter5.ipynb b/Chapter5_LossFunctions/Chapter5.ipynb deleted file mode 100644 index 54346a99..00000000 --- a/Chapter5_LossFunctions/Chapter5.ipynb +++ /dev/null @@ -1,1482 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Chapter 5\n", - "____\n", - "### Would you rather lose an arm or a leg?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Statisticians can be a sour bunch. Instead of considering their winnings, they only measure how much they have lost. In fact, they consider their wins as *negative losses*. But what's interesting is *how they measure their losses.*\n", - "\n", - "For example, consider the following example:\n", - "\n", - "> A meteorologist is predicting the probability of a possible hurricane striking his city. He estimates, with 95% confidence, that the probability of it *not* striking is between 99% - 100%. He is very happy with his precision and advises the city that a major evacuation is unnecessary. Unfortunately, the hurricane does strike and the city is flooded. \n", - "\n", - "This stylized example shows the flaw in using a pure accuracy metric to measure outcomes. Using a measure that emphasizes estimation accuracy, while an appealing and *objective* thing to do, misses the point of why you are even performing the statistical inference in the first place: results of inference. The author Nassim Taleb of *The Black Swan* and *Antifragility* stresses the importance of the *payoffs* of decisions, *not the accuracy*. Taleb distills this quite succinctly: \"I would rather be vaguely right than very wrong.\" " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Loss Functions\n", - "\n", - "We introduce what statisticians and decision theorists call *loss functions*. A loss function is a function of the true parameter, and an estimate of that parameter\n", - "\n", - "$$L( \\theta, \\hat{\\theta} ) = f( \\theta, \\hat{\\theta} )$$\n", - "\n", - "The important point of loss functions is that it measures how *bad* our current estimate is: the larger the loss, the worse the estimate is according to the loss function. A simple, and very common, example of a loss function is the *squared-error loss*:\n", - "\n", - "$$L( \\theta, \\hat{\\theta} ) = ( \\theta - \\hat{\\theta} )^2$$\n", - "\n", - "The squared-error loss function is used in estimators like linear regression, UMVUEs and many areas of machine learning. We can also consider an asymmetric squared-error loss function, something like:\n", - "\n", - "$$L( \\theta, \\hat{\\theta} ) = \\begin{cases} ( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\lt \\theta \\\\\\\\ c( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\ge \\theta, \\;\\; 0\\lt c \\lt 1 \\end{cases}$$\n", - "\n", - "\n", - "which represents that estimating a value larger than the true estimate is preferable to estimating a value below. A situation where this might be useful is in estimating web traffic for the next month, where an over-estimated outlook is preferred so as to avoid an underallocation of server resources. \n", - "\n", - "A negative property about the squared-error loss is that it puts a disproportionate emphasis on large outliers. This is because the loss increases quadratically, and not linearly, as the estimate moves away. That is, the penalty of being three units away is much less than being five units away, but the penalty is not much greater than being one unit away, though in both cases the magnitude of difference is the same:\n", - "\n", - "$$\\frac{1^2}{3^2} \\lt \\frac{3^2}{5^2}, \\;\\; \\text{although} \\;\\; 3-1 = 5-3$$\n", - "\n", - "This loss function imposes that large errors are *very* bad. A more *robust* loss function that increases linearly with the difference is the *absolute-loss*\n", - "\n", - "$$L( \\theta, \\hat{\\theta} ) = | \\theta - \\hat{\\theta} |$$\n", - "\n", - "Other popular loss functions include:\n", - "\n", - "- $L( \\theta, \\hat{\\theta} ) = \\mathbb{1}_{ \\hat{\\theta} \\neq \\theta }$ is the zero-one loss often used in machine learning classification algorithms.\n", - "- $L( \\theta, \\hat{\\theta} ) = -\\hat{\\theta}\\log( \\theta ) - (1-\\hat{ \\theta})\\log( 1 - \\theta ), \\; \\; \\hat{\\theta} \\in {0,1}, \\; \\theta \\in [0,1]$, called the *log-loss*, also used in machine learning. \n", - "\n", - "Historically, loss functions have been motivated from 1) mathematical convenience, and 2) they are robust to application, i.e., they are objective measures of loss. The first reason has really held back the full breadth of loss functions. With computers being agnostic to mathematical convenience, we are free to design our own loss functions, which we take full advantage of later in this Chapter.\n", - "\n", - "With respect to the second point, the above loss functions are indeed objective, in that they are most often a function of the difference between estimate and true parameter, independent of signage or payoff of choosing that estimate. This last point, its independence of payoff, causes quite pathological results though. Consider our hurricane example above: the statistician equivalently predicted that the probability of the hurricane striking was between 0% to 1%. But if he had ignored being precise and instead focused on outcomes (99% chance of no flood, 1% chance of flood), he might have advised differently. \n", - "\n", - "By shifting our focus from trying to be incredibly precise about parameter estimation to focusing on the outcomes of our parameter estimation, we can customize our estimates to be optimized for our application. This requires us to design new loss functions that reflect our goals and outcomes. Some examples of more interesting loss functions:\n", - "\n", - "\n", - "- $L( \\theta, \\hat{\\theta} ) = \\frac{ | \\theta - \\hat{\\theta} | }{ \\theta(1-\\theta) }, \\; \\; \\hat{\\theta}, \\theta \\in [0,1]$ emphasizes an estimate closer to 0 or 1 since if the true value $\\theta$ is near 0 or 1, the loss will be *very* large unless $\\hat{\\theta}$ is similarly close to 0 or 1. \n", - "This loss function might be used by a political pundit who's job requires him or her to give confident \"Yes/No\" answers. This loss reflects that if the true parameter is close to 1 (for example, if a political outcome is very likely to occur), he or she would want to strongly agree as to not look like a skeptic. \n", - "\n", - "- $L( \\theta, \\hat{\\theta} ) = 1 - \\exp \\left( -(\\theta - \\hat{\\theta} )^2 \\right)$ is bounded between 0 and 1 and reflects that the user is indifferent to sufficiently-far-away estimates. It is similar to the zero-one loss above, but not quite as penalizing to estimates that are close to the true parameter. \n", - "- Complicated non-linear loss functions can programmed: \n", - "\n", - " def loss(true_value, estimate):\n", - " if estimate*true_value > 0:\n", - " return abs(estimate - true_value)\n", - " else:\n", - " return abs(estimate)*(estimate - true_value)**2\n", - " \n", - "\n", - "\n", - "- Another example is from the book *The Signal and The Noise*. Weather forecasters have a interesting loss function for their predictions. [2]\n", - "\n", - "\n", - "> People notice one type of mistake — the failure to predict rain — more than other, false alarms. If it rains when it isn't supposed to, they curse the weatherman for ruining their picnic, whereas an unexpectedly sunny day is taken as a serendipitous bonus.\n", - "\n", - "> [The Weather Channel's bias] is limited to slightly exaggerating the probability of rain when it is unlikely to occur — saying there is a 20 percent change when they know it is really a 5 or 10 percent chance — covering their butts in the case of an unexpected sprinkle.\n", - "\n", - "\n", - "As you can see, loss functions can be used for good and evil: with great power, comes great — well you know.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Loss functions in the real world\n", - "\n", - "So far we have been under the unrealistic assumption that we know the true parameter. Of course if we knew the true parameter, bothering to guess an estimate is pointless. Hence a loss function is really only practical when the true parameter is unknown. \n", - "\n", - "In Bayesian inference, we have a mindset that the unknown parameters are really random variables with prior and posterior distributions. Concerning the posterior distribution, a value drawn from it is a *possible* realization of what the true parameter could be. Given that realization, we can compute a loss associated with an estimate. As we have a whole distribution of what the unknown parameter could be (the posterior), we should be more interested in computing the *expected loss* given an estimate. This expected loss is a better estimate of the true loss than comparing the given loss from only a single sample from the posterior.\n", - "\n", - "First it will be useful to explain a *Bayesian point estimate*. The systems and machinery present in the modern world are not built to accept posterior distributions as input. It is also rude to hand someone over a distribution when all they asked for was an estimate. In the course of an individual's day, when faced with uncertainty we still act by distilling our uncertainty down to a single action. Similarly, we need to distill our posterior distribution down to a single value (or vector in the multivariate case). If the value is chosen intelligently, we can avoid the flaw of frequentist methodologies that mask the uncertainty and provide a more informative result.The value chosen, if from a Bayesian posterior, is a Bayesian point estimate. \n", - "\n", - "Suppose $P(\\theta | X)$ is the posterior distribution of $\\theta$ after observing data $X$, then the following function is understandable as the *expected loss of choosing estimate $\\hat{\\theta}$ to estimate $\\theta$*:\n", - "\n", - "$$ l(\\hat{\\theta} ) = E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", - "\n", - "This is also known as the *risk* of estimate $\\hat{\\theta}$. The subscript $\\theta$ under the expectation symbol is used to denote that $\\theta$ is the unknown (random) variable in the expectation, something that at first can be difficult to consider.\n", - "\n", - "We spent all of last chapter discussing how to approximate expected values. Given $N$ samples $\\theta_i,\\; i=1,...,N$ from the posterior distribution, and a loss function $L$, we can approximate the expected loss of using estimate $\\hat{\\theta}$ by the Law of Large Numbers:\n", - "\n", - "$$\\frac{1}{N} \\sum_{i=1}^N \\;L(\\theta_i, \\hat{\\theta} ) \\approx E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] = l(\\hat{\\theta} ) $$\n", - "\n", - "Notice that measuring your loss via an *expected value* uses more information from the distribution than the MAP estimate which, if you recall, will only find the maximum value of the distribution and ignore the shape of the distribution. Ignoring information can over-expose yourself to tail risks, like the unlikely hurricane, and leaves your estimate ignorant of how ignorant you really are about the parameter.\n", - "\n", - "Similarly, compare this with frequentist methods, that traditionally only aim to minimize the error, and do not consider the *loss associated with the result of that error*. Compound this with the fact that frequentist methods are almost guaranteed to never be absolutely accurate. Bayesian point estimates fix this by planning ahead: your estimate is going to be wrong, you might as well err on the right side of wrong." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Optimizing for the *Showcase* on *The Price is Right*\n", - "\n", - "Bless you if you are ever chosen as a contestant on the Price is Right, for here we will show you how to optimize your final price on the *Showcase*. For those who forget the rules:\n", - "\n", - "\n", - "1. Two contestants compete in *The Showcase*. \n", - "2. Each contestant is shown a unique suite of prizes.\n", - "3. After the viewing, the contestants are asked to bid on the price for their unique suite of prizes.\n", - "4. If a bid price is over the actual price, the bid's owner is disqualified from winning.\n", - "5. If a bid price is under the true price by less than $250, the winner is awarded both prizes.\n", - "\n", - "The difficulty in the game is balancing your uncertainty in the prices, keeping your bid low enough so as to not bid over, and trying to bid close to the price.\n", - "\n", - "Suppose we have recorded the *Showcases* from previous *The Price is Right* episodes and have *prior* beliefs about what distribution the true price follows. For simplicity, suppose it follows a Normal:\n", - "\n", - "\n", - "$$\\text{True Price} \\sim \\text{Normal}(\\mu_p, \\sigma_p )$$\n", - "\n", - "\n", - "In a later chapter, we will actually use *real Price is Right Showcase data* to form the historical prior, but this requires some advanced PyMC use so we will not use it here. For now, we will assume $\\mu_p = 35 000$ and $\\sigma_p = 7500$.\n", - "\n", - "We need a model of how we should be playing the *Showcase*. For each prize in the prize suite, we have an idea of what it might cost, but this guess could differ significantly from the true price. (Couple this with increased pressure being onstage and you can see why some bids are so wildly off). Let's suppose your beliefs about the prices of prizes also follow Normal distributions:\n", - "\n", - "$$ \\text{Prize}_i \\sim \\text{Normal}(\\mu_i, \\sigma_i ),\\;\\; i=1,2$$\n", - "\n", - "This is really why Bayesian analysis is great: we can specify what we think a fair price is through the $\\mu_i$ parameter, and express uncertainty of our guess in the $\\sigma_i$ parameter. \n", - "\n", - "We'll assume two prizes per suite for brevity, but this can be extended to any number. \n", - "The true price of the prize suite is then given by $\\text{Prize}_1 + \\text{Prize}_2 + \\epsilon$, \n", - "where $\\epsilon$ is some error term.\n", - "\n", - "We are interested in the updated $\\text{True Price}$ given we have observed both prizes and have belief distributions about them. We can perform this using PyMC. \n", - "\n", - "Lets make some values concrete. Suppose there are two prizes in the observed prize suite: \n", - "\n", - "1. A trip to wonderful Toronto, Canada! \n", - "2. A lovely new snowblower!\n", - "\n", - "We have some guesses about the true prices of these objects, but we are also pretty uncertain about them. I can express this uncertainty through the parameters of the Normals:\n", - "\n", - "\n", - "\\begin{align}\n", - "& \\text{snowblower} \\sim \\text{Normal}(3 000, 500 )\\\\\\\\\n", - "& \\text{Toronto} \\sim \\text{Normal}(12 000, 3000 )\\\\\\\\\n", - "\\end{align}\n", - "\n", - "For example, I believe that the true price of the trip to Toronto is 12 000 dollars, and that there is a 68.2% chance the price falls 1 standard deviation away from this, i.e. my confidence is that there is a 68.2% chance the trip is in [9 000, 15 000].\n", - "\n", - "We can create some PyMC code to perform inference on the true price of the suite." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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E9hXqPFdEnjbGXDS+Ig8//DD33nsvzc3NAFRXV7NixYqxP4aDw2Wa1rSmNa3p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IjsFzaPiPzZ2DraV9RE8tE/iiUZyGUBNDUPiIiTbCLwU2PMM9bmPhFZaL0/2UJ2Xdb2JeO2n7HA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\nbpVS84sj3wFMp7Vr1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Ljl1VOsvbYZp8ue5wiVUoVK5wwopSbU8Zafowd6iUWT+PtDiAj1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\nsSLyJDCjqt8VkSeAQVVtNiD+a8L2BnuBl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VW9B/gc8Eci8jvtGzUsM7P0Yq5gacOswveB\n/cAB4CLwVGcvx2wmIpIlfAv7J6qab99m+Yu5XJRefkKYXgp0MH/plmBgNYOjmR6gqhejzyngbwmr\nkE2IyC4AWcdB7kxXWI+0caHtmBujc3nAgKrOXr9LNxtNVSc1AjxDmL+ApZeeJyIxwkDgf6vq30Wr\nLX8xS2pLL3/VTC+dzF+6JRh4E7hdRG4WkThhY4nnO3xNZoOJSFpE+qL5DPBZ4ChhWvhKtNtXgGZG\n/TzweyISF5H9wO3AIVUdB3Ii8oCICPBv244x3WU90sb/XeJc/xp4eSN+gNk40QNd078izF/A0ktP\ni/7fPgscU9Wn2zZZ/mKucLX00tH8pdOtqtdrIqwWcpKwYcW3O309NnUkDewnbHF/BHi3mQ6AYcLR\nrE8BLxKOeN085k+jNHMC+Bdt6++L/iGOEo523fHfZ9M1p48fEY6GXiOsS/nV9UwbQAJ4DjhNWP/z\n5k7/ZpvWNb08RthA7x3gbcIHu52WXmwCHgKC6N7zVjQ9YvmLTWtIL5/rZP5ig44ZY4wxxhjTo7ql\nmpAxxhhjjDFmjSwYMMYYY4wxpkdZMGCMMcYYY0yPsmDAGGOMMcaYHmXBgDHGGGOMMT3KggFjjDHG\nGGN6lAUDxhhjjDHG9CgLBowxxhhjjOlR/x/UbAH+j555wAAAAABJRU5ErkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%matplotlib inline\n", - "import scipy.stats as stats\n", - "from IPython.core.pylabtools import figsize\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "figsize(12.5, 9)\n", - "\n", - "norm_pdf = stats.norm.pdf\n", - "\n", - "plt.subplot(311)\n", - "x = np.linspace(0, 60000, 200)\n", - "sp1 = plt.fill_between(x, 0, norm_pdf(x, 35000, 7500),\n", - " color=\"#348ABD\", lw=3, alpha=0.6,\n", - " label=\"historical total prices\")\n", - "p1 = plt.Rectangle((0, 0), 1, 1, fc=sp1.get_facecolor()[0])\n", - "plt.legend([p1], [sp1.get_label()])\n", - "\n", - "plt.subplot(312)\n", - "x = np.linspace(0, 10000, 200)\n", - "sp2 = plt.fill_between(x, 0, norm_pdf(x, 3000, 500),\n", - " color=\"#A60628\", lw=3, alpha=0.6,\n", - " label=\"snowblower price guess\")\n", - "\n", - "p2 = plt.Rectangle((0, 0), 1, 1, fc=sp2.get_facecolor()[0])\n", - "plt.legend([p2], [sp2.get_label()])\n", - "\n", - "plt.subplot(313)\n", - "x = np.linspace(0, 25000, 200)\n", - "sp3 = plt.fill_between(x, 0, norm_pdf(x, 12000, 3000),\n", - " color=\"#7A68A6\", lw=3, alpha=0.6,\n", - " label=\"Trip price guess\")\n", - "plt.autoscale(tight=True)\n", - "p3 = plt.Rectangle((0, 0), 1, 1, fc=sp3.get_facecolor()[0])\n", - "plt.legend([p3], [sp3.get_label()]);" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 50000 of 50000 complete in 14.8 sec" - ] - } - ], - "source": [ - "import pymc as pm\n", - "\n", - "data_mu = [3e3, 12e3]\n", - "\n", - "data_std = [5e2, 3e3]\n", - "\n", - "mu_prior = 35e3\n", - "std_prior = 75e2\n", - "\n", - "true_price = pm.Normal(\"true_price\", mu_prior, 1.0 / std_prior ** 2)\n", - "\n", - "\n", - "prize_1 = pm.Normal(\"first_prize\", data_mu[0], 1.0 / data_std[0] ** 2)\n", - "prize_2 = pm.Normal(\"second_prize\", data_mu[1], 1.0 / data_std[1] ** 2)\n", - "price_estimate = prize_1 + prize_2\n", - "\n", - "\n", - "@pm.potential\n", - "def error(true_price=true_price, price_estimate=price_estimate):\n", - " return pm.normal_like(true_price, price_estimate, 1 / (3e3) ** 2)\n", - "\n", - "\n", - "mcmc = pm.MCMC([true_price, prize_1, prize_2, price_estimate, error])\n", - "mcmc.sample(50000, 10000)\n", - "\n", - "price_trace = mcmc.trace(\"true_price\")[:]" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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ppZRSefG06Fj2L+W5kXymueR8xhgjIvm9Tp4uZ8xAQZfO9vZS23XqXKzb1K1b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\nARERERkWd2ft2rXcdtttrFmzBoBUKsXHPvYxmpq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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "\n", - "import scipy.stats as stats\n", - "\n", - "x = np.linspace(5000, 40000)\n", - "plt.plot(x, stats.norm.pdf(x, 35000, 7500), c=\"k\", lw=2,\n", - " label=\"prior dist. of suite price\")\n", - "\n", - "_hist = plt.hist(price_trace, bins=35, normed=True, histtype=\"stepfilled\")\n", - "plt.title(\"Posterior of the true price estimate\")\n", - "plt.vlines(mu_prior, 0, 1.1 * np.max(_hist[0]), label=\"prior's mean\",\n", - " linestyles=\"--\")\n", - "plt.vlines(price_trace.mean(), 0, 1.1 * np.max(_hist[0]),\n", - " label=\"posterior's mean\", linestyles=\"-.\")\n", - "plt.legend(loc=\"upper left\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that because of our two observed prizes and subsequent guesses (including uncertainty about those guesses), we shifted our mean price estimate down about $15 000 dollars from the previous mean price.\n", - "\n", - "A frequentist, seeing the two prizes and having the same beliefs about their prices, would bid $\\mu_1 + \\mu_2 = 35000$, regardless of any uncertainty. Meanwhile, the *naive Bayesian* would simply pick the mean of the posterior distribution. But we have more information about our eventual outcomes; we should incorporate this into our bid. We will use the loss function above to find the *best* bid (*best* according to our loss).\n", - "\n", - "What might a contestant's loss function look like? I would think it would look something like:\n", - "\n", - " def showcase_loss(guess, true_price, risk=80000):\n", - " if true_price < guess:\n", - " return risk\n", - " elif abs(true_price - guess) <= 250:\n", - " return -2*np.abs(true_price)\n", - " else:\n", - " return np.abs(true_price - guess - 250)\n", - "\n", - "where `risk` is a parameter that defines of how bad it is if your guess is over the true price. A lower `risk` means that you are more comfortable with the idea of going over. If we do bid under and the difference is less than $250, we receive both prizes (modeled here as receiving twice the original prize). Otherwise, when we bid under the `true_price` we want to be as close as possible, hence the `else` loss is a increasing function of the distance between the guess and true price." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For every possible bid, we calculate the *expected loss* associated with that bid. We vary the `risk` parameter to see how it affects our loss:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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iSZMmLF++nFOnTnHDDTfw8ccfc/XVV5eLc/311zNw4EA+/fRTbrzxRqZPn07n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\nVespW5ZH+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Mg85XUUv7cev8NDVIdksqYNxnCKZOEf4685StXzV+Er3oUhKYeUO+ZhzurV\npDrVOqp5YsF97CnaQrQlll9NebRZZ6H2ef2sWraXjV/noxTExFm46LJe9B6UfVbccbcfKqRg7vsU\nvv0JfrsDgJhO7eh4y0zazZ6IKS60YX2FEG2L5EQESU6EEEI0jLu0luL316M7vUR3TCVz6jkYzMYG\nf99XujcwC3V1IabMHqTcMQ9jcvsm1am4qoBH591NSc0RUuMz+e2Mp8hN796kMn+KrdrBh29tprSo\nFk2Dc87ryIhLu2GNaviTmLZIKUXV6g0cfuE9ypevhuA1RMrIIXS6bRbpY89HMza8LQghmp/kRAgh\nhIg4V7GNkvfXo7t9RHdJI3PKIAymhl80eg6vp+rF2Sh7FeZOw0i59R0MsU0bLWl34SYen38f9S4b\nnTJ68sD0p0iJT29SmT/l4J5yFr+3FZfTS0JyNJN/Nois9onNdrzWwO9yUzx/OYdffJf6XQcAMFgt\nZE8bR6dbZxLfp1uEayiEaGkSRARJToRoKOmHKkJxJrUXV2E1xR9sQHn8xHTPIHPSQDRjw5OVXbtW\nUPPKjSiPA2ufcSTf+DKaJaZJdVq9cwnPfvpnfH4v53QZyT2THyGqiWX+GF1XfPPZfr75/AAo6NIz\nnYkzBxAVHZ6nD62xrbhKKzjy6gKOvL4AT2Ug58OakUqHG6fR4bopWNNTIlzDs1drbC/i7CJBhBBC\niNNyFlRSMn8TyusntlcWGRP7hxRAONa/h+2tX4DuI3rYz0ic/S80Y+MvvpVSLFzzCu+uegaAcefM\n5Iax92E0NM8/aw67h8XvbeHwvko0DUaM687wC7ugGc7M3Afblt2BIVoXrTg+RGvCgJ50vHUm2ZPH\nYrA2fAQuIcSZSXIigiQnQgghTs1xqILShZtQPp24vjmkT+jX4ItnpRT2lU9R9/F/AxA79h7ir/hj\nkxKPfX4vc5c9wufbFqGhce3Fv2bi0KubLZm5+EgNH761mTqbi+gYM1fMHkjHbmnNcqxI0r0+Sj/5\ngvy571Pz7bbARoOBzMsupNNts0g6d8BZkTAuxJlGciKEEEK0OPuBMkoXbQa/In5Ae9LG9WnwhaTu\ntmN7+5e4Ni8EIP7Kh4m76K4m1cfhruPJhb9lW/5aLCYrv7jiYc7tMaZJZf4YpRRb1h3h84934fcr\nsjskMulng0hIim6W40WKp6KaI28uouDV+bhLKgAwJcbT/mdXkDtnhswqLYQ4JQkigiQnQjSU9EMV\noWjL7aV+TwllH28FXZEwOJfUMb0aHED4Kg5TPfdafMU70axxJF37HFH9JzapPqU1hfxj/r0UVhwg\nMSaF+6c/Sbfsfk0q88d4PX6WL9rBzk1HATjnvFwumtgLo6n5Jqxr6bZSu20P+S+9T/HCFehuDwCx\n3TvR8ZaryJkxAVPsmRUsnWna8rlFnBkkiBBCCPEdSils3x6m6su9ACQO60TK6B4NDiDcuz+j+vVb\nUI4ajOndSL75DcxZPZtUp7wdi5m7/O84PXbapXbmt9OfIiOpeSYxq66ws+itTVSU1GMyGxk/tS+9\nB+U0y7Famu7zUfbpV+S/9D7Va7cENmoa6eNG0vGWq0gdNVS6LAkhGkRyIoIkJ0IIIUD5dSpW7KRu\naxEAyaO6kzS8c4MuLJVS2D/730D+g9Kx9h1P0rXPY4hOaHR9HO56Xl7+KHk7FwNwbo8x3DbhD8RF\nNb7Mn7JvRymfztuGx+0jOS2GKdecQ1pmaDNPt0aeyhoK3/qQglfm4zpaBpw0q/RN04np1LR5OoQQ\nrZfkRAghhGhWfqeH0g+34CqoQjMZSJ/Yn7ieWQ36ru62Y3vnblybFgAQN/5+4sb/Fs3Q+O4/e4u2\n8u+Pf0+ZrQirOYrrx9zHmAFTm+VOue7XWbV8H99+dQiAHv0yGT+tP9aotv3PZO2OfRTMncfR+UvR\nXcEuS91y6XjzVeTMvAxTbPMMhyuEOPO17bNjGElOhGgo6YcqQtFW2ounyk7p/I14qx0YYy1kTh1M\nVHbDJlDzVRym+uXr8B3dEch/uOZZogZc3ui66LqfBWte5oPVL6IrP50yenL3pL+Rk9qp0WX+FHud\nm4/e2UzhoWo0g8boCT0ZMqJji3frCVdb0X0+ypbmBbosfbPp+Pb0seeTe8tVpI0+t0nBnWgd2sq5\nRZy5JIgQQoiznLOgktJFm9FdPiwZ8WRNPQdTQsOSat17Pqf6tZvDlv9Qbivm35/8nj2FmwG4Yth1\nzBp1F2ZT88xLUHi4mo/e3oy9zk1svJVJswfSvnPbnEDNa6uj8M0PyX95Hq6iUgCMcTG0n305uXNm\nENulQ4RrKIQ4k0hORJDkRAghzka1WwupWL4TdEVMt3QyLh+AwXL6+0vNkf/w9a5lvLTsrzjc9STH\npnHn5X9hQKfzGl3eT1FKsWF1Pl8u2YPSFe07JzNp9iBi463Ncrzm5DhcyOEX36Po7U/wO5wAxHTp\nQMc5M2g3ayKm+NgI11AIEUmSEyGEECJslK6o+movtm8PA8ERmC7s0aBJ5H6Q/zDuN8RNeLDRXWSc\nbjuvrvwHX27/CIAh3UZz+4Q/kBCT3KjyTsfl9LJswXb2bg/crR82qjOjxnXHEMIM3JGmlKJ67RYO\nP/8OZUtWQfCGYOqooXS8bRbpY8+XLktCiGYlQUSQ5ESIhpJ+qCIUrbG96B4fZZ9sw7G/DAwaaZf2\nIWFAw0bn8VXmB+Z/CFP+w/7i7fzvR7+jtKYQs8nK9RffyyWDpjdbPsLe7SWs+HAnjnoPFquRCdP7\n06Nfw5LHm1tD2oru9VHy4UoOP/8utVt3A6BZzORMG0en22YR36dbS1RVtAKt8dwizi4SRAghxFnE\nV+eiZP5GPGV1GKwmMqcMIrpjaoO+G8h/uAXlqMaY3jWY/9CrUfXQdT8frnuN9/Oew6/7yU3vzt2T\n/kb7tC6NKu906mtdrPxoF/t2BJ4+tOuYzITp/UhOaxtdfTzVtRS+uZD8lz/AXVwOgDklidwbp5F7\n41SsGQ37OxRCiHCRnIggyYkQQpzp3CU2SuZvwm93Y0qKIWv6YCwpp7+IVkph//x/qfsomP/QZ1wg\n/yGmYaM3fV9FbQnPfPJHdh3ZAMBlQ67mZ6N/gcUU/nwEpRTbNxTxxeLduF0+zBYjoyf0ZOC5HRrU\ndSvS7AcKyH/xPYreXYzf6QIgrkdnOt4+i5xp4zFGt70cDiFE0yilUBzvxcixK3ldKfy6Qlfg1wPv\n/UpRsGe75EQIIYRonPo9JZQv3oby6UR1SCZzyiCM0acf8SiQ/3APrk3zAYgbdx9xEx5qdH/7tXtW\n8sLSh7G7akmMTeXOy/7MoC4XNKqs06mpcrB84Q7y91cC0LlnOpdO6UNCUsNGnooUpRRVqzdy+IV3\nKV+++kS+w0Xn0un22aRdNFxmlRaiEZRS+BV4fDoev45XV3j9KvD+lEuF168fX3r9Co+u8PpOfNen\n6/h0FXj51fH33u+tB/YDn64Hv3fipevqeCCggv9RnAgWAnU/ESyE6u/NdI9cgoggyYkQDSX9UEUo\nIt1elFLUrD1E9ap9AMT3b0fapX3QGpBE/P38h8SrnyF64KRG1cPlcfL6Z4/z2daFAJzTZQR3XPZn\nEmPDP5yqris2fp1P3vJ9+Lx+omPMjLmiN70GZrfqi++vPv+CruVODr/wDnXbA39fBquFnBnj6Xjr\nLOJ7NU9XL9E2Rfrc0hy8fh27x4/do2P3+oPv/Tg8fpxeHbdfDwYACrdfx+sLLD1+HY8vcPHvDl7s\nu4P7HQsY3MFAQD+DOuBowLFTWuC9htGgYdQILjUC93u8zXJ8CSKEEOIMpXw65ct2UL/jKAApo3uQ\nOKzTaS+klVI4N7xP7bz7Ua66Juc/HCjewb8//gPF1fmYjRauuegexg+e1SwX9OUldSydv52SQhsA\nvQdmc/HlvYmJa555JsLBVVxO4dsfs+X5V3DYfABY0pLJvWk6Ha6/Emt625y3QpxdlFI4vTr1Hj91\nbh/1bj91nhOBwHdfgWDB4f3udo+/+a/wDRpYjAYsRg2z0YDZqGE5vtQwGwxYTMGlUcMc3O9U+5sN\nGiaDhslowGQAk8EQ2GYMbjcE9jEaAuUEthmC3znxmUELBADHzoha8D/HAoPj20/aFoqNGzeG7c/v\nZJITESQ5EUKIM4nf4aF00WZchdVoZiMZl/cntnvmab+n26uxvX8vrs2LALD2m0jS1c80Kv/B5XHw\n7qpnWbLxHZTSaZ/Wlbsn/ZXc9O4hl3U6Pp/O2i8OsPbLg+h+RVyClUuv7EvXXhlhP1Y4KL+f8s/W\nUPjmIspXfIPy+wGI69WFTrfPJnvqpRijJN9BtDyPT6fG5aPO7aPO7T8eDNSfFBjUu33BYCHweX1w\nW1NjAIMGsRbjiZf52HsD0WYjVlPgYt5qMmA2GrAaNSzBbYHAwIDVpAU/CwQDxwKGwHcNGNtALlS4\nyTwRQgghGsRTWU/J/I34apwY46xkTRuMNfP0k8C5d62k5u1foteWoFliSZj2N6KHX9uoJwYbD6zi\n5eV/p6K2BE0zcPmwa5k18k4s5qjG/KSfVHykhiUfbKeyrB6AgcM7cOH4nlijWt8/cc6iUore/pjC\ntz8+Pqu0ZjKSNWkMHa6/kpSRQ1p1lyvR9nj9OjaXjxqnj5rg0uYKvLc5fdS4vMc/t7l8OLx6o49l\nNRmItxiJswZe8RYTsdZjwYDhuwHC9wKFGIuBKJNB2n8b0vrOsBEiORGioc7Efqii+bRke1FKUb/j\nKBUrd6M8PiyZCWRNPQdT/E9fuCuPg9qP/oJj1YsAmDufS9I1z2JK6xxyHWrqK3h15eOs2bMcgC6Z\nvbl1/O/onNU79B90Gh6Pj9XL97Hh63xQkJwaw7hp/ejQuXV1/9F9Pio+W8ORNxZRvvIb0AMXaTGd\n2tH+2im0mzURa3pKoK3IBZRooLy8PIYMP5/iWg9Ha90crXVTXOemynksOAgEBXaPP6RyjRokRptI\nsJqOBwInggIjcVYTcRYj8VYj8cf3MRJrNWJpQxM2iqaTIEIIIc4Afrub8mU7AxPIAbE9M0mf0A+D\n5adP856CTdS8eQf+sn1gMBF/2UPEjr0bzWAM6fi60vlsy0Le+vIpHO56rOYoZo68iwlDZmE0hP+f\nmvz9FSxdsIPaaieaQWPYqE6cP7YbZnNo9W5OzsISCt/6mMK3Pzo+t4NmNpE56WI6XDeFlAsGy6zS\n4rTsHv/xIOHYq6jWzfb1B2H36YdoNmiQFGUiMcpEUvSxpfk768lRJhKjTSRFmYi1GOVpgGgQyYkI\nkpwIIURbZd9XRsWyHfgdHjSLibSxvYjrm/OTFwLK76N+5b+oX/IY6D5MmT1IuvZ5zB0Ghnz8ospD\nvLD0YfYUbgZgUJcR3HzpQ6QnZjf6N/0Yl9PLF4t3s31DEQAZ2fGMn9aPzHaNm7Mi3HSfj/IVX1P4\nxiLKP1tzfHjWmC4d6HDtFNrNvAxLWnKEaylaE6UUde4fBgpHaz0U1bqxuXw/+l2zQSMr3kJOgpWc\nRCs58VZSYswngoWowJMCgwQFZzXJiRBCCPEduttHxWe7qd8euKCOyk0h47J+mBJ+eh4EX/lBat68\nA2/+egBiLrydhCv+iGYJbf4Er8/DwjWvsHDNy/h1H4kxKdww9n7O73Vp2O9k6n6dHZuOkrd8H/Y6\nN0aTgQvGdGXoqM4YW0EXCkdBMUVvf0Th2x/jLqkAQLOYyZw4mg7XTiFlxGC5u3sWcvt0Kh3ewMvu\npcLhpcrhpcLuodLho9LhodLuxf0TGckWoxYIEk56tQsu02LNZ2WisGgdJIgIkpwI0VCSEyFC0Vzt\nxVlQRfmn2/DVutBMBlIu7EHC4NyffvqgFM5vXqN24e9RHgeGxGySrn4Ga8+LQj7+riMbeXHpwxyt\nygdgzICpXH3R3cRFnT6BOxRKV+zdUcrq5fuoqrAD0K5jMuOn9SUlPS6sxwq5bkpRvnw1Ba/Mp+KL\ntSeeOnTNpcO1k2l3VWhPHeTc0rbUu30U1bqpdHipsJ8IFI4HDQ4vde6G5SPEmA1k/yBQCDxhSIkx\nn/JJQl5eHpnSXkQESRAhhBBtiO7zU/3VPmwbAhfv1qwE0if2x5L60xfU/tpSbO/cg3vnMgCiBk8n\nccY/MMQkhXT8elctb33x1PFJ43JSOnLr+N/Tu0N4b8IopTi8r4K8ZfsoPVoLQGJKNCMu6U7vAdlo\nEb77WvHVt+z723PYNu8CAk8dsq64mA7XTiH5/EHy1OEM4vHpFNS4OFzt4lCVM7CsdlJhP/0EXiaD\nRmqMOfCKDSzTYsykBNfTgp/FWFpPLo8QDSU5EUGSEyGEaO3cJTbKFm/DW2kHTSP5/C4kndfltLNP\nu7Z+gu3dX6HbK9GiE0mc8TjRQ6aHdGylFN/sXs5rnz2OzV6J0WDiyvPmcOV5N2E2hXcit6L8alYt\n3Uvh4WoAYuOtnD+mK/2Hto9416WaDdvZ+8jzVOVtAMCakUqnO39Gu1mXY0lpHXkZonH8uqKkzs2h\nKheHq50cCgYNR2vdp5zl2GrUaJcYRXrsdwOCY8FCaoyZhCiT5COIiJOcCCGEOEspXadmzSGqvzkA\nusKcEkvG5f2xZv30RavuqqV2/n/hXPcWAJYeo0m6+t8Yk9qFdPxyWzEvL3+ETQdXA9Cz/SBuG/97\n2qWGPgTsTykrriVv+T4O7g6MZBQVbebc0V0457xczBG+U1u36wD7Hn2BsiWrADAlxtPlF9eQO+cq\nTLGh5ZKIyFJKUeXwcajayeGTniwUVLtOmZtg0KBDopVOKdF0To6iU3I0nVOiyIq3Sj6COKtJEBEk\nORGioaTfsghFU9uLp8pO+eJtuIttACQM6UjKqO4YTjOUqefAN9T83534qwrAHEXCFX8iZtStIQ0p\n6td9LNnwLu/l/Qe310WMNY6rR9/DmIFXYtDC90SgutLO6uX72b2tGBSYLUaGjOjEsFGdsEaZw3ac\nxnDkF7H/Hy9x9INloBTG6Cg63jaTznddgzkxPqzHknNL+Pl1RaHNxf5KJweCr4NVzh8d8Sgt1kzn\n5Gg6JUfROSWwzE2KwmKKfPL+90l7EZEmQYQQQrRCSilqNxVQ9eVelE/HGB9FxmX9iO6Y+pPf0931\n1C/9B/bP/w1KYWo/gKRrn8Oc1Suk4289vIb/++Ip8sv2AnBez0u4YexvSI5Lb/Rv+r46m4tvPtvP\ntg1FKF1hNGoMHJ7L8Iu6EBtnDdtxGsNVWsHBJ1/lyJuLUD4/mtlEh+uuCfzIewAAIABJREFUpOuv\nbsCa8dN/ByIynF4/h6pcHKh0cKAqEDAcqnLiOcXThTiLkU4pwacKwYChY3IU8Va5LBKioSQnIkhy\nIoQQrYWv1kn5kh048ysBiOubQ9rYXhisP35XXul+nOvepm7xX9FrS0EzEHfJr4kbfz9aCDkLh0v3\n8NaXT7P18BoAUuMzmXPpgwzpdmHTftRJHHYP6748yOY1Bfh8OpoGfQe344Kx3UhIimzXIE91LYee\neZP8ue+jO91gMJAzYwLd7ptDTMeciNZNnFDt8B4PFPZXOjhQ6aTI5uZUVzSZcRa6pkbTNTWabqkx\ndE2NJj3WLMnv4qwhORFCCHGGU0pRv6uYyhW70N0+DNFm0sf1JbZH5k9+z733K2oX/h7f0e0AmHMH\nkzDt71g6DW3wsStqi3lv1bOs2rEYhSLaEsuV58/hssGzsZijmvS7jvG4fazPO8z6vEN4gkNf9uiX\nxYhLupGaEdnhWn12B/kvvseh/7yFr7YegMyJo+n+29uI6xne3A8RGqfXz85SO9tK6tlX4eRAlYMq\nxw+7Ixk16JgcRZfUGLqlRtM1JZouqdHydEGIZiL/ZwVJToRoKOmHKkLR0Pbis7upXLEL+95SAGK6\npZM2ri+m2B/v1uMr20/th3/Cvf1TAAxJ7UiY9Geizpna4NyHelcti9a8wpIN7+D1ezAaTIw7ZyZT\nz59DQkx4Zlb2ef1sXnuEtV8cwOkIDIvZqXsaI8d1JyvCM03rbg9H3ljEgX+9iqciMBpU6oXD6PHQ\n7SSe06dF6yLnloA6t4/tJYGg4f/bu+8oO677wPPfX1W93DkjNHIiEkECDCIkZlKiLEuUjrLXsi05\nyl7J4zmywnjXXu9YGmvGe1Yer2d215wdSWMFS6KCbYqkSAUSIgkwIefcjUbn8HKquvtHVT+8RjfA\nbhBAA43f55w6Ve9WvffqPVxU1+/d+7vXDxyyk0ZHiocsljXFWB60LCxv9rsjha+BiQevFq0varZp\nEKGUUrPIGENqzxmGf34Ir1BGwjYt999Ezfr5F+xu4WVGSD31ZbLbHgOvjERqqHnwj0nc8wfTnnW6\nVC7y9Ov/xOMvPkYm78/DcNeat/Ohuz9Je8PCy/LZ8rkSu7af5tUXTpFNFwGYv6iBtz28is5lTZfl\nPS6VcV3OfOdJjv6nx8h39wJQf8taVv2736f5rdNvwVFv3ki2xJ6+NHvO+oHDieHchG5JlsDq1jgb\nOmpY0xZnRXOcjtqwDp2q1CzTnIiA5kQopa624lCawaf3k+/2fwGPLW2h5aG1hOqnDgRMuUh222Ok\nnv6PmOwoiBC743+i9p1fwK67eJencZ7xeOHAU3z7+b9nYKwHgLWdm/m1e/+Y5fMuzy/vqbE8r75w\nkt07uirdltrm17H1wRUsW906q33R3Wyensef4uT//S0yR/wJ+2pWL2Xl53+Ptre/TfvJXwX96WKl\nlWHP2TRdY4UJ+0OWVIKGDfNqWNuW0MnYlHoT5mROhIh0Al8D2gAD/D/GmL8VkSbg28Bi4CTwQWPM\naPCczwMfB1zgU8aYp4PyzcB/B6LAE8aYTwflkeA9bgWGgA8ZY05drc+olFLn88ouoy+dYHT7cfAM\ndjxM8wNrSKzumPIm1hhDYd+TJH/4v+IOHAMgvPJu6h7994QWrJ/2++49tYN//PlXONF3EICFLcv5\ntXs+xaZlWy/LzfNQf5qXnz/B/p09eMGIOIuWN3P73UtZvKJ5Vm/Qc11nOf3fH6f7H39EaTQFQGzR\nfFZ85hPMf9/DiK03qVeCMYae5LmgYffZNH1Bq9S4iGOxti3Bhnk1bOxIsLo1QeQaHFJVKTXRbHdn\nKgH/xhizU0RqgFdF5CfAbwE/McZ8WUQ+C3wO+JyIrAU+BKwFFgDPiMhK4zen/BfgE8aYHSLyhIi8\nwxjzJPAJYMgYs1JEPgT8NfDh809EcyLUdGk/VDUT59eX3OlhBp/eR2kkC0DtxoU03bMK+wLzIZS6\n95D84Z9RPOJPcma3raTuPX9JZO3D074pPz1whG/84j+zM5gsrrGmlQ++9Q+4Z/27sKw3f/Pcc3qE\nHb84wdED/QCI+AnTt9+9lI6Fs5fzYIxh5MWdnHrsO/T9+DnwPMDvtrT4tz9Ax6/ejxWe3Xkoqs2F\na4vrGY4N5djbl2Zvb4Z9fWlGchOToBNhm/XtiUpLw4rmGKEbKJfhcpkL9UVd32Y1iDDG9AK9wXZa\nRA7gBwfvBu4JDvsq8HP8QOI9wDeNMSXgpIgcBe4QkVNArTFmR/CcrwGPAk8Gr/XnQfn3gL+70p9L\nKaXO5+aKDP38MOm9ZwAINSdofXgd0YVTJy+7Y72knvgrf7ZpY5B4I7Xv+Czxrb+F2NO78R1K9fGd\nbf+VX+z558qIS+++4zd555aPEAm9uaFUjWc4fniAl587QfdJvzuW7Visv3UBW962hMbmxJt6/TfD\nzRU4+/2nOfUP3yG1/ygAEnLoeO+DLP7EB2i4dd2sndtckyu5HOjPVAKGA/1Z8mVvwjH1UYcNHX7Q\nsHFeDUsaYzrTs1JzwGy3RFSIyBLgFmA70G6M6Qt29QHjnX3nAy9VPa0bP+goBdvjzgTlBOsuAGNM\nWUTGRKTJGDNc/f6bNm26bJ9FzW36y4+aia1bt5La18PQzw/hZYtgC413Lqfh9qXIFF02TDFL+mf/\nF5ln/xZTzIDlkLj7d6h5+2ew4g3Tes9sIcUPt3+VJ175BqVyAduyeWjT+3nfXb/zpkdccl2Pg7vO\nsuO5Ewz1+0OhRqIOm+5cxK1vWUyidvYmicud6fO7LP2PH1Ia8ZPFwy2NdP7Ge+n82KNE21tm7dym\n43q4tgxlS+zrS7OvN8PevjTHhnKTRk5aUBdhfUeCde01rO9IsKAuorkmV8D1UF/U3HZNBBFBV6bv\nAZ82xqSqLzbGGCMimv2tlLrulEayDP5kf2XSuGhnIy0PryPcNPlXeuN55F77Lql/+Uu8UT/hObLh\nV6h791/gtC6f1vsNJnt56rV/4qe7HidT8Pv937n6QT589x/R0dj5pj5LsVBmzyvdvLLtJKmxPAA1\ndRG2vHUJG2/rJDxLY/EbYxjZvotT//Ad+n/8HMb1E7nrbl7Dkt/5oN9lKTL9yfbUOcYYusYK7OtN\ns7fPb2noSU7MZxgfOWlde4L17TWsa0/QGL92uogppa6cWQ8iRCSEH0B83Rjzg6C4T0Q6jDG9IjIP\n6A/KzwDVfwkX4rdAnAm2zy8ff84ioEdEHKD+/FYIgK985SskEgkWLVoEQH19PRs2bKhE+tu2bQPQ\nx/q4sn2tnI8+vvYeP//cc2QO9bI63cjLx/ZihW3qNi3ioQ/5eQzVxxtj+NnX/hPZHf/I5tBpAF51\nl5HY+gnu+/AfTOv9vvWDr7H90LP0WQfwjMvwqRyLW1fxp7/7v7Ny/ga2bdvGUU5d0ufJpAt87R++\nz9H9/cxrWQXAcOY4N908j49+7GFsx5qV79srlljWl+HUY99h++6dAKwL19Hx6IP03r4Sd+US5r/t\nbVftfC7H4/Gy2Xr/W25/C4cHsvzw6Z9xejRPqvUmxvJlksf877du+SZiIYv6wYMsbYzy6DvuZ01r\nnFe3vwjlAd669Nr6Puf64/Gya+V89PG183jPnj2MjY0BcPr0abZs2cIDDzzA5TarQ7yK3+TwVfzE\n539TVf7loOyvReRzQIMxZjyx+hvA7QSJ1cCKoLViO/ApYAfwr8DfGmOeFJFPAhuMMX8gIh8GHjXG\nTEqs/pu/+Rvz8Y9//Ap/YjUXbNumyWzqwvI9oww+tY/ioN/VZ5/08s5PfgQ7PvHXcGMMhQPPkP7x\nlyh1+TdpVsMCah/5HLHbPoy8QcKz65XZcfinPPHKNznSs9t/vtjcufpBHtnyEVbO3/CmPkffmTF2\n7ehi/+s9lIM+7vMXNXD7PctYvroVmaU+7fmefk5/9XG6vv4jSsOjAISbG+j82KN0fuy9ROe1zsp5\nXQ5X89rieobTo3kO9mc40J/lwECG0yN5zr8jaIo7lRaG9R01LGvSfIZrhf4tUtN1pYZ4ne0g4q3A\nc8BuqFy7Po8fCPwTfgvCSSYO8foF/CFey/jdn54KyseHeI3hD/H6qaA8AnwdP99iCPiwMebk+eei\n80Qopd4Mr1Bi+LkjJHd2AeDUx2h5eC3xJZP74ReOPE/qib+idMIfC8Kqa6fmoT8h/paPIc7Fcwoy\n+RQ/3f19nnrt2wwm/UnSEpFa7r/5fbz91g/SUtdxyZ+hkC9zcFcPu1/upq8nWSlfvqaV2+9ZxoLF\nl2cG65kqjiTp//Fz9P7zsww998q5LksbV7P4tz9Ix7vvx47OXi7G9WAkV+Jgf5aD/RkODmQ4NJAl\nW5qYAO1YwvLmGDe1JbipLc6a1gQdtWHNZ1DqOjcn54kwxmwDLjSu24MXeM4XgS9OUf4qMOmnN2NM\nAfjgmzhNpZS6IGMM2SP9DD57ADddAEtouG0JDW9ZjhWa2JpQPLGd1BNfrAzXaiWaSTz4aRJbP46E\n4xd9n7PDp3nytW/x8z0/olDKATCvcTGPbPkwd6/7VaLTnKl6qvPv7R5j98vdHNx9llLRv0GPxkKs\nu3U+G2/rpLmt5pJe+80ojSbp+/Fz9P7opww9/zKm7J+XODYd73mAxb/9QRq2rNcb3CmUXI9jQzkO\nDmQ50J/hYH+Gs6nipOPaa8KsaYsHQUOC5U0xwjo/g1JqmmY1iLiW6DwRarq0CVkBGNcjfaiX5Kun\nKPT6v9pH5tXT+vZ1hFtrK8dt27aNOxbXkHriixQOPAOAxOpJ3PdHJO7+Xaxo7ZSvD/4N/v7Tr/DE\nK9/gtWPPY4IG2/WLb+edWz7KpmVbseTSbvoK+RL7d55l98tdDJxNVcoXLm3k5ts6WbmuHSd0dSdg\nK42l6H/yeXp/9CyDz72MKZUBENum+Z7b6Hj3A7S/427CzdMbpep6c6nXlmS+zP7+TCUB+vBglpI7\nsZdBxLFY3RL3WxjaEqxpS9CsCdDXNf1bpGabBhFKKTUDbq5Iclc3yddP+y0PgBUL0bh1BXWbOif8\nMl7q2U/yiS8ymPVHppZIDYl7fp/EvX+IFb/wJGzFcoEXDjzFj1/9Jqf6DwMQssNsXfsI79zyERa1\nrrykczfGcLZrlF07ujm05yzloDtLLB5i3eYFbNyykKbWq9vqUEqm6X/qeXp/9FMGf769EjhgWTTf\nfRsdv3of7Y/cQ7hldrpSXWuMMfSmiuztS7OvL8O+3gynRvOTjuusj3BTECzc1BbXuRmUUpfdrOZE\nXEs0J0IpdTHFoTRjr5wivb8HEyQah5oT1G9eTM3a+RO6LpX7jpB68q/J7/w+GAOhGIm3/TY1938K\nq6b5gu8xmhnimZ3f4yevf4exrD+IXH2imYc3vZ8HN72f+kTTJZ17Pldi/+tn2P1yN4N96Ur5omVN\nbLy9kxVr23GuYjeWcipD/1PPc3Y8cCiW/B2WRdNdt/gtDo/cTaT10j7vXOJ6hmPDOfb1+kHD3r40\nw9nyhGNCtgTDrNawvt3vmlQX1d8IlVK+OZkToZRS1zJjDLmTQ4y9cpLcyaFKeWxpC/WbFxNb0jyh\n5aE8dIr0U18m9/K3wXhgh4nf9ZvUPPjH2PVTJzwbY9jf9SrP7nqcHYd/Stn1b6gXt63inVs+yl1r\n3k7Imfk8B8YYzpwcYfcr3Rze01sZYSmeCLN+8wI23Lbwqs4qXU5n6H/6l35XpZ9txysEffRFaLrr\nVjrefT/tv3LvDR84TJwBOsOB/sykGaDrIjbr2mtY15FgXXuClS1xwrbmMiilri4NIgKaE6GmS/uh\nzn1eySW9v4exV09RGsoAII5FzboF1G9eRLh5Ypcfd/QM6af/D7IvfR28MlgO8Tt/nZqH/y0v7jvJ\nW6cIIJLZEZ7b+y88u+v7nB055b8HwuYV9/DOLR9lbefmS0oaHh3OcnhvH3tf7WZ4IFMpX7yimY23\ndbLipjbsq9TqkDvTx8AzLzDwzAsMPffyhMCh8c5NdLz7ATredS+Rtgu3zsxlJdfj1EieI0M5jg5m\n+cXzz5NuvWnSDNDz68KVVoZ1HTV01usM0Er/FqnZp0GEUkoFyqk8yZ1dJHd14eX8FgG7JkL9rYuo\n3bgQO3auRcCUixQOPEPu1e+S3/tjKBdALGK3fZiat38Gp2VpcOTJc88xhgNdr/HMru9NaHVorGnl\nvg3v4b6Nj9JaP29G52yMYaA3xZF9fRzd389A77kk6URtxG912LKQhqaLj/50ORjXZfT1/Qz85JcM\nPPMiqX1Hzu0UofHOm+l41/20v+teoh3X73wOlyJXcjk+nOPYUI4jg1mODeU4OZKnXBUxJMcKNLT6\nM0CvrZoBukkToJVS1yDNiQhoToRSN65C75if73Col/GfgSMdddRvWUJiVTsSdBUxnkfx+IvkX/0u\nuV0/xGRHK68R3fQoNe/4LKGO1ZNeP5kd4fl9/8qzux6nZ/hcq8PNy+7iwZvfxy3L34ptTf83Hc8z\n9Jwa4ch+P3AYG8lV9oUjNstWt7J6wzyWrWnFvsLdXErJNIM/2+63ODz7YmUCOAA7HqP5nttoe2gr\nLQ+8hWj75Dkz5qJUoczRoRzHBrMcGfIDh67RyRO5CbCgPsKK5hgrmuOsbI2zpjVO7CqPiqWUmts0\nJ+IqOPTCNhZt3ESs5uqPia6UurqM55E50k/y1VPkzwQ3vgKJ1e3Ub15MZH5DpctIqWcfuVe+Q+61\n7+GNnqm8hjN/HbHNHyB26/uwGxdOfP2g1eHZXY+z/fCz51odEi3cu/E93L/xvTNqdSiXPU4fG+LI\nvj6OHegnmzk37n88EWbF2jZWrG1n0fLmK5okbYwhc+y0HzT85JeMbN9VmcMBILZoPq0P3UXbQ1tp\nesstWJGZ53NcT0ZzJQ4PZjk6mOPoUJYjgzn60pPnZLAFFjfG/IChJc6K5hjLmmLEwxowKKWuTxpE\nBHbu3Mm9Qws4u+15jJfC81KUvTQlk6HgFSiaEkVbcEMRnIZGahcsYvGmzbR0LnzjF1dzivZDvX65\n2SLZE4Nkjw+QOzGIV/BHubEiDrUbF1J3yyJC9f6kbeXhLr/F4bXvUj57oPIaduNCore+n9iW9xOa\nt3bSe6Ryo0Gug9/qMHwqR/PiOJuWbeWBm9/LrcvfNu1Wh0K+zIlDAxzZ38fxQwOVieAA6ptirFzb\nzsp17czrbMC6gsN3esUSwy/trAQO2RPdlX1i2zTeuYm2h7bS+tBWEisXz+n++iXX40B/hpe7U7za\nneToUG7SMRFbWNp0LlhY0RJnSUP0DSdy02uLmgmtL2q2aRBRxbgpxK5F7Hpsux4biACT2iVSwEFI\nHtxH0nsFz0viemlKXoaiyVE0RQp4lB0b4jXE2ubTtnoNizZsJByJXPXPpdSNyhhDcSBF9vgg2WMD\nFHpGJ+wPNSeo29RJ7foFWGEHLz1EZts3yb36HUontleOk3gjsU2PEtvyAUJLbkcsa9L7HOx+nWd2\nfm9Sq8O6dRv4vV/7E9rq50/rnDOpAscO9nNkXx+njw3hVk0a1javlhVr21m5tp2WjpordrNujCF7\nopvhF19n8KcvMfiLHbjpbGV/qLGOlvvv9Lsp3XsHoYa6K3Ie14qzyQKvdCd55UyKnT0pcqVzoyWF\nbWFNa4IVLX6XpBUtMTrrozong1JqztOciMB4TsTo4ACndu5k9OQxiiODWPkcYc8jjENEIoSsOCEr\ngW3VIlYdyAwS3kwZ46VwK60cWb+VgzJFS/CiUUL1zdQvWcaSTbfS0NZ25T6wUnOUV3LJnRoie3yA\n7PFB3FTVRFyWEOtsIr68lfiyFkKNCbxChsLeJ8m99l0KB571R1cCCMWIrn+E2JYPEFl9H3LeMKvF\ncoFD3TvZc2o7rxz5BT3DJwE/12Hj0rfw4Kb3ccuyt+LYF79GGGPoP5vixOEBThwa4MzpUSqd5wUW\nLm5kxdp2Vqxtu2LJ0cYYsse7GH7hNYZfeJ3hF1+n0Ds44Ziam5bT+qDfTalh8zrEnrvdcHIll11n\n07zaneSV7hRnkoUJ+xc3RtmyoJbNC+vY0FFD5CrOsaGUUjOlORFXSUNLKw0PPgQ89IbHFotFuvfv\n5+yBveT6z0ImiVMqEzYWEQkRtmKErASOVYNl1YGVQOxGHLsRB4gCtee/6BiwC4Z3vc6wlznXrcrL\nUPRyFClRFI+y42Alaom1z6N9zToWrF1HODy3+x4rdSGlsZwfNBwbIN81XJkMDsBOhIkvayW+rJXY\nkmassIM70k3x+JNkDvyE/O5/xRSDoVAtm8iaB4hu+QDRDe/Eipxrh/SMx+n+I+w5uZ3dp17iYPdO\nSuVzN5cNiWbu2/go92189A1bHfK5EqeODvmBw+FBMqlzr2PbwuIVLaxc186yNa0kai5/66UxhszR\nU5WAYeSF1yn0D004JtTUQNNdt9C89VZaH7yLWOfMRo26nhhjODGcD1obkuzrzVCqGjWpJmxzaxA0\nbF5QS1uNXmuVUkqDiMClzBMRDodZtmkTyzZtmtbxA91n6Nqzk+TpE5RGh7ELBULGEMEhYkUISZxQ\nEHCIVQtWAstKEAbCwKRpoYpAF5iufrqfPlvJ5Sh5aUomR9HLU6BM2Ra8SBSnvpH6zkUs2ngrDfPn\nz+l+y1eS9kOdfcbzKPSMkTk2QPb4AKXB9IT9kY46P3BY3kqoJY7be4DiiR8x9uJLFE9sxxvtmXB8\naPEWYls+QHTTo9i154YeHUz2sufkdvac3M7e0ztIZkcmPG9x2yo2LL6DDUvuYN2iLVO2Omzbto2t\nW7dWtTYM0tM1iqm+Sa2LsHRVK0tXtbBkZQvhyOW9NBtjyBw+6bc0vLiT4RdfpzgwPOGYcEsjTW+5\nhaa7bqHprltJrFoyp68RY/kyr53x8xpeOZOcMAu0AGta42xZWMeWhXWsbo1fle5Jem1RM6H1Rc02\nDSKuotaFC2hduGBax+ZzOU7v3kX/kYPkB/ogk8Zxy0SwCBMmbEWnaOVowLYbsPFbOSYZ85eRvXsZ\nMa8FXav8Vo6Sl6NIgSIurmNjYnGiTS20LF/G/HU3E2tonNM3FOraVs4UKPYlKfQlKfQmyXcP4+Wr\nbvrCNvElLcSXtRKZH8UM7qF4/LukH99O6dSrmMLEIENi9YSX3kF42VuIbnp3ZU6HbCHN/iM/Z8+p\nHew5+VJlONZxTbXtbFxyB+sX3876xbfTkLjwJGnjrQ07njvOnudLE1obLEtYsLSRpataWba6lZb2\ny5vfYIwhfeiE39LwwmuMvPg6xaGJ+SDh1qZKwND0llvmdEJ00fU4NpTj0ECWQwMZDg1k6R6b2EWp\nOR5iy8JaNi+o49YFtdRF9c+jUkpdjOZEBK73eSLOnu7izO5djHWfxB0bxi7kCHsQFntiLofUBK0c\nU4YZF+YV8Ewaz8tQ9rKUTI6SKVISD9cWiEWJNjTS0NlJy8o11HYsxI7oBElqZowxuOmCHyz0JSuB\ng5suTDo21Bj3g4Z2wcrtpXRqB8UT2ymf2QvGm3Cs3bLUDxqW3k5o6R047asRy6Lsljh2dh+7T25n\nz6ntHO3Zi2eqhisNJ1jbuZkNS/zWhvlNF/513hjDQNDacPwNWhsWr2gmEr08/z+8cpnM0dOk9h4m\nuecwyb2HSe07Qmk0NeG4SHsLTXfdQmPQ2pBYvmhOBg2eMZwZK3AwCBYODfgTu5XPmwY6bAvr2hOV\n1oYljdE5+X0opZTmRKiLmreok3mLOqd1bCFf5NS+ffQd2k9uoAeTTuKUS4QNRHAIWxHCVhzHSmBL\nLWLXgRXBIoJlN1fyOSYoA4P+Mvz6YYY5jPHyGJPG9TK4JkfJK1CSEq5lIOzgJOLEm5uonddBbfsC\n4s3zsGtrkJCtf8xvAMYY3FSeQm+SQr/fwlDsS+JmJ4+xL2GbSFsd4eYwdiSNVTyKd/aXlJ7fTmqk\ne+LBlkOocxPhpXcQWnYH4aV3YNe1k8yOcGLwGN1n99C95wd0Dx7nZP8hcuP5EIAlNqsW3MyGxXew\ncckdLJ+37oKJ0cVCmYHeFANnU5ztHuPkkYm5DWIJC8dbG1a1XpbRlNxcgdSBY36gEAQNqQNH8fKT\nv7NIR4vfyhC0NsSXLpyT/6+GsyUODWQ5OJDhYH+Ww4NZMlVD4YLfPWlxQ5Q1bXFWtyZY3RpnaVMM\nR0dQUkqpS6ZBROBSciKuV5FomFWbb2HV5lve8FhjDCNDo5zYs5uRU0cpDPYhuTShcokQEBGbiIQJ\nWTFCEsO2EliW39ohVhQhimW3EOK8wMMAaX8pnnIZ4jRDnA7es4zxMngmh2fyuBRwpYyxwYo6ODVx\nog31xJuaibd2EGpswamrw46FKzMLX0naD3VmjGfw8iXcbJHiUPpct6S+JF6uNOl4K+IQanRwohls\nepHsIbyR3Xh7j1LKDHH+MyRaV2lhCC+9g0Lbcs4kz9I1eIzu/gN07/8XuoeOT8pnGDe/aTEbltzJ\nhsV3sHbRrcQjE4c7MMYwNpKrBAwDZ1P09yYZG548P8BUrQ3btm2jdd6yGX9vpdEkyb1HJgQMmaOn\nMa476dhY5zzqNqyidv0q6tavom7DKiIdLXMqaDDGMJorc3o0z6FBv4XhYH+GgczkOtQSD7G6Nc6a\nNj9gWNkSJ3EdTOqm1xY1E1pf1GzTIEJdlIjQ1NJI0333APe84fGeMQwPpeg6dIy+4wfI93djsqM4\npTwR4xERi7DlEJYwIStCSKLYEsOWOGLF/dwOCSN2PRb1k9+g4C9mCDLHSmToAroqu42XDYKPHJ4U\nMY6HRBycmgjhulpijY1EGlsINzZj1zdgx8JYEWdO3WxdScYYTMnFzZXwckXcbBE35wcIXq6Imyvi\nZku4uSLeeHl+8k3eOAlBKJ7Hkj6swlEYfRWvZxdy3MMDvPOPDyew25YT6liDt3Ajg/XtnMaje+gE\nXYNH6D7yFGOZoaneimgozsKWZSxsWU5nyzIWtiyjs2UlTVWJ1KX+ddYUAAAUTUlEQVSiy9muUQZ6\nU/QHAcNAb4pioTzp9SxbaG6robWjlrZ5dSxa3kRrR+2M65JxXbKnekgfOk7qwPFKwJDrOjv5+7Jt\nalYvnRgwrF85p+ZpSObLnEkWODNW4EyyQPdYnjNjBXqSBbKl82sExEMWq1r9FoY1rXFWt8ZpSejo\nSUopdaVpTkTges+JuF65nmF0LEtvVz99XT0M9ZwiN9SFZEewS1nClIiIIWoJEcsmbIUJS5iwRHCs\nOI7EsaQGrGCRS2uJMKaEMUWgjKEMlguWARssR7AcCyvkYEXCOJEITjSKFYlgRaJIJIIVi2NFY1hh\nB3FsxLb8tWNhOee2xbEmTVR2tRhjMGUPr1jGFMt4RRevUMYr+ospBGXFc2VeoYwpun5wEAQO1cOn\nTvOdEdvFsosIY1jF4zD2OpI7hLiDTLrlFguraRFeUyf52jbSiXqGQzH6bJuz5TzDmQH6R7oZyQxO\n9WZEQjEWNi8LAoZzQUNzbQci4k9AVyiTGiswNpKd0MIwMpRhqktiPBGmdV4trR21tM6rpa2jjqbW\nBPYM5gcwxpDv6Sd98Djpg8dJHTxO+tBx0odPTNkdyYqGqb1pxYSAofam5dix63/CykzRDYKEPN1j\n5wKGnmSBVGFyS8u4mrDNgvoIK1vilYChsyGKpT8CKKXUBWlOhJqTbEtobkzQ3LiUdRuXAlsverzr\nGZL5EsMDYwx1DzDYPcBwXx/pkS7K2T5CboooBWK2S8wWYrZDxAoRtcKEJUpYYjgSDxLMazBWDVhx\nRELI+RMHjv8UXvJ7X7nB4v+uXgqWiaP+TI8H4i9i+yP1iC2II0HwYQECIv66shCUca6s+rEApqrM\ngFc6Fwh4Je/cJGZvSgkxGcRLgTuGlEfBSyFuEvFSfrk3vp0EL4NMalMAN1ZPrnYFqXg9Q6EofbZN\nlylxophhrJCCTLe/XEDYiVQFC8tZ2LKM+Y1LiUoj2VSR1FiBTCpP8nCB7a/0kx7rIp3Mk04VKBWn\nvlEVS2huTdA2r7YSNLTNqyNRO7Mb98LAsN+yEAQM6UMnSB88TjmVmfL46IJ2alYv81sZ1q2gdv0q\nEisWYTnX5yXaM4ahbIm+VJHeVJHedJGzVa0LY/nJLTvjYiGLBXURFtRFmF8fYWF9hAV1URbUR6iL\naL6UUkpdK67Pv1BXwI2UE3E9sy2hMR6mcXEryxe3vuHxxbLHSK7EcP8YI2f66e4ZZqx3iLHRAfKZ\nLkxpEMskcSgSssuELJewDWHL4FhC2BJCIoTEIoRFSGz2dY+wZ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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 7)\n", - "# numpy friendly showdown_loss\n", - "\n", - "\n", - "def showdown_loss(guess, true_price, risk=80000):\n", - " loss = np.zeros_like(true_price)\n", - " ix = true_price < guess\n", - " loss[~ix] = np.abs(guess - true_price[~ix])\n", - " close_mask = [abs(true_price - guess) <= 250]\n", - " loss[close_mask] = -2 * true_price[close_mask]\n", - " loss[ix] = risk\n", - " return loss\n", - "\n", - "\n", - "guesses = np.linspace(5000, 50000, 70)\n", - "risks = np.linspace(30000, 150000, 6)\n", - "expected_loss = lambda guess, risk: \\\n", - " showdown_loss(guess, price_trace, risk).mean()\n", - "\n", - "for _p in risks:\n", - " results = [expected_loss(_g, _p) for _g in guesses]\n", - " plt.plot(guesses, results, label=\"%d\" % _p)\n", - "\n", - "plt.title(\"Expected loss of different guesses, \\nvarious risk-levels of \\\n", - "overestimating\")\n", - "plt.legend(loc=\"upper left\", title=\"Risk parameter\")\n", - "plt.xlabel(\"price bid\")\n", - "plt.ylabel(\"expected loss\")\n", - "plt.xlim(5000, 30000);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Minimizing our losses\n", - "\n", - "It would be wise to choose the estimate that minimizes our expected loss. This corresponds to the minimum point on each of the curves above. More formally, we would like to minimize our expected loss by finding the solution to\n", - "\n", - "$$ \\text{arg} \\min_{\\hat{\\theta}} \\;\\;E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", - "\n", - "The minimum of the expected loss is called the *Bayes action*. We can solve for the Bayes action using Scipy's optimization routines. The function in `fmin` in `scipy.optimize` module uses an intelligent search to find a minimum (not necessarily a *global* minimum) of any uni- or multivariate function. For most purposes, `fmin` will provide you with a good answer. \n", - "\n", - "We'll compute the minimum loss for the *Showcase* example above:\n" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "minimum at risk 30000: 14049.32\n", - "minimum at risk 54000: 13027.94\n", - "minimum at risk 78000: 12284.47\n", - "minimum at risk 102000: 11702.10\n", - "minimum at risk 126000: 11586.99\n", - "minimum at risk 150000: 11070.72\n" - ] - }, - { - "data": { - "text/plain": [ - "(-1000, 80000)" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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djLrqUW+LVO0wv1+GquKhhx5i7ty5bp8seOrMwu8iMhd9q6gdfZPnO0AY8KmI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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import scipy.optimize as sop\n", - "\n", - "ax = plt.subplot(111)\n", - "\n", - "\n", - "for _p in risks:\n", - " _color = ax._get_lines.color_cycle.next()\n", - " _min_results = sop.fmin(expected_loss, 15000, args=(_p,), disp=False)\n", - " _results = [expected_loss(_g, _p) for _g in guesses]\n", - " plt.plot(guesses, _results, color=_color)\n", - " plt.scatter(_min_results, 0, s=60,\n", - " color=_color, label=\"%d\" % _p)\n", - " plt.vlines(_min_results, 0, 120000, color=_color, linestyles=\"--\")\n", - " print \"minimum at risk %d: %.2f\" % (_p, _min_results)\n", - "\n", - "plt.title(\"Expected loss & Bayes actions of different guesses, \\n \\\n", - "various risk-levels of overestimating\")\n", - "plt.legend(loc=\"upper left\", scatterpoints=1, title=\"Bayes action at risk:\")\n", - "plt.xlabel(\"price guess\")\n", - "plt.ylabel(\"expected loss\")\n", - "plt.xlim(7000, 30000)\n", - "plt.ylim(-1000, 80000)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As intuition suggests, as we decrease the risk threshold (care about overbidding less), we increase our bid, willing to edge closer to the true price. It is interesting how far away our optimized loss is from the posterior mean, which was about 20 000. \n", - "\n", - "Suffice to say, in higher dimensions being able to eyeball the minimum expected loss is impossible. Hence why we require use of Scipy's `fmin` function.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "______\n", - "\n", - "### Shortcuts\n", - "\n", - "For some loss functions, the Bayes action is known in closed form. We list some of them below:\n", - "\n", - "- If using the mean-squared loss, the Bayes action is the mean of the posterior distribution, i.e. the value \n", - "$$ E_{\\theta}\\left[ \\theta \\right] $$\n", - "\n", - "> minimizes $E_{\\theta}\\left[ \\; (\\theta - \\hat{\\theta})^2 \\; \\right]$. Computationally this requires us to calculate the average of the posterior samples [See chapter 4 on The Law of Large Numbers]\n", - "\n", - "- Whereas the *median* of the posterior distribution minimizes the expected absolute-loss. The sample median of the posterior samples is an appropriate and very accurate approximation to the true median.\n", - "\n", - "- In fact, it is possible to show that the MAP estimate is the solution to using a loss function that shrinks to the zero-one loss.\n", - "\n", - "\n", - "Maybe it is clear now why the first-introduced loss functions are used most often in the mathematics of Bayesian inference: no complicated optimizations are necessary. Luckily, we have machines to do the complications for us. \n", - "\n", - "## Machine Learning via Bayesian Methods\n", - "\n", - "Whereas frequentist methods strive to achieve the best precision about all possible parameters, machine learning cares to achieve the best *prediction* among all possible parameters. Of course, one way to achieve accurate predictions is to aim for accurate predictions, but often your prediction measure and what frequentist methods are optimizing for are very different. \n", - "\n", - "For example, least-squares linear regression is the most simple active machine learning algorithm. I say active as it engages in some learning, whereas predicting the sample mean is technically *simpler*, but is learning very little if anything. The loss that determines the coefficients of the regressors is a squared-error loss. On the other hand, if your prediction loss function (or score function, which is the negative loss) is not a squared-error, like AUC, ROC, precision, etc., your least-squares line will not be optimal for the prediction loss function. This can lead to prediction results that are suboptimal. \n", - "\n", - "Finding Bayes actions is equivalent to finding parameters that optimize *not parameter accuracy* but an arbitrary performance measure, however we wish to define performance (loss functions, AUC, ROC, precision/recall etc.).\n", - "\n", - "The next two examples demonstrate these ideas. The first example is a linear model where we can choose to predict using the least-squares loss or a novel, outcome-sensitive loss. \n", - "\n", - "The second example is adapted from a Kaggle data science project. The loss function associated with our predictions is incredibly complicated. \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "##### Example: Financial prediction\n", - "\n", - "\n", - "Suppose the future return of a stock price is very small, say 0.01 (or 1%). We have a model that predicts the stock's future price, and our profit and loss is directly tied to us acting on the prediction. How should we measure the loss associated with the model's predictions, and subsequent future predictions? A squared-error loss is agnostic to the signage and would penalize a prediction of -0.01 equally as bad a prediction of 0.03:\n", - "\n", - "$$ (0.01 - (-0.01))^2 = (0.01 - 0.03)^2 = 0.004$$\n", - "\n", - "If you had made a bet based on your model's prediction, you would have earned money with a prediction of 0.03, and lost money with a prediction of -0.01, yet our loss did not capture this. We need a better loss that takes into account the *sign* of the prediction and true value. We design a new loss that is better for financial applications below:" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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/z2Xy4uYTWnph3+a0aSpPjJRIJJLykHP2Iqf+/bk2Y+c74Qmcfc37CEvuH9LS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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 4)\n", - "\n", - "\n", - "def stock_loss(true_return, yhat, alpha=100.):\n", - " if true_return * yhat < 0:\n", - " # opposite signs, not good\n", - " return alpha * yhat ** 2 - np.sign(true_return) * yhat \\\n", - " + abs(true_return)\n", - " else:\n", - " return abs(true_return - yhat)\n", - "\n", - "\n", - "true_value = .05\n", - "pred = np.linspace(-.04, .12, 75)\n", - "\n", - "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred],\n", - " label=\"Loss associated with\\n prediction if true value = 0.05\", lw=3)\n", - "plt.vlines(0, 0, .25, linestyles=\"--\")\n", - "\n", - "plt.xlabel(\"prediction\")\n", - "plt.ylabel(\"loss\")\n", - "plt.xlim(-0.04, .12)\n", - "plt.ylim(0, 0.25)\n", - "\n", - "true_value = -.02\n", - "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred], alpha=0.6,\n", - " label=\"Loss associated with\\n prediction if true value = -0.02\", lw=3)\n", - "plt.legend()\n", - "plt.title(\"Stock returns loss if true value = 0.05, -0.02\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note the change in the shape of the loss as the prediction crosses zero. This loss reflects that the user really does not want to guess the wrong sign, especially be wrong *and* a large magnitude. \n", - "\n", - "Why would the user care about the magnitude? Why is the loss not 0 for predicting the correct sign? Surely, if the return is 0.01 and we bet millions we will still be (very) happy.\n", - "\n", - "Financial institutions treat downside risk, as in predicting a lot on the wrong side, and upside risk, as in predicting a lot on the right side, similarly. Both are seen as risky behaviour and discouraged. Hence why we have an increasing loss as we move further away from the true price. (With less extreme loss in the direction of the correct sign.)\n", - "\n", - "We will perform a regression on a trading signal that we believe predicts future returns well. Our dataset is artificial, as most financial data is not even close to linear. Below, we plot the data along with the least-squares line." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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JUgz9HP/aTduarXGfTmx9+1JO8oMUv7DSiL6IiEiOlPuIdSqlsoJJa6U7/llv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\npqam6RdDiiPTJNqYZJNocxm/hoaGZne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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Code to create artificial data\n", - "N = 100\n", - "X = 0.025 * np.random.randn(N)\n", - "Y = 0.5 * X + 0.01 * np.random.randn(N)\n", - "\n", - "ls_coef_ = np.cov(X, Y)[0, 1] / np.var(X)\n", - "ls_intercept = Y.mean() - ls_coef_ * X.mean()\n", - "\n", - "plt.scatter(X, Y, c=\"k\")\n", - "plt.xlabel(\"trading signal\")\n", - "plt.ylabel(\"returns\")\n", - "plt.title(\"Empirical returns vs trading signal\")\n", - "plt.plot(X, ls_coef_ * X + ls_intercept, label=\"Least-squares line\")\n", - "plt.xlim(X.min(), X.max())\n", - "plt.ylim(Y.min(), Y.max())\n", - "plt.legend(loc=\"upper left\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We perform a simple Bayesian linear regression on this dataset. We look for a model like:\n", - "\n", - "$$ R = \\alpha + \\beta x + \\epsilon$$\n", - "\n", - "where $\\alpha, \\beta$ are our unknown parameters and $\\epsilon \\sim \\text{Normal}(0, 1/\\tau)$. The most common priors on $\\beta$ and $\\alpha$ are Normal priors. We will also assign a prior on $\\tau$, so that $\\sigma = 1/\\sqrt{\\tau}$ is uniform over 0 to 100 (equivalently then $\\tau = 1/\\text{Uniform}(0, 100)^2$)." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 100000 of 100000 complete in 28.1 secPlotting alpha\n", - "Plotting prec\n", - "Plotting beta\n" - ] - }, - { - "data": { - "image/png": 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mHVvpOu17ARcs5u6/V+8ZBL/Hr21Xofpj0pGl3b9zc12GkX79+pGeno5dSCRh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\ntv38g1oH7L/3NYjm9Z47dy7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IRgDSO9YrcT1DaU925vfs/c8cdi+Yxvv/mML/jHsw2n5k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\n4Y8O2xNwTVwRVLoRF1pTkhUxjdG7L+UjFj9iI3T8ck1cPe33ZfvV9Rt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n4BkRScIlE3lWVVeKyFIRycD1p74D+AmAqm4SkReBTUApMFsrv3hn45po1RTX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\npk1ERDKh2qkwab/kVy6OtIVWD1KLmObdY8klljwgrlxiElofFlo7Ca1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AaUv8P3idPaPtBOuFYZyzWDRfocTdPiF8rD18b4ZJcKpUHYX35//srNINqVV+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\nJKHkEkoeEFYuIbHWh1lrJ77OV2nW4gFf5ysNfm1H55xzqfE1ohqfH8P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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import pymc as pm\n", - "from pymc.Matplot import plot as mcplot\n", - "\n", - "std = pm.Uniform(\"std\", 0, 100, trace=False) # this needs to be explained.\n", - "\n", - "\n", - "@pm.deterministic\n", - "def prec(U=std):\n", - " return 1.0 / (U) ** 2\n", - "\n", - "beta = pm.Normal(\"beta\", 0, 0.0001)\n", - "alpha = pm.Normal(\"alpha\", 0, 0.0001)\n", - "\n", - "\n", - "@pm.deterministic\n", - "def mean(X=X, alpha=alpha, beta=beta):\n", - " return alpha + beta * X\n", - "\n", - "obs = pm.Normal(\"obs\", mean, prec, value=Y, observed=True)\n", - "mcmc = pm.MCMC([obs, beta, alpha, std, prec])\n", - "\n", - "mcmc.sample(100000, 80000)\n", - "mcplot(mcmc)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It appears the MCMC has converged so we may continue.\n", - "\n", - "For a specific trading signal, call it $x$, the distribution of possible returns has the form:\n", - "\n", - "$$R_i(x) = \\alpha_i + \\beta_ix + \\epsilon $$\n", - "\n", - "where $\\epsilon \\sim \\text{Normal}(0, 1/\\tau_i) $ and $i$ indexes our posterior samples. We wish to find the solution to \n", - "\n", - "$$ \\arg \\min_{r} \\;\\;E_{R(x)}\\left[ \\; L(R(x), r) \\; \\right] $$\n", - "\n", - "according to the loss given above. This $r$ is our Bayes action for trading signal $x$. Below we plot the Bayes action over different trading signals. What do you notice?\n" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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Xkj1Bpzh/R/zJlv7j2f3wC1yOPYV388BC28qIvpNr164d586dw9XVFTc3N7p0\n6cKbb75Jw4YNHd21a7Js2TKWLl3K999/b5v35ptvOrBHV8/+Ofz+/v7ExMQUu05ERAQPPvgge/fu\ntc17/PHHy6R/QgghhCh96ZnZvPVbDD8dvZBvWTeLD0/1boxnFddS29+lA0c5NOMDzv20BQAPvzo0\nm3o/DYbdwq7duwtcRxJ9J6eU4tNPP6Vnz56kpaUxZcoUnnrqKT755BNHd61CyszMxM1NLgtROsxa\nWyoMEj/zkxianzPGMPJcCo9+fZjM7Pzf3k/t1Yibm9Uq1f2lnjzDkdcXcGL596A1rt6eBP37Hhrf\nPxxXz6pFriulOybi4eHBoEGDOHTokG3eunXr6NWrF40aNSIkJIRZs2bZlg0fPpwFCxbk2kZYWJht\nFP3w4cPccccdNGnShK5du7J69Wpbu/Xr19O9e3csFgvBwcG8917BtV/R0dEMHjyYpk2b0qxZMx54\n4AESExNty+Pi4hgzZgzNmzenadOmTJs2jcOHD/PEE0+wbds2LBYLQUFBAEyaNIlXXnnFtu6SJUvo\n1KkTTZo04e677yY+Pt62rHbt2ixevJjOnTsTGBjI1KlTCz1vM2fOZOzYsYwfPx6LxcKNN97Ivn37\nbMvbtWvHO++8Q1hYGBaLhezsbLZt20a/fv0IDAykZ8+ebNq0ydb++PHjDBgwAIvFwpAhQzh//rxt\nWUxMDLVr1yY727iz/sKFC0yaNIng4GCCgoIYM2YMKSkpDBs2jPj4eCwWCxaLhfj4+FwlQABr1qyh\ne/fuBAYGMmjQIA4fPpyrz++99x433HADjRs3Zvz48aSlpRV6DoQQQghx9bTWLNsZT9/wnTy8+lCu\nJL+BjwdLRwSzbkL7Uk3yMxKTOPTKh2y8fhgnPvsO5eqCZfyd9Nq6kiaPjS02yQdJ9E0hp947JSWF\nL7/8ks6dO9uWeXl5MW/ePI4fP87y5ctZtGiRLZEfOXIkK1assLXdu3cv8fHx9O3bl+TkZIYMGcKw\nYcM4cuQI4eHhPPnkk7Zk8tFHH2XOnDnExMSwZcsWevbsWWj/Jk+ezIEDB9i6dSsnTpxg5syZAGRl\nZTFy5EgsFgt//fUX+/btY8iQITRv3py33nqLzp07ExMTQ1TUP8+SzSmD2bhxIy+//DKLFi3iwIED\nBAQEMGHChFz7XbduHRs2bOC3335j9erVbNiwodA+/vDDD9x+++1ER0czdOhQRo8eTVZWlm35F198\nwYoVK4gjAXSpAAAgAElEQVSOjiY+Pp6RI0fy5JNPEh0dzUsvvcTYsWNtCf39999P+/btOXr0KE8+\n+SSffvpprvIdew8++CBpaWls2bKFw4cP89BDD+Hp6cnKlSvx8/MjJiaGmJgY/Pz8cm0jMjKSiRMn\nMnPmTCIjI7n55psZNWoUmZmZtvP01VdfsWrVKnbt2sW+ffv49NNPCz1+4RhmqS0VBZP4mZ/E0Pwc\nHcNTl9K4d8V++i3cxeLtp3ItG9nOlx/Gh7J4WGvqeVcptX1mp2dwbMFyNna7i+h3PyE7NR2/gTcR\n9tuntH5lMlXqXFfibUmNQjF+8Lu+VLbTP37zVa2nteaee+7B1dWVlJQU6tSpw8qVK23Le/ToYft7\n69atueOOO9i0aRO33nor/fv3Z/LkyURHRxMYGMjy5csZMmQIbm5ufP311zRq1IiRI0cCEBISwoAB\nA1i9ejVTp07F3d2dgwcP0rp1a3x8fGjbtm2B/QsMDCQw0LgJpHbt2jz00EO88cYbAGzfvp3Tp0/z\n0ksv4eJifKbs2rWr7biKsnLlSkaPHk1ISAgAzz77LEFBQcTFxeHv7w/AY489ho+PDz4+PoSFhbF3\n71769OlT4PZCQ0MZOHAgYHxz8MEHH7Bt2za6deuGUoqJEyfSoEED277/9a9/cfPNNwPQu3dvQkND\nWbduHWFhYezatYuvvvoKd3d3unfvTv/+/Qs8nvj4eDZs2EBUVBQ+Pj4AdO/evdDjt5/35Zdf0rdv\nX3r16gXAv//9b+bPn88ff/zB9dcb78kHHngAX19fAPr378+ePXuKPKdCCCGEKJnXfj7GzwXU3gO8\nPag5rep5lfo+dXY28V//xOHX5nH5uPFYzuu6taPFc49Qs0PwVW1TEn0np5Ri6dKl9OzZE6013333\nHQMHDmTLli3Uq1ePP//8k5deeomDBw+Snp5Oeno6t99+OwBVq1bl9ttvZ/ny5UybNo0vvviCJUuW\nAEZJzfbt221JOhgj8MOHDweMspk333yTl156ieDgYJ577rlc3yTkOHPmDE8//TRbt24lKSkJrTU1\na9YE4MSJEwQEBNiS/Ctx+vRp2rdvb5v28vKiVq1anDx50pbo5yS5ANWqVSMpKanQ7eUk8TnntEGD\nBrlKgexvbo6NjeWrr77ihx9+sM3LysqiZ8+enDp1ipo1a1KtWjXbsoCAAE6cOJFvnydOnOC6666z\nJflXIj4+3nacOX1u2LAhp079M5pQr14929+rVq2a63iEc3DG2lJRchI/85MYml95xjAxNZM7lxY8\naNajUQ2m9m5ENffSu7nW3sXte9k//S0S/zoIgFezxrR49mHq/qtHoVUDJSGJfjGudiS+LCilGDBg\nAJMnT+b3339n4MCBTJw4kYkTJ7Jq1SqqVKnC9OnTc9WMjxgxgocffpiuXbvi6elJp06dACOxvf76\n6/niiy8K3Ff79u1ZunQpWVlZfPTRR9x3330FjhjPmDEDV1dXNm/eTI0aNfjuu++YNm2abR9xcXFk\nZWXh6pr7wijuTZtT1pIjOTmZ8+fP50rYr4R9Ip6dnc3Jkyfx8/MrsD/+/v4MGzaMuXPn5ttObGws\nFy9eJCUlBU9PT9u8vMcHxvFfuHCBxMTEfMl+ccdfv3599u/fb5vWWnPixAnq169fYPtr+UdACCGE\nqMy+PXCOdzbFFrisu6UGL/YNKrN9ZyQmceTVecQs+RK0xqNebZpOnUDDEbfhUgoPB5EafRPIKenQ\nWvP9999z8eJFmjc3fgEtOTmZmjVrUqVKFbZv387nn3+eK+nr0qULSimee+4522g9QL9+/Th69Cgr\nVqwgIyODjIwMduzYweHDh8nIyGDlypUkJibi6uqKt7d3gYlszv49PT2pXr06J0+e5N1337Ut69ix\nI76+vrz44oukpKSQmprK77//DkDdunU5efIkGRkZBR7r0KFDWbZsGXv37iUtLY0ZM2bQqVOnXKPc\nV+Kvv/7i22+/JTMzkw8//BAPD48Cv6EAuOuuu1i7di0//fQTWVlZpKamEhERwcmTJwkICCA0NJSZ\nM2eSkZHB1q1bWbt2bYHb8fPz4+abb2bKlCkkJCSQkZHB5s2bbcef8yGgIIMHD2b9+vVs3LiRjIwM\n3nvvPapWrUqXLl0KbH81z+0XZc/RtaXi2kj8zE9iaH5lFcOsbE3f8J30Dd9ZYJL/9qDmrJvQvsyS\nfK018d/+TETPUcQs/gLl6kLgv+/hhi0rCBg9uFSSfJBE3xRGjRqFxWKhUaNGvPrqq3z44Ye0aNEC\ngDfeeIPXXnsNi8XC7NmzueOOO/KtP3z4cPbv38+wYcNs87y9vfn888/54osvCA4OplWrVsyYMcOW\neK9YsYLQ0FAaNWrEkiVLmD9/foF9mzp1Krt376Zx48aMGjWKgQMH2j5ouLq6smzZMqKjo2nbti0h\nISG2J/v06tWLli1b0rJlS9uHFvhnZLpXr15Mnz6dsWPH0rp1a2JiYggPD8/Xzl5ho9pKKW655Ra+\n/PJLgoKCWLVqFR9//HGhH14aNmzI0qVLmTNnDs2bN6dt27a8//77tifpLFiwgO3bt9OkSRNef/11\n230OBfVj3rx5uLu707VrV1q0aGE7j82bN2fIkCF06NCBoKAg4uPjUUrZ1m3WrBnz5s1j2rRpNGvW\njPXr17Ns2bJCH/1pv64QQgghChYRbfyw1S3/3VXg8jX3hbJuQvsyqcHPcfnEaXaOm8auCc+QFn+O\nGh2DuX79Ylo88xBuXtWK38AVUJVlJHDDhg26Q4cO+eafPHnyqstBzGL58uV8/PHHfPfdd47uikPM\nmjWL6Oho5s2b5+iuOJXK8N4XQgghAPqG7yx02Z0h9ZjYtex/iFRnZXH8v6s4MnMBWckpuHp70uKZ\nhwgYczuqkMHHktqxYwd9+vTJN+InNfoVXEpKCuHh4dx///2O7orDVJYPs0IIIYT4x/ELl7n/84OF\nLl86IrhUH4tZlMS9h9k3ZRYJuw4A4Htbb1q9/DhV69ct0/1K6U4FtmHDBlq0aIGfnx933nmno7vj\nMFLWIhxF6oPNTeJnfhJD87uaGI5dvo++4TsLTPJdFKyb0J51E9qXS5KfmXyZgy++x5Z+40nYdYCq\nDerRYcks2i98tcyTfHCiEX2lVH9gLuAKhGutZxXQ5h3gFiAFGKe13qmUCgA+BuoBGvhIa/1O+fXc\nefXp04fY2ILvIq9Mcp4CJIQQQoiKKT0rmwGL/ip0+f+FBXBryzrl2CM4+9NW9k97g8uxp0ApGk24\ni2ZPTcTNu+zq//NyikRfKeUKvAfcDJwAtimlvtZaH7BrcyvQVGvdTCnVFfgQ6AZkAI9rrXcppbyB\n7Uqp9fbrCiGEI8gzvM1N4md+EkPzKy6GK/46Tfi2k4UuX3NfKK4u5futftrZ8xx4di7xq38EoHpw\nM9rMnkaN9q3LtR/gJIk+0AWI1FofA1BKfQYMBuyT9UHAEgCt9e9KqZpKKV+tdTwQb52fpJQ6ADTI\ns64QQgghhKggirq5tnU9L+YOal7o8rKis7OJW/YNh2Z8QGbCJVyqedDsyftpNHFYqT0u80o5S6Lf\nELCvMYkDupagjT9wOmeGUqo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i1hTOytmfoy+EEEIIkUtxo/c/jA/FReXLbUQhLu7YT+Ts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\nLIuF9z7Fhsm+XyANOqTQ446rSDl5qNriKrGn3vsbDk/luO6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Qj754jnOONe9PYdF9T1Gw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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "figsize(12.5, 6)\n", - "from scipy.optimize import fmin\n", - "\n", - "\n", - "def stock_loss(price, pred, coef=500):\n", - " \"\"\"vectorized for numpy\"\"\"\n", - " sol = np.zeros_like(price)\n", - " ix = price * pred < 0\n", - " sol[ix] = coef * pred ** 2 - np.sign(price[ix]) * pred + abs(price[ix])\n", - " sol[~ix] = abs(price[~ix] - pred)\n", - " return sol\n", - "\n", - "tau_samples = mcmc.trace(\"prec\")[:]\n", - "alpha_samples = mcmc.trace(\"alpha\")[:]\n", - "beta_samples = mcmc.trace(\"beta\")[:]\n", - "\n", - "N = tau_samples.shape[0]\n", - "\n", - "noise = 1. / np.sqrt(tau_samples) * np.random.randn(N)\n", - "\n", - "possible_outcomes = lambda signal: alpha_samples + beta_samples * signal \\\n", - " + noise\n", - "\n", - "\n", - "opt_predictions = np.zeros(50)\n", - "trading_signals = np.linspace(X.min(), X.max(), 50)\n", - "for i, _signal in enumerate(trading_signals):\n", - " _possible_outcomes = possible_outcomes(_signal)\n", - " tomin = lambda pred: stock_loss(_possible_outcomes, pred).mean()\n", - " opt_predictions[i] = fmin(tomin, 0, disp=False)\n", - "\n", - "\n", - "plt.xlabel(\"trading signal\")\n", - "plt.ylabel(\"prediction\")\n", - "plt.title(\"Least-squares prediction vs. Bayes action prediction\")\n", - "plt.plot(X, ls_coef_ * X + ls_intercept, label=\"Least-squares prediction\")\n", - "plt.xlim(X.min(), X.max())\n", - "plt.plot(trading_signals, opt_predictions, label=\"Bayes action prediction\")\n", - "plt.legend(loc=\"upper left\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What is interesting about the above graph is that when the signal is near 0, and many of the possible returns outcomes are possibly both positive and negative, our best (with respect to our loss) prediction is to predict close to 0, hence *take on no position*. Only when we are very confident do we enter into a position. I call this style of model a *sparse prediction*, where we feel uncomfortable with our uncertainty so choose not to act. (Compare with the least-squares prediction which will rarely, if ever, predict zero). \n", - "\n", - "A good sanity check that our model is still reasonable: as the signal becomes more and more extreme, and we feel more and more confident about the positive/negativeness of returns, our position converges with that of the least-squares line. \n", - "\n", - "The sparse-prediction model is not trying to *fit* the data the best (according to a *squared-error loss* definition of *fit*). That honor would go to the least-squares model. The sparse-prediction model is trying to find the best prediction *with respect to our `stock_loss`-defined loss*. We can turn this reasoning around: the least-squares model is not trying to *predict* the best (according to a *`stock-loss`* definition of *predict*). That honor would go the *sparse prediction* model. The least-squares model is trying to find the best fit of the data *with respect to the squared-error loss*.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Kaggle contest on *Observing Dark World*\n", - "\n", - "\n", - "A personal motivation for learning Bayesian methods was trying to piece together the winning solution to Kaggle's [*Observing Dark Worlds*](http://www.kaggle.com/c/DarkWorlds) contest. From the contest's website:\n", - "\n", - "\n", - "\n", - ">There is more to the Universe than meets the eye. Out in the cosmos exists a form of matter that outnumbers the stuff we can see by almost 7 to 1, and we don’t know what it is. What we do know is that it does not emit or absorb light, so we call it Dark Matter. Such a vast amount of aggregated matter does not go unnoticed. In fact we observe that this stuff aggregates and forms massive structures called Dark Matter Halos. Although dark, it warps and bends spacetime such that any light from a background galaxy which passes close to the Dark Matter will have its path altered and changed. This bending causes the galaxy to appear as an ellipse in the sky.\n", - "\n", - "\n", - "\n", - "\n", - "The contest required predictions about where dark matter was likely to be. The winner, [Tim Salimans](http://timsalimans.com/), used Bayesian inference to find the best locations for the halos (interestingly, the second-place winner also used Bayesian inference). With Tim's permission, we provided his solution [1] here:\n", - "\n", - "1. Construct a prior distribution for the halo positions $p(x)$, i.e. formulate our expectations about the halo positions before looking at the data.\n", - "2. Construct a probabilistic model for the data (observed ellipticities of the galaxies) given the positions of the dark matter halos: $p(e | x)$.\n", - "3. Use Bayes’ rule to get the posterior distribution of the halo positions, i.e. use to the data to guess where the dark matter halos might be.\n", - "4. Minimize the expected loss with respect to the posterior distribution over the predictions for the halo positions: $\\hat{x} = \\arg \\min_{\\text{prediction} } E_{p(x|e)}[ L( \\text{prediction}, x) ]$ , i.e. tune our predictions to be as good as possible for the given error metric.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The loss function in this problem is very complicated. For the very determined, the loss function is contained in the file DarkWorldsMetric.py in the parent folder. Though I suggest not reading it all, suffice to say the loss function is about 160 lines of code — not something that can be written down in a single mathematical line. The loss function attempts to measure the accuracy of prediction, in a Euclidean distance sense, such that no shift-bias is present. More details can be found on the metric's [main page](http://www.kaggle.com/c/DarkWorlds/details/evaluation). \n", - "\n", - "We will attempt to implement Tim's winning solution using PyMC and our knowledge of loss functions." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Data\n", - "\n", - "The dataset is actually 300 separate files, each representing a sky. In each file, or sky, are between 300 and 720 galaxies. Each galaxy has an $x$ and $y$ position associated with it, ranging from 0 to 4200, and measures of ellipticity: $e_1$ and $e_2$. Information about what these measures mean can be found [here](https://www.kaggle.com/c/DarkWorlds/details/an-introduction-to-ellipticity), but for our purposes it does not matter besides for visualization purposes. Thus a typical sky might look like the following:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Data on galaxies in sky 3.\n", - "position_x, position_y, e_1, e_2 \n", - "[[ 1.62690000e+02 1.60006000e+03 1.14664000e-01 -1.90326000e-01]\n", - " [ 2.27228000e+03 5.40040000e+02 6.23555000e-01 2.14979000e-01]\n", - " [ 3.55364000e+03 2.69771000e+03 2.83527000e-01 -3.01870000e-01]]\n" - ] - }, - { - "data": { - "image/png": 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2KKWWaZ8LKaVWK6WOKaVWKaUKuhz7jlLquFLqiFKqrUt6PaXUP1reF9mh0+Fw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\niiVTb3JLKYpFuHChbwIT3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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from draw_sky2 import draw_sky\n", - "\n", - "n_sky = 3 # choose a file/sky to examine.\n", - "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", - "Training_Sky%d.csv\" % (n_sky),\n", - " dtype=None,\n", - " skip_header=1,\n", - " delimiter=\",\",\n", - " usecols=[1, 2, 3, 4])\n", - "print \"Data on galaxies in sky %d.\" % n_sky\n", - "print \"position_x, position_y, e_1, e_2 \"\n", - "print data[:3]\n", - "\n", - "fig = draw_sky(data)\n", - "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", - "plt.xlabel(\"x-position\")\n", - "plt.ylabel(\"y-position\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Priors\n", - "\n", - "Each sky has one, two or three dark matter halos in it. Tim's solution details that his prior distribution of halo positions was uniform, i.e.\n", - "\n", - "\\begin{align}\n", - "& x_i \\sim \\text{Uniform}( 0, 4200)\\\\\\\\\n", - "& y_i \\sim \\text{Uniform}( 0, 4200), \\;\\; i=1,2,3\\\\\\\\\n", - "\\end{align}\n", - "\n", - "Tim and other competitors noted that most skies had one large halo and other halos, if present, were much smaller. Larger halos, having more mass, will influence the surrounding galaxies more. He decided that the large halos would have a mass distributed as a *log*-uniform random variable between 40 and 180 i.e.\n", - "\n", - "$$ m_{\\text{large} } = \\log \\text{Uniform}( 40, 180 ) $$\n", - "\n", - "and in PyMC, \n", - "\n", - " exp_mass_large = pm.Uniform(\"exp_mass_large\", 40, 180)\n", - " @pm.deterministic\n", - " def mass_large(u = exp_mass_large):\n", - " return np.log(u)\n", - "\n", - "(This is what we mean when we say *log*-uniform.) For smaller galaxies, Tim set the mass to be the logarithm of 20. Why did Tim not create a prior for the smaller mass, nor treat it as a unknown? I believe this decision was made to speed up convergence of the algorithm. This is not too restrictive, as by construction the smaller halos have less influence on the galaxies.\n", - "\n", - "Tim logically assumed that the ellipticity of each galaxy is dependent on the position of the halos, the distance between the galaxy and halo, and the mass of the halos. Thus the vector of ellipticity of each galaxy, $\\mathbf{e}_i$, are *children* variables of the vector of halo positions $(\\mathbf{x},\\mathbf{y})$, distance (which we will formalize), and halo masses.\n", - "\n", - "Tim conceived a relationship to connect positions and ellipticity by reading literature and forum posts. He supposed the following was a reasonable relationship:\n", - "\n", - "$$ e_i | ( \\mathbf{x}, \\mathbf{y} ) \\sim \\text{Normal}( \\sum_{j = \\text{halo positions} }d_{i,j} m_j f( r_{i,j} ), \\sigma^2 ) $$\n", - "\n", - "where $d_{i,j}$ is the *tangential direction* (the direction in which halo $j$ bends the light of galaxy $i$), $m_j$ is the mass of halo $j$, $f(r_{i,j})$ is a *decreasing function* of the Euclidean distance between halo $j$ and galaxy $i$. \n", - "\n", - "Tim's function $f$ was defined:\n", - "\n", - "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 240 ) } $$\n", - "\n", - "for large halos, and for small halos\n", - "\n", - "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 70 ) } $$\n", - "\n", - "This fully bridges our observations and unknown. This model is incredibly simple, and Tim mentions this simplicity was purposefully designed: it prevents the model from overfitting. \n", - "\n", - "\n", - "### Training & PyMC implementation\n", - "\n", - "For each sky, we run our Bayesian model to find the posteriors for the halo positions — we ignore the (known) halo position. This is slightly different than perhaps traditional approaches to Kaggle competitions, where this model uses no data from other skies nor the known halo location. That does not mean other data are not necessary — in fact, the model was created by comparing different skies. \n" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "def euclidean_distance(x, y):\n", - " return np.sqrt(((x - y) ** 2).sum(axis=1))\n", - "\n", - "\n", - "def f_distance(gxy_pos, halo_pos, c):\n", - " # foo_position should be a 2-d numpy array\n", - " return np.maximum(euclidean_distance(gxy_pos, halo_pos), c)[:, None]\n", - "\n", - "\n", - "def tangential_distance(glxy_position, halo_position):\n", - " # foo_position should be a 2-d numpy array\n", - " delta = glxy_position - halo_position\n", - " t = (2 * np.arctan(delta[:, 1] / delta[:, 0]))[:, None]\n", - " return np.concatenate([-np.cos(t), -np.sin(t)], axis=1)\n", - "\n", - "import pymc as pm\n", - "\n", - "# set the size of the halo's mass\n", - "mass_large = pm.Uniform(\"mass_large\", 40, 180, trace=False)\n", - "\n", - "# set the initial prior position of the halos, it's a 2-d Uniform dist.\n", - "halo_position = pm.Uniform(\"halo_position\", 0, 4200, size=(1, 2))\n", - "\n", - "\n", - "@pm.deterministic\n", - "def mean(mass=mass_large, h_pos=halo_position, glx_pos=data[:, :2]):\n", - " return mass / f_distance(glx_pos, h_pos, 240) *\\\n", - " tangential_distance(glx_pos, h_pos)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 200000 of 200000 complete in 193.7 sec" - ] - } - ], - "source": [ - "ellpty = pm.Normal(\"ellipcity\", mean, 1. / 0.05, observed=True,\n", - " value=data[:, 2:])\n", - "mcmc = pm.MCMC([ellpty, mean, halo_position, mass_large])\n", - "map_ = pm.MAP([ellpty, mean, halo_position, mass_large])\n", - "map_.fit()\n", - "mcmc.sample(200000, 140000, 3)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we plot a \"heatmap\" of the posterior distribution. (Which is just a scatter plot of the posterior, but we can visualize it as a heatmap.)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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hQqUkNLSJBAdXlJIl75CFCxdmOn9Ws2rVKgkJqS3gvDIQMSSks3z77be+lpYj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vSqGAwWUZR84u+fV+bPn+9tWY8kDodDdu/eLRMnTpR27bpLeHhZ0evNYjIFitUaJjZbYTEa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\nv39/qduW1jgLqqE0vLc/u3xSdtOgQ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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "t = mcmc.trace(\"halo_position\")[:].reshape(20000, 2)\n", - "\n", - "fig = draw_sky(data)\n", - "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", - "plt.xlabel(\"x-position\")\n", - "plt.ylabel(\"y-position\")\n", - "plt.scatter(t[:, 0], t[:, 1], alpha=0.015, c=\"r\")\n", - "plt.xlim(0, 4200)\n", - "plt.ylim(0, 4200);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The most probable position reveals itself like a lethal wound.\n", - "\n", - "Associated with each sky is another data point, located in `./data/Training_halos.csv` that holds the locations of up to three dark matter halos contained in the sky. For example, the night sky we trained on has halo locations:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 1.00000000e+00 1.40861000e+03 1.68586000e+03 1.40861000e+03\n", - " 1.68586000e+03 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", - " 0.00000000e+00]\n" - ] - } - ], - "source": [ - "halo_data = np.genfromtxt(\"data/Training_halos.csv\",\n", - " delimiter=\",\",\n", - " usecols=[1, 2, 3, 4, 5, 6, 7, 8, 9],\n", - " skip_header=1)\n", - "print halo_data[n_sky]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The third and fourth column represent the true $x$ and $y$ position of the halo. It appears that the Bayesian method has located the halo within a tight vicinity. " - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "True halo location: 1408.61 1685.86\n" - ] - }, - { - "data": { - "image/png": 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hQqUkNLSJBAdXlJIl75CFCxdmOn9Ws2rVKgkJqS3gvDIQMSSks3z77be+lpYj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\nze7du3O2qSoJCQnUqVMHgKioKKKio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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig = draw_sky(data)\n", - "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", - "plt.xlabel(\"x-position\")\n", - "plt.ylabel(\"y-position\")\n", - "plt.scatter(t[:, 0], t[:, 1], alpha=0.015, c=\"r\")\n", - "plt.scatter(halo_data[n_sky - 1][3], halo_data[n_sky - 1][4],\n", - " label=\"True halo position\",\n", - " c=\"k\", s=70)\n", - "plt.legend(scatterpoints=1, loc=\"lower left\")\n", - "plt.xlim(0, 4200)\n", - "plt.ylim(0, 4200);\n", - "\n", - "print \"True halo location:\", halo_data[n_sky][3], halo_data[n_sky][4]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Perfect. Our next step is to use the loss function to optimize our location. A naive strategy would be to simply choose the mean:" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ 2324.11251994 1122.86392315]]\n" - ] - } - ], - "source": [ - "mean_posterior = t.mean(axis=0).reshape(1, 2)\n", - "print mean_posterior" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Using the mean:\n", - "Your average distance in pixels you are away from the true halo is 41.7538021788\n", - "Your average angular vector is 1.0\n", - "Your score for the training data is 1.04175380218\n", - "\n", - "Using a random location: [[ 796 2958]]\n", - "Your average distance in pixels you are away from the true halo is 2414.39326766\n", - "Your average angular vector is 1.0\n", - "Your score for the training data is 3.41439326766\n", - "\n" - ] - } - ], - "source": [ - "from DarkWorldsMetric import main_score\n", - "\n", - "_halo_data = halo_data[n_sky - 1]\n", - "\n", - "nhalo_all = _halo_data[0].reshape(1, 1)\n", - "x_true_all = _halo_data[3].reshape(1, 1)\n", - "y_true_all = _halo_data[4].reshape(1, 1)\n", - "x_ref_all = _halo_data[1].reshape(1, 1)\n", - "y_ref_all = _halo_data[2].reshape(1, 1)\n", - "sky_prediction = mean_posterior\n", - "\n", - "print \"Using the mean:\"\n", - "main_score(nhalo_all, x_true_all, y_true_all,\n", - " x_ref_all, y_ref_all, sky_prediction)\n", - "\n", - "# what's a bad score?\n", - "print\n", - "random_guess = np.random.randint(0, 4200, size=(1, 2))\n", - "print \"Using a random location:\", random_guess\n", - "main_score(nhalo_all, x_true_all, y_true_all,\n", - " x_ref_all, y_ref_all, random_guess)\n", - "print" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is a good guess, it is not very far from the true location, but it ignores the loss function that was provided to us. We also need to extend our code to allow for up to two additional, *smaller* halos: Let's create a function for automatizing our PyMC. " - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from pymc.Matplot import plot as mcplot\n", - "\n", - "\n", - "def halo_posteriors(n_halos_in_sky, galaxy_data,\n", - " samples=5e5, burn_in=34e4, thin=4):\n", - " # set the size of the halo's mass\n", - " \"\"\"\n", - " exp_mass_large = pm.Uniform(\"exp_mass_large\", 40, 180)\n", - " @pm.deterministic\n", - " def mass_large(exp_mass_large = exp_mass_large):\n", - " return np.log(exp_mass_large)\n", - " \"\"\"\n", - "\n", - " mass_large = pm.Uniform(\"mass_large\", 40, 180)\n", - "\n", - " mass_small_1 = 20\n", - " mass_small_2 = 20\n", - "\n", - " masses = np.array([mass_large, mass_small_1, mass_small_2], dtype=object)\n", - "\n", - " # set the initial prior positions of the halos, it's a 2-d Uniform dist.\n", - " halo_positions = pm.Uniform(\"halo_positions\", 0, 4200,\n", - " size=(n_halos_in_sky, 2)) # notice this size\n", - "\n", - " fdist_constants = np.array([240, 70, 70])\n", - "\n", - " @pm.deterministic\n", - " def mean(mass=masses, h_pos=halo_positions, glx_pos=data[:, :2],\n", - " n_halos_in_sky=n_halos_in_sky):\n", - "\n", - " _sum = 0\n", - " for i in range(n_halos_in_sky):\n", - " _sum += mass[i] / f_distance(glx_pos, h_pos[i, :], fdist_constants[i]) *\\\n", - " tangential_distance(glx_pos, h_pos[i, :])\n", - "\n", - " return _sum\n", - "\n", - " ellpty = pm.Normal(\"ellipcity\", mean, 1. / 0.05, observed=True,\n", - " value=data[:, 2:])\n", - "\n", - " map_ = pm.MAP([ellpty, mean, halo_positions, mass_large])\n", - " map_.fit(method=\"fmin_powell\")\n", - "\n", - " mcmc = pm.MCMC([ellpty, mean, halo_positions, mass_large])\n", - " mcmc.sample(samples, burn_in, thin)\n", - " return mcmc.trace(\"halo_positions\")[:]" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n_sky = 215\n", - "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", - "Training_Sky%d.csv\" % (n_sky),\n", - " dtype=None,\n", - " skip_header=1,\n", - " delimiter=\",\",\n", - " usecols=[1, 2, 3, 4])" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " [-----------------100%-----------------] 1050000 of 1050000 complete in 2202.2 sec" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/isaac/.virtualenvs/data-science/lib/python2.7/site-packages/scipy/optimize/optimize.py:1758: RuntimeWarning: invalid value encountered in absolute\n", - " tmp2 = numpy.abs(tmp2)\n" - ] - } - ], - "source": [ - "# there are 3 halos in this file.\n", - "samples = 10.5e5\n", - "traces = halo_posteriors(3, data, samples=samples,\n", - " burn_in=9.5e5,\n", - " thin=10)" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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OHjYmhj7I7N8wh0NWNHslZHm92D/u7nWve2WlaRjngPaMIUDRr5kxRkQVq0pq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v2u1dKQEBQojVcCP7UeB2Onizk4HnWWvfKYQ4E/i9tfa7+TNfBX4J3At81lq7b379pcAx1tpu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PfPlwsWEIsNJqxZ8HoCpRyi0WggyPh+b+UEHlQKn+rBtm0UEiWc4FDYEfibuDAMIvE40Wgc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mui9P0kIIgW05SQpCCF8c12sPgeJXGZDYfiq9NwnXlPZeiMJ48FoNpcafSqU455y/sMMO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\nPSjyWpNwbXbfaAjB2ppgWRb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VhdDrWhVkS2qhbTPOtmJYlsV++x3Gl1/uSDS6iTZtfubV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VSa\nQi5PWCzipNIoS6IFpFIO2VQa1/OQmTSZ9lYsKUsLnu95SMvinnvv5ZDDrqSzMxazXEg6vSpvvzmZ\nb37zmxC57oMI2HlRqr7bkSMlLKyUjbAsUq1ZABM+1ppMKoWwLXCc0ntvlieykR1qTxNob65dDvJm\nzpzJmmuuT2fnncDWANj2zzjjjOX5zW9+3ehjl6yeyTUMQ3QQEAYBOgzRQYi2DeABTK1FrUthZxWa\n+plKCIRl8fIrr3DUUSfz3nufIeU3WHHFHG+99eIixObAD0uk9qQnpR4QkPQUF4tFUCHC7uJu1bN4\n+r7PAw88wHPPTWbu3IVsssm67L///n0qUl7Nyp8lUKY8kyq6plqGChFCYrWYCgISwLIQUZgp3uTE\n7yz2iBtvjlfywAWhj2OlzUIfBKUFOT5eCEHRLRAojy0335W33jwbw7f7nNbWMSxYMAuo7Rnry8Ic\njwmllAFnUAJAlcZG+cY4UAptWTipyBPaR9BSq22VxmtyfCqlCFy31FdVqEtJS729X633V8nLWyta\nUskqzVG2bXeVVotAt1XnGKl0/WZGqb7stgycJaxSB9dSGtXvOl221SzZ8WJQUSkjKAZwsSigjsI0\nhCbd2M6YSbLWxNVTmLLaM8+YMYN11t+SBQv+AOwDPMKqq57Ee9NeNKCy6EIYYqUSPDytCT2fIF9g\n4cKFCD9EhCFFFYLS+PkcKTuFEpoOz2XgwIEMWm4QOghxUbQOGUQ2bcCbtKzo+imUUiz/jZF0dj5D\nnMWZyRzJL385nN+c9ivDTSDinwVBSX09n8sZL1kEIAVmV2dFxyoglW0hHUkJNNMa2aH2BL4a3f0+\n9NBDjBu3P8XicSi1HK2t5/L66y8wcuTI3j9oFatnco2PiWtjer5PJp0u8Y/qyZ7TWvPyyy8zc+ZM\nttpqK9rb2+sGZ3Eb6g3je55H6PlYKYdUtBFZmnbz5Qu9m8+jih525L1USmG1pHES4DfuN+WbQQWm\ndqhtUygUkLa5vlv0aW3Nmnt5AVIIrJiOYBn9Nc/zKLh5Ljh/Apf8aT6uewUwkwEDNmTBgpk9Pkcj\n4AwoyTPUIoZXopRopytM3Wy+WT3j1ZQh6x5JSaV6D856A2waAUHlYycGlzpKXhNCmO+WSvXZgdFb\n0PhVtWXgLGGVOq1l2wYI9BKcJUFWiS/Wy/BovNOTxBpdBpzJGoWBy1339cT/42fe+Qd7899J6xEE\nZ0V/7cBxhjFv9mcIIaJwEwjbMlmlnoclLYq5HLM//wJHg62gkM/heS7z5s1HBCGDlxuIrzSdbift\nbQNoHTAArTVWOk3L0EFks1mUCrGdFLZlYadNUsYpp53JXy6bQ7F4ddSepxg16nimTZvcjTirte4W\nCnaLRZN9pRTFoouXz0MQkE23EKCx21tpGzCg9A6aPSn3ZXKpxzOmlOom9dJb3sVbb73FX/5yNV98\nMY8TTzySLbbYolfn12P1PH/ymGrelN68x/KFMPDDEv8o/ntvpUh8zyOMFnzP93EsA86aSSlophkQ\nVUS5Ll6+gFAmFOypgEw2i51Olzxmybb7vk/gugghujIUIxAc97XkBsFzXUScRS5NuTQRned5Hh99\n9BHrrrs5rvsRMIuhQ3fkiy/er9TkRdrf17BmHM4OAxUlL1Qmhic9Z2EYUnA97EyabDbbb7I5PfXh\nMAqdJ+ezeqQx+nq/+J7NCh8GQYCXzxN6XomuYrVkyLS0LHVj5Mtmy8BZmVXaGfS2I1fakWppFKnL\nNX162hnqKIst/p+w7Zoek1qctlrtnT59OmPHbkax+BGQjf7yFsNW2J3XJ//XcEVsm4LvlbSkLGnh\nhSHzZs1CdeQpzpvPjFmzaHUyFD2XnO+StWyQguUHD0FIi1xQpLW1DY0mm20lO3AggSVoy2YRKYdU\nJkO2JYN0HObOn8+o1ceSzz+P8WOTycoAACAASURBVJ4tJJUaTrHYUdEbU8ry0xqlNUGxSOgHhIUi\nKgyj92Ah0iksx2mYhNtM62mn3YjnbObMmVx88aW88cZ7DB06iO2335zx48eTzWZ7PLeZ9sUXX/De\ne+/heR4jR45kxIgRTbt2ctxq3TjROwgCgtAveQOUUou1BFdvLZ4rAt/HL7q4+QJYgkxra6moeiUv\nfbFYRMS6U1GYqlpISmtNsVAA37wXLaL6lNGx0jJAe/fd9uGxxzYkDDdk3XUv4JVXHu+TV6bZ5yRB\nd+eChThCMHnKFG78+z95e9oHzJs3lzFj1uTcc09l/fXX7/HezbBm8cF6Y80EZ77vU+zowCbiSGtF\ndrnlurzMy6zPVg2cNTfe8yUyIUTDuyillCFHEnV8bXRsAqVwYt6LUtgR4bbaQJRSEgiBiK6jhcDp\nQX8nmaoNIBOTVzUTQvDcc8/hONtTLGYTvz/KZptsRNo26fgaTW7hQlQx4gOhkNLCKgZ05jr537v/\no833+Vwp/JzPcssPQBUVSvvMBoYOW4G0SOEWXAYObEc6Eq9o+Baugrb2NrACXNuEuoZ94xucd95Z\nnHbaOPL5pzEkY5v58+czaNCgbu0vcWgAR0o8z0MojS0EoQahNFIKpG1K/VR6R0syVCWE+H/2zjve\njqL8/+/Zdsot6QklCNJCE5AqAuIXEEGkiIig/gAjVQiIX/gKqBS/ooIoX8VCx4JUpYhKDSAoiBRR\nOoROSEIISe69p+3uzPz+mJ29e0/OOffcloTyvF68yN2zOztlZ+aZ5/k8n6c/mgtw/IEbTX0yapz2\n6qy1Zvvtd2Pu3O0Jw/2Axdx44x+YNeskTjvtFL72tVljvpDOnz+fAw6YyT//eT/5/PpAjjB8jlVW\nWYVvfesEvvzlQ9qyRLfahLPz1mx4CpyELkKZ/hyK2PLse4QQKdZqeUu7CoidB1JKch2F1L2US2gr\n6kUphes5xJFMMZxaihRHWv9+KSWe46A8D6E1YRgRo3CFSc9kv6MfnXcmO3x0d8plh8OP+IZ5ro74\nebAxbFeG8owQAj8IqNZq3HLLX/jWmT9i8WIoVw5BqYOASbz00s08/fQhvPDCv4dUj3qZO3cuL774\nIvl8nnXXXXfAerVMnVrM+3oZDbef4zjEUuIkBgsFA0jDhyJa6zRYxmH5Kg6lUonFixczffr05fjW\nFS/vWeWsXob7IWutkVFkLFg6wRIUi2jrHkxA/pZ2wroVsouoECaiMKyZSEPDxxUjWpysHMchhjTR\nstSaoI0J/NJLL1EqrZO50kM+/yNmHflLhNJIJH19ZUrzF1IQLkveXkxfrUJx/Dh8BT1vL6XD9fAd\nH1Urk0cR9lUI8nkqlSp9QpErdKJVjJ/zQYGMYmphRFdXN4HngdRJ6qx+mo3jjjuGhx76NzfcsCfl\n8tfxPIfOzs5l6t9skXYTN2lVJVFR7kBupZXJCjIaB4N6UUoxd+6LhOE9wCTApNaBZzjzzK9x7bV/\n5L77bh21CMJGsvvu+/PkkzsQxzdQq+VszXjppXs47rgTeOqp5zn33LOaPr8M8D2JYK4fu+zGldI1\nMPiGV/+sJfiUkWyo4C1PXEy7bbfrlE5oGXQCfbBl2P/XQy3aeb+17ChtAjh83zfRsb6D43mEUYjS\nMSIGtGDNNddk9l0388QT/2HvffYmiqKUtDZ1PYfxAMLV5TUPS6USn/7053n00Tcplc7DUPVk3/1P\n1lhjZBbd//mf0zj//J+Ty20A1KhWn2fbbXfk1FNnsdtuuw1bKa23sslIDsvKVn+Y9UbQ/9aAkPXU\nuMuB5uLnP7+Ak046BaXg6KOP5LzzfjDm71xZ5D3r1mwkQ12MrflfVWuGegKD0/KtHz4BG8dxTKVU\nJvA9PM8jBvLF4oCFM+vaTMtPOMIa1cXiQuJEocNxUrdGq3pfdtllHHfcHymVbgRqFAoHsO/eE7jg\n/84xrgAlWfDWItwlPfQuWYJXi1i0cBFvuYqufAeyWsVb2svCUi/FXJEl8xYAgokTJ7E0LFPs7iI/\nvoOiXyDoKoLrkhMukQPjpkxm+urTwRGIYp7O8ePw8/l0wZJScvbZ5/Lzn1/GrFlHcvLJXx90zOI4\nJqpUDOdVYql0ggBHiFTJhdGnJhkracf90ew73W+/L/HnP3cRhr9g4EakyOe/xKc+5fKHP/x2zOoe\nBAWi6AVgtQa/LiSXW5e5c19k0qRJDZ8fCv3FcEHOjfoW+iPaLDZOa43K0B+MtUt8KC4o2w6kHBA8\nYfnEwlqNKKE8IOEeVFrjJC7gRm7NLBbSugUdbfBokYpNJLlrcHlamqwdcaQodpj5a8tEi36lQpqc\nin4Cxl8erjyAWq3GttvuzLPPzqBavRCoT1/2Bzo6juJvf7tj2G5NpRRBUEDK5wGr5PUA19PR8UPW\nX38it9zye6ZNmzbkskeLr2w0ZagY50bP33LLLfz4xxdz//13o5TiM5/Zn4sv/mnDQzjADTfcwBe/\neByVyt3ARAqFjXnkkbvYcMMNR6lVK4c0c2u++xnehiD2ZNMOA7HdIB3Xxc0FEPh4+Vx6UskmBo9r\nIZ5UqCQ3nUd/bs9seZY1Wccx1XIZnaR/asRubq1tfhDg5QyPmOUmayUHHHAAxeKjdHbuQ0fHxnzs\nYy4/O/+HuMU8TiGHEg6+67Fg0ULoqfL2gjd57fXXEYt66Js/nwVvzOe1txbh9kTMf/k15sx7jfKS\nHua9MZc358+jr7dEh/Ap5nJU+ypUe/qIwpC876NlTG9YxckH5IoFnDoLouu6nHrqN5g799m2FDP7\njBsEJvosCMgVi+RyOYJk4/GDAMd1UcNQzGbPns0OO3yKWbNOHJCSaCzFuj+aRaMppahWq0RxaLi5\nMt/GZZf9jA984AF8/xhgSaZUh2r1Em6++UaWLFnCWMnMmUdSKMwEFjT4dS6gkqTpw5fBkmUP9mwz\nBnV7CLIp11RC6ArLZsNY0WK/EZHQNcRxTJSJOq2WSqhqiIgkUalMubfPtBOnLTydSDBm5bCGcjVS\nSyq1sol6VBqFQioTjCFjU24j3GQsI7SQ6Vo32inMmsl1113HnDkB1eolDFTMXqRQ+DITJx7Pfffd\nPiK8meM4bLHF9ghxU+ZqN3AopdLjPP74LmyxxQ4sWNBoLrzzxLqK3eS/oShmYRjymc98kQMO+Dqz\nZ+9DpfIctdrz3HDDYr773bMbPiOl5LDDjqNSuRqDQ56I636cRx55ZPQatZLL+27NYUj29O5oTTUh\nrxRCpESWWmtK5TKBZR0XBiNlN4NWYjYg0b8BNcFK1eNlWlkNrTJZKBR44omHueWWW1h3nZPYZqut\nkLHZ5GUYg4zxHIHv+fSFvbz55lLGOwHVUo2lvT3k/IDecpmKDIn6SozTgp6eRThLTJTqojCmq6OD\nnAqJlWJqYRzdhQLFcePwC0XcfA6vq5N8R8eo5LWzi8YywR11fUQbCndW7r//fvba6yAqlXN55JE/\n8eSTBzJ79h+Xi9WtmftDa02tVkMLCQjiWKW5FF3XZfz48TzwwJ0cd9w3uPHGGUTRYcTx/sA04Ekc\nxzV8XmMk55//Q3K5b3LRRTPw/R0plTYFNMXisyh1D7/61eVNT8kwuhiZ4UgzxW8sLRZ2XuokuMW+\nabC2Z6EQIsG7lvv6cISAKEZF0qRTCiOQCum6iMAnlw2OyZRf796NI0ku7/db7kOIQonnuygtMESw\nxhqWtiWxntVqNRAaTLXAMcqa53mpQbediOThRi2/+urrRJEG/gHEwIt0dl6LUv/g+ONn8T//8wTj\nx49vq6xW8tvf/pLtttuFpUsjlDoe0tFziOMzePPNJZx22llceOFPh1RuK1f7ipThwjE+//kvc/vt\nfVQqjwH9/H+12i688cbjDZ+59957iaIpwPbptSiayKJFi4b8/neqvO/WzMhQQ5SBlH5DJW7NIFlE\n4ihCRpEpL+FQ84UDroN23ZZuTSlNAmEnCRdv5uJo18XT6L5sRgSlFEuXLKGypIe8cKlVqyxdsphn\nnn8O9VYP4ZJelixaiK5WWbxoMVE1Jp/3TJ7Kcg3HESgdE9ckwbhOOleZSue0VeiY3E33+PGstdrq\niJyPM66bSWutwfhJE0fEPdZonOppG2QcN+2Xdsb54x//NH/9637ATGAeQmxMEMR89rMHcMEF59HV\n1TXs+g9XpJREcZhGKGqtjdXCW5Zr6Omnn+anP72QP//5TpYuXcTkydP43vdO5fOfP2DM69nT08Mt\nt9zCs88+B8Daa3+QPfbYo6k7MyuDjc1YuDXts/VM/JYoeTSzS7Rqi82a0S4+qxHRb4RGx5K4XAGl\nEWAs1R1FwwmYWJSb9a3t+ziOkTpKswfUajUEDkpLarWQQjFn+kkK8rlCqjwJIdIIWK011VoVxzWk\nsUK7aeRwuVxO+dXiUFFM+AhtnZRS6T0AKoZi3ZrZTHp7e/nOd77PTTfdQRDkWGutNTjwwD35zGc+\nQ0dHR/sD1IY8//zzfHa/g3nxpcWUSl8D9gcmJ79eyIc/fBWPPnrPkMtdnnjHsZR7772XT33qK5RK\nj5NVzCCko2N7LrvsJA44YNk16fTTz+R736sSx99Pr3V378j115/BLrvsMvYVX47SzK35vnKWyFAW\nfbuIZ5m3LeN5Ug+zaEpJrBSB56Edx9Bd+H6aeLbZ+7VunQIl+0wW+NvMHdsIzxJrPSC3Z7m3j6iv\nhI4lshoyb+F8Fi9cxOJXX+eVp16AnsU4YcTChUtBxuQdhzDnUa3WcBB0uwGu0sjuAL+zwLgPfpAp\na66Jn/OZPG4CHRO68aZMYK0NZlDs6Gh7M22khDXiqKtXxtwEKJ4dk3ZzqCql6OiYSLX6PDAFOAxj\nZP4Wudy32WyzV3jggTvbPsnPnj2bH/3oQv71r8eoVPrYYout+OUvf8iMGTPaet6K5UrKpjAS2iU/\nSJqhd5uMZONq9exIlaWhykipDhqlyNKOQGpNWKkiowjPdQkKBfzAT6M6bUaAVutGvXIkI00ul6NW\nqxErk99SK3AdL1XOrFglWGnzvcpYpQqh7wVpZgIhhHHLo/CcAN8LUmU5DMM0e4Gtj+cEg0Ycj4VS\n06zMlLIjDPnrX//K+b/4NbPvuh3HKSCEQ0dHjmuuuYz/+q//GnEd3qly7rnncuqpc4mibPq4MoXC\nweywQ8ytt17fcB3dd98vcdNNuwKHJlcWks+vx8KFr7e0vr8TpZly9r5bM5Fm1BSN0mIIYXIDWvoM\nnYDPLSBdKEVUq6E1uJ5LJCV+EFBs4afPRtYIMBitRLFoFGWT3UjcpP60uahbsLNI2hxJ4wIRrocr\nHPr6+gjD0ICKhcPkcd28tnAB5WqV7sDj7cV9LHIcOlyPSi2k5CqiWhXf85gYeeQRVCtlZK1Kdy5H\nn4jontjN1FVWMSk/2lTMGkWvNRqnOI4HpN5yEqWsPr9dLCXCcQal11iyZAlmrkxJrtwJ3AFMp1a7\nlCef/CiXXfYrDjtsZss2GNzEsVx77W2UyycD3wGK3HPPDWy99Q68+urzQ3KvmE1VpK5MNORyufeU\nYgYji3Zt5TI2mDQHndznj3BzH2vrh+M4RJhvWAhBBHiJIul3FPG0xtEaL7H82TqEYYiUZl5IBSqT\n4ixbdrFYTN2K+Q4vjW6NYnMQdWwC8jrLteMYDFoUgRYaXJFwo6k0ohP6MYDogRjA4Y7tSKMc2zkM\nZqNolTIp5dxcjl123ZWdd9mFSCl6enqI45hVV1111LOTvNNknXXWwfcvJYr2ASYgxF0Uiz9jt922\n46qrLm16wF1rrVWB/owTnvd/7Lnn3iuVYrZ48WKuuuoqHn30KbbYYiNmzpw5qmnbVrwj+x0gWbA+\nUprE4J5n8tO5Lm4yAbUQJsG346T8Zo4GnZxQB1sksgEJ9kTbzBpWr6RoKQeAw7NiU+ZYS1KchOH7\nQYBIQvHdwMfxXWKtiZWx+nU5Hp25HE7Ox/FcZKnMkqVLkVGMG1ZZWqkRCIcJwqEsjEUnlIK+MKZD\nCeJSjRjNGqtOZ0L3OHIZhXMwGQnwe6Rl5HI5pKxh7GpgcCsWyO5QKp3Nd787eCLxM8/8Htde+zTl\n8mPAEcAGwAfQ+niEWIdHH310SO2xQHDX8fC9gHwTXivot6rKhNfqfWku2fktlGp7vrZbZrOgnvp5\naRWodkUk641KMJVBPkekNa7rUsjlyOfz5Do6ELkcXj6PHwTmXRilwnEck/oqsbzVi+OYdFhBYm2D\nJADH8VKlQ8bmuaylrFqtppxn2ehNtEgzOqjYzEWlFCpmGSXG87xB76mXZgEf7Uiz8ZJSoq2XBBqu\nIdmAEt/3mTp1KtOnT3/PK2YA++67L2efPYt11/1vpk8/iIMOepI///kyrr/+ipbBQbvuuhMdHVcA\nCxHiArq7f8P55zcOHlgR8sorrzBjxuaceOJ9XHrpupx00q1ssMEWLFy4cNTe8b5bM5FWbs1W7odG\np60wDNG12sC65XJDJgFtdfKux72JpE6NUrfUl6UzLk37d6QUYblMz5IllBa+zaI336Rv3gKit95m\n4YK3eeOVl+h9cxGl3j7iqIrnBHi5APyAgpenpkwS5nwxz4TuTorjJ5FffRprb7I+q6y5Jp3jx+OO\n72TitGkpfUErqe9zleD6nAS/l6U4aOTWzCZ8zrZTOybd02Du69VWW595864FNgc+ApwN7JQ+lctN\n4aWXnmDVVVdt2oZVVlmXBQv+AGxW98tc8vlNeOWVZ5k6deqgfTFUaYeO490kI7VQjSaT+lDLHErd\nW7nXbIS4k1iMrWKRzbFp6xXF4QBIg8BpO0eijQ6t1Wq4njlAytiQ3GbdlGiR0j9YWgir4FmS3yiK\niKIIPzBWufrvdKgBAcOhoGjUd/a6tpb3Bsm+02TxCZcl0BYUZWWSlRnXprXm8MOP4/LLL2Czzbbj\niisuYKONNlrR1Upl990/y513bo6U306v+f4JfOELVX71q18Oqaxmbs13neVsuNYC61YkOYW2O7Gy\n1q7UVeY4JuVJ4gbQyUluKHVrdJKzi4hMFgupNWEYouI4PXU3s6Bl62kBzvUndq0UxJKor0ROaoTj\n0gcoz2XClGkUJnbjFwI68kUqImLB4rcovfU2TlSiGCsqcRUhXHzPpRyH+K5DWIupyRh8Dy+Xa3vD\ny1oV4jimr1RKE++C4YCz4+Q4TsOxy5ahlErpBlzPG3ScDzhgX3K5XyR/7Qhcla0dudyavPHGG4OM\noWIgpQXAwxSLO/PNb548JooZjMyC8E6TLL5J6ebW45VRhqqYNbPEZS03VqGJwrDhvY7jIDCW/SiK\niMI4XavaqW8URUgV43gZq5aWKYaNJIuA0pJYhSZyU/eXr1U/+W8ul6OjowPP9RtSfDSy3LUSq+DZ\ndc2+azh9CqRuyzhZd1HKwFaEIRgXiXckVgoJBMlaNFxL//KUdiy7K1KEEFxyyfmEYZVHH713pVLM\ntNbMnv0XpPzagOtRNJPbb589au9599ldrTWpCcN2K2mGRxlqiL/ruijfN8pOUq5WKokrb69u9W5L\npKRSLqd5O1PMWyJ2sokET6akJMjlGi5OWXwbSVvCMASl8RwPL/CJHYcJEyZQqlUJlQTPZUJvD/Gi\nJZQcSUdN0dtbRjohi3RMrljE93wW9fXgBIKpxW56K2U6iFl30iRy47ro6uxsewGwdYzjmHKlQqDB\niSW1OCaXkPxmx6rR2NkysidcoRRSqUH7/4wzTuX66z/CokV7o9TjxPHbxPF/A+sl/V0Z1G1x4YXn\n8cUv7o8Qn0DrIp73FPAiv/zleXzhCwe11Q9jIYOB4lfW03QjGW66q6yMFoVHI1xqszJbYZkajUFb\nmNhk3mspUVJBYPLKWqUq63pTUpr0Zm1kVbCS9rUSoDERmUnkcBhGBIGfHj7Te5ODgYfBmo5l2iLr\n9q9PkdSszGyfuq6LSg6+9vAqhIn69qzSa4O7tB4Al/CTsV65Z8pAGex7WllkZasPmG/U93PEcQXI\nRu3HuO7oqVTvOuVsLD62RsrMYBuaVSwAHCFS0O5w6qa1TlM7CSGQSqWpoIIgMFa1OEZpw5UU+D5I\nSVirkWsSyVevzJg2GObvXKGD0pKlKKHpLnYQVSPCShU6C4yfMJHakqXIWsykjg5qOkZKeHvpYsqB\nwwc6JxOUa/T0LGHShE6KXkAoIwodxWHl09Nak3NdHA1CgKdMmH8wiGs0OyYAftay2Ub/jx8/nqef\nfoQrr7ySD3zgGJ55Zg6nnroX5fKvgHl4Xg8bb7xxyzrsu+8+PPvsltx5551EUcRaa32enXbaqW33\n9nA3qsFSEjUDTY8UUP1OlcHmdzuyTKQn/RHDjcpstjk2CmLx6r711GXJQOXNFQI3CAzontgkKyeJ\nTrb/ToJigkxgjm6k6GW+O1tfKSUI4/oLQ2MlAxA45PO+wZdphRDGmoYUBL6H44iGhyellKHocBIF\nOeHldtzEBTuM76/RutZOWqz0GxDCuJ8Tt6uUMqVTsYfrrMvaKqNuEBgPxAgV/Pdl5RfHcfjEJz7F\nLbf8kCg6B6OWSwqFMzjkkM+P2nvedcrZWEmrKK/6yW8xUPbuKE7Snwxhkcme5u1CnOaoS0D99m/P\n9wmTk7PlWbOnu3aUQKVMJgNQSK3oDSs4rofregRS0ikj8p7LG1WjBI4vh7zBYhAOBeFTrUXoKKRD\nd6BzEaVqSGe1hlYgwxBHGoXKz+VSK93s2bMZN24cH/3oR9vqCyWVCa5oAzhdPyZRgkez7pR2paOj\ng8MPPxyAT37yk+RyAf/7v4eglOTqq69sC/A7ffp0Dj300Lbf2awNQ7EEN7MgQGtLU7PfssS+K5s1\nbbQIO5vN73alkbKlE3D+SMtJlbYkYCGKIrQDnnAMZiujvNmxjzKKhFUQlernNWxWq3oFPQ6TA6Yr\nQGhqVUOjoZRCKk2Q7w8OcISL53ks7QnB0biuQxTFePmByuVLL73EKad8h9mz78HzPGZ+5SBOPPFr\nKSWMEMm8GoYVtN3+tFbErMVUJ32ntaZWNVQkQikiMOz4GUtaGEVUSiUC10MnB+ZChkNtJHksl4es\naMLnd7pcdNF57Ljj7sybtyNhuAVBcDebbroq3/zm/4zaO951yplezh9bO9QOFpfg2w2yjbrVn+aD\nXM64LJJFH8eBRAkDcH3fXFMqVWDaSUxrrXKe1kSJx7Gjo5Ol1SqB6zEl8Mnnc7y1aAlTJpZ5LawQ\njXsbtcSnkHPw0PTES9BuQN73cGSMrtSQQZVybw9hrUa53Ectjun0PObPn88OO3yShQsLxPGrXH/9\n5ey+++5N6+d5HtUwxHXNhhA5gnySEaCZopAdE621wVQk+JBQGXLf3DAiqY466nCOOurwIT83HBmJ\n26EeSN1sk0ij0QQDQORZ8PbKbk1rpYiOloyFq7fZ5tgMp2TXgyiKEL6L5/bn1Mwqb1Yp1I5j/rO4\ntKTcWGtcm2uzwVpZr6BrZPL+ZL4ITS2s4boOSFI3IFqAS5JL00MpB0cItKMJaxFO3ny3L7zwAltt\ntSPl8leR8hagynk/PomXXnyNiy85v2HARL2VcKRicaxWWbWYYNsHtWoVVa3iIgijCNdz0b6f9pPj\nOMYlrDS4hnhcxiZafaTpyZaXjIa1+L0s06ZN46mnHuKmm27i5ZdfZostfspOO+00pMP/YPKui9aM\nM8nD7SYzlh9dfcJyIQRKiAHKmV0sswEDQ6mT1obsMA3pdpzUXZndNLLuTxuI0E7kpooiZBgSVWpE\ntRqlUpnS0iXEYYRc2otyBItLffS+8gZ9S5dSevMt3pg7l7i3Slzpo1apGgCy59KFS9XR+B3jWHv9\ndZi43tqMX/8DbLDNVni5HDt+bA9ee21/4vg04CL23fc+brjhipbtt8qG1oZXLt1IIHX5ZPshG6Vp\nx0cJQRSGCK1NYILvr9TRVMONIFSqNbO6VbYQyf8xEXIWSC1VQnCrwHOTDBUMjOxd0UmYl6fcfffd\nfOMbZzFv3lx+/OPvsM8++zRUTltFe2fvaeQutH9bZatVOa0iEq0iE0VRf/RkGCOkTOeM1Bovn08t\npdl3Nyo/SgKRvMRFG8WGPNbzPBOcFKuUPLZaraKFeV7GGtdx+78lz8P3fXbYfg8eeWQfTLojK0tx\n3Wm89dZ8CoVC6tZUMgliSP4eTtTxMu5mq7wm1nQFOBmeNyklYaWCiGIcR6CUIex2C3nz7kShq1Qq\n6HIVNzAZF6RUUMhTKBTartu7WSqVCpVKhYkTJ67oqqz0ksz7d3+0po06FMkGPZpRKD09PTz88MO8\n/vrr6TUhzOlKxzE6js1Jq0E0ZDZScrgKgXW92DLq/3YSpc3N8Jc120SyUTpCCCJpkj17woSIe5hy\ny0ikhs6OTgqTJ9I1aSL5SRNZa/oHmDJtKp3TplKYOJGOcROY0DmJar4AuRxTJ41HC0FULpGrKBa+\n8jrnfP9c5s3bJFHMBDCecrnWsK1pXZMTqeV9syc8IUxElJQyZemWYWgUMCEG9L/UGhnH+Ag8Yag4\nRB0mbWWT4XJgxbGJpLMuXMcjtaJBv6UJbb4dGwmnMRiiIAhwHW/E3+ryEquQjAWf24UXXsKee36B\nhx76Cq+//kMOO2wWYVRr+N1YS0SzKOBG8w5Ypp8HK8dGJPZHZcb9eLD0+f70TI5rkpjXl1e/dtSX\nbxXJOJKp0h6GIUr2U3XYTBXCgWq1inANZlXggFBGqcfB842C39fXx6OP3o9SR9X1Xjeum6dWq5nv\nUbipwum4/TmGhxN1XN+fjusitE553lyxLM9b/9xLynBNEEV2XXddl5pWSKmIophI6/d5zRK58cab\nmDJlDVZZ5QMcfvislXqdXZnlXfc1jVUUyq9//VuOPvo4fH8twvB1pk9fg9NO+zoHHXRgmugcILCu\nzFE0GVuwr7Bkty3aNBh2pr5/rMvV9TykI5BKUywW6avVCHyXVaauSm+5F6nAK+SYoLrpwGOe4zBx\nynjGKUV1aZmop4daXCZXrNZPFAAAIABJREFULuHj4eY6GdfdRUdnB9rVxL19XHz5b6lWH6I/rmke\nU6eOT90yVlILQGItdFxBgnwhcAcmeg/DEB1FKeBfSolKNiG7YWej5mw2h1a4m5VBxtLtYL8RoVmm\nTPubTgJYRgvTNZgMx3U4li7Xxx9/nBNOOJVK5X5gXQBiGTB//nw+uNbaDZ/Jzr16d9xQ1qVWc9ha\nrWzCcyElUimE7xMLgahT4NN3Z6zNreAOWTexVJJcPkgt9MJ3UFKjlUbqxC1oz/eivz32eYtBCyOT\nCF0Lhev6SNlDf/YNgD+w2mprMHXq1AFtN/O3aVXblvoyW4njOAjXRXjGsqiESCmAsnPSFYKgWACp\nUFqjnf41abDvb6wjoqMooq+vj3w+v9xTu82dO5cvfvErlMt/Adbjyiv3ZLPNLuDYY7+63OrwbpF3\nnXI2VvKNb5xBpXIzlcoOgGTOnLs4+uiTueKKP3DD73+Tpm2o5x5a2cUuOMIxFqWoWsOJJY7voSJJ\nLpcjVyyyuK+HrvHdRK5PMQiY1p2nTyo8RxBXasgli6n1VCmHFWPmdyDfNY7OCeMRjsNdD/wdIbYH\n+je2rs7r2XO3w6lVq+QTegwbwaW0dReD6/kmRZUgxe5pbfKPojWOVGne0mwQhFYKT5joq0iavIN+\nMiYK8FdyAGyrzb7Zgut5HmE5NGGtGLemV1x2mtcrXXaTtd+vVcKWF6ZrOEpWowAGmXEFN0st1E79\nDz/8BKrVM7GKGWjC2iImjJ84qAWzUTCHcJxRo1rQWuMnbsn00KG1wXhhxs6OKzrJWtIkarSRZL87\n6+JMk6V7CeFqGKKETq1i5vvUuK7pZ1eYHML2NyUVnudywAGf5/e//yLV6s+A8cANFIvf4sor/7hM\nvcbiYOA4DtJxUtJZa5G2YyqEwA8CnKR/fWdg7tFs3xTy+TSYKhAmn3KkVMt8rCMJ9BlMSqUSn/3s\nwdx9922Ai5Q1tI6ZOnVttt12G3beeRt23XVXNtxwwzFT2K655lqU+gywDQDl8g8477zj3/PKWRzH\nPPzww1SrVTbffPO20va965SzsYpCKRY7AXuMc4FPUCp9nPvuO5DPHTiTm66/InWnjXYgQjZSSymF\nwoBQrQxl82nYP4l7Q8YxKooRgUdQKBCpsuFKyufo9Bz8ICDuqlFesoTxtQIirOC4Pk6X5m1XMGWK\nh3AE5XKFznyRmgv5cePonjKRm35yEeVyFkz/FPAMn9rtk6lbwXEcwloNVIyKjeXMC7wBFjDfC4iT\n9voJDiaOJY5OTsWOk1rGrKXC8zzj6k6AvAoTYLGyu+ystLugWxdoLpdLwc5esTGzer3S5QV1GKiM\nEjbWB41lQOhCDeDlaneczLcQ4fmJlSQyKYSs+81eG0zxe+yxx3j88WfQ+rDM1b8zZcrqTJw4sS2l\ncZnITWhJtTBa1pThKtON3p9VjrTWBl/mO6k7PItFdByHXNCfVzDfYQJRoigiFxglRqP4yfk/YJVV\nf8zFF32cWq3MttvuwI9+dCtbbrnlqLVlsP7xfJ8IDN+h56VBM9k+cF13UDeldbfa9UZJCXEMnoEF\nNJqnY8kv9thjj3HnnX9ByqeBtZKrEfPnP8dNNz3Ibbf9A9f9Mfm8Zt999+Kkk2YxY8aMEb83K3fd\n9SDV6qcyV7bjtdeep7e3l66urqbPvZvlt7/9HccccwKwKo7TRbX6OAcffAg///mPWmbLWblNB8OQ\nwTAbw5UTTzyajo4Tgb7MVZ9K5Ur++tfHuPfvfx/V92VFCIHrecQZF5dMAPKNsCytsDfN+se+I8gF\nFLo66Z40gcL4bnTOJ5dPmLwLARMnT2LylKl44zpYbbXVmDhhPLlCgQ+suhqimCPX1cm0tdbAX2US\na226MatvthFT11+Xt5f20L9gQLHwbU464Vi8DPu3UgqhNTKWuJiFq1KqUK1UqVWqUIuJymVUGBqK\nkQSL5vge2hFox8FJsCGN2iw8DzcIyLXISbkySnZBt1i7ehyHtT4pbbio7MbWqp12A7bvgGUxUO3I\naOK+su2o1ircddddXH755Vx99dU899xzA+6tZ4TPphGyGKUUFzUE3NIdd9xBFO0P9C+cxeI5nHzy\nrBEpTc3WpaHOYYuJEsJkCZGJK81agZrhyZqNU7bPs1kW7DckcNK+1agBgSQWH2YVGevWtPVIc8Em\n5eSCPGeddTpvvvky5fJi7rnnTw0Vs2y/jSb+USfrhicEQYa7rN0xSCOck35XShGFoSH9TXC7tt7D\nzRIw3Pn00Y9+lJkzD6OjYw/gTxhjgg9sDMykWr2IUuklFi26hV/9ahKbb74je+55AC+88MKQ69hM\n+voqQHfmio/nddHb2ztq73gnyQMPPMBRR51Eb+/t9Pb+m6VL/0at9iJXXPEsp5xyestn3zk71BBk\ntCc0wFFHHcG++36IYnE34KXMLzmiaDf+85//jBmA2oJvHUitCXbit7Nx10uz/nFdk5vTdV1yuRxB\nR5Hu8ePwigVyXUWmrboaMh8QdHUwadJUcrkCec+nI59Hak2hUKRYLNA5rovpa67B+CmTmLLqKkyc\nMjl5j+Vr+yGTJj/J0UcdhvDMOy1ezEQp6tS94Hk+QrgEnsn95wvHYG1EP2+X5/uIIMDP51NMiF08\n7cZtOYzeCSD3ZtJq0c5an9pVQpptykOt00jTwGSVLOu6vf/++1lj+gbst98pzJp1F0cc8Qc233wn\nNt98B/7zn/8A/ZYVqyCMFt7s1VfnE0XTM1duZvz4pzniiPZoVJoFczSbd0Odw9nDhpfP4+Xz5uDh\neWlwQP0YtBonG6Fp35n9dlLrUCbIIJvI3F6LwtjgzrQkDEPiOE7H0ipogZ/Dc/uDUZrVdSylWV/b\n6/YebdeijGT7UCRrTKw1EoHr2TFt/f0NFugzkvkkhODCC3/KFVd8n3XW+RadnZsDFwGvZ+8CNkLK\nM6lWX+S22z7MZpt9hAcffLCtdwwm6667BkI8n7lSQsre92zU5s9+dinl8kmYHM1WJlGp/JILLriw\n5bPvSuVsLMRxHH7zm4s4+eS9KBS2olg8ELgU+CmedwObb775YEUMS4YzWYd78nJdF8f3U44kL5/H\nywX4+RyFYhHhOnR2daI8B6U1YaVC2NuHiCSO69Dd2UGxu5vuSZMZP2kSHV2duEGAHwQceOBe5POn\nUCh8jqlTL+Tee2+le/Jk/ELBgPfj2Lh/VJLmSoNwXAqFglnIUIkCEaenemuJEJ5nolQT16xdPIEB\nOTjfqUqZ4zgmj2qtRlyrmejUDH3LUCVLuWCtbO0qdPXSrlWv1ffY73o2uKIwDNln7wNZvPhienr+\nSan0W3p7r6NSeZV///vLbL/9LmnEdFbhMTjD/o3PUjgMJd8iwBprrEo+/wTG8nANxeJMrr76shRX\nOpjUW8laKU3DFdtu65YzDPtxU0W72TgNVxnIWtXiSKYBAVprYhkRyyitB/RT/Vgy20qlglTxgLpq\nrZkzZw4PPfSQoeVoYbkaal+289xgfVHvktTJmpXzPWO99DwcPxO0xbLf2mCenXaUxFYihGDffffl\n+ef/xTXXfJ+99/4rHR2b09W1KbncMcBvMZCShYCHlMdSKu3LrFmntP2OVrL33rvR0fEH+iFAt7Hh\nhlu0PXfebZLP53Ddvga/hDhOa1f2u47nrN32DBfjobVm3htvcNONN3L7HQ/gBx6HH/5FPvGJTwy7\n3q3E8l0Bae5MEguX5fiq5/EBTIg4jfmWWkk2UlIkLgC7oAMorSn19iKrNao9Zao9S6nVqhSCnCFm\nDALGT5yIk7g4852deJ5HpVLhZz/7BR0dRb7whYMGACKznF5KKaqVCiQbdi0MQRtrmtYmg0EuVyBf\nKCzD49aIc04k+I93ukRRRFgupxQACozynIngzYLqm3FCZe+zm1WQcDwZUPnQOMwG42Nrp15ZTJ3W\nmufmzGHLrT5OtTqPRrBY35/FKadM5swzl3ULNJrXQ53rb731FptssjWLFy9mlVVW44YbrmCLLbZo\nu0/q69MO/9lg9wwmrfjP7O+NxgmMkhHHxvJlSIndhtx49WMIRpGuhYbfDC0QOLie08+Rl9QD+oML\npJRIFaeULfaeI444jiuv/D2+PxkhFvHjH5/FwQcfPACw38433mgM7HNaa6JaRC55LsuVWKtWcew6\nhEm/lV0/6tM2lXt7ufjyX3PhRVcxb/6rTJ2yOnvv8wlOO+0Uxo0bN+i31ui7tGuYdccbq787rKhL\n+11pKXno4Yf5+/33c89fH+Vf/3qU3t7FVKu9OI7LRhttxQ9+8E123/2TQyq/kUgp+dCHPsILL2xD\nGO5CoTCL66+/tCXR+LtZnnzySbbZ5uOUy5cCn8bYw16kWPx/fOMbe3LaaafaNWqZwX1PKmeNFsNs\nHrzhTKqxkuyCkLp93IEunGx9tNap1cieZB3fbwpubdSWOI6Jq1Xc5J3VMMTzfXK5HFJKauUKURSi\nY0mtVCEOQ8KwhtKafKFIUMiT6+ogVywSZMLQ221jWKuBVbjiGNd3B7Q98HOptSBbbrbe0E+4+W7g\nHwrDEMJwIEYsCNI8nbZ/bGBFsz7PbuJaGyqSrNVppCSfQyFNzdYpqzhIKfnI9p/k8ce3IIrOBrK5\nSGMKhU9y9tmfYdasY9uu51AliiLeeustVllllRHN73bJhEe6pgzWz83GyRI2a62p1QzlhZPFiTVY\nY7KKRBSHKC1T5U5J815LxiqlNG5ny6WH6VupYnwvSMltK+UqkyatQhzPx2CWHqFYnMn++2/LxZec\nn7pQh0OIXN83SqnUtZrt6ziOUQnvY2rxchv3YV9fHzvs9ClefGEK5cp/AxsAr5DP/4K1136axx77\nO15iMa0fUztX4yhK19hskFKtWgU9UEm0iuxQv4nhEFmPVBYtWsTxx5/MU089z+mnn8A+++wzpu9b\n2eXuu+/m8MNPYO7cuXheN9DD1742izPP/Fb2APm+cgbLfrRKKUPRkKFZWFncYEM9VduTl0wwalpr\nlOs2TIDerOwoigYoAlEUGaUoCIjCkLgWImWMkoaEsVatoCKTjFx7Ll7RWLbSZOOOkzJwD9ZGKSVK\nSvwkRZOKImKdhOwPcop8tyhngynMMLBtQ/lG2t2oRlrfZu9rRznTWvPW4sUceOBXePDBh9F6X6rV\nNQiCBfj+rWy33Ub85S/XtYx0WllkeW2Q7Voom2Uk0Mk4WWs0MKjiY5Uzq3RJaaxnjnDxfLdpBgqE\nJgwjfM83hwst6O3tZbXVPkgYLoaUgbCHYvG/+N73D+WrXz0SrRgY1TtM5azZc+1aOZVSXHTRRZx4\n4o2Uy7cyEGem6ezcgd/85kQ+veeeAzwaNvm8ktKk2Ytjotism0C6TkspieVAJbFe0W6m9DXLlGJ/\nb/fbe/nllwnDkLXXXvsdt36urPL6669TKpVYZ511BvRpM+Xs/V6nP0owC4JtxJe0IsRiFNolI3Uc\nh5rlPxJiIOlq3aRsFtbtOA4xIHQ/wz66PyjBywX4TrKIaE3QUUAojeMkLjchwBJfWqxHi9D0Zm10\nHAcphMkjiEALyGUoMBotUrYcZakzBpHlaQVtR+o3WUv94LouyvcNJg9S6xgMLTy/njsKLUYMpLf4\np/p2WMutkhrHtZFyho7B4gZtnerpXaZOncrdd/+JZ599lltvvZXXX5/Haqt9kG23/RXbbbddw4PG\nyjSOVsaK2qdeLAasFe1Eo3GycyYC0AzI2Zlaq2ncp47jmEhOKY3ShIPnGX6zOI4HBD9ooVGS9G+/\nGKQHA9/3mTRpEh/84AyeffYmYL/kDd2Uy7/mW9/cmS996SDGdRvC6qHynrXLl5ZdP7TWCEjXQ9t2\n24ePP/4s5fKuLBsAIBCikK6VqccjilCJEqsjmbpzXU2aAUVk1mkb4FNf32brAwyEt8RSGmJxmtO3\nNJLXXnuN/fY7mCeffBrXLdLZKbjllj+MGab6vSTTp08f/KaMvKcsZwM3DJlaIcIERG4/3FgpYylK\nlImVyZLWjljzfFYauTabuUw9z0tP03EU4TgOnu8TxjGe4wzgBZKmoDTnnNaaWpL43ebbu+TyX/P7\nG+5kzpxn6eoax7e/fQIHH/ylhnWvP73aE6dV1rKKWSPXdBxFqOS6YmDevMHetTKMc7NTvpMQZzZy\nWw7VOjMURWY4Sk+jMRQJ/YtVvOv7eiTKVbt4uxUlK6vimJX6PmyW1xIG5gMFGn6XcRyn1h+LJdUK\nXK8fP1ZvwbrzzjvZZ5/DKZcfAiandevu/iSXXHIY+++//zLvb7cv68egVTntrAt33HEH++57GOXy\n3fQTa0c4zs+YPPknvPjik+STZyzGLs3wEsc4wjWBPZWaifR0TVYCv1BIreGN6tdsfUh+bLiWtwvX\nKZVKrLfeZrz55peR8hQMPupXrLnmD5kz59/vW9DGSJpZzt4z0Zp2wrUTyVcf2SSShWt5h30PV1zX\nBccw/pO4CVWDultgeT9Xj0z5w2yovh8EKW4s5/vo7GaKiYYjiSZUyjD1O8m1m26+mbXW24xvnXYn\nf//7V1iw4C/MmXMOhx12JEuWLGlYd3t6bRbNlAYsJMERdoysC9dxk/x5SW5RlGpKETEcGpKxEK11\n0/6wv8dRhFAm5ZSuq+Ng4fn1Yk//g2EB7Yb95sIF3HX3bObOndvW91/frxZX4yeuUwAtB0YUtlun\nZu8bKo3I8pR22ma/65GuMcMtR4iBEbOO4yyT19LOu2xEKJg1IAiCgYe2pA6xjCiVS8Y65ArCWpQe\nkOsjZ3fddVeOPvogisWdMRGFRpQaR6VS6Z+nGeWq3TZmxwBoOyqz0bqgtWbnnXfmjDOOp1DYiu7u\njzKue08KhTXZYos/8sADd1EsFhvOSRt5LaUEIZAOOL6H53sDvo3hzofsPoeUKRdkO+X87ne/Y+nS\nTZDym/SrBoewaFFtGY5BKwsWLODKK6/k97//PaVSqe16vi+Dy3tGFa53/bgAGTO/yOTH9ER/dGJ6\nirKTWo5euo2xEiGSZMeJNcvPLGZZa0rq0kjal7ogkgUl7ZuMSd/z/RSsb60gfhAgE1O8vfbVr36d\nK674M+Xy74CPZWo3HtAUCgUDFm5wmrMLU/0JNkoSeLtCmEU1wabVL2oWbxGFoclJCsQM3yo21paP\nQw/9Kr/5zYWsv/6HufTSn7DNNtsMcMEIh5Zuy6G6vtsVKSWnnnoG55//c/L5TQijpzn/p+dy2GEz\nh12mVfgQhi4lisbOyjXccRvOc7VajRNP/CbXXXcjQZDnc5/7NF/72jGsscYabb1vNHKE1s+X7Fo1\nWJt0ciizq0MUxzjewPvqMzngNHafK6VwXEHgBkRRhOcZC47ruoicSMD9bkPX6znnfJc111ydU07Z\nCSH+Cyk7EOIedt75x6PWVyNh6c/28fHHHs2hXzqI/zzxBL29vWwwYwbrbbBBWo6dk47j4Mp+a6FW\n4Ljm71w+j5vUP7vvNJNWLtpYSrSUBo6SwEFse9tp2+zZD1Au71F3VaAzlrqslMtlNt10W0qlD+M4\nZbQ+mu985zROOGHWoO96XwaX94xy1kocxyEWAscqZBnFzGIurOIy1Ik8HJdQK3N7u+VZBWeAq6vF\nffbfWXEcxyhElmfHcfpB/nVlZE3ev/zlRVxxxZ2Uy48A4zJ3SorFmRx66FEm52WiYDVTmlIsoLYL\nkVE2bXi7Sk7njmOSt1ulJIwihJQIqYgExuInJWGicFoFrh080GhtnK3kr3/9O/Agzz33Krvt9lnO\nOed0jj76SMAsvO1YgRrhiUYq11xzDRdccDNhOIcwnAI8w3HHfYyPfWwH1l9//abPZftVa02slMG/\nKAVKYZJgD33zaPW++g1LeGJY4zbc8f7ud8/mkksep1q9AQg5//wruPDCLbjiiovZZ599Wj6fuqpU\nYhUSOk1fZRUr285W5bTCkA7WpvpnPcchihXC73drZiMu25H0mxT9+EIz95q73B3H4dhjv8oBB+zP\nn/70J6rVKp/4xCmsvvrqaT3bURBHIq3WhXqr2riuLj62447pYbJh+6GfdFdJ8klWFK01URim71S0\nTkpvy2yGLbTYQYvnVHa9bLPdEyeOQ4g3GdiMv5PLxWywwQbL3P/MM89QqXRSKt2QXHmOb31rP15+\n+TX+7//OXqkNGO8Eec9gzgbDETTDJNgEuVmcRDsRL62wU80W3FZ1HCo+qt37rQIaR9EyeCDALB5W\nORgk6hLMRtPVNZlK5QFMeLmVNykUjmDjjZdw791/IpfLpe9v1p/1EYq1xMJn08NYzJvOKGZRgiXM\n4rBibcgvY6XwEib5bFRaK4W33UivkcjHPrYn9933/4ADgTkUi3vyve/N4vjjj03fuSKwceusszkv\nvngusGt6LQiO4fvfX4evf/3rLZ/Nup9tSiWLY9KoAYrHaPRno0i14YzbcMd7jz0O4NZbPwMclLn6\nEMXintx550185CMfaTheWmtDuCpk2kda65QqJqxFBLlkDRgES9eKy2w4EbMqs05Zl+VQufS01kNq\nQ6Mysu8a7rjWl91uVCYsi/nKYruiMEy9Du3My0ZMAUqMLFo6K0opquVyanWJgXyGs66VPPnkk2y9\n9cepVK7EJC6/i2Lxq/zud79k3333Xeb+119/nfXW25xq9Q366W4WUyzuyFlnHcnXvva+Ba0dSb6l\n9y7mLHXJNcEyicwESdN5OE66kbeL57FSfxJVCVBdRRGl3l7iWs2QDWbwDq2wDkPFRw3WXhiIZfIS\n65NOwP/25OUmVjHP83CTa61k/vz5xLEEbGTKW7ju9ykUNuGoI9bnrjtubEuxldJwJ0VRRBhGBvMX\nxwY7F8cGI0eC46DfMmj/7fs+IjmtIkzEqe+6OG6iECT9V4/tGC3sz1DkyCO/QGfnJclf61Iu38Ip\np3yXu+66C2hvLEcq9e3WWvPKK08B2w+4LwxXZd68Nwctz36nnu+m35LGzCkLYK7HHY2k7+vHcXnL\nlltuRC53X93VrSmXz+Woo05qOm+UMjkrSdZmm0YpJWf1+i0hg2Hphoo9bPWsxZAKhzRHKQzMp9lM\nybLWHUe4uI5nCG2F21Z2hmy/NMIROs7AfKpDKTNbv8HmU7PvKdtPYAKOnKSs7EHafsf2gG+/aYs5\nixOiWZX06WjmDg0SvLDwPENv1OZc2njjjbnmmstYa63/xvdXY8MNf8Cf/3xVQ8UMTPThxht/CLgm\nc3UC5fIfOeWUb/P222+PuD3vZXnPKGcw+AJeD6aMLeB1hBujVazAWKI8qVIusiyFRzMZCci3VXuz\nCp+TcVmOZJFYbbXV2G+//QmC1SkUViGfX4dP7fEY/3zgDs794VkUCoU0CCGOYyI5EM9gx0AnVrO4\napTYsBbiYPBtwvOMFTKJAMyOl7X8aW2oRCJIgwPaOa3Xj7897Y9kMxhM9t9/f1z3CeCh5MraVCq/\n47Of/RJvvfUWMDrKR7PvyFop6oHeXV1TgHkDyujsvI/NNttkSO+sL9v2qcBJN/hGfZ8qCsP49oe7\niTd7brB6zJp1NIXCjcBf6n45iMcf/0fap/V9Yzdwz/NGnCO0mdLRTptg4DrnJAeZeuWo3e+w/j6r\nbNnE6cM9+GQVv5H21XDmU30f+0kgRPZwZ79jHcdUy2V0skYNJ+/scGQka8Vee+3FSy/9hzAs8dRT\nD/Lxj3+85f2/+MXZFIv/Dfwnc3VtHGcPrr322iHXfTRlzpw5HHbYsWy44UfYdNMd+d///Z4hWn6H\nyLteOSuXyzz77LOUy+VB721mnRrOx97oFAu0tH41ekYIYUzw2tB/RGFoLHuMjpLQatMZzklcCMHV\nV1/G3Lkv8NSTD9CzeAHXXnUp666zjrGeCKNgxRnwejZPpB0DrbWx2jkOjiPwXRetB46F1hrPcVLL\npopjQ/fh+8TJuBVyOXSSSF1qw7llFbj6tsgEUJu6M+i3wo12cu2s5HI5fv7zH1MsHgJUk6u7UC4f\nyKGHfnVU3tFIScr2eSMrxf7770cQnIFxjgD8hq6uF1JKg8HEcRxkbCyXQKIgmE0rG3Vq66YTJcHO\nDetubxZV10qGu4k3eg7ghTlzOOwrxzB99Q0oFicwderaHHnkcWmU7bRp0/jTn66js/NQXPc7wFtJ\niQ9TLI5L3fhWbJttyiSrtHqueXeKG4r7ubLaUTAbrVXN2tRIIR8L66O1XluPhP13K2mlXI+1lVQp\nRRiGhMlaayWrTFvMqrWMNfJ+aK3x6Ld8OhgLpCv6sWgyigjDMH1+pJb7kVhPhyPbbLMNl132MwqF\n3YB70+vl8sa88MLLY/beweS2225j88234/LLJ/PMM+fy+ONn8P3v/5099th/uXlERiorDHMmhHgZ\n6AEkEGmttxFCTMTYSNcEXgYO0FovSe4/BZiZ3H+c1vr2BmVq6w7TWvPDH57H//7vWQTBNKrVuXz0\noztz8cXnNQUzjzabt8Ut6ESxQjVnhR6A9ajDzjTirxkNJaEdfEIz7MVg0irtVLZN9h0kLuXIbsaA\nDENkGKEdkWI6LK2HAoTjIJL+DWs1hDapZ3Sq1PVjB5UQAxb3RsEWg+XWG0wG66tWv2ut2Wuvz3Pn\nnVOp1X6WXK1QLM7gvvtuHHZuRyutsFTNfuvr6+PTn/48//rXczhOjs7OiFtvvZ4PfehDDdvRqH1Z\nviutNUiJ63gpb5t2HANYTr6JLBZQYqKqR2s+Dleuv/4GvvSlw4njI4iiLwKrAfMJgnPYaKPneeSR\ne9MF/9VXX+Wkk07nT3+6EdftxnUjLr3053zuc/sP6B+tdZqKSCduLkvIaq1a0L/Jw+hGCreT7qld\nfNlgAUzGhRemoHqpNUEweOaO4a49I5Fma6I9JFtPh0xclGmgAAPTYQnRnyfTriFa65QU1lAzRSZo\nWTgE+Tye76eZXbJlDrXdK6Lfbr31Vg46aCZSbkiptDX5/FVcddX57L333mP+7noplUqstto69PRc\ny0CmgJiOjhn87W+IEO9SAAAgAElEQVQrF6luM8zZilTOXgK21Fq/nbl2DvCW1vocIcQ3gAla65OF\nEBsBVwJbA6sDdwLra61VXZm61NuLB9xy22184eBvUi7fDnwAqCLEL+nuPof775/NRhtttEydrEl6\nLIDXVkGxCcW11uA45PL5liebsUz/MpaJwlsBjKWUeJnTo9Ya7TgmGlMbkG0cx0ShwcMFvk+kFX6h\nQJDLpQuOUipdMIW1JibKhsUL2vKt8le/aNmFTErDf6ekHDTtVSMZ7NtpZ7NbunQpm2yyLXPnnojW\nhyX1/AGf//zzXHnlpSMej2abcau6aa154okniKKIzTbbzESyNWgn0PR6GJoUP1JKhNQEQdCfaBtw\nkvdZNz9uQsqZKN8rUjnr6+tj6tQ1qFTuALaq+1WTz0/j34/dxzof/OCAdlerVRYsWMDqq69ucKt1\nfRxHMiVk1XrkOU6HKu0EPjSyFGUVRWieiDzb3jiOCcs1cvkEyyo1fiat2opQJppJfQ5bKSXKui3t\nOpG0SSsoFAr9ls3kGRtcBRBGkcGAZQ58Ya2GjEOEMlHLrmcsmrjuSnEYGa6EYchNN93EM888w1Zb\nbcUee9TTciwf+cc//sEnP3ksPT0PL/Nbd/dm3HXXZWy55ZYroGaNpZlytqKpNOortDewU/LvXwP3\nACcD+wBXaa0j4GUhxBxMOMk/6gv0MBP80X/9i3J5f4xiBpBH6xNYutRn5szj+cc/7li2MmJs+KJs\n2a7rolw3jX7UiYKhk1NYo1On1oZKwk7PRnQPI63XgEjUUZL6cPQ4UaR8YehIylFkgMKJGV6Q+NiT\nPojDiDgKcTwTHu57PkIbLibh+yZKCsN5FiYRmiRKmlCKSiZEXSYuUpm4FCCT3sSeVBNXgmcBtFoP\nSTEfjDupHQqAcePGMXv2H9l664/R1xej1FEodTA33rgxSl08IveEEII4NBuL4xgAuuVHsm6vRuH5\nQHqQscpto3ZCYy62bJ2ttcwQcCYbk+MAxoXj+X4/s7lV+JQa89RHreSf//wnvj+DSqVeMQP4D54H\nUydPxqZ7s4eGQqHAWmutld5ZP/6uZ1y+whfL0PWMFj1EK6WnFV9WVmy9lZZUy9U06lJGCUdh3Tct\nM1YjQ6FhlLogZwhuEQPdbPVK61hQ1QxX0gNXUpcwDHF9FyGcZcbJ3uu7bhpc5fk++Sx/ptOfYk5q\nCUKldDLvBgmCgM997nMruhp0dnYSxwsxEJF85peb8f3FbLzxxiuoZkOTFYk508CdQoiHhRCHJ9em\naa0XJP9eAExL/r0a8Hrm2dcxFrSmssb06XQU/9Xgly/z8MP3NrhuZCzxDNnoR9d10TbNUh2eJgsq\nHSybwUikUYSWPS2PVFGrB84iRIq/AMh5HnFyMsy2SUqJDCPCUhldDol6+gjLZbTdpKOIpYsXo2q1\nlAHbFYIwsbporYmlJOe6hGFIqVw2lrBMSqss/sMqFAPyVDoOYjmeWJ9//nlOOulkLrvsctZdd10e\neeRvTJ/+U/L5Q4BXqVSWLINtGYroRKn1HQdHmQ3QKhFZq2n9d98Kp9auWEJSz/PwfZ8gH5jcq8m4\nWxd1Wo+My77+G1oR5M+bbropSr0AXA0pcrSMEBdQKO7OeT/5HhpNLawhVdx2Hw0XE9euDDZ27bw/\nq1BqPXjkaLN32nXGKmyS/m+5Gd5xrMWuefXieR5x0vYoiohkv9WQpA3W60FiSdRaD+BZzAZXWXb+\n7LxyXRfP9dPnlTTleZ63XPFiw5GHHnqII488jpkzv8rNN9+cHixWJtlkk03YbbcdKBY/AVwL/JEg\nOJZx447gj3+8mnw+P1gRDUVrzdtvv82rr77aMMBntGVFWs6211rPE0JMAe4QQjyT/VFrrYUQrVa5\nhr+dcdZZiATDUSj+h1p4FnFs84QBPEtn58TRaQHDN8kvE3ygB546Ha3TxN312QxGS7KWQosHssrg\naGRCyCo9cUIbkuJOlMJL8GPQb2mTUhLVQmQtInAcRCyp1HrxfI8gF1CrVvGkRhFTi63FxcNzXWNl\ncV18z0PGEgeNh8GKeL6fBmA06sf0RIvBOg11URyM0LaZpeLxxx9nu+12plz+CsXihdx221+55ppf\n8eST/+Tb3/4u11xzMDvtNHNE45J+a9bVUq0itUm+jBbkEldxo+fqLSO2bY3a2aj9jTZaa4HTjk6+\nEd9ktEiwgtm2iTH47ocikydP5vbb/8j/+39H8+qrR+D744iit9lqq+35wdlXsfnmH8YwqCdKRZPv\nptH4W5oRi7VMD2dNrFhDkXYstSPt2xQmkLRJxirltLNYRillopi4ODnjqvaSg0GU5O1dEXLIIUfz\n+99fzaabbs3pp3+d3XffPR2LfLFIFEXEUpLPBWlKOz8ICBOcpJcELAz4bttUKoUQBEGAlG56GLTK\nmxgjz81oyG9/+zuOOuokKpVj0brAddedySab/ITbb7+Brq6uZe6fN28eS5cuZcaMGcu9Hddd92su\nvvgSrrvuSqIoZqedtuKYYx5l1VVXHVI5Wmv+8pe/cPrpP+LJJx9BKYHndaBUH7vssjvnn/8DPphA\nGtqVe+65h3vuuWfQ+1YKElohxOlAH3A48HGt9XwhxKrA3VrrDYQQJwNorX+Q3H8rcLrW+sG6cnS1\nUkElnDzz33yTT+91IK++WqNW2xkhJK57FRdf/FO++MWDRox1GCpGLXu/lCbfpSV1VUoRK4VvAdqZ\n35YH9mAssW1gsCnV3j78pPxIa/JdnSkuzL6zVqvx9psL8Sshvu9Ti0JqcUxxwjg6OzuIQtN/tSjG\nEeaEKXyfjs5OE/VpGoNW2qRIkQpcB8f3DZ7M7SeMHODWxACVgdT1OVTM4XACAnbZZR/uvns3tD4G\nKFMsbsQ991zH1ltvbeo0CuNiywCoVqtIHSO1whMenuciHK8htq5VEvZWAQEDMIzCBAVYi0itUiOX\ngN5l4spsRW2zMmCRbOLqRYsW0dPTy7RpU8kF+f4k4Qk3mSOSNEVOY9xmO+D5Rr8Nt86jQdY6GJks\n9Fu6skEO6XXdn4rNxqzbKFVHuIhk9tUnWB/rsV5vvS2ZM+ckADo6zmDLLdfmkkt+wnrrrQf043Ht\n+mAxqEEuN8DqloWFjCZeud21pL4eY9lvq6++AW+8cRnw0eSKJJc7hC99aTyXXPKz9L4HH3yQY475\nBk888Tie10VXl8M999zCjBkzxqxuYyFaaz73uUO49daHKJW+A/wXMDn5dSGOcyGTJl3MSy89RUdH\nx7Df0wxztkKUMyFEEXC11r1CiA7gduBMDBX5Iq312YlCNr4uIGAb+gMC1tV1lRdC6LhWG7hZCMF9\n993Hww8/jOM47LXXXsyYMWNUwP/D2TgHYMksVgqIpEwjDLUeOvP0SGWslTMpJSqKiOM4tRB6uRxB\nEJixiGPjuotjKn0laouXIJQmyAUo10EUC3QUiwZPVq3iug5KabTQFIpFPDfBwpAAchP3SxhF+EnU\nJY4D1jLp9HNsZTeXegC6zix4o734xXFMZ+dEarWXAWPN9bxvcNJJOb73ve+k/TbScbHfupaSKA4J\nZYTvGsZ3gaFvcINgmTLbCWJo9q7svHI9zyhm1Spexs3VKhp2NObnaEkjRUfgpLQQ1sXh+34acTlY\nPcda8RzO2A1Wz/Sg2KTOgwWWZF2etp/A8N2N1RxrJmec8V3OOeephA0/xHHOp1D4AVdffTmf/vSn\nBxxoUlyw75vk8E2+TXvvSNsx2LdvfxcW/pL8biOdh/re559/njPPPIf/z955x9lV1P3/PXPKLbtp\npAEpQCihd0Ioj0I0goIIAqGj4A8Lggrq4wPYQGygAoqAICCKNEVBFAQUEB5BHopEgZBEmiEJJWXb\nLafN/P6Yc+6ee/fu7r27d5Ow8n298kpyzzkzc+ZM+c63fD6vvrqCL3/5Mxx00EF122TbLkp1AbnU\nlTU4zkzWrn2DtrY27rjjTo4//jRKpYuBEwAbIb7NoYf+g9/97uZmu2K9yl133cVxx51LofB/VL9z\nIiG53AyefLJ+gmGj0p9ytr7cmlOB38aDyAZ+qbW+TwjxJHCbEOJjxFAaAFrr54UQtwHPY7KbT69V\nzPoTKSXz5s1j3rx5Vb8PFsBdK77vs2LFCmbOnDnswOxKYLVloePf0mbxirsxic1ZBwvWYG65VpQf\niThoP1KAUZy9WCGzAb/soaKIfDZDkM9hRQqZcXGzWbL5HEoIAs8j42aIVIi2wM1kezcNKXEdB8dx\nDLQGJrYt0rpCLuyVSmbQRxHlICCbz/diDtXET6SDfKH1pPdvvPEGUraRKGYAYbgHTz7ZC97Yiu+S\njKcAkMKJk0vi038qMaDecwMlCtSTevMqiVNy4oy3xI2vlKI/FXOw+ZnERta6hUZC+nNJJnyJ0u3l\npq3NAk6er7WSjXQQfPLt0n2U1N2MAtGM63Og8ZJcS0J1LLsXtHV9uK6/+MWzuOaaXSmVbgGORanP\nUyjsx4IFR3L++V/gC1/4nJl39MbmVsWlUn9stuI9GkkukmASxaoso6LpRJIXX3yRvfZ6F93dn0Kp\nA/nwh0/mz382dGNpEUIwe/buLFp0D/Dh1JWNcJyxrFq1iq6uLk466TRKpd9j7CjEbduXF1+8awg9\nsX6ls7MTGEP90PzVZDJfYOedt2e77bYbkfrXi8Nfa/2y1nrX+M+OWutvx7+v0Vq/V2u9jdb6fTrG\nOIuvfUtrvZXWelut9b39lR3Ei1ErAypXrlzJ9Olbs/32c5kyZTPuv99keg4F8C/Z8JP4Lp3aXNJl\n6XgxG2jTSTaokQjgH64SUts2IUQlPsOyjXvAlpLQ95GpGAtHSEAwbtw4MmPayYxpJ9eWB8yi5Ng2\n0rGRtkM2kwEhCFU1C4CUBqLEcl2k45CJ0/ajKKpk80opsemlpYG+3zOIoioGhyRmrVWSyWRQqkx1\n+KQi3e2t+i7J5mhJm0wmg0aAMrEvOuWaqfdcqxJkEldmQl2TYEU1K1rrGCS0jAp9gnKZIAXk2WpJ\n+q42eL6/vqm1EtUG46/LIPikLk0KWHUYCR4w8Loz0HhJ92NSzkgwbjQibW1t3HXXreRyZ2LO/ABz\nKZUe4+tfv4Zzz/06lm2v12SUoa7vzTx31lnn0d19Jkp9FTieYvE8Lr74irr3Xn75t8nnzwTSiXZ/\nwXVh5syZXHnl1fj+AtKKGYDj/J53vav6t7eDHHPMMcybN5N8fhsymTOB7yLlOYwd+yFyudkcf3yO\n++777YiNi/UNpdFySdKYZQq/KSERTkszFokLLvguHR1HEQTfp1R6gMMPP5YHH/w9c+bMaRp6Y6BT\nUTNl1Zq+Wx3AP1RJFoYwCLASdwYGPDYpP9mUkoXDuDVN5mUUhjiOjePYRMIxgbMxFpuKIlSksGwL\nNESBMskAcexYbfnNvkvFYpmO5VAKtK5Ab7RyGk6cOJGxY8fz1lvPAya923GeYt99d+nTrlacyNOW\nDStnV35rpStpoHkVYE77WmiUAKcfa07yWxi7+oUQVeUoZXg6rWQcCQ1KtQR+oj/p7xvUm4eiDsTE\nSLatP6lNCjCociCEPeR2DdfqNxRr7FCkEQvh7rvvzlVXXcInP/leSqV7gZ2AmRSLD/HDH87H9wO+\n//1v9XluXXgZgji7XMblIyU6lQEaxqEOYdwGO54jlhAN7wtr167l3nv/gFI/Tf26Oy+8cGufewHm\nzZvHtdf+gNNOex9SbgPkiKJnuO22mxFCsHDhEnx/fs1Tj5DJ3MBXv7pwWH2yPsRxHH73u1v4xz/+\nwT33/JE331zNhAlj2Hbbk5g798dMnz598EKGIaNOOZNSYmlNuVQiEy86Zd/vg3xfuxELUjAKNQP5\n6aefJwjOjv83j2LxKg4//HhefXVRxbrVCmlmE27WLbsuJB3bJMIQL2ZCkIDvebiZDEhZyUZVgOU4\nlItFhB8QegGBjpBZkz2YyWTMIiglUpjQ4bIXg/gqhReFSKsN3/NMZiCgY3yheouRbduUfR87yXwE\nsjUo5ck3iKLIJGfEY0Noky6faeEiLITgxBOP4corv0u5fAOwBtu+kcMP/2PL6qhX50iOkfS8gupD\nhrQspGtXNhiIA69Vins2TuqQlkDakiBUOI6DbfUlpk8Ddq4vqTcPo1gp6k+klIR+2KssIbHdkbce\npRWWRITVXL2NZIEOJiM9BptRIE8++URc1+HUU+dTKt0BzAWmUCw+yFVXzWGffXbvQ1c20BhvhVS8\nDHEIgJM6lCSHz6T+BCdNCIMZ2My+8Nxzz5HL7YDvt6d+1SjVPzzGsccewxFHHM7DDz+M53kccMAB\ntLeb5/fdd1fuu+8WyuX3ARrLuoZs9sf85jc3NZ0luSHJzjvvzM4777zO692wQFRaIGEYUiqVUX5g\nFhIh+rivEkk2Ca0McGl//H1Tp04GXk/98mG6uzflzjvvbLp9Q3GFvl0kvTBobWAsKi5NzDs7roud\nzUL8t+O6BnfGsnDzOdrbe1OyrfhPmoPRdRywYutopIlKZVTZqwTGDuR6TNLkcV204+CkMq/quQJa\n7eqtJ+effx5bbLGI9va55PO7csYZp7HLLrsM/uAGLP25tur9XgspQ2wVS+ZmAjeRjKmEZ1ZEGs/3\n48xmE2/Y6nk0VLeSlI2RrrcyLGGwdiilCAMT8uF5JfxSGeWHqLjukW7LUGUo7RrIbVyvvGOPPYZf\n//o62toOQ4ib4lI2oli8hVNOOZ1///vffepopbu/ngxWftriPVTrt2FoqOVTfoS5c3cb8LlMJsP8\n+fM59NBDK4oZwGc/eyZHHjmTXG4H2tt3ZcGCZSxc+Dfmz6+1pr0jjcgGAaXRKhFC6O5Vq+kp9JC3\nXWQcn2TZFiLODKyV/rJykmBfgB/+8Iecd97fKZV+nnryMk45ZTHXXWf8880E2rYiU2tDymZLJN2X\nXrmMCCOEbah4+svMi6IIv1RCBCFSCrQGPzLPZWJXaBgEIAReuYwKDLG5ikKEAiEFUoOyJJm2OLi/\ngYzZwPermBqEEJXg2kgbjLkoDKvdaiPUv2EYcs8997DxxhtXIDTWhYx0xmC9+mqz+aSspmgKwxAl\nqaL2SXOApvlawzBENRCbOdS2NpKRB9UQCoVSCWlZtLW19du3CTRHAjGitUZoi2yDVGHNvEOSEKC1\nrigpCRizbZl+07HFpZHMzsEyMls5noaacToQBMxAa+azzz7Le997GJ2d8ymXvwlMwra/zhFHvMJt\nt/1sWO/SrDSasZkcehNGAhmvW43sC2+99RYzZmyN5y3DBL53kstty6OP3rNBcU+OdonnTp8PNDpM\nNikRUjAm30YktAnmDkN8pfol2U0Wea9cRochRIb/MvB9o2hEEQuOPhr4A/Cv1JOzefbZpb1lJITd\n/Vjf0ic2YNinrpGw6gx2Sh3setoqKC0Ljxj2wbbrBp1XTuzx4qKU+bsSzxGZODQhJWXfJwzNRuN7\nZcJQGUJ010BtWHacyUR13FLS3gRhP4ois6kHQYXqKfQ844pNrDlBgI4Vs1ApAzo5goqvbdt88IMf\nXOeK2XDR/4ciiTVHICtKVdqSjJQIepHX+7M6CWFYB1zXxbbtln+bPiDRUImlTM9zMJtfoVzmhJM/\nycRJm7DRRlM58siTKBQKlTleO3dq3YND+QYDzcfk+2pUleWoP+tlowkK/SVHjMR4GmriRH+Wy3rf\nNF3ejjvuyKJFT3HyyVlyue2R8juE4S784Q93tjxhY7C1dLD1PXkXwChjMVRRFIYNJzJMnjyZI488\nilzuSOBntLXN4+STj3lHMdtAZNQpZ8nCY9xXNrhOJd6sdkIkQeZhECDCiDAIzeYOFX+/EIKpkyfz\njW98mXz+SGBtXNPLTJ1qAOkGm/T9KW8bkithMAWzEQVUCIFl28blKCVt+TxaGOwxUUcxC2MFKeM4\nRFIQCFBS4LgGsyeKInQUUYwta1lM/IVWmoRKRyuF5TqIODPTTm0WSXt1GFIuFivKt+95hiy9zvdK\nf8s0DUv6xLqhfLPhyLrMGISBlYX0JuS4Lq7r1qUVajQkYKS+UX/zXAjBKad8mjvuKBGGKwiCFdx9\nd4ajjvpIpT3puaNiV2yipAVeUDmM1JtX9WQwZaj2+1a4PIUg0oYyKLEIN+sOHq6CN9LSnwLZiEyY\nMIGf/OQynnzyIY4+egnTp3+ZD37wiJa6zBtZS5P3GOwQX29Maq2rYD0Gmgs33HAVX/jCf/G+9/2e\nK6/8HFdeecmoWePe7jLq3JrFri7CIMCNQfmk4+DE7sy0KwspkTHuUhiGhJ4HgB270qDataKE4Oyz\nz+G6625FqYOAO/jTn+5kv/32q6BJp2OV0i68ekCiOo51G6pbstVuzcHAThsFQ611PfUHplt7n+95\nkChVvk8mBqf1w9DAb0QKqenFbcq6WPF3lY7J6qx1HSXlJ99HxFm7nucRBiFZ17QlVMrEvMVwG7XM\nDUr0ZoGmEcNDpYy7dhhxH+tD0ht72rIzFAT5Rt1YiSsvPUf6Q9IfTp2tmhf1yhEpLMJ0CERnZyfT\nps3C85YDSQyORzY7neef/z9mzpzZZ+4oYZgTlI6p2mJLItAQyPBgDABhGBJGQWVcQi/Ya/obJNeG\nC1jbCkaCWhmqW3Og8kYqFKTZudBKYGmiqAJAC1TKGsr7bojhMqNd/mPcmnY2i5PPE1kW2HYFUsP3\nDR5Sgi+mgqDXgqYUAhO7FAYBWogqUluFUdR+9KPv8fDDd/Cd7+zEQw/9gf322w8wnevHrjAdhvhB\nMOhgHszaNpgM9/l1IbWZQzqqPuEnJ7QgXgxs28BiWEJWnf4sywJplKggCPDDwADOxlaWRt1aycJj\nAVIKg4kXK/AJr6awbWQqtsjzfUPj4vsmji5uexiGaBVSLhcJYpd4o1aP9SnJhocwfe/7vlE0msSb\navT0P9T7+5PEmpC4qWpP962aF/XcSlacvRvEY0LFivyiRYvIZrejVzEDyJDJ7M2zzz5bt/wkG1kK\nw2/ajGtWqRRmWZ13S1s+IhWa+6Le+VSZZymr8HBJ2BtNgmhGWtGu2vJGIsEnmVORCglCn3K5zIsv\nvshJJ32cHXfcj2OOOYWlS5cOu560JO8iHQcVh45AdVjHUObC22Ff+U+RUQelgdbYiTVEKTRQDkPQ\nGhmpKgw0bJtQa4MC7Rh3nG3bWPHCVS9Veo899mCPPfaoqdJkESabhJs6nUJ9XBwpZa8VbwOQRoi7\nG8H2Sd9XUWyFqNCNgIGwkJaFHwTYxEpbFJGLLWGWbZEkc9uOQxCfDCMU2raQ0qm4qRVUkcanrQJR\nfE0IQQBY2sQhainJuq5RSqRE0Itkn+CZKWJYh7hcIQQqDCuk6EJiNjwhkFZieWoeoXtdS6/7Scbk\ny71UOs1sVEOBchEKEkoAMYyhX3u6Hw7G30AWj0QRTEs9iIMpU6bg+68CEaQ4D5R6lcmTJ9edO1Zs\nObNsSRi7JZ2EgqdOCEB6gyyXSkihiYKQwPfJ5fMIZIXpIfnGFgmxdq/ld6D3Hs64TRSpwfDLmrEw\nJeW2cj61ujyIlRehKwkejz72KB867HjK5U8TRcezaNGj3Hvvf/Hii88xceLEAdfSZvpHCFFRskcK\n1uMdWX8y6ixnFZ+7MNl3CSp8El8R+QGRH6Aig86fBE8K264gyVfiNJoI2h/o/v5O4en4mSgVg9aI\nRaHVkBxJvFhEvMXUnOQbPXWm75PJyU4poxQlVg+M5cmSsspylSww5TgWTQUBpVIJN1aYpePSNm4s\nY8ePq1i6wADF1saVJRmeoTZoUk4mU9X2NOVPJUszFVjrlUr4pRJR2SPw48DvJEGgRX0+EtJMvEiz\nY3y4UpsMMNQ6BzrdNzMvhmLNq9dnW265JVtuuTlC/CR15+/I5XqYM2dO3bmjtcmelFIaF7pjoURf\nbsTaNiaKmWVZZDIujmWhIl3Vn/3F96XLHIlkkMHGU6uspyMtQ4m5qjAxaM3xx32cQuF6oujrwAEo\ndS7l8iH85CdXA/2vpUPtn/76fSh7xGiGenq7yeiznPUjUkoCNFqb2BHbNcCWCGEUifi+oaA9N2JV\nqndiq0Kjj92t0JglIJngrToxaa1Npk/8/ygMETVtaPTUmb5PW1aFGDoBEjWYSwEOGGuT1li2TRC7\nLXUcA6Z17wB1HMMJmSwaMlbsEiBSpZSxwsXfICiXTYxQfF04jkH3T59Q6bVgVrKfhCCMIsJiCQHo\nIMQLTMaojGmnhBBEAThuzEwQaSxHND12mrUiNFLeYOCb9Xgi++PWHEiaQUnX2iTeJDGWKopAyorl\nqZXSzLwYivWvv/e+/fYb2H//+ZTLv0brPFI+wZ133tkb7zXA3Km4akVfpaZPG6nmgB0Kr2grgGSH\nIhsicHatNDKHaqXi0hWap556mmIxBxxadY/n7ciL/1pilPLU4T8tre6foewRrd5X6kmpVKKzs5ON\nN964peWONhl1ypnCDLAw3sSFlJRjWARbSkJLIqwUNIIQWKnBaMUbPTS+YfY3oPvbfGt/j6LIKAjC\nBOgmloDBJmUrTfStXBhq389xHMLUtVApE3wfW7mUUvjKBPyLIED7AYHSuNkMaBNbZNu2cYPGLumA\n2BpWc7KsJCFEBpoDwHLsXhBKKY0rM+U+SqxhxNY9o+gJpGOjpDTuI6XIOb2W1cSVYMleGiSriYVs\nKJvAYNLIptuo+2kwaVYJskQMe6IUUhuolcECk/ubh4MphiPhukqXXe+9t9lmG5YtW8Ldd9+N53kc\ncsjNjBkzpt9yhqokW5ZFoVQik0liHzVjs/m65Wul4/lXvR5FUQRCv+P+qiNDUVyFEGQyGTzPY+2a\ntVjWpn3uaWt7iP33O2ydK6NDmQsjOX/++c9/st9+8/A8j1NOOZUrr7zknXHYj4y6bM1k8QnjAG0n\n3syj0ICXVjIkLQOO2h+wHzSe3ZKGBaiKeaoDBgjVoJVRbEK34jgWBf0Cto6kNJtBNJDiORh4Z2Ip\nDIMA4mxZP3eC2nEAACAASURBVIzI2bZRWkqeAZfNZlBaY8dZlWlqJhFbPHXsMo2iCD8IcGzbJGYo\njbQkRAYPrRLL0893TzCsbClNsHWhaIjVAT8Msdvy5HK5li0kI5HdNhJltkKGMrYGm4etsDqu78y0\nRt6hto1BFEHKVWlZVgVMNrnf932TqSmN0mdbjjkgpUBvfS/AzSTzanhZkM2874aeCTicOaS15o03\n3mDWrB0olR4HtgI0cC2TJn2DJYueYuyECU2Pe2DYY722nlaW14zsssv+/OMfpwBH0tY2nx/84BN8\n/OP/b53VvyFKrDf0+QijUjmrTTEWUprNIYZSiKLI+PpjZQB6QQoH2kRqBzX0Klpaa/wYwkMIkwlo\ny15KmaQsoKqOMIHg0LpSjrIsMjFa+LqaSInFKQ014tTAU6Tv7W+RbWQj1lrjlcvI+L4gioiCEKm1\nsZB5HkprZDZjLJvxt5FCVPULsfXF97yK1c8PQxNDFvdn4AdEaDKOA1L2STevfS8Vuzi9UgkrscxI\nSa6traWxF+saemB9LsiNbsppy46MXdfJ781CDTTTtmb7ZV33Zbo+rXWF3ir5f3rcJOMq+XcURUhh\nVZ5z4nhLpRTo3szXDUkhXZ/1DTSHGpUrrriaL3zhPGz73cByNprQyZ13/JLtd9ihqcP+UGFOBnrn\n9akgd3R0MGXKDIJgNeACTzJu3AdZtWpZvyDx/wnSn3I26nokcc+p2GUpMGeXJKsPqNAJpS1bYRRV\nYpTqSb0MMRG7IGtjntKuyTT4bcWqpnoJbKE3GN8smLpPgGgrstJaKcN1gSbvG0YRAio4dL7nI5Wq\nUD7ZmQzELmktBJ7vE4YhdpxNaceKdtIWKSUZxzFZt/E17dhYUoLohSvo70CSDqy1LKvCx5qJlfqB\npNlNoFWxX7Xtr+eyHAkXarPtGswFWjXWo4gwhTU30m0bCr7UUOZko2NkoExK8y1VQ+NGKcNTWiiV\nEAIsWxKEAflcPp4vI2tVrfceI+kyq1d/Mu6NRVE1RPVVYROQvdyuzcjpp3+c979/Po899hgTJkxg\n//33J5fLNRQbWNs/URQ15WYdbHwmwN7NhtC0QpYsWUIutzVBkNAo7olS43nuuefe9nzCIyGjTjlL\nJIlLSeAbpOOYNPjYvVVPwahV4tKxLPXuj5SivyEt48y+iiWvRiFQ8aQhteknmTLJRFmXAbRJXJBI\nA+8Ooa5GAsWTAHEVK1ahUliuSz6bJYoinDhOLQgMeX0Ul2VJSYRJLLBjpTexwFmWRRgrfYl1TCtF\nNlH8gqDXElanTfXeox4Xaz2ptyBaNVbZ2kW5VbFftdJfoPH6CAAfrF1pSY91y7JQsdWnAl68gWSM\nDXVONqrUDaZIDzZuEqVfaRNXFvoRjpsAKCukZcp3bHfYh4HB3nd9Hgigd9yD8VAgNGFkfq/XlnSb\nkyzXoc6RzTffnGnTplXq76+sVlsSBxqflTEYRZXEJ8u2jQGjgXasWLGCe+65B9d1WbBgAZk47KNR\nGTduHEp1V/2m9e4sXLjwHeWsjow65axKKROCQGsDxRAHcFdZsGqeFaI3OUBrjaDX+tVfXUmAsxAG\nS8uNrWgJenykenHVdGyJEbEFJyFtht6YgrcDTo0QAj9WrGRs1Uo2z0asJAlivxN/kzCKEI7Jnq1y\nw0WGW1OHESAQtowBZE1dvudha02kNKEKKtRRmTjw3EmdVN0EZDb1fKukdkEUSuF5HrYTu5r62ZjW\npRXh7SSVMSRMXOHbYU4MJo0qdY0mdQyU+WkONub/jgORDiq/J27QkVaUNoQDQW1boJpaaqiHmEYU\nmYHKSp5P1rgEyqeewt5KC7tKPApKmSx2HSdnCTHgwUFrzWWXXc4553wNy3o/Wi/j9tv/yB13/LKp\n+qdPn47nrQB8jFsTyuXJrFixYkjvM9plwziOtlAqLrM4wD4TJwEEvk9YLoPvE5RK+J6HH4a9k4Te\nTTs5YaTxZoQQffBfrDiwPMFJy+bzYFkVt5rUMfuAEHFmooJIGXdqKgU+7U6rnZjrCnOmKd7C2NUI\nVFEYVX2DmvdJXLuVOBh6YQCIDPl45Pv4nkcYhgRxcL6IWR6kZf6dKHTJZmdwooxVtB5OVFXbY0un\n6Mea2Yik36O/59MLc3ozWF8yEujtrZZk/Kk4QaQCCN0kTMRIy4aKA5Uel0AFWd+2baJQV3g1hbbI\npCjqap8dTTHIIzHuE+taIxhx9fo1/XwYBUSxFi1EfTT+RKkWyIbaP9j4TA4+tZh7ycGhXjvOO+98\nzjvvJ5TLT1Eo/JJi8U7uvvu3VZAujUhbWxvTpm0JPF75LQzf4txzv8J2283hJz/5CaVSqakyR7Os\n/1WlxZJkatpSYiexQkqh4kBxIYThWYzjzUJlUOLTmZQqNv1GsaUrCdSvBxyYVkSSU5ST+rctZSVI\nXQEKA5CbkIMPJPUm0mCBoENdZButK60U2bGyNFhdtcquiqIK6G6SVWsBOgwpdXfjl0qGMikMKyDB\n9dqULETJv0UqaLx2kUoU5v4WoEakv4V5Q92wE0kW+FbR4IyEpA9VEMcTpvhqNxRpdk4m0ugYGYpC\nUW9cglHQbMuhPT+GXKYNx8qQz+erymtG2WhGNoQDQTLubctBaKsSdJ6Qzlfo+1L/Tq711+ZGD15C\nCHzPUDpFKsQrG6qtBBw4OWAiqtkf+lvDk3o1asBvNND4HGi97E8eeughLrvspxSLDwBbJK1BDoEX\nF+ALX/gU2ex59EaCP4bWj/PCC+fz+c//gWnTtubaa6/f4Ob9+pBRl60Zel4VeTWA7/tEUYRbcS9G\nYEmshNw6VrC01gaZPs7aBAxAbQzB0EhcSRArIcmJX2tNGJebFuk4Lc1QWVdZOEMh7a0lOQ/DkCCK\ncKwYoDYMcTMZfM+HIERkHKRtG2LoxNolpEkUsG0c1zXm/jBEaE1XVxfPPv88juuy00470d7eXmlb\nOstNKNVUu+u9R38Zlum6hBAV2AIYWsbXf6Ik4yQMQ7q6usjlcuTa2/t1K1XCE8Tbg3R+OAkBA0mj\n47JeWcPNGh4sM3BdZWYOVld/rsRKPGvq/wkG33D6K+E1rRwO40SmJE42iYX1fJ+sa/ATa9uSrOFK\nqZZldtfrp4H2jr32mseTT54KnFgpQ4gfcfDBD3P33b9quv4wDNl11/147rnJwATg38BD9AYZ/R/5\n/Kl87GPv57LLLtrg53QrJP4GfV50wznet0jS8RhhaLjn0Ib30IuVtEhriAdmPbqM/k65A1mmKgM8\nnvxBTEqsiDfmVBZgIyeWZiUd0zJUy1AjUq9vhBANWeySPhJxPJgWAjuTqYCTGoqnuK9N5C6WMO5M\nKxNzYUaGXikMArp7evjkpz/N9M0244OHHcbBBx/MlClTOO200+jo6KiyatbSZQ3HuuX7PkuWLGHx\n4sW8+OKLlEqlPhbUDd1SlZZm3RMjJUopvvDfX2H8xE2ZsfkObDR5U+bNO4wlS5ZU7knGkA5DwnKZ\n8G1EOt9f+MJQ7xtMlFKUy2WC0Dek3C3uo8Gsbq16j3r1ptebRqx/SVuEEBUPihACHUVEceIRULmW\nPlyn62rGIpguR1q92ZKhH+DHlHCO1WvlkpZV1bahWvcHWovrfZP+rG2vv/46//znM8CCVAlryOW+\ny1e/+vmm2pWIbds8/vgDHHPMBCzrd8AXqY7+nkOx+DDXXfcAl19+5ZDqGC0y6pQzqA4olpah3HEz\nGSzHIbIsRMatClpPAvuF1gbkEQMEqyyrwvsIDMh7Vh0D5VbFQMnEbdqkK2RDlNqJnECSDMQHJ4TB\nMvNjHDUtYsJeYZInAqUo+QGBUigrTiyIFWjXdXDjE6dQ2iRfKMWat95ir7324he/+AWlUomuri66\nuroolUr8/Oc/Z4899qCjo6PfdjfzDVavXs1tt93GRz7yCbbacg/GjZ3E3nMOY999jmKPPQ5iwoSN\n+cQnPrtONqZWyh//+Ee23HJXbNtm44234Lnnnluv7fnGN77D1dc8Srn8PJ63miB4k//93/ey2277\n8tRTTwG980zrXv7cJGZmfcb1rU+ppzAIIfA8j8VLF7HP3PeRz41n+vRtueSSS/E8b9Bnb7nlFj7w\ngQXMn38kN954Y10Ffn3EVtZTxNJwE820YzClbiB38WAHr9p+VZGxnvmBh4gzZsM4UWiw2Mr+FMJ6\nSupQuUvrrVevvfYamcwMkuB9WEs+fzinnnosc+fObajcetLW1sYtt/yCu+/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9kquu+gFH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I7t64FNHEulSBvbKTUN/KoCW/nxGQYxCvDZAUzC+CSIMgKYViVJVuIkL+9NUIL06uynKK8n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\nsQSDy8nPn8WXX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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "fig = draw_sky(data)\n", - "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", - "plt.xlabel(\"x-position\")\n", - "plt.ylabel(\"y-position\")\n", - "\n", - "colors = [\"#467821\", \"#A60628\", \"#7A68A6\"]\n", - "\n", - "for i in range(traces.shape[1]):\n", - " plt.scatter(traces[:, i, 0], traces[:, i, 1], c=colors[i], alpha=0.02)\n", - "\n", - "\n", - "for i in range(traces.shape[1]):\n", - " plt.scatter(halo_data[n_sky - 1][3 + 2 * i], halo_data[n_sky - 1][4 + 2 * i],\n", - " label=\"True halo position\",\n", - " c=\"k\", s=90)\n", - "\n", - "# plt.legend(scatterpoints = 1)\n", - "plt.xlim(0, 4200)\n", - "plt.ylim(0, 4200);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This looks pretty good, though it took a long time for the system to (sort of) converge. Our optimization step would look something like this:" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(10000, 3, 2)\n", - "[[ 2941.11736958 3482.87483555 3097.57462199 2940.34938955\n", - " 1293.79961354 171.05131012]]\n", - "Using the mean:\n", - "Your average distance in pixels you are away from the true halo is 883.931977628\n", - "Your average angular vector is 1.0\n", - "Your score for the training data is 1.88393197763\n", - "\n", - "Using a random location: [[4106 2346]]\n", - "Your average distance in pixels you are away from the true halo is 1647.74122801\n", - "Your average angular vector is 1.0\n", - "Your score for the training data is 2.64774122801\n", - "\n" - ] - } - ], - "source": [ - "_halo_data = halo_data[n_sky - 1]\n", - "print traces.shape\n", - "\n", - "mean_posterior = traces.mean(axis=0).reshape(1, 6)\n", - "print mean_posterior\n", - "\n", - "\n", - "nhalo_all = _halo_data[0].reshape(1, 1)\n", - "x_true_all = _halo_data[3].reshape(1, 1)\n", - "y_true_all = _halo_data[4].reshape(1, 1)\n", - "x_ref_all = _halo_data[1].reshape(1, 1)\n", - "y_ref_all = _halo_data[2].reshape(1, 1)\n", - "sky_prediction = mean_posterior\n", - "\n", - "\n", - "print \"Using the mean:\"\n", - "main_score([1], x_true_all, y_true_all,\n", - " x_ref_all, y_ref_all, sky_prediction)\n", - "\n", - "# what's a bad score?\n", - "print\n", - "random_guess = np.random.randint(0, 4200, size=(1, 2))\n", - "print \"Using a random location:\", random_guess\n", - "main_score([1], x_true_all, y_true_all,\n", - " x_ref_all, y_ref_all, random_guess)\n", - "print" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## References\n", - "1. Antifragile: Things That Gain from Disorder. New York: Random House. 2012. ISBN 978-1-4000-6782-4.\n", - "1. [Tim Saliman's solution to the Dark World's Contest](http://www.timsalimans.com/observing-dark-worlds)\n", - "2. Silver, Nate. The Signal and the Noise: Why So Many Predictions Fail — but Some Don't. 1. Penguin Press HC, The, 2012. Print." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.10" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/Chapter5_LossFunctions/DarkWorldsMetric.py b/Chapter5_LossFunctions/DarkWorldsMetric.py index 0b59edf4..ce652277 100644 --- a/Chapter5_LossFunctions/DarkWorldsMetric.py +++ b/Chapter5_LossFunctions/DarkWorldsMetric.py @@ -58,7 +58,7 @@ def calc_delta_r(x_predicted,y_predicted,x_true,y_true): for perm in it.permutations(a[num_halos-2],num_halos): which_true_halos=[] which_predicted_halos=[] - for j in xrange(num_halos): #loop through all the true halos with the + for j in range(num_halos): #loop through all the true halos with the distances_perm[count,j]=np.sqrt((x_true[j]-x_predicted[int(perm[j])])**2\ +(y_true[j]-y_predicted[int(perm[j])])**2) @@ -141,7 +141,7 @@ def convert_to_360(angle, x_in, y_in): theta: the angle in the range 0:2pi """ n = len(x_in) - for i in xrange(n): + for i in range(n): if x_in[i] < 0 and y_in[i] > 0: angle[i] = angle[i]+mt.pi elif x_in[i] < 0 and y_in[i] < 0: @@ -204,7 +204,7 @@ def main_score( nhalo_all, x_true_all, y_true_all, x_ref_all, y_ref_all, sky_pre x_predicted=np.array([],dtype=float) y_predicted=np.array([],dtype=float) - for i in xrange(nhalo): + for i in range(nhalo): x_predicted=np.append(x_predicted,float(sky[0])) #get the predicted values y_predicted=np.append(y_predicted,float(sky[1])) #The solution file for the test data provides masses @@ -271,9 +271,9 @@ def main_score( nhalo_all, x_true_all, y_true_all, x_ref_all, y_ref_all, sky_pre W1=1./1000. #Weight the av_r such that < 1 is a good score > 1 is not so good. W2=1. metric = W1*av_r + W2*angle_vec #Weighted metric, weights TBD - print 'Your average distance in pixels you are away from the true halo is', av_r - print 'Your average angular vector is', angle_vec - print 'Your score for the training data is', metric + print('Your average distance in pixels you are away from the true halo is', av_r) + print('Your average angular vector is', angle_vec) + print('Your score for the training data is', metric) return metric @@ -316,10 +316,9 @@ def main(user_fname, fname): #first input would be #a float, if succeed it #is not a header - print 'THE INPUT FILE DOES NOT APPEAR TO HAVE A HEADER' + print('THE INPUT FILE DOES NOT APPEAR TO HAVE A HEADER') except : - print 'THE INPUT FILE APPEARS TO HAVE A HEADER, SKIPPING THE FIRST LINE' - + print('THE INPUT FILE APPEARS TO HAVE A HEADER, SKIPPING THE FIRST LINE') skip_header = sky_prediction.next() @@ -331,7 +330,7 @@ def main(user_fname, fname): if does_it_exist > 0: #If it does then find the matching solutions to the sky_id selectskyinsolutions=true_sky_id.index(sky_id)-1 else: #Otherwise exit - print 'Sky_id does not exist, formatting problem: ',sky_id + print('Sky_id does not exist, formatting problem: ',sky_id) sys.exit(2) @@ -342,7 +341,7 @@ def main(user_fname, fname): x_predicted=np.array([],dtype=float) y_predicted=np.array([],dtype=float) - for i in xrange(nhalo): + for i in range(nhalo): x_predicted=np.append(x_predicted,float(sky[2*i+1])) #get the predicted values y_predicted=np.append(y_predicted,float(sky[2*i+2])) #The solution file for the test data provides masses @@ -409,9 +408,9 @@ def main(user_fname, fname): W1=1./1000. #Weight the av_r such that < 1 is a good score > 1 is not so good. W2=1. metric = W1*av_r + W2*angle_vec #Weighted metric, weights TBD - print 'Your average distance in pixels you are away from the true halo is', av_r - print 'Your average angular vector is', angle_vec - print 'Your score for the training data is', metric + print('Your average distance in pixels you are away from the true halo is', av_r) + print('Your average angular vector is', angle_vec) + print('Your score for the training data is', metric) if __name__ == "__main__": diff --git a/Chapter5_LossFunctions/draw_sky2.py b/Chapter5_LossFunctions/draw_sky2.py index 26b1f470..6f4ca58f 100644 --- a/Chapter5_LossFunctions/draw_sky2.py +++ b/Chapter5_LossFunctions/draw_sky2.py @@ -2,14 +2,13 @@ from matplotlib.patches import Ellipse import numpy as np -def draw_sky( galaxies ): +def draw_sky(galaxies): """adapted from Vishal Goklani""" size_multiplier = 45 fig = plt.figure(figsize=(10,10)) - #fig.patch.set_facecolor("blue") ax = fig.add_subplot(111, aspect='equal') n = galaxies.shape[0] - for i in xrange(n): + for i in range(n): _g = galaxies[i,:] x,y = _g[0], _g[1] d = np.sqrt( _g[2]**2 + _g[3]**2 ) diff --git a/Chapter6_Priorities/Chapter6.ipynb b/Chapter6_Priorities/Ch6_Priors_PyMC2.ipynb similarity index 92% rename from Chapter6_Priorities/Chapter6.ipynb rename to Chapter6_Priorities/Ch6_Priors_PyMC2.ipynb index 919d492c..f3c7533f 100644 --- a/Chapter6_Priorities/Chapter6.ipynb +++ b/Chapter6_Priorities/Ch6_Priors_PyMC2.ipynb @@ -11,7 +11,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#Chapter 6\n", + "# Chapter 6\n", "\n", "____\n", "\n", @@ -27,7 +27,7 @@ "\n", "Up until now, we have mostly ignored our choice of priors. This is unfortunate as we can be very expressive with our priors, but we also must be careful about choosing them. This is especially true if we want to be objective, that is, not to express any personal beliefs in the priors. \n", "\n", - "###Subjective vs Objective priors\n", + "### Subjective vs Objective priors\n", "\n", "Bayesian priors can be classified into two classes: *objective* priors, which aim to allow the data to influence the posterior the most, and *subjective* priors, which allow the practitioner to express his or her views into the prior. \n", "\n", @@ -926,7 +926,7 @@ "figsize(12.0, 8)\n", "beta = stats.beta\n", "hidden_prob = beta.rvs(1, 13, size=35)\n", - "print hidden_prob\n", + "print(hidden_prob)\n", "bandits = Bandits(hidden_prob)\n", "bayesian_strat = BayesianStrategy(bandits)\n", "\n", @@ -1042,8 +1042,8 @@ " \"AMZN\": (0.03, 0.02),\n", " }\n", "\n", - "for i, (name, params) in enumerate(expert_prior_params.iteritems()):\n", - " plt.subplot(2, 2, i)\n", + "for i, (name, params) in enumerate(expert_prior_params.items()):\n", + " plt.subplot(2, 2, i + 1)\n", " y = normal.pdf(x, params[0], scale=params[1])\n", " #plt.plot( x, y, c = colors[i] )\n", " plt.fill_between(x, 0, y, color=colors[i], linewidth=2,\n", @@ -1103,7 +1103,7 @@ "\n", "stocks = [\"AAPL\", \"GOOG\", \"TSLA\", \"AMZN\"]\n", "\n", - "enddate = datetime.datetime.now().strftime(\"%Y-%m-%d\") # today's date.\n", + "enddate = \"2015-04-27\"\n", "startdate = \"2012-09-01\"\n", "\n", "stock_closes = {}\n", @@ -1120,7 +1120,7 @@ " _previous_day = np.roll(stock_closes[stock], -1)\n", " stock_returns[stock] = ((stock_closes[stock] - _previous_day) / _previous_day)[:n_observations]\n", "\n", - "dates = map(lambda x: datetime.datetime.strptime(x, \"%Y-%m-%d\"), x[1:n_observations + 1, 0])" + "dates = list(map(lambda x: datetime.datetime.strptime(x, \"%Y-%m-%d\"), x[1:n_observations + 1, 0]))" ] }, { @@ -1144,12 +1144,12 @@ "source": [ "figsize(12.5, 4)\n", "\n", - "for _stock, _returns in stock_returns.iteritems():\n", + "for _stock, _returns in stock_returns.items():\n", " p = plt.plot((1 + _returns)[::-1].cumprod() - 1, '-o', label=\"%s\" % _stock,\n", " markersize=4, markeredgecolor=\"none\")\n", "\n", "plt.xticks(np.arange(100)[::-8],\n", - " map(lambda x: datetime.datetime.strftime(x, \"%Y-%m-%d\"), dates[::8]),\n", + " list(map(lambda x: datetime.datetime.strftime(x, \"%Y-%m-%d\"), dates[::8])),\n", " rotation=60);\n", "\n", "plt.legend(loc=\"upper left\")\n", @@ -1179,9 +1179,9 @@ "figsize(11., 5)\n", "returns = np.zeros((n_observations, 4))\n", "\n", - "for i, (_stock, _returns) in enumerate(stock_returns.iteritems()):\n", + "for i, (_stock, _returns) in enumerate(stock_returns.items()):\n", " returns[:, i] = _returns\n", - " plt.subplot(2, 2, i)\n", + " plt.subplot(2, 2, i+1)\n", " plt.hist(_returns, bins=20,\n", " normed=True, histtype=\"stepfilled\",\n", " color=colors[i], alpha=0.7)\n", @@ -1258,7 +1258,7 @@ "for i in range(4):\n", " plt.hist(mu_samples[:, i], alpha=0.8 - 0.05 * i, bins=30,\n", " histtype=\"stepfilled\", normed=True,\n", - " label=\"%s\" % stock_returns.keys()[i])\n", + " label=\"%s\" % list(stock_returns.keys())[i])\n", "\n", "plt.vlines(mu_samples.mean(axis=0), 0, 500, linestyle=\"--\", linewidth=.5)\n", "\n", @@ -1302,8 +1302,8 @@ " plt.subplot(2, 2, i + 1)\n", " plt.hist(mu_samples[:, i], alpha=0.8 - 0.05 * i, bins=30,\n", " histtype=\"stepfilled\", normed=True, color=colors[i],\n", - " label=\"%s\" % stock_returns.keys()[i])\n", - " plt.title(\"%s\" % stock_returns.keys()[i])\n", + " label=\"%s\" % list(stock_returns.keys())[i])\n", + " plt.title(\"%s\" % list(stock_returns.keys())[i])\n", " plt.xlim(-0.15, 0.15)\n", "\n", "plt.suptitle(\"Posterior distribution of daily stock returns\")\n", @@ -1852,7 +1852,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 36, "metadata": { "collapsed": false }, @@ -1869,7 +1869,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 37, "metadata": { "collapsed": false }, @@ -1880,7 +1880,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 38, "metadata": { "collapsed": false }, @@ -1888,7 +1888,7 @@ { "data": { "text/html": [ - "
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\n", "\n", " \n", " \n", @@ -1936,7 +1936,7 @@ "4 Italy 4" ] }, - "execution_count": 4, + "execution_count": 38, "metadata": {}, "output_type": "execute_result" } @@ -1960,7 +1960,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 39, "metadata": { "collapsed": false }, @@ -1968,7 +1968,7 @@ { "data": { "text/html": [ - "
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\n", "
\n", " \n", " \n", @@ -2040,7 +2040,7 @@ "4 Scotland England 0 20 3 5" ] }, - "execution_count": 5, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" } @@ -2055,7 +2055,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 40, "metadata": { "collapsed": false }, @@ -2078,7 +2078,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 41, "metadata": { "collapsed": false }, @@ -2134,7 +2134,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 42, "metadata": { "collapsed": false }, @@ -2143,7 +2143,7 @@ "name": "stdout", "output_type": "stream", "text": [ - " [-----------------100%-----------------] 200000 of 200000 complete in 130.0 sec" + " [-----------------100%-----------------] 200000 of 200000 complete in 87.0 sec" ] } ], @@ -2224,7 +2224,7 @@ "metadata": {}, "source": [ "\n", - "#Diagnostics#\n", + "# Diagnostics#\n", "\n", "Let's see if/how the model converged. The home parameter looks good, and indicates that home field advantage amounts to goals per game at the intercept.\n", "\n", @@ -2236,7 +2236,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 43, "metadata": { "collapsed": false }, @@ -2250,9 +2250,9 @@ }, { "data": { - "image/png": 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3dPzz4vP5+O8LV7OhOir9Tdz+7Csu5cL/LOVuv4CXgdr+PPXVFt5c8QNfBTRQ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\nAU4ys+OA7cAlwJzEOsuAecASMzsbeGWw+qpzzz2XW2/tGiTEb+P/Z4x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6D1bwuQiLNAGsqWMWLw43Kn4pqA0tbcYYY6JV8ADLmCiUys0CYdx1V7FLYIwx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\nDrNZncOxHJzyZvUfLKq7CE8DFqrqgcCxwN0i0ji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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2269,26 +2269,26 @@ "source": [ "It looks like we have decent parameters and that the intercept was a good idea. I'm not so sure about how autocorrelated the Tau terms are but that is for me me to brush up on my Bayesian models. \n", "\n", - "#Simulation#\n", + "# Simulation#\n", "Now we pull in some observed data (i.e. the table from last year) and include some remarks about Qualification" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [], "source": [ "observed_season = DATA_DIR + 'table_2014.csv'\n", - "df_observed = pd.read_csv(observed_season)\n", + "df_observed = pd.read_csv(observed_season, encoding = 'iso-8859-1')\n", "df_observed.loc[df_observed.QR.isnull(), 'QR'] = ''" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 46, "metadata": { "collapsed": false }, @@ -2375,37 +2375,35 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 47, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/maxwell/anaconda3/envs/bayes/lib/python3.5/site-packages/ipykernel/__main__.py:63: FutureWarning: by argument to sort_index is deprecated, pls use .sort_values(by=...)\n" + ] + } + ], "source": [ "simuls = simulate_seasons(10000)" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { + "image/png": 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Dc+4eA/AYAK7B4XlQVjNHcM8CfxgRrwLeBMyVdBQwH7g5Io4EVgALACQdA5wJ\nHA28E7hCKZcB8Hng3Ig4AjhC0jtG9NWYmZllLdfgJH0T+Gz+OzEi+iVNBVZGxFGS5gMREYvy+t8G\nLgI2ACsi4pjcflbe/rwGz+EanFnFuQZn7TTqNThJM4Ae4FZgSkT0A0TEFmByXm0asLGw2ebcNg3Y\nVGjflNvMzMxGXNMBTtIBwL8AH4mIp9h11827SyPIOXePAXgMANfgaN88mDp1BpIq+VfGuGZWkjSO\nFNz+MSKuy839kqYUUpQP5/bNwMGFzafntqHaG5ozZw4zZswAYOLEifT09NDb2wvseLPrvLx69epK\n9acTywOq0h8v77y8w8By7+gsbxloa3X7vFSR8eqG74P+/g3ALSS9+d+VHVoeuN2Xby+mVU3V4CRd\nDTwSEX9YaFsEbI2IRZIuBCZFxPx8kskS4HhSCvIm4PCICEm3AvOAVcC3gM9ExI0Nns81OLOKcw2u\nftr2npbSeg1u2CM4SScA7wPulXQX6dV/HFgEXCvpg6QTSM4EiIg1kq4F1gDPAOcXotVc4MvAvsDS\nRsHNzMxsJPiXTCpq5cqVz6cQxiqPQbXHoG17++cIFo/tI7h2zYO6HcH5l0zMzKyWfARnZqW4Blc/\nPoIzMzPrAg5wFbXrqdhjj8fAYwD4Ojg8D8pygDMzs1pyDc7MSnENrn5cgzMzM+sCDnAV5Zy7xwA8\nBoBrcHgelOUAZ2ZmteQanJmV4hpc/bgGZ2Zm1gUc4CrKOXePAXgMANfg8DwoywHOzMxqyTU4MyvF\nNbj6cQ3OzMysCzjAVZRz7h4D8BgArsHheVDWsP+jt9lImDp1Bv39GzrdjYamTDmULVv6Ot0NMxth\nrsFZW3RBbr/Tneg6rsHVTxd8Tl2DMzMzc4CrKOfcAVZ2ugMd53mAa3B4HpTlAGdmZrXkGpy1RRfk\n9jvdia7jGlz9dMHn1DU4MzMzB7iKcs4dXIPzPABcg8PzoCwHODMzqyXX4KwtuiC33+lOdB3X4Oqn\nCz6nrsGZmZk5wFWUc+7gGpznAeAaHJ4HZTnAmZlZLbkGZ23RBbn9Tnei67gGVz9d8Dl1Dc7MzGzY\nACfpSkn9ku4ptE2StFzSWknLJE0o3LdA0npJ90uaXWifKekeSeskXT7yL6VenHMH1+A8DwDX4PA8\nKKuZI7irgHcMapsP3BwRRwIrgAUAko4BzgSOBt4JXKF0zAvweeDciDgCOELS4Mc0MzMbMU3V4CQd\nCtwQEa/vmDQ0AAAHkklEQVTJyz8AToyIfklTgZURcZSk+UBExKK83reBi4ANwIqIOCa3n5W3P2+I\n53MNrma6ILff6U50Hdfg6qcLPqdtqcFNjoh+gIjYAkzO7dOAjYX1Nue2acCmQvum3GZmZjYqRuok\nk6qG/K7lnDu4Bud5ALgGh+dBWeNKbtcvaUohRflwbt8MHFxYb3puG6p9SHPmzGHGjBkATJw4kZ6e\nHnp7e4Edb3adl1evXl2p/ozE8g4Dy73DLLe6ftnl1MdOj0+3Le8wsNw7OstbBtpa3T4vVWS8uuX7\nYPQ/b80uD9zuo6xma3AzSDW4Y/PyImBrRCySdCEwKSLm55NMlgDHk1KQNwGHR0RIuhWYB6wCvgV8\nJiJuHOL5XIOrmS7I7Xe6E13HNbj66YLPaUs1uGGP4CR9hRRaf0nSA8BC4FLga5I+SDqB5EyAiFgj\n6VpgDfAMcH4hUs0FvgzsCywdKriZmZmNBP+SSUUVU2Z1UG7PcCXFNOLoqe7efpXnQdv29s8RLB7b\nR3Dtmgd1O4LzL5mYmVkt+QjO2qIL9gw73Ymu4xpc/XTB59RHcGZmZg5wFbXrqdhj0cpOd6DjPA/w\ndXB4HpTlAGdmZrXkGpy1RRfk9jvdia7jGlz9dMHn1DU4MzMzB7iKcs4dXIPzPABcg8PzoCwHODMz\nqyXX4KwtuiC33+lOdB3X4OqnCz6nrsGZmZk5wFWUc+7gGpznAeAaHJ4HZTnAmZlZLbkGZ23RBbn9\nTnei67gGVz9d8Dl1Dc7MzMwBrqKccwfX4DwPANfg8DwoywHOzMxqyTU4a4suyO13uhNdxzW4+umC\nz6lrcGZmZg5wFeWcO7gG53kAuAaH50FZDnBmZlZLrsFZW3RBbr/Tneg6rsHVTxd8Tl2DMzMzc4Cr\nKOfcwTU4zwPANTg8D8pygDMzs1pyDc7aogty+53uRNdxDa5+uuBz6hqcmZmZA1xFOecOrsF5HgCu\nweF5UJYDnJmZ1ZJrcNYWXZDb73Qnuo5rcPXTBZ9T1+DMzMzaHuAk/aqkH0haJ+nCdj9/t3DOHVyD\n8zwAXIPD86Csce18Mkl7AJ8FTgIeBFZJui4ifjB43cWLF7eza03ZZ599OOOMM9hzzz1H/blWr15N\nb2/vqD9Pta0GejvdiY7yPAC2dLoDned5UE5bAxwwC1gfERsAJF0DnAbsEuDmzl3R5q4N77nnljFl\nyhTe9ra3jfpzPf7446P+HNXnMfA8AH7e6Q50nudBOe0OcNOAjYXlTaSgt4unn67eEdyECSexffv2\nTnfDzMya0O4A17Tx49/V6S7s4uc/v5u99tqrLc/V19fXlueptr5Od6DjPA/wgTyeB2W19TIBSW8E\nLoqIX83L84GIiEWD1qvqeapmZtYhrV4m0O4AtyewlnSSyUPA7cB7IuL+tnXCzMzGhLamKCPiOUkX\nAMtJlyhc6eBmZmajoZK/ZGJmZvZCVe6XTCTtIelOSdd3ui+dIKlP0t2S7pJ0e6f70wmSJkj6mqT7\nJd0n6fhO96ndJB2R58Cd+d8nJM3rdL/aTdJHJX1f0j2Slkjau9N9ajdJH5F0b/4bE3NA0pWS+iXd\nU2ibJGm5pLWSlkmaMNzjVC7AAR8B1nS6Ex20HeiNiNdFRMNLKMaATwNLI+Jo4LXAmEtjR8S6PAdm\nAq8Hnga+0eFutZWklwG/D8yMiNeQSipndbZX7SXpVcC5wHFAD/Drkl7e2V61xVXAOwa1zQdujogj\ngRXAguEepFIBTtJ04BTgHzrdlw4SFXtf2knSeOCtEXEVQEQ8GxFPdrhbnXYy8MOI2DjsmvWzJ7C/\npHHAfqRfQBpLjgZui4hfRMRzwH8Av9nhPo26iPgu8Nig5tOAgQukFwOnD/c4Vfsi/RTwMar7c9bt\nEMBNklZJ+nCnO9MBhwGPSLoqp+e+KOlFne5Uh70b+GqnO9FuEfEg8H+BB4DNwOMRcXNne9V23wfe\nmtNz+5EOAA7ucJ86ZXJE9ANExBZg8nAbVCbASfo1oD8iVpOOYlq63qFGTshpqVOAuZLe0ukOtdk4\nYCbwuTwO20ipiTFJ0l7AqcDXOt2XdpM0kbTXfijwMuAASe/tbK/aK/9O7yLgJmApcBfwXEc7VR3D\nHghVJsABJwCnSvoRaW/1bZKu7nCf2i4iHsr//oRUcxlrdbhNwMaI+J+8/C+kgDdWvRO4I8+HseZk\n4EcRsTWn5/4VeHOH+9R2EXFVRBwXEb2k33VZ1+EudUq/pCkAkqYCDw+3QWUCXER8PCIOiYiXkwrJ\nKyLi7E73q50k7SfpgHx7f2A2KUUxZuQUxEZJR+SmkxjbJx29hzGYnsweAN4oaV+l/4nzJMbgCUeS\nDsr/HgL8BvCVzvaobQZn8q4H5uTb5wDXDfcAlf0tyjFqCvCN/FNl44AlEbG8w33qhHnAkpye+xHw\ngQ73pyNyzeVk4Hc63ZdOiIjbJf0LKS33TP73i53tVUd8XdKLSWNw/lg46UrSV0j/V9YvSXoAWAhc\nCnxN0geBDcCZwz6OL/Q2M7M6qkyK0szMbCQ5wJmZWS05wJmZWS05wJmZWS05wJmZWS05wJmZWS05\nwJmZWS05wJmZWS39f6x9fDYiTOXnAAAAAElFTkSuQmCC\n", "text/plain": [ - "" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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D7U8hjWkDjIyI9fn2ejZP+R1NOt3tsIb0BF/KtzuspTDryOy1In9h625mm1lfuIF0Ld8R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\nzAYUJzYzMxtQ/j//IVxi94/NqgAAAABJRU5ErkJggg==\n", - "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2417,31 +2415,21 @@ "median = simuls.points[simuls.team == 'Ireland'].median()\n", "ax.set_title('Ireland: 2013-14 points, 1000 simulations')\n", "ax.plot([median, median], ax.get_ylim())\n", - "plt.annotate('Median: %s' % median, xy=(median + 1, ax.get_ylim()[1]-10))" + "plt.annotate('Median: %s' % median, xy=(median + 1, ax.get_ylim()[1]-10));" ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { + "image/png": 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XvX6/01VtP+2Dsvbn2NhYX+vXYboO58Owxd9+Pj4+Tll6+h6epL2AS9s1vG7z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\nD0bEc0nJ75yK4+mJpF2Bb5J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"text/plain": [ - "" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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Vq9YO9mqw6OkXGPc3HYO9GiKyGWpV5NSTS1t/5Vuxau2A/spI13Zi2iuV/Exr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\n365MW+6/f6jfrkzD0K2Mect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- "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2453,21 +2441,29 @@ "median = simuls.gf[simuls.team == 'Ireland'].median()\n", "ax.set_title('Ireland: 2013-14 scores for, 1000 simulations')\n", "ax.plot([median, median], ax.get_ylim())\n", - "plt.annotate('Median: %s' % median, xy=(median + 1, ax.get_ylim()[1]-10))" + "plt.annotate('Median: %s' % median, xy=(median + 1, ax.get_ylim()[1]-10));" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/maxwell/anaconda3/envs/bayes/lib/python3.5/site-packages/ipykernel/__main__.py:3: FutureWarning: by argument to sort_index is deprecated, pls use .sort_values(by=...)\n", + " app.launch_new_instance()\n" + ] + }, { "data": { - "image/png": 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eb81pyGe285xAsx85ysy2NbPXteuqcS7NG4E/55HTP9Dsf/+knd491VOz/xvNRPPU7CPW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\nRU5ErkJggg==\n", 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2490,7 +2486,7 @@ "ax.set_ylabel('Team')\n", "ax.set_title('% of Simulated Seasons In Which Team Finished Winners')\n", "_= ax.set_yticks(df_champs.index + .5)\n", - "_= ax.set_yticklabels(df_champs['team'].values)" + "_= ax.set_yticklabels(df_champs['team'].values);" ] }, { @@ -2514,22 +2510,23 @@ } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python 2", + "display_name": "Python [conda env:bayes]", "language": "python", - "name": "python2" + "name": "conda-env-bayes-py" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.10" + "pygments_lexer": "ipython3", + "version": "3.5.2" } }, "nbformat": 4, diff --git a/Chapter6_Priorities/Ch6_Priors_PyMC3.ipynb b/Chapter6_Priorities/Ch6_Priors_PyMC3.ipynb new file mode 100644 index 00000000..c5ec49bd --- /dev/null +++ b/Chapter6_Priorities/Ch6_Priors_PyMC3.ipynb @@ -0,0 +1,1834 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6\n", + "`Original content created by Cam Davidson-Pilon`\n", + "\n", + "`Ported to Python 3 and PyMC3 by Max Margenot (@clean_utensils) and Thomas Wiecki (@twiecki) at Quantopian (@quantopian)`\n", + "\n", + "\n", + "---\n", + "\n", + "This chapter of [Bayesian Methods for Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers) focuses on the most debated and discussed part of Bayesian methodologies: how to choose an appropriate prior distribution. We also present how the prior's influence changes as our dataset increases, and an interesting relationship between priors and penalties on linear regression." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Getting our priorities straight\n", + "\n", + "\n", + "Up until now, we have mostly ignored our choice of priors. This is unfortunate as we can be very expressive with our priors, but we also must be careful about choosing them. This is especially true if we want to be objective, that is, not to express any personal beliefs in the priors. \n", + "\n", + "### Subjective vs Objective priors\n", + "\n", + "Bayesian priors can be classified into two classes: *objective* priors, which aim to allow the data to influence the posterior the most, and *subjective* priors, which allow the practitioner to express his or her views into the prior. \n", + "\n", + "What is an example of an objective prior? We have seen some already, including the *flat* prior, which is a uniform distribution over the entire possible range of the unknown. Using a flat prior implies that we give each possible value an equal weighting. Choosing this type of prior is invoking what is called \"The Principle of Indifference\", literally we have no prior reason to favor one value over another. Calling a flat prior over a restricted space an objective prior is not correct, though it seems similar. If we know $p$ in a Binomial model is greater than 0.5, then $\\text{Uniform}(0.5,1)$ is not an objective prior (since we have used prior knowledge) even though it is \"flat\" over [0.5, 1]. The flat prior must be flat along the *entire* range of possibilities. \n", + "\n", + "Aside from the flat prior, other examples of objective priors are less obvious, but they contain important characteristics that reflect objectivity. For now, it should be said that *rarely* is a objective prior *truly* objective. We will see this later. \n", + "\n", + "#### Subjective Priors\n", + "\n", + "On the other hand, if we added more probability mass to certain areas of the prior, and less elsewhere, we are biasing our inference towards the unknowns existing in the former area. This is known as a subjective, or *informative* prior. In the figure below, the subjective prior reflects a belief that the unknown likely lives around 0.5, and not around the extremes. The objective prior is insensitive to this." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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ja9GRm5cBqO1RMtu0An47fxq2byd4536OvfoBJ/xKcX+TOnQZNZwS9R5gl7n4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\nol1TPv30U9566y2OHz8OQEFBAWfOnHFsL0vUAXx9fQHIz8/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ZW8ox8DDjOSxOZkwRQlTN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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "from IPython.core.pylabtools import figsize\n", + "import matplotlib.pyplot as plt\n", + "\n", + "figsize(12.5,3)\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", + "\n", + "x = np.linspace(0,1)\n", + "y1, y2 = stats.beta.pdf(x, 1,1), stats.beta.pdf(x, 10,10)\n", + "\n", + "p = plt.plot(x, y1, \n", + " label='An objective prior \\n(uninformative, \\n\"Principle of Indifference\")')\n", + "plt.fill_between(x, 0, y1, color = p[0].get_color(), alpha = 0.3)\n", + "\n", + "p = plt.plot(x,y2 ,\n", + " label = \"A subjective prior \\n(informative)\")\n", + "plt.fill_between(x, 0, y2, color = p[0].get_color(), alpha = 0.3)\n", + "\n", + "p = plt.plot(x[25:], 2*np.ones(25), label = \"another subjective prior\")\n", + "plt.fill_between(x[25:], 0, 2, color = p[0].get_color(), alpha = 0.3)\n", + "\n", + "plt.ylim(0,4)\n", + "\n", + "plt.ylim(0, 4)\n", + "leg = plt.legend(loc = \"upper left\")\n", + "leg.get_frame().set_alpha(0.4)\n", + "plt.title(\"Comparing objective vs. subjective priors for an unknown probability\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The choice of a subjective prior does not always imply that we are using the practitioner's subjective opinion: more often the subjective prior was once a posterior to a previous problem, and now the practitioner is updating this posterior with new data. A subjective prior can also be used to inject *domain knowledge* of the problem into the model. We will see examples of these two situations later." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Decision, decisions...\n", + "\n", + "The choice, either *objective* or *subjective* mostly depends on the problem being solved, but there are a few cases where one is preferred over the other. In instances of scientific research, the choice of an objective prior is obvious. This eliminates any biases in the results, and two researchers who might have differing prior opinions would feel an objective prior is fair. Consider a more extreme situation:\n", + "\n", + "> A tobacco company publishes a report with a Bayesian methodology that retreated 60 years of medical research on tobacco use. Would you believe the results? Unlikely. The researchers probably chose a subjective prior that too strongly biased results in their favor.\n", + "\n", + "Unfortunately, choosing an objective prior is not as simple as selecting a flat prior, and even today the problem is still not completely solved. The problem with naively choosing the uniform prior is that pathological issues can arise. Some of these issues are pedantic, but we delay more serious issues to the Appendix of this Chapter (TODO)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We must remember that choosing a prior, whether subjective or objective, is still part of the modeling process. To quote Gelman [5]:\n", + "\n", + ">...after the model has been fit, one should look at the posterior distribution\n", + "and see if it makes sense. If the posterior distribution does not make sense, this implies\n", + "that additional prior knowledge is available that has not been included in the model,\n", + "and that contradicts the assumptions of the prior distribution that has been used. It is\n", + "then appropriate to go back and alter the prior distribution to be more consistent with\n", + "this external knowledge.\n", + "\n", + "If the posterior does not make sense, then clearly one had an idea what the posterior *should* look like (not what one *hopes* it looks like), implying that the current prior does not contain all the prior information and should be updated. At this point, we can discard the current prior and choose a more reflective one.\n", + "\n", + "Gelman [4] suggests that using a uniform distribution with large bounds is often a good choice for objective priors. Although, one should be wary about using Uniform objective priors with large bounds, as they can assign too large of a prior probability to non-intuitive points. Ask yourself: do you really think the unknown could be incredibly large? Often quantities are naturally biased towards 0. A Normal random variable with large variance (small precision) might be a better choice, or an Exponential with a fat tail in the strictly positive (or negative) case. \n", + "\n", + "If using a particularly subjective prior, it is your responsibility to be able to explain the choice of that prior, else you are no better than the tobacco company's guilty parties. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Empirical Bayes\n", + "\n", + "While not a true Bayesian method, *empirical Bayes* is a trick that combines frequentist and Bayesian inference. As mentioned previously, for (almost) every inference problem there is a Bayesian method and a frequentist method. The significant difference between the two is that Bayesian methods have a prior distribution, with hyperparameters $\\alpha$, while empirical methods do not have any notion of a prior. Empirical Bayes combines the two methods by using frequentist methods to select $\\alpha$, and then proceeds with Bayesian methods on the original problem. \n", + "\n", + "A very simple example follows: suppose we wish to estimate the parameter $\\mu$ of a Normal distribution, with $\\sigma = 5$. Since $\\mu$ could range over the whole real line, we can use a Normal distribution as a prior for $\\mu$. How to select the prior's hyperparameters, denoted ($\\mu_p, \\sigma_p^2$)? The $\\sigma_p^2$ parameter can be chosen to reflect the uncertainty we have. For $\\mu_p$, we have two options:\n", + "\n", + "1. Empirical Bayes suggests using the empirical sample mean, which will center the prior around the observed empirical mean:\n", + "\n", + "$$ \\mu_p = \\frac{1}{N} \\sum_{i=0}^N X_i $$\n", + "\n", + "2. Traditional Bayesian inference suggests using prior knowledge, or a more objective prior (zero mean and fat standard deviation).\n", + "\n", + "Empirical Bayes can be argued as being semi-objective, since while the choice of prior model is ours (hence subjective), the parameters are solely determined by the data.\n", + "\n", + "Personally, I feel that Empirical Bayes is *double-counting* the data. That is, we are using the data twice: once in the prior, which will influence our results towards the observed data, and again in the inferential engine of MCMC. This double-counting will understate our true uncertainty. To minimize this double-counting, I would only suggest using Empirical Bayes when you have *lots* of observations, else the prior will have too strong of an influence. I would also recommend, if possible, to maintain high uncertainty (either by setting a large $\\sigma_p^2$ or equivalent.)\n", + "\n", + "Empirical Bayes also violates a theoretical axiom in Bayesian inference. The textbook Bayesian algorithm of:\n", + "\n", + ">*prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior* \n", + "\n", + "is violated by Empirical Bayes, which instead uses \n", + "\n", + ">*observed data* $\\Rightarrow$ *prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior*\n", + "\n", + "Ideally, all priors should be specified *before* we observe the data, so that the data does not influence our prior opinions (see the volumes of research by Daniel Kahneman *et. al* about [anchoring](http://en.wikipedia.org/wiki/Anchoring_and_adjustment))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Useful priors to know about\n", + "\n", + "### The Gamma distribution\n", + "\n", + "A Gamma random variable, denoted $X \\sim \\text{Gamma}(\\alpha, \\beta)$, is a random variable over the positive real numbers. It is in fact a generalization of the Exponential random variable, that is:\n", + "\n", + "$$ \\text{Exp}(\\beta) \\sim \\text{Gamma}(1, \\beta) $$\n", + "\n", + "This additional parameter allows the probability density function to have more flexibility, hence allowing the practitioner to express his or her subjective priors more accurately. The density function for a $\\text{Gamma}(\\alpha, \\beta)$ random variable is:\n", + "\n", + "$$ f(x \\mid \\alpha, \\beta) = \\frac{\\beta^{\\alpha}x^{\\alpha-1}e^{-\\beta x}}{\\Gamma(\\alpha)} $$\n", + "\n", + "where $\\Gamma(\\alpha)$ is the [Gamma function](http://en.wikipedia.org/wiki/Gamma_function), and for differing values of $(\\alpha, \\beta)$ looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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s2YiNjUVYWBieeuop+VhJSUnyEoWlpaW4++67ERYWhvHjx6OoqAgpKSnQarUA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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "gamma = stats.gamma\n", + "\n", + "parameters = [(1, 0.5), (9, 2), (3, 0.5), (7, 0.5)]\n", + "x = np.linspace(0.001 ,20, 150)\n", + "for alpha, beta in parameters:\n", + " y = gamma.pdf(x, alpha, scale=1./beta)\n", + " lines = plt.plot(x, y, label = \"(%.1f,%.1f)\"%(alpha,beta), lw = 3)\n", + " plt.fill_between(x, 0, y, alpha = 0.2, color = lines[0].get_color())\n", + " plt.autoscale(tight=True)\n", + " \n", + "plt.legend(title=r\"$\\alpha, \\beta$ - parameters\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Wishart distribution\n", + "\n", + "Until now, we have only seen random variables that are scalars. Of course, we can also have *random matrices*! Specifically, the Wishart distribution is a distribution over all [positive semi-definite matrices](http://en.wikipedia.org/wiki/Positive-definite_matrix). Why is this useful to have in our arsenal? (Proper) covariance matrices are positive-definite, hence the Wishart is an appropriate prior for covariance matrices. We can't really visualize a distribution of matrices, so I'll plot some realizations from the $5 \\times 5$ (above) and $20 \\times 20$ (below) Wishart distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "n = 4\n", + "for i in range(10):\n", + " ax = plt.subplot(2, 5, i+1)\n", + " if i >= 5:\n", + " n = 15\n", + " plt.imshow(stats.wishart.rvs(n+1, np.eye(n)), interpolation=\"none\", \n", + " cmap = \"hot\")\n", + " ax.axis(\"off\")\n", + " \n", + "plt.suptitle(\"Random matrices from a Wishart Distribution\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One thing to notice is the symmetry of these matrices. The Wishart distribution can be a little troubling to deal with, but we will use it in an example later." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Beta distribution\n", + "\n", + "You may have seen the term `beta` in previous code in this book. Often, I was implementing a Beta distribution. The Beta distribution is very useful in Bayesian statistics. A random variable $X$ has a $\\text{Beta}$ distribution, with parameters $(\\alpha, \\beta)$, if its density function is:\n", + "\n", + "$$f_X(x | \\; \\alpha, \\beta ) = \\frac{ x^{(\\alpha - 1)}(1-x)^{ (\\beta - 1) } }{B(\\alpha, \\beta) }$$\n", + "\n", + "where $B$ is the [Beta function](http://en.wikipedia.org/wiki/Beta_function) (hence the name). The random variable $X$ is only allowed in [0,1], making the Beta distribution a popular distribution for decimal values, probabilities and proportions. The values of $\\alpha$ and $\\beta$, both positive values, provide great flexibility in the shape of the distribution. Below we plot some distributions:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Lt0TCU3saV2nonLR8/tAVV413BzbFZCTh2tEYTMaA3E8SaSGEEEKIc9zVJ2k4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vSwh7oDXv2Yx3BP1b1QwoHoXhhz1L1wpZBCYLd2UejcRLF7C/mebQ/WG75P4v5t0n3XSfdfJzF8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\nTqpWf5z26POkYLJKWOcxyYswn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "\n", + "params = [(2, 5), (1, 1), (0.5, 0.5), (5, 5), (20, 4), (5, 1)]\n", + "\n", + "x = np.linspace(0.01, .99, 100)\n", + "beta = stats.beta\n", + "for a, b in params:\n", + " y = beta.pdf(x, a, b)\n", + " lines = plt.plot(x, y, label = \"(%.1f,%.1f)\"%(a,b), lw = 3)\n", + " plt.fill_between(x, 0, y, alpha = 0.2, color = lines[0].get_color())\n", + " plt.autoscale(tight=True)\n", + "plt.ylim(0)\n", + "plt.legend(loc = 'upper left', title=\"(a,b)-parameters\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One thing I'd like the reader to notice is the presence of the flat distribution above, specified by parameters $(1,1)$. This is the Uniform distribution. Hence the Beta distribution is a generalization of the Uniform distribution, something we will revisit many times.\n", + "\n", + "There is an interesting connection between the Beta distribution and the Binomial distribution. Suppose we are interested in some unknown proportion or probability $p$. We assign a $\\text{Beta}(\\alpha, \\beta)$ prior to $p$. We observe some data generated by a Binomial process, say $X \\sim \\text{Binomial}(N, p)$, with $p$ still unknown. Then our posterior *is again a Beta distribution*, i.e. $p | X \\sim \\text{Beta}( \\alpha + X, \\beta + N -X )$. Succinctly, one can relate the two by \"a Beta prior with Binomial observations creates a Beta posterior\". This is a very useful property, both computationally and heuristically.\n", + "\n", + "In light of the above two paragraphs, if we start with a $\\text{Beta}(1,1)$ prior on $p$ (which is a Uniform), observe data $X \\sim \\text{Binomial}(N, p)$, then our posterior is $\\text{Beta}(1 + X, 1 + N - X)$. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Bayesian Multi-Armed Bandits\n", + "*Adapted from an example by Ted Dunning of MapR Technologies*\n", + "\n", + "> Suppose you are faced with $N$ slot machines (colourfully called multi-armed bandits). Each bandit has an unknown probability of distributing a prize (assume for now the prizes are the same for each bandit, only the probabilities differ). Some bandits are very generous, others not so much. Of course, you don't know what these probabilities are. By only choosing one bandit per round, our task is devise a strategy to maximize our winnings.\n", + "\n", + "Of course, if we knew the bandit with the largest probability, then always picking this bandit would yield the maximum winnings. So our task can be phrased as \"Find the best bandit, and as quickly as possible\". \n", + "\n", + "The task is complicated by the stochastic nature of the bandits. A suboptimal bandit can return many winnings, purely by chance, which would make us believe that it is a very profitable bandit. Similarly, the best bandit can return many duds. Should we keep trying losers then, or give up? \n", + "\n", + "A more troublesome problem is, if we have found a bandit that returns *pretty good* results, do we keep drawing from it to maintain our *pretty good score*, or do we try other bandits in hopes of finding an *even-better* bandit? This is the exploration vs. exploitation dilemma.\n", + "\n", + "### Applications\n", + "\n", + "\n", + "The Multi-Armed Bandit problem at first seems very artificial, something only a mathematician would love, but that is only before we address some applications:\n", + "\n", + "- Internet display advertising: companies have a suite of potential ads they can display to visitors, but the company is not sure which ad strategy to follow to maximize sales. This is similar to A/B testing, but has the added advantage of naturally minimizing strategies that do not work (and generalizes to A/B/C/D... strategies)\n", + "- Ecology: animals have a finite amount of energy to expend, and following certain behaviours has uncertain rewards. How does the animal maximize its fitness?\n", + "- Finance: which stock option gives the highest return, under time-varying return profiles.\n", + "- Clinical trials: a researcher would like to find the best treatment, out of many possible treatment, while minimizing losses. \n", + "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", + "\n", + "Many of these questions above are fundamental to the application's field.\n", + "\n", + "It turns out the *optimal solution* is incredibly difficult, and it took decades for an overall solution to develop. There are also many approximately-optimal solutions which are quite good. The one I wish to discuss is one of the few solutions that can scale incredibly well. The solution is known as *Bayesian Bandits*.\n", + "\n", + "\n", + "### A Proposed Solution\n", + "\n", + "\n", + "Any proposed strategy is called an *online algorithm* (not in the internet sense, but in the continuously-being-updated sense), and more specifically a reinforcement learning algorithm. The algorithm starts in an ignorant state, where it knows nothing, and begins to acquire data by testing the system. As it acquires data and results, it learns what the best and worst behaviours are (in this case, it learns which bandit is the best). With this in mind, perhaps we can add an additional application of the Multi-Armed Bandit problem:\n", + "\n", + "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", + "\n", + "\n", + "The Bayesian solution begins by assuming priors on the probability of winning for each bandit. In our vignette we assumed complete ignorance of these probabilities. So a very natural prior is the flat prior over 0 to 1. The algorithm proceeds as follows:\n", + "\n", + "For each round:\n", + "\n", + "1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", + "2. Select the bandit with largest sample, i.e. select $B = \\text{argmax}\\;\\; X_b$.\n", + "3. Observe the result of pulling bandit $B$, and update your prior on bandit $B$.\n", + "4. Return to 1.\n", + "\n", + "That's it. Computationally, the algorithm involves sampling from $N$ distributions. Since the initial priors are $\\text{Beta}(\\alpha=1,\\beta=1)$ (a uniform distribution), and the observed result $X$ (a win or loss, encoded 1 and 0 respectfully) is Binomial, the posterior is a $\\text{Beta}(\\alpha=1+X,\\beta=1+1−X)$.\n", + "\n", + "To answer our question from before, this algorithm suggests that we should not discard losers, but we should pick them at a decreasing rate as we gather confidence that there exist *better* bandits. This follows because there is always a non-zero chance that a loser will achieve the status of $B$, but the probability of this event decreases as we play more rounds (see figure below).\n", + "\n", + "Below we implement Bayesian Bandits using two classes, `Bandits` that defines the slot machines, and `BayesianStrategy` which implements the above learning strategy." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "rand = np.random.rand\n", + "\n", + "class Bandits(object):\n", + " \"\"\"\n", + " This class represents N bandits machines.\n", + "\n", + " parameters:\n", + " p_array: a (n,) Numpy array of probabilities >0, <1.\n", + "\n", + " methods:\n", + " pull( i ): return the results, 0 or 1, of pulling \n", + " the ith bandit.\n", + " \"\"\"\n", + " def __init__(self, p_array):\n", + " self.p = p_array\n", + " self.optimal = np.argmax(p_array)\n", + " \n", + " def pull(self, i):\n", + " #i is which arm to pull\n", + " return np.random.rand() < self.p[i]\n", + " \n", + " def __len__(self):\n", + " return len(self.p)\n", + "\n", + " \n", + "class BayesianStrategy(object):\n", + " \"\"\"\n", + " Implements a online, learning strategy to solve\n", + " the Multi-Armed Bandit problem.\n", + " \n", + " parameters:\n", + " bandits: a Bandit class with .pull method\n", + " \n", + " methods:\n", + " sample_bandits(n): sample and train on n pulls.\n", + "\n", + " attributes:\n", + " N: the cumulative number of samples\n", + " choices: the historical choices as a (N,) array\n", + " bb_score: the historical score as a (N,) array\n", + " \"\"\"\n", + " \n", + " def __init__(self, bandits):\n", + " \n", + " self.bandits = bandits\n", + " n_bandits = len(self.bandits)\n", + " self.wins = np.zeros(n_bandits)\n", + " self.trials = np.zeros(n_bandits)\n", + " self.N = 0\n", + " self.choices = []\n", + " self.bb_score = []\n", + "\n", + " \n", + " def sample_bandits(self, n=1):\n", + " \n", + " bb_score = np.zeros(n)\n", + " choices = np.zeros(n)\n", + " \n", + " for k in range(n):\n", + " #sample from the bandits's priors, and select the largest sample\n", + " choice = np.argmax(np.random.beta(1 + self.wins, 1 + self.trials - self.wins))\n", + " \n", + " #sample the chosen bandit\n", + " result = self.bandits.pull(choice)\n", + " \n", + " #update priors and score\n", + " self.wins[choice] += result\n", + " self.trials[choice] += 1\n", + " bb_score[k] = result \n", + " self.N += 1\n", + " choices[k] = choice\n", + " \n", + " self.bb_score = np.r_[self.bb_score, bb_score]\n", + " self.choices = np.r_[self.choices, choices]\n", + " return " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we visualize the learning of the Bayesian Bandit solution." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "figsize(11.0, 10)\n", + "\n", + "beta = stats.beta\n", + "x = np.linspace(0.001,.999,200)\n", + "\n", + "def plot_priors(bayesian_strategy, prob, lw = 3, alpha = 0.2, plt_vlines = True):\n", + " ## plotting function\n", + " wins = bayesian_strategy.wins\n", + " trials = bayesian_strategy.trials\n", + " for i in range(prob.shape[0]):\n", + " y = beta(1+wins[i], 1 + trials[i] - wins[i])\n", + " p = plt.plot(x, y.pdf(x), lw = lw)\n", + " c = p[0].get_markeredgecolor()\n", + " plt.fill_between(x,y.pdf(x),0, color = c, alpha = alpha, \n", + " label=\"underlying probability: %.2f\" % prob[i])\n", + " if plt_vlines:\n", + " plt.vlines(prob[i], 0, y.pdf(prob[i]) ,\n", + " colors = c, linestyles = \"--\", lw = 2)\n", + " plt.autoscale(tight = \"True\")\n", + " plt.title(\"Posteriors After %d pull\" % bayesian_strategy.N +\\\n", + " \"s\"*(bayesian_strategy.N > 1))\n", + " plt.autoscale(tight=True)\n", + " return" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + 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al8A0NqEhIucCtwAXisinIrJRRJa03SfIGLMS2C0iO4A/Al8NY5Ujlit2IKOu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\nAW7MIKyXFlAUNqDWum9lyLYXs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fI2B3jwwcN3/P9z8uRJXnjhBQAK\nCwtxOBw8/PDDrIS4r0DMhC+9DXxRCPHz+c999rOfFSMdXeRny0nGJoOB6vJNHNghu2+cvXoZ4K5p\nn7l8EV//MOUTASbO1XKhSR4zq1VyfHNDxBPtm2q1ga5SO+adm3nff/gE5h2bOXXmDJAcN4VEtevq\n6vjsZz+bNNeTLO35ca7r+frhiGDMVsl3Lw0weEP+vJvKdqDTqNgcaGd7jpG99y1+U79w+hR1b7WS\nqS8BoG+0mcoDhezafx/vfv8KXX0NbHukYtk39aXas9tWevxPfHIuxodTe1d0fDzbTn+YExRhm/Jh\nuyzfD/btO8CnPn/wtv9fzz33HHV1dRQWyoOmw+Hgz//8zxPqwiRJ0t8CHiHEl+ZvP3HihBh95gtE\n/MFbH5+ixby9Cuu+bVj3bcOyd9tdPfFy8uTJDV1ZeK1Q+mVpEtk31wam+J/vdjHonpupN+rUfGJn\nNjXZ6xu+ff7legZncsbsRRYC6SPRe+tKmZ1cms9mWypf2J1N6jqE4P78e1dwO+XV/tU48s1nNSsQ\ncRUQkiRpgFeAV4UQX7n5+bs1hGm5BCddTF6qZ/JiHZMXrxNyyTZmDRFPVFTMorWayHhwH/aHDpD5\n0H50joxEXHLCUQaKxUlEv9T2u/nqmV66JmLDlXblGflQjQOL/tYLmrW/aaarbhCQ41G3P1KBKVP+\n3MdzBaL2yvlVDRTJsgIxy6udTs71unmoa4TZu/zn/+Yo+rSUOzpPIkKYJEnKBIJCCKckSXrgdeAf\nhRC/mr/fiRMnRIlIwdPajbu+BXd9K+76ZoKTty/klF5RjHXfVqz7tmPZU0NaaQHSOoRHrAfK/W9x\nlH5ZmkT0TSAU4d8uDfDTuuGYBKcduQY+tj1rxQXgVop7zMNb37kUbe96fxVtnXVxExAPFxg50TN3\nb6qw6vgve3LQrbGIOPVGCx1Ncj2II++vYs+h4lWfM5lCmL4FNCwmHhRAazFhf/g+7A/fhwhH8LR2\nMXmxDuPF67hvtME8a7PghIvBl95g8KU3ADBt3UTGg/vIOLwX695tqPW6RL2NdUUZJBZnPftl1BPg\n6+f6eLs9NhHOYdDy0e1ZVNrTlzhyju7rg1HxAFC6MzcqHuLNageJZOPBPCOXhqdx6TSY/XI8cU/7\nOJtqEp9EtwxygO/M5EGogB/dLB5mUWk0GKtKMVaVwm89hhACX/8w7uvNuBtacV1vwdc7uOA4T0sn\nnpZOer//CwC0NjOWXVuw7N6CZc9WzDs3ozGszWdtrVHuf4uj9MvSrHfftIxO80/vdMVMLOm1Kj6y\nLYs9+caEiPmWCz3Rx7ZcEwarnu3W+I0LD+Ub0UgSr3fLSc0tE36+cmWIL+zKRqteu/drzzZGBUQy\nODHFTUBIknQ/8AmgTpKkK8hOG38lhHgtXq9xNyGpVRgqSzBUlpD/iQ8SdE3hvNLA5MXrTF6sIzju\njNnfVdeMq66Zjq9+D5UuBeu+bWQc3kPGA3sxbd2EpN44riwKG4NgOMLP6kf4/pVBvME5d6UUtcTj\nlRk8VG5blgvFxKCbayfm6j3YiyzkVipuO8slTaviwTwjbSOuqIBobxndEAJCCFEHrKhCnCRJ6POy\n0Odl4XjsAUBexXU3tOKqb8Vd34KnpTOmPg9AcNzJyBunGXnj9OyJMFSVYtlTg2V3DZbdW0gvK1SS\nsxUUVkE4Ivhh7RDfuzzAvFqhVNnT+OSubCx6bUKua9rpo69xONouXCO3ogfyDKgkeLVLFhHXR718\nrXaYz+1woF4jd6bMLGP0cX8SVKSOm4AQQpxiNsND4Y44e/UyB3bsIvPBfWQ+uA8hBNPtPVEx4a5v\nQYTnfsBF/AHG3rvI2HsXga+htZqw3b+bjMN7yTy8B31RnrKEf5ez1v1yuc/Fs6d76XH6Y7bL4Ur2\nZQ8OXref8z+vJzLz+U0z6di0v3BNP5+rDWFKRg7kpFPflgqTsiPqjRsjvC/B15QItBYTtoO7sB2U\nNUnY52equVMOe2poZaqxjZDbE3uQEEw1tjHV2Ebvv/985jxGzLtqZlYpajDvrE5Ki23l/rc4Sr8s\nzXr0Tc+kj396p4umkenothS1xDM1dg4VWxL6+6PpbBezkflmhyG60r0W48L9uQb8YcGbvXI404Uh\nD9+6PsLvb7WvicvU/IJyU0lQUE6pRJ2ESJJEelkh6WWF5H30/YQ8Xly1N3BeacB5pQFvz0DM/sEJ\nF0OvvMXQK28BoC/Iia5OZBzaTUqmNRFvQ2EDMuD2841z/ZzsjJ3dyDam8JFtWWyyLz+HKRQMc/7l\nevwzVUDVWjXVD5ai1i6cZ0gG96VZkiX3YT5alcTOMhvTveOoBYTcfkZGPdjXKAxso6BO1WHeVol5\nWyUgF47y9Q3hbmxjqqEN9402pjt7Y8JDAYKTbkbfPMPom3JiOpKEYVNxdJXCvLNatpBVVnYVFKJE\nhODlhlGeP9+Hf96yQ7E1ld/bnYPdcGd5WfHGPeahp2Eo2i6K8+rDYmPDQ/kGfOEIpwfkiYv3+qaw\n6DR8uNIW19eGuYJy0XoQ3YmtB7FmdSAW415Poo4X/pFxnFcbZUFxuSHGKnYxjDUVUTFh3b9tw8YD\nK6wdnkCYH9YO8eL1YYLzBgadRuL9VZkcKbXe0bKsEIJLv2ykv1mO10SCrUfLsWYbb32gwpKEIoJX\nf96AeVoWZLZ9hXz66eplH5+oOhDLYS3HhvC0V16lmFmFcDe2RQ0sboVan4ppeyXm7Zsx76zGvLMa\nfWHOXbO6q6BwJwxPBfh/3+3iSv/cd0ctwRObMzlWYVuXug634/zP6xlsk52XLNlGtj1cvi6vGxGC\nl9omuTzijW77dE0mRwpMcX+tq2e7uX5Jrq69+/4iHnpi86rOl0xJ1ArrgM5uw/HI/TgeuR8hBN6u\nPpyXG5i80oDrWhMRX2zYift6C+7rLXQ+9wKSWo1pexW2gzuxHdyFdd9WRVDcw4Qjgl83j/FvlwaY\nmFfwB2BvvpFnahyYUu/8NtF0umtOPABle/IV8bBKNCqJjBwToTa5X5ubRvCHImvu/LHRUafpMe/Y\njHmHPNDOJmdPNcorFFONbXjaeyESiTku7PVF6/bMorWZMe+ols+3Uz6nzh7/mUYFhWRBCMEbreM8\ne7qX6Xm5cLmmFH53dw75CQyhmc9YnzMqHkA26lgvVJLEU2UWPMEITZPy769/qx8lU6+hJjO+EyOZ\n88bRRCdSKwIiCZjNgVgJkiSRVpxPWnE+OR96lEgwxFRTezTcyd3YHjMwinAY5+V6nJfr6fjq95Je\nUCixrosTj3652u/ma2f7aB/3xmwvtOj47a1ZlGboV3Tejqv9NJ/rjrZzKjLJ27R+SdN3Yw7ELJvL\nrNTNCAjDlJ9fN4/xZLWSkH4nzE/Oth+Ta5TM5lJMNbYy1dTB1I0OAmMTC44NjjtjQ5+A1PxsLDtn\nRUU1pm2b4nYPVe5/i6P0y9LEs28mvUG+crKHU11zUQ4ScKzCyvurMtGuUxXm2yGEoPFkR7RtL7Ji\nsMX+cF/rcUEtSXxkk5Vv1o8x4AkSEfAvV4b42wN55BvjF9qVmTWXqzXc7yIUDKNZJCx4PVAExF2G\nSqvBVLMJU80mCj71tJw/UdeE80oDrrpmptt7YF7Y2kYTFAqrp3vSx7cu9HO6Kzb0zZyq5qktdvbk\nm1a8HN3fPELdm3OOS9YcI+V78ld1vQpzWDLSQaOCUITUcIRfXOjj/VWZa+b6sVokScoHvgtkARHg\nG0KIf07sVS3k5lwKgMDYBFNNnUw1tcviormD8NT0gmN9vYMM9g4y+Is35Q0z+RSm7ZsxbduEeVsV\nxi0VaNJXJsgVFBLBqc5JvnyyB6dvbmU6M03L7+7OWfHk0lox1D7O+ExegKSSKN6ek5Dr0KlVfKrK\nxtfqRnAFInhDgv95cYC/uy8PywpW8hcjVa/FZEnFNekjHBYM9DopKEnMKqiSA3GPEXRN4b7ejLP2\nBq5rTUx39MYIipuR1GpMO6qw3bcT24EdWPbUoLXEP65PYe0Z9QT498uDvN48FpNTqlVJHKuwcazC\ntqpwmNGeSc6+WEdkJofCYEtj+7HyRZOmFVZO3TvtTPTK4u9GhoFPPr2FI2W3N0pIUCG5bCBbCHFV\nkiQDcAl4SghxY/5+G2FsEJEIvoERWVA0dTDV1IGntQsRDN3+YEkivbwI8/ZKTFsrMW2rxFSzCY1R\nmZxRSC6m/CGeO9vHb1rGY7YfKjbzTI0j6UImI+EI73zvMu4xWdznbsqkfG9BQq9p0BPkG/Wj0UTz\nYlMKf70/N259d/atNlobZKva+4+Vc9/Rled6KDkQCstGazLE2CAuEBTtPTH7i3AY56V6nJfkFYpZ\nT3Xr3m1Y92/Dum8bqfnZSmJhEuP2h/hx7RA/qx8hEI4Vi3vzjXxwix3rKj27JwbdM3at8vn1Rh1b\nHypbtniIZyXq1ZJslahvJiPXFBUQGdMBflY/vCwBkQiEEIPA4MzjKUmSGoE84MYtD0xCJJVqLvTp\n6H0AREIhvJ19sqBolkXFdFffAtcnhIgWvOs//np0c1pZIaat8iqFadsmTFsr0ZqVXCGFxHC+x8mX\n3+thdDoY3WbSqfnkrhyqs5JT7HbWDkTFg0qjWrO6D7D8sSE7XcvHNln598ZxIkCnK8BztcP88a6s\nuCSbO3JNUQHR27kw1HK9UAREErCaHIjVcqeCYr6nes93fwZAaq4Dy75tWPdtx7p/G8aq0rjZHyqx\nrouznH7xhyL8vGGEH9UO4fbHFtuqyNTz9BYHRdbVJ8BNDro589NrhALya6ToNWw9Wo42Tku2d8rd\nnAMBxCSjW31B3hry0DjsYbMjOQf4WSRJKgZ2AOcSeyXxQ6XRkF5eRHp5EVlPHAHk5GtPazeelk6m\nWrvwtHTh7R1YKCqA6bZuptu6GXzpjeg2fVFuVFA0qvwc+8hvKYnaN6GMC0uzkr7xBMJ87WwvrzfH\nrjrsyjPyse1ZpKUk5yqyzxPgxunOaLuwJouU1MUnw9Z7XKiwpPJkqZmft8uTPZeHpznePMFH4mDv\nmpU7FwXS1zVBOBxBnYB8FEVAKMSwlKBwXWvCVd+Kp7VrgVuJr3+YwZfeiA6CGmM6lj1bZ1YotmPe\nsRl1WnI4NdwLBMIRXm8a4we1Q4x6gjHP5Zt1PLXFHrcfm5NDbs78tI7QjEDRpKjZ+lA5qQn2A7+b\n0Rt1pBpS8E0F0AiBxRfkZ9eH2Xy0JNGXtiQz4UvHgT8RQizwUD1+/DgjHV3kZ8uxyyaDgeryTdGJ\nlbNXLwNsiLZan0pDeApKMznwoUcBOHX+HP6+YTar0vC0dHL22hX8g2NUS3IseUNE9pCvVqXj7ern\nUkcLyDXvUH/x27SYNaQV53Ho8GFMW8q57nOSmuvggcOHAflHIxD94Xi3t+vq6pLqejZy+2Kvi79+\n/uc4fSFMZTsACHZd42i5jY/ufRiAS+fkqu679x9MqrY0biMUCNPV14AuTcuhqu2ALBaAqGCovXKe\ntpbGmPbNzy+nDfl3tP/enfsY84b41clTALzCDnINWlL66wHYt/cAAOcvnL2jdv2NKwxNtJBlrSAU\njPDKz39NhsOwrP/vkydP8sILLwBQWFiIw+Hg4YcfZiUoORAKd0TY52fqRjuu6y1y9dfGViJe/y2P\nkbQaTFsr5SJNu7Zg2b1FCXtaAwLhCK81jfHDRYRDRpqWD1ZnsjPPGDe/7skhN2eO1xH0yzHgmhQ1\n246VY7De+XdcCWG6M5rPdTPYKlsWtlvSac8w8O8f24I9fWnhlqg6EJIkaYBXgFeFEF9ZbJ97cWwI\n+wNMd/TimVml8LR2Md3ZiwiFb38woNLrMFaWYqypwFhdgammAmN1mWJ6obAsPIEwXz/Xx6tNYzHb\nd+Ya+Mj2LIy65J5fHu4c5+yL16PtmofKsOWubX7mSsaGiBB8v2mcpgn5d5JGgr/cn0vFKlf/T7/R\nSnvTCACH31fJvsMrm0BSciAU1g11qi7WUz0cxtPei7u+Gff1Flz1LQTHY919RDAUdXrqmtmWYrdh\n2S2LCfOuGsw7qtCk31s/IOJFIBThteYxfnh1KCZ2FcCoU/N4ZQb3F1vi6tQz1jvJuZfqo2FLmhQ1\n2x5emXhQuHOsOcaogLB5A7QKePXGGL+7OzHuI7fhW0DDUuLhXkWtS8FYVYqxqjS6LRIIMt3VL+dL\ntM6Jiog/uOD4iNcvFxS92hizXV+Ui6lmE8bq8hlRUa5M2CjEcLprkq+e7o2ZaEpPUfPR7Vnsykv+\nHJxQMMy1N1qibXuhZc3Fw0pRSRIfqbDy9bpRhrwhQgK+fHmQvz+YR+Yqcg8ducaogOjpGF+xgFgN\ncRMQkiQ9D3wAGBJCbIvXee8FEpkDsVoktRpDRRGGiiJynn4EIQT+wZGomHDXt+Lt7l9wXGBknOHX\n3mP4tffkDSoVxs1lsqDYWY1ldw3p5YWcOn1aiXVdhJMnT7L3wEFeaxrjR7WLC4dHKmwcKraQEmfX\njMG2MS6+0kgkLIeyqbVqtj5cvsB3O1Hc7TkQAJasuUHe7A+iCUd4tWmMj+/MRpNElq6SJN0PfAKo\nkyTpCiCAvxJCvJbYK0tOVCna6P0U5LFh/9Yd+PqH8LT1MN3eg6e9G097D8GxxYtIebv68Xb1M/TL\nt6PbNCYDhqpSjFVlM39LMWwuI8WanD+6boeSA7E0t+qbUU+AZ0/3xtR1ANieY+BjO5J/1WGWxvc6\nmHbNzOinqCnbe3ur8ESOCzq1ik9W2fha3SieUAR3IML/ujTE3xzIRb/C8Xl+HkRvx3hC8iDi+Wn5\nNvAvyJ7fCvcokiSRmuMgNceB/ZH7ATmPYqqhFXdTO1ON7UzdaCfs9cUeGInIIVH1LfR89yVAHvQ6\ni21kHbuBZVc1pu1VSjIh4PKF+E3zGF/prI/x6AZZODxaYeP+NRAOAN31g9T+ujnq/KtNlROmDdbV\n+YInQ+jSLMkcujSLVqfBmJGGe2waCbD5AgyrVZztcnKoxJLoy4sihDgFJGcG5gZBUqvQF+SgL8iB\nI3M/gIKTLjzts6Kih+m2Hrw9/YhwZME5Qq4pJs9fY/L8tZjtuqxMDFUlMcIifVOJUrPiLiMcEfyi\ncZR/u9gfU03akKLmw9sc7MozbpgVquHOcTquzk1Klu7OWzJxOt6sZmywpmr4nUor324YIyygxx3g\na7XD/MkKnZkM5lTSjTo8bj/BQJiB7kny17keRFxzICRJKgJ+sdQKxL0Y56qwEBGO4O0ZwH2jLSoo\nprv6blmPYpbUvCzM26swba/CtK0S87YqUjKS5wfTWjLg9vNi3TCvNY1F/aVnWWvhIISg6XRXTIXp\nVEMKW4+Wozfq4v56Cren42o/PfVDAPQY9TTaTezMNfI/3r+4J3iiciCWgzI2xIdIIIi3ux9Pew+e\ntm6m23vxtHcvWgBvSSSJtKJcWVBsLsNQWYqhqpT0skJU2o0xQ60wR9OIh6+e7qVpJPYzcKDQxDM1\nDtKT1GFpMfzeIG9/9xJ+TwAAW56JLQ+WbhjxA7Ib04ttc6uHT5SY+WhVxorONb8exIGHyjj0SMWd\nX4+SA6GwkZDUKtKK80grziPrfbKLSMjjxdPSibuxjakb7bgb2wg53QuO9fUN4esbYuhX70S36Qty\nZDGxowrT9s2Yt1XeVcXumken+cm1Id7rmFzgBGnVazhabuP+YjMpa7R8GQqEufzajWjMPUC6JZWt\nR8tJWWX9CIWVY80xRgVEhlceUK/0uxlyB8gyKi5Y9yKqFG3UVnYWIQSB0QmmO/vwdvYx3dnLdGcf\n0939iMDC3AqEkJ/v7JsLMUU2w0gvLSC9ohjDphIMm4pIrygmvawQdaoyiZBsjE8H+fbF/gXWrA6D\nlo/vyKY8c2MJdiEEV169ERUPWp2GTQcKN5R4ANjlSGPYG+Rkv+y89ssOJ7mGFB7Iv/Pck5x8c1RA\ndLWOrkhArIZ1FRB3k1VfPNuz25LlehLR1qTracQLm3M58DsfQAjBe2++ydXzF3nSnM9UcycXmhoQ\noRDVKtllJGp92DOAt2eAt37xS7mtSkdflEtHjon08kKOPv0BTFsrOVdXCySHdd7t2oFwhK8df43T\nnU7GM6oAcLVdBcBUtoOUgXr25JuoMKWxt6wMWBurPL8nQKDPiGvEQ1dfAwDbd++n+oES6usvye1V\nWuPFuz27LVmuZ63anT31dA+2U5i9mbRQGH/TZfwaFW+05vCJndk899xz1NXVUVhYCLAquz6FxBCP\n/DhJktDZbejsNqx7t0a3i3AE38DwjFjojYoGX9/gojUrRDAUrcA9xFvzX4C0olxZWFQUk76pGMMm\n+fFaVdpWciCW5u1332XEUsn3rwzGhCupVfDYpgweqbChTUDNgNXScr6H4XlF0zbdV3hHoUvJlBv3\naKGJUW+IGzPOTN++PkJWupZNd+jMlF1gjj4e7HXi8wZJXcdJPSWEKQnYyEnUa838vomEQni7B+QC\nTc1yVVdPWw8iFLrNWWT0hbkYt5Rj2lKBcUs5xi2b0BcklzvJ8FSAXzaO8mrTGJO+he9rU6aeRzZl\nMN1ey+4DB9f0WgZaR7n6enPUphUgr9JO6a48pCRK1L2ZZBoo1pq6t9qY6HcB0JhhpMecRp5Jx7c+\nvHnB51oJYdp4JGJsiASCeHsGZEHR0ct0lywwAsPjtz/4JnTZmRg2lZBeUSSLiwpZXKRkWld131UE\nxEKEEJzucvKP33sFf/aWmOe2Zqfzoa2OW9o8JzND7WOce6k+2s6vdlC6M++OzpFs44I/HOHr10cZ\nmpbHV2OKir+7Lw972p0JgF/9+BrjI/Jk6lOf2EnFlqw7On4140K8BUQxsoDYutjzyiChEG8iwRDe\nrr4ZQdHFVEsH0x3L91LXmAxzdodbZv5VlqDSrd+NNiIEV/rcvNw4yrlu54LJP7UEO3KNHKuwUWBZ\n+4J84VCEhvfa6bgyl6gmqSQq9hWQXbayWE2FtaG/aYTWi70AjKfpuJgt5wN9+clNVGfFzv4qAkJh\nNYQ803h7BvB2D+Dt7sfbPcB0dz/+wdFl5a/NR2M2yuFQZQWklRbKj8sLSSspUBK4V8C1ATfPX+in\ncTg2zyHLkMJvb3MkfZX6W+Ea9XDyh1ejluEmezrbj1Uk9STWcpnwhaLOTAD5Bi1/e1/eHTkzXTnT\nRf1leazetjefR5+puaNrSIocCEmSXgCOABmSJHUD/1UI8e14nV9BYTFUWs2CmF/ZS70PT7O8UjHV\n0om3q29RURFyTTFx9ioTZ69Gt0kaNenlRTGiwlRdTkqmNa7X3u/y85uWcd5oGWdoKrDgeUuqhkMl\nFg4WmTGlrk+0oWvUw5XXmnAOzxULTknTsvlQMWa7Yc1eVykktzJseSa4KD+2egOoI4KwSuKNlvEF\nAiJRKBbfdwea9DSMVWUYq8pitof9AXy9gzHiYrq7H1/f0JITOSGnG+eVBpxXGhY8p8uxz4iLQtLL\nCkmbeawvyFGSuG+idXSab13s52JvbL5gqkbFE1UZHC61xrX+z3rjdfs597PrUfGgS9NSfbgkYeIh\n3mODNVXDxyutfGvGmal3KshzV4f5093Ld2bKK7JGBURr4zCPPCXWrX/i9m0UQnw8Xue611BCmJZm\nJX0je6nLMbhZT8jbIsFQ1J1kuq076lKymDuJCIWZuiG7Q3vtu6IAACAASURBVHH89ej2lEzrnId6\nVansTlJZgta0/B/WnkCYdzsm+U3zGNeHPIvuU5Gp50iplZpsw5I3/0vnTkdzFeJBJByh9WIvzWe7\niMxzeLLlmai8rwjtBvEHh+Rbql5LUg060sypTDt9SEJg8/oZSU/l7fYJPnMgb00cuVaAYvG9QjbC\n2KDWpUR/7M9HhMP4BkZiRIV3Jl8t4vUveT7/wAj+gRHGT12O2S5p1LL5RmkhTSkhDh0+LLeL8kjN\nc6DSbJx71GppHZ3mB7WyscZ81Coo8rTyBx96bMPUdFiKgC/I2Rfr8Lrlz4pKrWLLkdIVW7Ym67hQ\nZNLxVKkl6sx0dWSa7zWM8anqjGWF+WVmG9HpNfi9IaanAgz0TpJbGN/JzqXY2J8wBYVlotJq5ga5\nmfoUQggCIxN42rtjRIV/YGTRcwRGJxg/eYnxk5ditqfmZWGonBEWlSWyuKgoRp0mhxsFwxEu97l5\nq22CU52TCyxYAdK0KvYWmHigxEL2OtuiOoenuPrr5phVB0klUbIzl7xKe1LliCgsJCPPxLRTrquS\nHwgxkg5TgTBne5wcLlmfgeRWCCFOzuTHKdxDSGo1+vxs9PnZcHBuZVEIQXDcibdvCF/vAN5e2VnP\n2zuIf2B40ToWIE/seFq78bR2Mxjx0PDK2bnX0qjRF+TMuPvlR13+9EWywFDr7w6XqOuDU/zg6hAX\nel0x2yVgX4GJJzZn0lE3dneIh5/W4R6bm+CrPlyCwXp3hjnucqQx4g3xXr88Br/R7cKsU/NU+e3v\n3yqVRH6xjbZG2Y2ppWFYERD3Esk+w5RI1rJvJElC57Chc9iwHdgR3R7yeGVXkqio6MHb1UvEv4jl\nIXPWsqNvnpl/clT5OUxk5dJuyGDI5mDcngWZWaCXb4IqCaod6RwoMrMlK/2OnDHisfrg9wa5caqT\nrroBuT7wDAZbGpX3FZJu2ZixyMk4y7SW2PLM9MxY+dmn/WBJB0niN83jSSEgFFbO3Tg2SJJESoaF\nlAwL5m2VMc+JcBjf4KgcEtU3NPe3Z4DAvMrbs0580eNCYTnhu6MXOLfgNXXZmdHVirTiPPTFeaQV\n5ZNWko/WktxF1CJCcLHXxQ9rh7g+uHDVemt2Oh+stpNjkkWSLY4r04nA7w1y7sU6JoemYrbb5lVe\nXgnJPi48UmjE6Q9zbcwLwE9bJjDr1BwpuP37LiidExCt9UMcfmzTunymFQGhoHATmnQ9pi0VmLbM\neSqLSAT/4OiMI0lf1FPd2zuweJyvEER6+jH39HNzVL/XZIbCfKyVxaSXF6GNFCJJBYgsO5Jq7UNO\nwqEIXdcGaDrTFeOwJKkkirflkL/ZcVckqN0rmDLT0ejUhPxh8Icw+4M4U1O40OtiwhvEugFqdSgW\n30p7tq3Py6J2pA9KMznwoUejz0f8AXZk5uLtHeTM+XMExiapDKjx9Y9QOybHgC+w+J5pX+nvgv4u\nqs8ufF5jTKfVoiXFYeO+nbvRF+RQ5x4jxWHj6AefQGsxJcTS2xeM4LZX8YvGURouy6LIVCZPdLnb\nrlKWoefTTz9KviWVS+dO0098LbwT0d5ctYuzL9ZRf11e5S/Kqwagq6+B2ivBhFtoQ/6anv9D2/fi\nCYW5clluf5sdGFPUhLvrANi39wAA5y+cjWn3DDbQO9hEfvZmJsam+dUrb2C26hf9fJ08eZIXXngB\ngMLCwlXZe8fVhel2KE4bi7MR4lwTRbL3zbAnwLXmQTqbe/F09mEdHCBjuB/L2AiqO/xuSfpUtMX5\naEsKSCkuQFuUh6YwD21hHmpzbJGZleRARMIRehqGaD7bHY0rncWaY6RsTz5pprV3eVqMeCZRrzbW\ndSMlUc/SfLabwTa50N+kw8h5g3yf/eyBPJ6pcQCJdWFSLL5XRrLf/xLFzf0S9vnxDYzgHxjG1z+M\nb2BE/ts/jH94DCKLh0UtB43JgL4gB31B9szf2Mda850XALsVXRNeXm4Y5Tct4/hCsdetkmBvgYlH\nKzKWLBYZ7/y49WK838WFl+vxT8+t9FfsL6DlXA+w+rEhHjkQ6zE2+MMRnq8fo98j94NGgv9tVxY7\nb+Ok9e5rTXS3yVbL+x4s4fBjlbfcf5akcGFSULgXCEUELZ4IlyYjXHaG6fEKwA6ldiidu8Gpg0GK\nxwfY5hqiaHKItKFBQv1DhAaGIbh43Qrh9RFobCXQ2MrNC9UqiwltYS7awny0hbl4gy58abZFxcXN\nhEMR+m4M03yuOxorP0uqIYWy3fnY8kwJXcZPBvelWTaScJjFXmSJCgirywvpepAk3u2YjAqIBCPN\n/FNQiDvqVB3pJfmkl+QveC4SChEYHsc3MIyvf0T+OzCMf+ZxxL/QAW8+IdcU7voW3PUtiz6vMRnQ\n52eTmusgNTeL1DxH9LE+z0FqjuO2tuAuX4h32id4o3V8gRUryK5KBwpNHC23YbvDOgHJjhCCrroB\nrr/VFjXwkFQSVQeLsBdZySnPTPAVzrEeY4NOreJ3N9v4xvVRxnxhQgL++fIQf3wbEVFSaY8KiPrL\n/Rw6VoFqjQsGKisQCgq3ICwE7R5BvTvMdVeEG1MR/LeYzLJrBTUGie0GyNex4Ee5iEQID48R6h8k\n2Dcki4r+QUJ9Q0TcU0uc9daozEa0RXloC/LkVYu8bDT5OYjMTHr6/XTWDsTM6gBodGoKt2SRu8m+\n5jcZhbVHRARnXqyTw5iAC7lWJlJTkIAXfqeGjHRtwlYg5lt8A0MsYvGtjA0KiUAIQcjpxj80hn9o\nFN/QKP6hUbk9OIp/cIRIYPHctzshJdMaIy70uVlocux0agyc9mp5z6UiIC28D2cZUjhSZmFfgRld\ncjiqxZWAN0jtGy0MtIxGt2lS1FQfLsGSFd+VnY3GpD/E8/VjTMzc09UStxQRkXCEF79zGZ9X/rw+\n87u7KKu6/eSRsgKhoBAnghFB57TgxpQsGBqnInhvUZNOjaAsTaI6HTanQWbKrW/ykkqFJtuOJttO\n6q7Yeoth11RUTIQGhggNjkT/EVx6EIs43fiv3cB/7QYCmM4uYnzTTlzFmxGa2NkqtQiTYwqRV2ZF\nm5Oq5DrcJUgqicwCC4Ot8ipEZSjMWeTc+FNdk3yw2p6wa1MsvhWSFUmS0FpMaC0mDJUlC56fFRi+\nwXnCYlZkzGxbjsAIjE4QGJ3Ade3Ggue2A1slCY/RzJTJgsdkRpeVSW5pDlnF2Wj6M5FCGYQdGahM\nyZ3wvVyEEAy0jFL3ZmvM5FaaJZUtD5aiN9wdrlmrwaLT8PtbMnm+fpQJf5jwzErEH2xzcDB3oXW8\nSq2itMpOw0wB2OsX+5YlIFaDIiCSACXOdWnWsm+EEIwEBC1TEZo9EVqmInRMC0K3WZSzaARVaRKb\n06EiTUIXpx/hapMBtakcXVV57HVGIkQmnIQGhgkNjRAaGOZqUz1VXikqLvymDJwl1UyWbyNgXlgt\nWuNxkdFwHtuNS6iD/rkQqdRU1DkOVNlZqByZqOyZc3+zMlFl2JA2mL96svp9rzX2ImtUQJgnPajS\nUomoJN7rSKyAUFg5ytiwOOvVL/MFhrGqdMHz8wVGYGScwMg4/tm/oxP4h8cITjghcutBRSUERtck\nRteM01QD8BaM3rSflKJF7chAnZmBxpGB2r7w77XuVnYfOZq0QmNi0E3Du+2M9TpjtmeXZ1C2Ox/1\nGq20bMRxwaJTLxARX6sdZsgT5Olyy4L/47LNjqiAaLsxjHPCi9m6dm6KG+uXgYLCCgkLwaBP0Dkd\nocsr/233RHAuno4Qg0ktKE+TKNdDeRpkaNd3KVlSqVBnWFFnWNHVyIlRxroS9EU1jAz7GOyfZsq7\n+ACVOtpP5vWzmDsakMQisVc+H+GObsId3Uu8uIRks86IigzUDvs8oZGByp6JZLWsi3uUwq2xOAzo\n0lPwewKIQJgsj48Bo566wSkmvasPw1BQUIhlvsBgRmB4w4IGd4RaZ5hrrgj9nhAGtxODaxKjcyLm\nn8U5gcU1gdbtvs0ryYhAkFDvIKHeQZYqxTcY8dCpt6K2WaLjRszjDCvqzLltKrNxXe7f7vFpms50\n0d8UW2dJm6qhYl8BmQWWNb+GjcisiPhO4xgjXvkHy89aJxiaDvLpmkxS5oUgm616HLkmhvtdRCKC\nc2+38egzNWt2bUoOhMJdRUQIxgKCfp+gzyfo8Ubomo7Q7RW3zF2YT4ZGUJQqUZoG5XrI1C7MZUgE\nfn+YsbEAo6N+xsYCBAKLvyG1WiIjI4WsrFTS1CEio+OIsXEio2OI0bGZ9hiR0THwLV0RdtmoVLLI\nyJj5Z7PKKxcZ8l+VzYoq04ZkNiGp1at/PYUl6b4+SGftAAC+9BTezZLrQHzhUAFZ090Jc2G6HcrY\noLAREUIwGhA0TUWi/7qmBbcaahxawTaDxFYD5M3kyYlgkPC4k/D4JOGJSSITLsITk4QnnIQnnEQm\n5OdEPO7XN6NRo7ZaUGdYFooOmwWVxYTaYkZtNaGymFAZDcsWHEIIhjvGab/Sz0jXRMxzkgTZFZmU\nbM9Bk6LMZd8ObyjCD5vHaXPOJf2XmnV8focD+7zE+sFeJ2/8vAGQi8x9+s8ewGJb+t6q5EAo3FNE\nhGAyCMP+CCMBeWWhzyfo90Xo9y1fKADoJEFhqkSRHopSoVAHhiRIVhNC4HaHcDqDTE4GcToDeDxL\nJ2NIElgsWjIydFitKajVs/cDDer8XMhf6B4hhADPNJGxcVlYjE8gJiaJjE8iJiYQ4xMIlxtuN8kQ\niSBGxwiPjnGLdBFZaFgtM0LDhspmQbKYUVnMNF2fIKRPY/tv7UFlMSOZjQkTGxvRxnWW7PL/n73z\njo/rqhL/94xm1Hu1JFvuPe6J4wSHhDiEFBJ6CyUbWGCBsCzLb5eyLL0tS2+mhA2wGxPAQGgJcXAK\ncWInTmTZcu+WLcm2ei9T7u+P96ZImpFG0kgjjc7383kfzX3vvvuujvTumXPvPecUcK76IsZnS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hdXaeaOb3dpSmzfNy+NRNCya1j6NhPHohVuvzNcAmEUkVS0tvAY6McI9i4585VIai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\nreNU1jlo6Whg8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hidden_prob = np.array([0.85, 0.60, 0.75])\n", + "bandits = Bandits(hidden_prob)\n", + "bayesian_strat = BayesianStrategy(bandits)\n", + "\n", + "draw_samples = [1, 1, 3, 10, 10, 25, 50, 100, 200, 600]\n", + "\n", + "for j,i in enumerate(draw_samples):\n", + " plt.subplot(5, 2, j+1) \n", + " bayesian_strat.sample_bandits(i)\n", + " plot_priors(bayesian_strat, hidden_prob)\n", + " #plt.legend()\n", + " plt.autoscale(tight = True)\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that we don't really care how accurate we become about the inference of the hidden probabilities — for this problem we are more interested in choosing the best bandit (or more accurately, becoming *more confident* in choosing the best bandit). For this reason, the distribution of the red bandit is very wide (representing ignorance about what that hidden probability might be) but we are reasonably confident that it is not the best, so the algorithm chooses to ignore it.\n", + "\n", + "From the above, we can see that after 1000 pulls, the majority of the \"blue\" function leads the pack, hence we will almost always choose this arm. This is good, as this arm is indeed the best.\n", + "\n", + "Below is a D3 app that demonstrates our algorithm updating/learning three bandits. The first figure are the raw counts of pulls and wins, and the second figure is a dynamically updating plot. I encourage you to try to guess which bandit is optimal, prior to revealing the true probabilities, by selecting the `arm buttons`." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + " \n", + " \n", + " \n", + "\n", + " \n", + "\n", + "\n", + " \n", + "
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Denote this best bandit's probability by $w_{opt}$. Our score should be relative to how well we would have done had we chosen the best bandit from the beginning. This motivates the *total regret* of a strategy, defined:\n", + "\n", + "\\begin{align}\n", + "R_T & = \\sum_{i=1}^{T} \\left( w_{opt} - w_{B(i)} \\right)\\\\\\\\\n", + "& = Tw^* - \\sum_{i=1}^{T} \\; w_{B(i)} \n", + "\\end{align}\n", + "\n", + "\n", + "where $w_{B(i)}$ is the probability of a prize of the chosen bandit in the $i$ round. A total regret of 0 means the strategy is matching the best possible score. This is likely not possible, as initially our algorithm will often make the wrong choice. Ideally, a strategy's total regret should flatten as it learns the best bandit. (Mathematically, we achieve $w_{B(i)}=w_{opt}$ often)\n", + "\n", + "\n", + "Below we plot the total regret of this simulation, including the scores of some other strategies:\n", + "\n", + "1. Random: randomly choose a bandit to pull. If you can't beat this, just stop. \n", + "2. Largest Bayesian credible bound: pick the bandit with the largest upper bound in its 95% credible region of the underlying probability. \n", + "3. Bayes-UCB algorithm: pick the bandit with the largest *score*, where score is a dynamic quantile of the posterior (see [4] )\n", + "3. Mean of posterior: choose the bandit with the largest posterior mean. This is what a human player (sans computer) would likely do. \n", + "3. Largest proportion: pick the bandit with the current largest observed proportion of winning. \n", + "\n", + "The code for these are in the `other_strats.py`, where you can implement your own very easily." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "figsize(12.5, 5)\n", + "from other_strats import *\n", + "\n", + "#define a harder problem\n", + "hidden_prob = np.array([0.15, 0.2, 0.1, 0.05])\n", + "bandits = Bandits(hidden_prob)\n", + "\n", + "#define regret\n", + "def regret(probabilities, choices):\n", + " w_opt = probabilities.max()\n", + " return (w_opt - probabilities[choices.astype(int)]).cumsum()\n", + "\n", + "#create new strategies\n", + "strategies= [upper_credible_choice, \n", + " bayesian_bandit_choice, \n", + " ucb_bayes , \n", + " max_mean,\n", + " random_choice]\n", + "algos = []\n", + "for strat in strategies:\n", + " algos.append(GeneralBanditStrat(bandits, strat))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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9xKZNm7BYLCQlJbF9+3YuXLhAlSpVaNSokfV8du3aZe0htz1fW5YtW0ZkZCQJ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#train 10000 times\n", + "for strat in algos:\n", + " strat.sample_bandits(10000)\n", + " \n", + "#test and plot\n", + "for i,strat in enumerate(algos):\n", + " _regret = regret(hidden_prob, strat.choices)\n", + " plt.plot(_regret, label = strategies[i].__name__, lw = 3)\n", + "\n", + "plt.title(\"Total Regret of Bayesian Bandits Strategy vs. Random guessing\")\n", + "plt.xlabel(\"Number of pulls\")\n", + "plt.ylabel(\"Regret after $n$ pulls\");\n", + "plt.legend(loc = \"upper left\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Like we wanted, Bayesian bandits and other strategies have decreasing rates of regret, representing we are achieving optimal choices. To be more scientific so as to remove any possible luck in the above simulation, we should instead look at the *expected total regret*:\n", + "\n", + "$$\\bar{R}_T = E[ R_T ] $$\n", + "\n", + "It can be shown that any *sub-optimal* strategy's expected total regret is bounded below logarithmically. Formally,\n", + "\n", + "$$ E[R_T] = \\Omega \\left( \\;\\log(T)\\; \\right) $$\n", + "\n", + "Thus, any strategy that matches logarithmic-growing regret is said to \"solve\" the Multi-Armed Bandit problem [3].\n", + "\n", + "Using the Law of Large Numbers, we can approximate Bayesian Bandit's expected total regret by performing the same experiment many times (500 times, to be fair):" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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QQpsAaVqJLqUsnGqchZaaDbU2ZrMZh8Ph2c7Nza3VQC4uLqa8vNzTwM7IyCA1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\nE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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#this can be slow, so I recommend NOT running it. \n", + "\n", + "trials = 500\n", + "expected_total_regret = np.zeros((10000, 3))\n", + "\n", + "for i_strat, strat in enumerate(strategies[:-2]):\n", + " for i in range(trials):\n", + " general_strat = GeneralBanditStrat(bandits, strat)\n", + " general_strat.sample_bandits(10000)\n", + " _regret = regret(hidden_prob, general_strat.choices)\n", + " expected_total_regret[:,i_strat] += _regret\n", + " plt.plot(expected_total_regret[:,i_strat]/trials, lw =3, label = strat.__name__)\n", + " \n", + "plt.title(\"Expected Total Regret of Multi-armed Bandit strategies\")\n", + "plt.xlabel(\"Number of pulls\")\n", + "plt.ylabel(\"Exepected Total Regret \\n after $n$ pulls\");\n", + "plt.legend(loc = \"upper left\");" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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0009z9OhRi2vCw8N56aWX2LBhAx07dgSgV69e5vaW9Lvmpl69ely5coUmTZoA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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "[pl1, pl2, pl3] = plt.plot(expected_total_regret[:, [0,1,2]], lw = 3)\n", + "plt.xscale(\"log\")\n", + "plt.legend([pl1, pl2, pl3], \n", + " [\"Upper Credible Bound\", \"Bayesian Bandit\", \"UCB-Bayes\"],\n", + " loc=\"upper left\")\n", + "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");\n", + "plt.title( \"log-scale of above\" );\n", + "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Extending the algorithm \n", + "\n", + "\n", + "Because of the Bayesian Bandits algorithm's simplicity, it is easy to extend. Some possibilities:\n", + "\n", + "- If interested in the *minimum* probability (eg: where prizes are a bad thing), simply choose $B = \\text{argmin} \\; X_b$ and proceed.\n", + "\n", + "- Adding learning rates: Suppose the underlying environment may change over time. Technically the standard Bayesian Bandit algorithm would self-update itself (awesome) by noting that what it thought was the best is starting to fail more often. We can motivate the algorithm to learn changing environments quicker by simply adding a *rate* term upon updating:\n", + "\n", + " self.wins[choice] = rate*self.wins[choice] + result\n", + " self.trials[choice] = rate*self.trials[choice] + 1\n", + "\n", + " If `rate < 1`, the algorithm will *forget* its previous wins quicker and there will be a downward pressure towards ignorance. Conversely, setting `rate > 1` implies your algorithm will act more risky, and bet on earlier winners more often and be more resistant to changing environments. \n", + "\n", + "- Hierarchical algorithms: We can setup a Bayesian Bandit algorithm on top of smaller bandit algorithms. Suppose we have $N$ Bayesian Bandit models, each varying in some behavior (for example different `rate` parameters, representing varying sensitivity to changing environments). On top of these $N$ models is another Bayesian Bandit learner that will select a sub-Bayesian Bandit. This chosen Bayesian Bandit will then make an internal choice as to which machine to pull. The super-Bayesian Bandit updates itself depending on whether the sub-Bayesian Bandit was correct or not. \n", + "\n", + "- Extending the rewards, denoted $y_a$ for bandit $a$, to random variables from a distribution $f_{y_a}(y)$ is straightforward. More generally, this problem can be rephrased as \"Find the bandit with the largest expected value\", as playing the bandit with the largest expected value is optimal. In the case above, $f_{y_a}$ was Bernoulli with probability $p_a$, hence the expected value for a bandit is equal to $p_a$, which is why it looks like we are aiming to maximize the probability of winning. If $f$ is not Bernoulli, and it is non-negative, which can be accomplished apriori by shifting the distribution (we assume we know $f$), then the algorithm behaves as before:\n", + "\n", + " For each round, \n", + " \n", + " 1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", + " 2. Select the bandit with largest sample, i.e. select bandit $B = \\text{argmax}\\;\\; X_b$.\n", + " 3. Observe the result,$R \\sim f_{y_a}$, of pulling bandit $B$, and update your prior on bandit $B$.\n", + " 4. Return to 1\n", + "\n", + " The issue is in the sampling of $X_b$ drawing phase. With Beta priors and Bernoulli observations, we have a Beta posterior — this is easy to sample from. But now, with arbitrary distributions $f$, we have a non-trivial posterior. Sampling from these can be difficult.\n", + "\n", + "- There has been some interest in extending the Bayesian Bandit algorithm to commenting systems. Recall in Chapter 4, we developed a ranking algorithm based on the Bayesian lower-bound of the proportion of upvotes to total votes. One problem with this approach is that it will bias the top rankings towards older comments, since older comments naturally have more votes (and hence the lower-bound is tighter to the true proportion). This creates a positive feedback cycle where older comments gain more votes, hence are displayed more often, hence gain more votes, etc. This pushes any new, potentially better comments, towards the bottom. J. Neufeld proposes a system to remedy this that uses a Bayesian Bandit solution.\n", + "\n", + "His proposal is to consider each comment as a Bandit, with the number of pulls equal to the number of votes cast, and number of rewards as the number of upvotes, hence creating a $\\text{Beta}(1+U,1+D)$ posterior. As visitors visit the page, samples are drawn from each bandit/comment, but instead of displaying the comment with the $\\max$ sample, the comments are ranked according to the ranking of their respective samples. From J. Neufeld's blog [7]:\n", + "\n", + " > [The] resulting ranking algorithm is quite straightforward, each new time the comments page is loaded, the score for each comment is sampled from a $\\text{Beta}(1+U,1+D)$, comments are then ranked by this score in descending order... This randomization has a unique benefit in that even untouched comments $(U=1,D=0)$ have some chance of being seen even in threads with 5000+ comments (something that is not happening now), but, at the same time, the user is not likely to be inundated with rating these new comments. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just for fun, though the colors explode, we watch the Bayesian Bandit algorithm learn 15 different options. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 6.78509844e-03 9.68721665e-02 3.16101371e-02 8.88059449e-02\n", + " 3.32812651e-02 6.59572621e-02 7.91635546e-02 5.97822577e-02\n", + " 1.17088549e-01 1.29945195e-05 3.66798062e-02 5.77077187e-02\n", + " 4.32774140e-02 6.94914246e-02 1.22741733e-01 5.13528129e-02\n", + " 3.29414904e-01 5.13320236e-02 5.35031763e-02 1.57610420e-02\n", + " 1.94570205e-02 1.11759388e-01 3.23349076e-02 2.04068995e-02\n", + " 1.47822753e-01 8.24022697e-03 3.20395660e-04 4.45643230e-03\n", + " 6.42090321e-03 7.29322919e-02 8.18486095e-02 5.05066236e-03\n", + " 1.73946201e-01 6.48018322e-02 7.70657954e-03]\n" + ] + }, + { + "data": { + "image/png": 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+dbFctq6h1KculivGXt/1qYtl69/fhlCf2vr9LWuvpk+fbvN9p5Cydgc9hIeH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\n3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JOPVvyP/lmXU3awkFI5j5763jw4/X/k/jOHBF8xaxNuZtrvXmi5vdZCCCTf80jKGoSU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\nQkxEiYoYQhXYJtmwTrNh0WxYRBZWqWJJCLSoR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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.0, 8)\n", + "beta = stats.beta\n", + "hidden_prob = beta.rvs(1,13, size = 35)\n", + "print(hidden_prob)\n", + "bandits = Bandits(hidden_prob)\n", + "bayesian_strat = BayesianStrategy(bandits)\n", + "\n", + "for j,i in enumerate([100, 200, 500, 1300]):\n", + " plt.subplot(2, 2, j+1) \n", + " bayesian_strat.sample_bandits(i)\n", + " plot_priors(bayesian_strat, hidden_prob, lw = 2, alpha = 0.0, plt_vlines=False)\n", + " #plt.legend()\n", + " plt.xlim(0, 0.5)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Eliciting expert prior\n", + "\n", + "Specifying a subjective prior is how practitioners incorporate domain knowledge about the problem into our mathematical framework. Allowing domain knowledge is useful for many reasons:\n", + "\n", + "- Aids speeds of MCMC convergence. For example, if we know the unknown parameter is strictly positive, then we can restrict our attention there, hence saving time that would otherwise be spent exploring negative values.\n", + "- More accurate inference. By weighing prior values near the true unknown value higher, we are narrowing our eventual inference (by making the posterior tighter around the unknown) \n", + "- Express our uncertainty better. See the *Price is Right* problem in Chapter 5.\n", + "\n", + "plus many other reasons. Of course, practitioners of Bayesian methods are not experts in every field, so we must turn to domain experts to craft our priors. We must be careful with how we elicit these priors though. Some things to consider:\n", + "\n", + "1. From experience, I would avoid introducing Betas, Gammas, etc. to non-Bayesian practitioners. Furthermore, non-statisticians can get tripped up by how a continuous probability function can have a value exceeding one.\n", + "\n", + "2. Individuals often neglect the rare *tail-events* and put too much weight around the mean of distribution. \n", + "\n", + "3. Related to above is that almost always individuals will under-emphasize the uncertainty in their guesses.\n", + "\n", + "Eliciting priors from non-technical experts is especially difficult. Rather than introduce the notion of probability distributions, priors, etc. that may scare an expert, there is a much simpler solution. \n", + "\n", + "### Trial roulette method \n", + "\n", + "\n", + "The *trial roulette method* [8] focuses on building a prior distribution by placing counters (think casino chips) on what the expert thinks are possible outcomes. The expert is given $N$ counters (say $N=20$) and is asked to place them on a pre-printed grid, with bins representing intervals. Each column would represent their belief of the probability of getting the corresponding bin result. Each chip would represent an $\\frac{1}{N} = 0.05$ increase in the probability of the outcome being in that interval. For example [9]:\n", + "\n", + "> A student is asked to predict the mark in a future exam. The figure below shows a completed grid for the elicitation of a subjective probability distribution. The horizontal axis of the grid shows the possible bins (or mark intervals) that the student was asked to consider. The numbers in top row record the number of chips per bin. The completed grid (using a total of 20 chips) shows that the student believes there is a 30% chance that the mark will be between 60 and 64.9.\n", + "\n", + "\n", + "\n", + "\n", + "From this, we can fit a distribution that captures the expert's choice. Some reasons in favor of using this technique are:\n", + "\n", + "1. Many questions about the shape of the expert's subjective probability distribution can be answered without the need to pose a long series of questions to the expert - the statistician can simply read off density above or below any given point, or that between any two points.\n", + "\n", + "2. During the elicitation process, the experts can move around the chips if unsatisfied with the way they placed them initially - thus they can be sure of the final result to be submitted.\n", + "\n", + "3. It forces the expert to be coherent in the set of probabilities that are provided. If all the chips are used, the probabilities must sum to one.\n", + "\n", + "4. Graphical methods seem to provide more accurate results, especially for participants with modest levels of statistical sophistication." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Stock Returns\n", + "\n", + "\n", + "Take note stock brokers: you're doing it wrong. When choosing which stocks to pick, an analyst will often look at the *daily return* of the stock. Suppose $S_t$ is the price of the stock on day $t$, then the daily return on day $t$ is :\n", + "\n", + "$$r_t = \\frac{ S_t - S_{t-1} }{ S_{t-1} } $$\n", + "\n", + "The *expected daily return* of a stock is denoted $\\mu = E[ r_t ] $. Obviously, stocks with high expected returns are desirable. Unfortunately, stock returns are so filled with noise that it is very hard to estimate this parameter. Furthermore, the parameter might change over time (consider the rises and falls of AAPL stock), hence it is unwise to use a large historical dataset. \n", + "\n", + "Historically, the expected return has been estimated by using the sample mean. This is a bad idea. As mentioned, the sample mean of a small sized dataset has enormous potential to be very wrong (again, see Chapter 4 for full details). Thus Bayesian inference is the correct procedure here, since we are able to see our uncertainty along with probable values.\n", + "\n", + "For this exercise, we will be examining the daily returns of the AAPL, GOOG, MSFT and AMZN. Before we pull in the data, suppose we ask our a stock fund manager (an expert in finance, but see [10] ), \n", + "\n", + "> What do you think the return profile looks like for each of these companies?\n", + "\n", + "Our stock broker, without needing to know the language of Normal distributions, or priors, or variances, etc. creates four distributions using the trial roulette method above. Suppose they look enough like Normals, so we fit Normals to them. They may look like: " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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KyJHyzw+7HatpfNnJGYrptGMrMAGISHkUIkN2DRvKGeNlzf8ppYa8Mn/OK+UE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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(11., 5)\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", + "\n", + "normal = stats.norm\n", + "x = np.linspace(-0.15, 0.15, 100)\n", + "\n", + "expert_prior_params = {\"AAPL\":(0.05, 0.03),\n", + " \"GOOG\":(-0.03, 0.04), \n", + " \"TSLA\": (-0.02, 0.01), \n", + " \"AMZN\": (0.03, 0.02), \n", + " }\n", + "\n", + "for i, (name, params) in enumerate(expert_prior_params.items()):\n", + " plt.subplot(2, 2, i+1)\n", + " y = normal.pdf(x, params[0], scale = params[1])\n", + " #plt.plot( x, y, c = colors[i] )\n", + " plt.fill_between(x, 0, y, color = colors[i], linewidth=2,\n", + " edgecolor = colors[i], alpha = 0.6)\n", + " plt.title(name + \" prior\")\n", + " plt.vlines(0, 0, y.max(), \"k\",\"--\", linewidth = 0.5)\n", + " plt.xlim(-0.15, 0.15)\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that these are subjective priors: the expert has a personal opinion on the stock returns of each of these companies, and is expressing them in a distribution. He's not wishful thinking -- he's introducing domain knowledge.\n", + "\n", + "In order to better model these returns, we should investigate the *covariance matrix* of the returns. For example, it would be unwise to invest in two stocks that are highly correlated, since they are likely to tank together (hence why fund managers suggest a diversification strategy). We will use the *Wishart distribution* for this, introduced earlier." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's get some historical data for these stocks. We will use the covariance of the returns as a starting point for our Wishart random variable. This is not empirical bayes (as we will go over later) because we are only deciding the starting point, not influencing the parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# I wish I could have used Pandas as a prereq for this book, but oh well.\n", + "import datetime\n", + "import collections\n", + "import ystockquote as ysq\n", + "import pandas as pd\n", + "\n", + "n_observations = 100 # we will truncate the the most recent 100 days.\n", + "\n", + "stocks = [\"AAPL\", \"GOOG\", \"TSLA\", \"AMZN\"]\n", + "\n", + "enddate = \"2015-04-27\"\n", + "startdate = \"2012-09-01\"\n", + "\n", + "CLOSE = 6\n", + "\n", + "stock_closes = pd.DataFrame()\n", + "\n", + "for stock in stocks:\n", + " x = np.array(ysq.get_historical_prices(stock, startdate, enddate))\n", + " stock_series = pd.Series(x[1:,CLOSE].astype(float), name=stock)\n", + " stock_closes[stock] = stock_series\n", + "\n", + "stock_closes = stock_closes[::-1]\n", + "stock_returns = stock_closes.pct_change()[1:][-n_observations:]\n", + " \n", + "dates = list(map(lambda x: datetime.datetime.strptime(x, \"%Y-%m-%d\"), x[1:n_observations+1,0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here let's form our basic model:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied log-transform to c and added transformed c_log_ to model.\n", + "Added new variable c to model diagonal of Wishart.\n", + "Added new variable z to model off-diagonals of Wishart.\n" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "import theano.tensor as tt\n", + "from theano.tensor.nlinalg import matrix_inverse, diag, matrix_dot\n", + "\n", + "prior_mu = np.array([x[0] for x in expert_prior_params.values()])\n", + "prior_std = np.array([x[1] for x in expert_prior_params.values()])\n", + "\n", + "init = stock_returns.cov()\n", + "\n", + "with pm.Model() as model:\n", + " cov_matrix = pm.WishartBartlett(\"covariance\", np.diag(prior_std**2), 10, testval = init)\n", + "\n", + " mu = pm.Normal(\"returns\", mu=prior_mu, sd=1, shape=4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the returns for our chosen stocks:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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9x7dyJGMfmsbvxzt37M6rd9umd0ZCQgKxsbGNzjdv7wrBSa21V719zkC61trf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7HmNjwix/B+nZVsq5601Bh+eO/QrWzdZht7yjvYUdJO7jnxJ756NQviA1icGEhyqOGyn3ub3crT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\nIOk7wDXAKEmy/TfgubKo/xD4aRk3yPY75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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 4)\n", + "\n", + "cum_returns = np.cumprod(1 + stock_returns) - 1\n", + "cum_returns.index = dates[::-1]\n", + "cum_returns.plot()\n", + "\n", + "plt.legend(loc = \"upper left\")\n", + "plt.title(\"Return space\")\n", + "plt.ylabel(\"Return of $1 on first date, x100%\");" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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at+4PDwy+3u8XsuXR1b3mbV+/sdSymbUKNyBKlEv/uXbOuX7rjl7TEw+dwbYd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\nByKfPGWNoZFfGS4EfmZmofg+/xJCWBunWCIi0samHd4qIiL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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(11., 5 )\n", + "\n", + "for i, _stock in enumerate(stocks):\n", + " plt.subplot(2,2,i+1)\n", + " plt.hist(stock_returns[_stock], bins=20,\n", + " normed = True, histtype=\"stepfilled\",\n", + " color=colors[i], alpha=0.7)\n", + " plt.title(_stock + \" returns\")\n", + " plt.xlim(-0.15, 0.15)\n", + "\n", + "plt.tight_layout()\n", + "plt.suptitle(\"Histogram of daily returns\", size =14);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we perform the inference on the posterior mean return and posterior covariance matrix. " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 5000 of 5000 in 40.4 sec. | SPS: 123.8 | ETA: 0.0" + ] + } + ], + "source": [ + "with model:\n", + " obs = pm.MvNormal(\"observed returns\", mu=mu, cov=cov_matrix, observed=stock_returns)\n", + " step = pm.NUTS()\n", + " trace = pm.sample(5000, step=step)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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uQPijbP1Rtv4oW3+UrT/K1q/uMI76okWLmDNnDrNnz2bJkiXs2rWr+b3evXtz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\niIiEkGrU85TqzvxRtv4oW39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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5,4)\n", + "\n", + "#examine the mean return first.\n", + "mu_samples = trace[\"returns\"]\n", + "\n", + "for i in range(4):\n", + " plt.hist(mu_samples[:,i], alpha = 0.8 - 0.05*i, bins = 30,\n", + " histtype=\"stepfilled\", normed=True, \n", + " label = \"%s\" % stock_returns.columns[i])\n", + "\n", + "plt.vlines(mu_samples.mean(axis=0), 0, 500, linestyle=\"--\", linewidth = .5)\n", + "\n", + "plt.title(\"Posterior distribution of $\\mu$, daily stock returns\")\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(Plots like these are what inspired the book's cover.)\n", + "\n", + "What can we say about the results above? Clearly TSLA has been a strong performer, and our analysis suggests that it has an almost 1% daily return! Similarly, most of the distribution of AAPL is negative, suggesting that it's *true daily return* is negative.\n", + "\n", + "\n", + "You may not have immediately noticed, but these variables are a whole order of magnitude *less* than our priors on them. For example, to put these one the same scale as the above prior distributions:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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k6WHgJknnAU8BZ7UykWYD9cS3rmFt55JWJ8OspepdB8L6kEJ/uhRiBI+BKJIU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\nM7WZWcp6u7kEJH1zycxsKKurBULStmS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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(11.0,3)\n", + "for i in range(4):\n", + " plt.subplot(2,2,i+1)\n", + " plt.hist(mu_samples[:,i], alpha = 0.8 - 0.05*i, bins = 30,\n", + " histtype=\"stepfilled\", normed=True, color = colors[i],\n", + " label = \"%s\" % stock_returns.columns[i])\n", + " plt.title(\"%s\" % stock_returns.columns[i])\n", + " plt.xlim(-0.15, 0.15)\n", + " \n", + "plt.suptitle(\"Posterior distribution of daily stock returns\")\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Why did this occur? Recall how I mentioned that finance has a very very low signal to noise ratio. This implies an environment where inference is much more difficult. One should be careful about over-interpreting these results: notice (in the first figure) that each distribution is positive at 0, implying that the stock may return nothing. Furthermore, the subjective priors influenced the results. From the fund managers point of view, this is good as it reflects his updated beliefs about the stocks, whereas from a neutral viewpoint this can be too subjective of a result. \n", + "\n", + "Below we show the posterior correlation matrix, and posterior standard deviations. An important caveat to know is that the Wishart distribution models the *inverse covariance matrix*, so we must invert it to get the covariance matrix. We also normalize the matrix to acquire the *correlation matrix*. Since we cannot plot hundreds of matrices effectively, we settle by summarizing the posterior distribution of correlation matrices by showing the *mean posterior correlation matrix* (defined on line 2)." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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YzC7u0w1yzuXqmdVrmDZvZbOr0edOGTPMG9m94Hd8rIGPk52fVriqrpjDazRk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\npxc/lfSRdcX/nWHNmjXcfffdtLe3Zwp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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cov_samples = trace[\"covariance\"]\n", + "mean_covariance_matrix = cov_samples.mean(axis=0)\n", + "\n", + "def cov2corr(A):\n", + " \"\"\"\n", + " covariance matrix to correlation matrix.\n", + " \"\"\"\n", + " d = np.sqrt(A.diagonal())\n", + " A = ((A.T/d).T)/d\n", + " #A[ np.diag_indices(A.shape[0]) ] = np.ones( A.shape[0] )\n", + " return A\n", + "\n", + "\n", + "plt.subplot(1,2,1)\n", + "plt.imshow(cov2corr(mean_covariance_matrix) , interpolation=\"none\", \n", + " cmap = \"hot\") \n", + "plt.xticks(np.arange(4), stock_returns.columns)\n", + "plt.yticks(np.arange(4), stock_returns.columns)\n", + "plt.colorbar(orientation=\"vertical\")\n", + "plt.title(\"(mean posterior) Correlation Matrix\")\n", + "\n", + "plt.subplot(1,2,2)\n", + "plt.bar(np.arange(4), np.sqrt(np.diag(mean_covariance_matrix)),\n", + " color = \"#348ABD\", alpha = 0.7)\n", + "plt.xticks(np.arange(4) + 0.5, stock_returns.columns);\n", + "plt.title(\"(mean posterior) standard deviations of daily stock returns\")\n", + "\n", + "plt.tight_layout();\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above figures, we can say that likely TSLA has an above-average volatility (looking at the return graph this is quite clear). The correlation matrix shows that there are not strong correlations present, but perhaps GOOG and AMZN express a higher correlation (about 0.30). \n", + "\n", + "With this Bayesian analysis of the stock market, we can throw it into a Mean-Variance optimizer (which I cannot stress enough, do not use with frequentist point estimates) and find the minimum. This optimizer balances the tradeoff between a high return and high variance.\n", + "\n", + "$$ w_{opt} = \\min_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n", + "\n", + "where $\\mu_i$ and $\\Sigma_i$ are the $i$th posterior estimate of the mean returns and the covariance matrix. This is another example of loss function optimization." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Protips for the Wishart distribution\n", + "\n", + "If you plan to be using the Wishart distribution, read on. Else, feel free to skip this. \n", + "\n", + "In the problem above, the Wishart distribution behaves pretty nicely. Unfortunately, this is rarely the case. The problem is that estimating an $NxN$ covariance matrix involves estimating $\\frac{1}{2}N(N-1)$ unknowns. This is a large number even for modest $N$. Personally, I've tried performing a similar simulation as above with $N = 23$ stocks, and ended up giving considering that I was requesting my MCMC simulation to estimate at least $\\frac{1}{2}23*22 = 253$ additional unknowns (plus the other interesting unknowns in the problem). This is not easy for MCMC. Essentially, you are asking you MCMC to traverse 250+ dimensional space. And the problem seemed so innocent initially! Below are some tips, in order of supremacy:\n", + "\n", + "1. Use conjugancy if it applies. See section below.\n", + "\n", + "2. Use a good starting value. What might be a good starting value? Why, the data's sample covariance matrix is! Note that this is not empirical Bayes: we are not touching the prior's parameters, we are modifying the starting value of the MCMC. Due to numerical instability, it is best to truncate the floats in the sample covariance matrix down a few degrees of precision (e.g. instability can cause unsymmetrical matrices, which can cause PyMC3 to cry.). \n", + "\n", + "3. Provide as much domain knowledge in the form of priors, if possible. I stress *if possible*. It is likely impossible to have an estimate about each $\\frac{1}{2}N(N-1)$ unknown. In this case, see number 4.\n", + "\n", + "4. Use empirical Bayes, i.e. use the sample covariance matrix as the prior's parameter.\n", + "\n", + "5. For problems where $N$ is very large, nothing is going to help. Instead, ask, do I really care about *every* correlation? Probably not. Further ask yourself, do I really really care about correlations? Possibly not. In finance, we can set an informal hierarchy of what we might be interested in the most: first a good estimate of $\\mu$, the variances along the diagonal of the covariance matrix are secondly important, and finally the correlations are least important. So, it might be better to ignore the $\\frac{1}{2}(N-1)(N-2)$ correlations and instead focus on the more important unknowns.\n", + "\n", + "**Another thing** to note is that the implementation of the Wishart distribution has changed in from PyMC to PyMC3. Wishart distribution matrices are required to have certain mathematical characteristics that are very restrictive. This makes it so that it is impossible for MCMC methods to propose matrices that will be accepted in our sampling procedure. With our model here we sample the Bartlett decomposition of a Wishart distribution matrix and use that to calculate our samples for the covariance matrix (http://en.wikipedia.org/wiki/Wishart_distribution#Bartlett_decomposition)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conjugate Priors\n", + "\n", + "Recall that a $\\text{Beta}$ prior with $\\text{Binomial}$ data implies a $\\text{Beta}$ posterior. Graphically:\n", + "\n", + "$$ \\underbrace{\\text{Beta}}_{\\text{prior}} \\cdot \\overbrace{\\text{Binomial}}^{\\text{data}} = \\overbrace{\\text{Beta}}^{\\text{posterior} } $$ \n", + "\n", + "Notice the $\\text{Beta}$ on both sides of this equation (no, you cannot cancel them, this is not a *real* equation). This is a really useful property. It allows us to avoid using MCMC, since the posterior is known in closed form. Hence inference and analytics are easy to derive. This shortcut was the heart of the Bayesian Bandit algorithm above. Fortunately, there is an entire family of distributions that have similar behaviour. \n", + "\n", + "Suppose $X$ comes from, or is believed to come from, a well-known distribution, call it $f_{\\alpha}$, where $\\alpha$ are possibly unknown parameters of $f$. $f$ could be a Normal distribution, or Binomial distribution, etc. For particular distributions $f_{\\alpha}$, there may exist a prior distribution $p_{\\beta}$, such that:\n", + "\n", + "$$ \\overbrace{p_{\\beta}}^{\\text{prior}} \\cdot \\overbrace{f_{\\alpha}(X)}^{\\text{data}} = \\overbrace{p_{\\beta'}}^{\\text{posterior} } $$ \n", + "\n", + "where $\\beta'$ is a different set of parameters *but $p$ is the same distribution as the prior*. A prior $p$ that satisfies this relationship is called a *conjugate prior*. As I mentioned, they are useful computationally, as we can avoided approximate inference using MCMC and go directly to the posterior. This sounds great, right?\n", + "\n", + "Unfortunately, not quite. There are a few issues with conjugate priors.\n", + "\n", + "1. The conjugate prior is not objective. Hence only useful when a subjective prior is required. It is not guaranteed that the conjugate prior can accommodate the practitioner's subjective opinion.\n", + "\n", + "2. There typically exist conjugate priors for simple, one dimensional problems. For larger problems, involving more complicated structures, hope is lost to find a conjugate prior. For smaller models, Wikipedia has a nice [table of conjugate priors](http://en.wikipedia.org/wiki/Conjugate_prior#Table_of_conjugate_distributions).\n", + "\n", + "Really, conjugate priors are only useful for their mathematical convenience: it is simple to go from prior to posterior. I personally see conjugate priors as only a neat mathematical trick, and offer little insight into the problem at hand. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jefferys Priors\n", + "\n", + "Earlier, we talked about objective priors rarely being *objective*. Partly what we mean by this is that we want a prior that doesn't bias our posterior estimates. The flat prior seems like a reasonable choice as it assigns equal probability to all values. \n", + "\n", + "But the flat prior is not transformation invariant. What does this mean? Suppose we have a random variable $ \\bf X $ from Bernoulli($\\theta$). We define the prior on $p(\\theta) = 1$. " + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "\n", + "x = np.linspace(0.000 ,1, 150)\n", + "y = np.linspace(1.0, 1.0, 150)\n", + "lines = plt.plot(x, y, color=\"#A60628\", lw = 3)\n", + "plt.fill_between(x, 0, y, alpha = 0.2, color = lines[0].get_color())\n", + "plt.autoscale(tight=True)\n", + "plt.ylim(0, 2);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, let's transform $\\theta$ with the function $\\psi = log \\frac{\\theta}{1-\\theta}$. This is just a function to stretch $\\theta$ across the real line. Now how likely are different values of $\\psi$ under our transformation." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 5)\n", + "\n", + "psi = np.linspace(-10 ,10, 150)\n", + "y = np.exp(psi) / (1 + np.exp(psi))**2\n", + "lines = plt.plot(psi, y, color=\"#A60628\", lw = 3)\n", + "plt.fill_between(psi, 0, y, alpha = 0.2, color = lines[0].get_color())\n", + "plt.autoscale(tight=True)\n", + "plt.ylim(0, 1);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Oh no! Our function is no longer flat. It turns out flat priors do carry information in them after all. The point of Jeffreys Priors is to create priors that don't accidentally become informative when you transform the variables you placed them originally on.\n", + "\n", + "Jeffreys Priors are defined as:\n", + "\n", + "$$p_J(\\theta) \\propto \\mathbf{I}(\\theta)^\\frac{1}{2}$$\n", + "$$\\mathbf{I}(\\theta) = - \\mathbb{E}\\bigg[\\frac{d^2 \\text{ log } p(X|\\theta)}{d\\theta^2}\\bigg]$$\n", + "\n", + "$\\mathbf{I}$ being the *Fisher information*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Effect of the prior as $N$ increases\n", + "\n", + "In the first chapter, I proposed that as the amount of observations, or data, that we posses, the less the prior matters. This is intuitive. After all, our prior is based on previous information, and eventually enough new information will shadow our previous information's value. The smothering of the prior by enough data is also helpful: if our prior is significantly wrong, then the self-correcting nature of the data will present to us a *less wrong*, and eventually *correct*, posterior. \n", + "\n", + "We can see this mathematically. First, recall Bayes Theorem from Chapter 1 that relates the prior to the posterior. The following is a sample from [What is the relationship between sample size and the influence of prior on posterior?](http://stats.stackexchange.com/questions/30387/what-is-the-relationship-between-sample-size-and-the-influence-of-prior-on-poste)[1] on CrossValidated.\n", + "\n", + ">The posterior distribution for a parameter $\\theta$, given a data set ${\\bf X}$ can be written as \n", + "\n", + "$$p(\\theta | {\\bf X}) \\propto \\underbrace{p({\\bf X} | \\theta)}_{{\\rm likelihood}} \\cdot \\overbrace{ p(\\theta) }^{ {\\rm prior} } $$\n", + "\n", + "\n", + "\n", + ">or, as is more commonly displayed on the log scale, \n", + "\n", + "$$ \\log( p(\\theta | {\\bf X}) ) = c + L(\\theta;{\\bf X}) + \\log(p(\\theta)) $$\n", + "\n", + ">The log-likelihood, $L(\\theta;{\\bf X}) = \\log \\left( p({\\bf X}|\\theta) \\right)$, **scales with the sample size**, since it is a function of the data, while the prior density does not. Therefore, as the sample size increases, the absolute value of $L(\\theta;{\\bf X})$ is getting larger while $\\log(p(\\theta))$ stays fixed (for a fixed value of $\\theta$), thus the sum $L(\\theta;{\\bf X}) + \\log(p(\\theta))$ becomes more heavily influenced by $L(\\theta;{\\bf X})$ as the sample size increases. \n", + "\n", + "There is an interesting consequence not immediately apparent. As the sample size increases, the chosen prior has less influence. Hence inference converges regardless of chosen prior, so long as the areas of non-zero probabilities are the same. \n", + "\n", + "Below we visualize this. We examine the convergence of two posteriors of a Binomial's parameter $\\theta$, one with a flat prior and the other with a biased prior towards 0. As the sample size increases, the posteriors, and hence the inference, converge." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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wWiFES5IOuHCWkpISCgsLpQPuxjw8PIiKimr039AlcsCVUpuB17TW2+pvb24O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\nPsq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V7Hr4eVe55+UXENQ30fB6dhVb+TanwXLzif74m417cX3ljaXMufH4adb8YqMJnzaZ\noo+WA5D391cITZmIyeJvWN0Alw/pzvrMEiqsDrJLqvm/7fn8pkF+uOiajE4bMVJ5eTkWi4WQkBCO\nHj3KwoULG+3v3r076enpp7zO008/zTPPPMPBgwd55513eOWVV9yqf/r06SxevJiffvqJ8ePH8+KL\nL2KxWBgzZkyLfh5v5EkAfgjI1FpvrC0vA+499qDnnnuOoKAgEhISAAgLC2Po0KGud5h1821KWcoN\n5171hvZI2bvL0l9av/zR/Y9y6OBeBpmC8AkNJmd0X/I3bWD8KOeL4JpNzpFxT8p2ByzTzmXsS/al\nkhxkYvhoZ4rLptRNQP0IdkvLS996lTk33trkfvvQBLp9G4K9uJQtWQfI+NtCLnj8IQA2rP0ZgDHj\nJnhcvnxId15c9jUA//ExcX7fSHb+ss6jv4+UW6dct83T6xUXF3t1msTJRpDnzZvHnDlz6NevHz17\n9uS2225j+fLlrv1z587l9ttv51//+hdXXXUVTzzxRJPXmTBhAqNHj0Zrzfz585k0aZJbbevbty8v\nvfQS99xzD7m5uQwdOpR33nkHHx+fU7a9taxatYpt27ZRXOyc1z8jI4PRo0eTkpLSouspT3LelFI/\nArdqrfcopf4KBGqtGwXhixYt0jfffHOL6xBdhzxUJ5pD+kvrqsrJ56eJs7BXOKcE7HP3zcRePtnw\nej7NqHTlfvuZ4KHBgUR5OO3gscacN5YN36074f6iL78j//k3ATAFBtD/m3/j0y3S0DbYHZqHvzlA\nVolzpD+lbwT3npNkaB3CGEbdW7Kzs706AG9NmZmZnH766Rw+fLhDzlByrBP9LTdv3kxKSkqL3g14\n+lu5A/iPUioVGA4ct4ap5IALd0kwJZpD+kvr2v3oP13Bd2ByPD0vbdkoz8kUVNl572D9g5dTe/oZ\nHny7I2zKJPwSnC+ujopK8ha/YXgdZpNi9un1aScr0o6yI6/M8HqE5+TeYgyjH2rubDy602mtt2it\nx2itR2itZ2itZb1dIYTo4I5u2EbOR/9zlfvceSPKx/gZSV7dW0FV7SJ2PS2KlGjj5/x2hzKb6Tbn\nalf56IdfUbV7/0nOaJmBPYIY3SvEVf7nz4ewOyRIEZ1TR39IsrW1+lBDampqa1chOomG+XdCnIr0\nl9ahHQ52/uUZVzlq0hmEjxpseD3rC2pYV1DjKs9OtGA2td8LdtDoYQSOGuosOBzkLHyxVUbwrhoW\njW/tz5lWWMnXewoNr0N4Ru4tnouPj6egoKBTpJ+0FvnNCCGEcMl6/ytKtuwCwOTnS/L8aw2vo9Km\nWbqn3FUeH+VD35DWm/N76uSL3Tqu262zoDY4Ll+9ibKV6w1vS7cgXy4eEOUqv74xh9Jqm+H1CCG8\nW6sH4JIDLtwleXeiOaS/GM9WWs6ex19yleNmX4qlZw/D63n/YAUF1c65sIN8YEa8sdP+Hevh+9yb\nHdc/qRehU85xlXMXvuRagMhIFw2IIirQmW5TXGXjrU25pzhDtCW5t4i2ICPgQgghAEj7x+vU5B8B\nwK97JPHXXmZ4HQdKbXx+qMpVntnLn2Af78kVjbruclSAc1ns6n3pHP3wS8Pr8DObmDW8/o3N5zvz\nOXCk0vB6hBDeS3LAhdeQvDvRHNJfjFW2+wDpS993lXvffg3m2kDUKHateXF3OXXPHfYPNjE2ypPl\nKNxTN/+3O3wiwoj8zSWuct7iN7CXGj9byci4EAb2CATAoeGFNYdk1ggvIfcW0RZkBFwIIbo4rTU7\n7nvalW4ROrQ/3c+fYHg9/8uuZm+pM9/ZrODqJItXzpQQfvmF+PRw5mnbjxSR/8LbhtehlGL2iJi6\nlHO25JTx04Eiw+sRQngnyQEXXkPy7kRzSH8xTs5HX3N0zS/OgslE3z/dYnhgfKTawdv76uf8vjDG\nlxhL24wB1a186S6Tvx/dbrrSVS546yOq92UY3SziwvxJ6Vu/4M/L67KotBqfcy6ap6vcW0aMGMHK\nlSub3Ld27VrGjh3bpu159913ufhi9x6YdsczzzzDnXfeadj1jCYj4EII0YVZi0vZ9fDzrnLcVRcR\n1CfB8Hr+lVZOhd2ZYtHdXzGlp5/hdZzIK28sbfY5weeMwzK4v7Ngs5P92POtkiIybVA3QvydM8Dk\nl1v5YOthw+sQornGjRvHunUnXj22tRj5xn/BggU8++yzhl3PaJIDLryG5N2J5pD+Yoy9T75CTcFR\nAPy6RZBw80zD69hYUMPqww3n/PZ3zYXdFpa+9Wqzz1FK0eP26xpNS1j6rfF9LtDPzBVD6x/I/GBr\nHjm1y9WL9iH3lo7Pbm/5J0menNscHgfgSimTUmqzUuozIxokhBCibRRv2UXGGx+7ysl33oBPUICh\ndZRZHby4u/4hxjGRZgaEtv6Dl0bwT04gbOp5rnLOEy/gqKw6yRktc2ZSGEkRzgderXYtD2SKNrN5\n82bGjx9Pnz59mD9/PjU1zjfKq1evZsiQIa7jnnvuOUaNGkVCQgITJkzgyy/rZwc6cOAAl156KUlJ\nSfTv359bbrnFtW/Pnj3MmDGDPn36MHbsWD755BPXvqNHjzJ79mwSExO54IILOHDgwAnbmZmZSVRU\nFG+++SaDBw9m8ODBLFmyxLV/4cKF3HjjjcybN4+kpCTeffddFi5cyLx581zHLF++nAkTJpCcnMy0\nadPYs2ePa9+IESNYvHgxZ511FvHx8Tgcjhb+Rt1nxAj4H4BfT7RTcsCFu7pK3p0whvQXz2i7nV/v\n/TvUBnrhZwyj2znG53z+K62CIzXOOoJ94Mp4Y2dWaW1R18/AHOZcPt6alUf+0vcMr8OkFNecHuMq\nr8ss4aeD8kBme+lK95Zly5bx8ccfs3nzZtLS0nj66add+xqmg/Tu3Zvly5eTkZHBPffcw7x58zh8\n2Jku9fjjj3Peeedx8OBBtm/fzq233gpARUUFV1xxBVdddRVpaWm89tpr/OlPf3IFvnfffTcBAQHs\n3r2bxYsX85///OeU7V29ejWbNm3iww8/ZPHixY1y2P/73/8yffp0Dh48yMyZMxv9DGlpacyZM4cn\nn3ySvXv3kpKSwuzZs7HZ6hfB+vjjj/nggw84cOBAm6zg6dEwhFKqF3Ax8BjwR0NaJIQQotVlvv0Z\nxak7AVC+vvS962bDH7zcWFDD97n16RRXJ1oI8fW+WU9OxhwSTNSNMzn83OsAFCx9l4jLJ+MXH2to\nPX2iAjgnOZwf9jsD7xd+PsTI2BCC/TvGpwWi+f4bY9xMQ1Nyf27Rebfeeis9e/YE4I9//CP3338/\nf/7zn4877rLL6tcEmD59Os888wybN29mypQp+Pr6kpmZSXZ2NrGxsa6HN7/++msSExOZNWsWAEOG\nDOHSSy/l008/5a677uKLL77g559/xmKxMHDgQK6++mrWrFlz0vbee++9WCwWBg0axOzZs/noo484\n++yzARgzZgxTpkwBwGJp/Eb/k08+YfLkya5j58+fz8svv8z69euZMMH5d5g7d67rd9EWPA3xnwH+\nBJzwszLJARfukrw70RzSX1quOv9IoxUve117GQG9Yk5yRvOVWR280CD1ZFSEmZERHTOYDL3wbPz7\n9QZA11jJeeLFVqln5tAehFmcv6MjlTZe25DdKvWIk+tK95bY2Po3kvHx8eTmNr0q63vvvcekSZPo\n3bs3vXv3ZteuXRQWFgLwyCOP4HA4uOCCC5g4caJrJDszM5ONGzeSnJxMcnIyvXv3ZtmyZeTn51NQ\nUIDNZmtUf69evU7aVqXUSdsbFxd3wnNzc3OJj49vdK24uDhycnKa/F20hRbfDZVSU4E8rXWqUuoc\noMlhjR9//JGNGzeSkOB8qj4sLIyhQ4e6PuKp6+hSlrKUpSzltikHv/U1tuJSfnWU4xcVwYTrpgGw\nZtMGAMaPGuNx+bW0CtJ3Oqc2jDttBLMSLK4FceqmBWyr8tTJF3t8vR63X8fXd9wLwKAVqylduZ5d\nfs6Pr8eMc46gbVj7s0flHZvXMYpyvsMZiLz75Qoij/TiussuALyn/3T2ch1Pr1dcXNzmQV1zZWVl\nub7PzMwkJub4N+KHDh1iwYIFfPrpp5xxxhkATJo0yfWcQvfu3V2zjaxdu5YZM2YwceJE4uLimDhx\nIh999NFx13Q4HPj6+pKVlUXfvn2Pa0tTtNaNjj906FCj9p7sE7yYmBh27tx53M/e8O9zqk8AV61a\nxbZt2yguLgYgIyOD0aNHk5KSctLzTkS19EEPpdTjwLWADQgAQoCPtdbXNzxuxYoVeuTIkS2qQwgh\nhLFyPvmWLfMecpUHL7qPyHHGPquzoaCGx7eVuspz+1gY0UFHvxvK+8drlPzPmXPql9SLvp+9isnf\n2OkUtdY8v/oQqTnOTw8Swy28cPlp+Jpl1uCOpi4lw1uNGDGCkJAQ3n//fQICArjmmmuYOHEiDzzw\nAKtXr2bevHls27aN3bt3c95557Fy5Up69+7Nu+++y4IFC/jHP/7Btddey6effsqYMWOIjY1l586d\nXHDBBfz8889ERkZy5pln8uc//5kZM2agtWb79u0EBwfTr18/brnFud7A4sWLSU9PZ+bMmSQmJjZ6\nwLNOZmYmI0aM4Morr+SZZ57h4MGDTJ8+nVdeeYVJkyaxcOFCDh48yIsv1n861XBbWloa5513Hv/5\nz38YP348L774Im+88Qbr1q3Dx8fH9RBmXYrKsU70t9y8eTMpKSktyqtr8f9orfWftdYJWutkYBbw\n3bHBtxBCCO9RfbiQX++vf8gqeuo5hgffx856MjrC3CmCb4Com6/EFORcPr7m4CEOL3nT8DqUUlw7\nMgZ/H+fLc3pRlcwNLlqFUoqZM2dyxRVXMGrUKJKTk7nrrruOO+60007jtttuY/LkyQwYMIBdu3Yx\nbtw41/5ffvmFCy64gISEBK677jqeeOIJEhISCA4O5qOPPuLjjz9m0KBBDBo0iL/97W+umVYWLlxI\nWVkZAwcOZP78+VxzzTWnbPOECRMYPXo0V1xxBfPnz2fSpElu/ax9+/blpZde4p577qFfv3588803\nvPPOO/j4+Lh+F22txSPgjS6i1CTgLq31ZcfuW7Rokb755ps9rkN0fqtWrepST58Lz0h/aR6tNZuv\nv4f8b1YD4Bcdxah//x2f2oDSKM/9WsoPec4X2BAfxUNDAgn2ad8HLzelbmr2apgnUvTFCvKXvOUs\nmEwkv/88gcMGGnLthr7Ze4R3U/MA8DUpXpoxgPjwjjWDTEdl1L3F20fAO5LMzExOP/10Dh8+3CYz\nlBzLq0bAG9Ja/9hU8C2EEMI7ZL3/lSv4Buj/53mGB9/f5VS5gm9wLrjT3sG30cIuPpeA4bUBt8NB\n1n1P4aiuOflJLZDSN6J+bnCHZvHqTJkbXHRpna3/t/rbCJkHXLhLRjNFc0h/cV9lVh67Hqxfkrnn\njMlEjB5qaB0Z5TZe3lPuKp8R6eM1qSdGjX4DKJOJ6AW/RVn8Aajel94qqSgmpbhxdM+6hTjZklPG\np78WGF6POJ7cW7xTe6SJtCZ5qkMIIToxrTXbFzyOrdQZHFvioul922xD66i0af6+vYya2sXjov0V\nVyf6G1qHJ155Y6mh1/ON6U63W37jKhe8+j4VW3ee5IyWSQi3cGH/KFd56fos9hdWGl6PEN4uPj6e\ngoKCdkk/aS2t/pPIPODCXV1p7lXhOekv7sl88/8oXOmcHhCl6P+X2zAHGJdLrLXmpT1lHKqwA+Cr\nYE5fCxaz94xWLX3rVcOv2VapKNMHdyM+zPlmxmrXPPH9Qaptrb9Mdlcm9xbRFjrPWwkhhBCNlO7c\nx+5HlrjKcVdPJWzYaYbW8U1ONSsb5H1fnehPbIDZ0Dq8UVuloviaTcwdF4df7Rua9KIqXll38vmS\nhRDeT3LAhdeQvDvRHNJfTs5aVMIvN92HvbIKgIDEOJJuucrQOg6U2nh1b33e9/goH8Z38zW0Dm/W\nVqkosaH+XD0i2lX+fGcBa9KLDa9HOBl5b3E45NOKjk5r3SoPgMoIuBBCdDLabmfLbY9QcdA5Umqy\n+DPw0TsNXTSmwubg7ztKsdbGFz0tilkJ3pP33VaOTUXJ/OOj2ItLT35SC5zdO5xRcSGu8qKV6RSU\nG5/yIozTrVs3srKyJAjv4I4cOUJYWJjh1231R9RTU1ORlTCFO2ReZ9Ec0l9ObO9TSyn4bo2rfNpf\nbiMoOd6w69scmn/sKCOn0hlY+JtgTt8AV5pEV1KXipL+u7+gK6uwZuaQefdjJL70GMpsXCqOUoob\nRvdk/5FKjlbaKKm289SP6Tx5UV9MnWx2iPZm1L3Fz8+P6OhocnNzDWiVaC/+/v4EBwcbfl3vmCNK\nCCGEIXK/+J79z73lKve6bhrdzh1r2PW11ry4u5xNR6yubdck+hNj8d4PVKdOvrhVr+8b053ou24h\n91Fnvn3ZyvUcfv5Nou80dhG6YD8zc8bG8tQPGWggNbuMD7bmMWt4jKH1COP4+fnJYjyiSeaHH364\nVSuorKx8uGfPnq1ah+gcEhIS2rsJogOR/nK80l372Xztn9BWGwARZwyj//3zUCbjRkj/c6CSr7Kq\nXOUpMb6cF2NcaktrOOfMc1q9Dv+EOLTVRtWOPQBUbNyKZWAf/JON7afdgvywa82eAud0hKnZZfSJ\nCpBVMg0k9xbhrpycHJKTkx9pybktHrJQSvVSSn2nlNqhlNqmlLqjpdcSQgjhGWtxKb/cfD/2Cmdg\n5h/bg9MeuQNlNm5k+qtDlXyUXj8P9fgoHy6L8+7guy1FXX8FgaPqFzg6dM+TVO/LMLyeywZ1p29U\nAAAaeOK7g+w6XH7yk4QQXsWTO7MN+KPWejAwHrhdKTXg2INkHnDhLpl7VTSH9Jd69ooqfrn5fir2\nZwJgsvgx+Mm78Q01Lm/x58PVvLq3wlUeHGrmmiT/DrE63abUTW1SjzKbiLlvHj4x3QFwlFeQfvuD\n2MuMDY59TIrfT+xF9yDnjDPVds1D/9tPTmm1ofV0VXJvEW2hxQG41jpXa51a+30ZsBOIM6phQggh\nTs1eWc3mG+/lyOrNrm39//w7gvoY9zH69qNWnvm1jLqJuJICTdzax4K5AwTfbc0cEkzsQ3egamec\nqTmQyaF7n0QbPBNGqL8PC86KJ8jP+aBnUZXnfA65AAAgAElEQVSNv/x3H6XVNkPrEUK0DkM+m1RK\nJQEjgHXH7pN5wIW7ZEYL0RzSX8BeVc0vN99fv9IlkDh3Ft1TxhtWx44iK09sK8VWG3338Ffc3i8A\n/w4048moEaPatD7/5AR6NHgAs/Tb1eT8bbHhQXhMiD/zJ/bCpzbHP7O4mke+OUCNXaa984TcW0Rb\n8HgWFKVUMLAM+EPtSHgjy5Yt49VXX3U91BAWFsbQoUNdHbzuox4pS1nKUpay+2VHdQ1vXn4zRZu2\nM8gUBEDBRWPwGRxH3dj3mk3OwHz8qDEtKr/67c98mF5JYLJzIMWevoVJCf4E+44G6lM76gJcby1v\nSt3MnBtvbdP6Q88dz4ZVP1H203oGmYI48u5nbMnNIOr6GZwxwfn33LD2ZwDGjJvgUfmWM4bw0tos\nSvalsmofLAry5b5zElm9ejXgHf1VylLuDOVt27ZRXOxcBCsjI4PRo0eTkpJCSyhPVvdRSvkAXwDL\ntdbPNXXMokWL9M03GzsVk+icVq2SeZ2F+7pyf3HUWEm99QEOf73KtS3+pitIuuVKw+r46lAVr+4t\nd6WdhPgo/tDfQlxgx1tmfsx5Y9nw3XEf0LY6bXeQ9/QrlH5fPyd75KxL6fnXP6BMxk7b+NWuApZt\ny3eVLzotijsmxmM2cAacrqIr31tE82zevJmUlJQW/Sfz9A7wL+DXEwXfQgghjOWormHLvIcaB9/X\nTyfxtzMNub7Wmrf3V7C0QfDd3V9xz8CADhl8tydlNhF99xxCzq1PCTry3ufkPPKc4ekoF50WxTnJ\n4a7y8t2F/O3bA1TbJB1FCG/kyTSEE4FrgPOUUr8opTYrpaYce5zkgAt3yYiDaI6u2F8qs/JYN+13\n5H31o2tb3OxLSZzzG0NmI7E5NEt2lTeaajAx0MSfBgTSzd97F9rxZm0VhCuluOb0GCYk1i+ZvSaj\nmHu/SqOkymZYPV1BV7y3iLbn09ITtdarARkOEUKINlC4aiNb5j5ETWGRa1vsby6m922zDQm+D1fZ\nWbyzjB1F9cHa4FAzt/axdKgHLr1RXRAOuNJRjrz3OY4aK7EP34nJ35i51M0mxW/H9CTM4sPy3YUA\n/Hq4nLu+2MtjU/rQI1jmbBfCW7T6kIbMAy7cVffAgxDu6Cr9RWvNgRfeYcNVd9YH3yYTyX+4nuT5\n13kcfGut+S6nigXrixsF3+OifPhdXwm+jdLUSHjRx/9l/6zfU52RZVw9SnHlsB7MGh7t2pZeVMWd\nn+/h4NHKk5wp6nSVe4toX/KZohBCeClbWTlb5jzI7r8tgdp0Bd+IMIY9/yBxV13scfBdXONg4fYy\nnt9VToXdmfFtAi6J9eX6JP9O8wDf1MkXt3cTgAZB+AX1KQ5Vv6ax7/J5FC//wdC6JvePZO7YWOre\nPxWUW/nDZ3v4YmcBnky+IIQwhkezoLhjxYoVeuTIka1ahxBCdCZaa/K+/IHdjyyhMjPHtT1kcD8G\nPrYA/+6RHtexoaCGF3aXUVRT/xrQ3V9xY28LycGSXdiatNYUf76CgqXvoq31nzpEXjONmPt+h8nP\nuFSRHXnlLPn5UKOHMUfGhfDHsxIkJUUID3kyC4oE4EII4UVKd+5j51+eabSyJUDPGReQfMcNmHxb\n/OgOAHtKrLy7v5LUo9ZG28/q7sMVvfwl5aQNVe09QO7j/8SaUz99oGVwf+Ieu5uAgX0NqyejqIqX\n1maRW1rj2hboa2Lu2DimnBZlyDMEQnRF7TkN4SlJDrhwl+TdiebobP2l5kgxv96/iNUpNzQKvn1C\ngzntodvpe9dvPQq+D5TaeHxrCfduKmkUfIf6Kn7fz8LsxM6b7123QI63sfTrTfySvxF85mjXtqod\ne9g3fQ6Zdz1GTWa2IfUkhFt4+ILeTOkfSd1fuMLq4JlVmTzw9T4OFVcZUk9n0dnuLcI7eTaUIoQQ\nwiMVGTlk/vsTDv37E6xFpfU7TCZ6zphM4m9n4hsa3KJra605UGZnWXola/JrGu1TwNgoH66I9yfY\np3MG3h2BOSiQmAd+T/Hn31Kw9D1XSkrxFyso+fpHIn5zCT1uuw6fqAiP6vEzm7hqeDQj40J4bUMO\neWXO/rDxUCm//XAnZ/YOZ9bwaPp1C/T4ZxJCnJqkoAghRBvTdjv5360l883/I3/FGjjmPhw+agjJ\nd95AUHJ8i65/pNrBj3nV/JhbTXq5vdE+BYyMMHNJnD8xFnkO35tUp2dR+MYyytc0Tj8yBQYQee10\nImZMwb93y/pEo3psDv5vez7f7D3CsRHAqLgQZg2PZljPYElNEeIUJAdcCCG8nLbbKd6yi/wVa8j+\nYHmjhyvr+Mf2IHn+dUSdNbrZwU9xjYNfjlj5MbearUetNLXEy/BwM5fG+nW5FS1feWMpc268tb2b\n4bbKHXso+NeHVO3Yc9y+gGEDCJ92AWEXn4dPZFgTZ7tvX2Eln/2az7bc8uP29esWwNm9I5iYFEav\nMItH9QjRWbVbAF678uWzOHPJX9NaLzz2mEWLFumbb765xXWIrmPVqlWyAplwW0foL1W5+RR8v46C\nH9ZRuHID1qMlTR4XfsYwYmdMJnL86Sgf94LjkhoHO4qsbC+ysa3ISuYxI911fBUMjzBzfrQfiUFd\nK/CuM+a8sWz4bl17N6NZtNaUr99C4esfUnPw0PEH+JgJOesMgs8+g6CRQ/Dvl4Qyt+zvm1FUxVe7\nCtmQWXLciDhAYriFCYlhTEwKp2+3AEydfGS8I9xbhHfwJABvcQ64UsoELAFSgGxgg1LqU631robH\npaWltbQK0cVs27ZNbnrCbd7UXxw2GxX7MindmUbJjjRKd6RRujON6gazWxzLJzSI6Knn0nP6+QT0\nijnhcVaHJqvCTma58yuj3E5muY3syhMvY66AfiEmxkX5cnqED5ZO+nBlZ6aUInjsCIJGD6N87WZK\nVqymfP0WsNW+0bLZKf1+jWtlTVNIEIGnDyZw1FAChw3AL6kXvjHdUaZTpxklhFuYNy6Oy4d057+7\nC1l9sBiboz4UTy+qIr2oine35BHoa6JPVCD9ugXQr1sg/boF0ivMv1MF5d50bxHeLTU1lZSUlBad\n68lDmGcAe7XW6QBKqfeAaUCjALy8/PiPtoRoSnFxcXs3QXQgrd1ftN2OtbgMa1EJ1qJSrMUlWItK\nqCksoirrMFXZeVRlH6Yq+zDVuQVoe9Mj0A35RoYRPnY4IWeMwHfs6VSYfdlv05Tl11Buc3C0RlNY\nbedItYPCagdHqh0U1egm00mOZVaQGGhiaLgPZ0T6EOkv+d2dgTKbCJ44muCJo7GXlFG6ch2lK36m\namfjwS1HaTllK9dTtnJ9/bl+vvglxOKXEIdfYhy+PaIwR4bjExGGT2Q45sgwzOFhmAItKKWIDvbj\nhlE9uWJId7bklLE5q5QdeeXU2OuD8Qqrg225ZWzLLXNt8zcregT7HfPlS0SALyH+ZoL9fAjxNxPk\nZ+4QizvJa5Fw15YtW1p8ricBeByQ2aB8CGdQfpwP5jzuQTWiq9ixYzUf7Hcn1BAdTzNS3RqmxTU6\nTdfv07Bj5xo+2FPt3KY1SmtwaFcZhwPlcDhXkNTa+b3dgbLZwG5H2WzO7202lNWGqqnGVF2Nqq5B\nVVdjstnwlN3Hh4KkPmT2H8TBfgPJ7RFLja4NQDZXeHRtE5AUZKJ/qJn+IWaSg8yddhpB4WQODSb8\nkhTCL0mhJjuP8nWpVO3YS+WOPdiPHh806hor1WnpVKeln/zCSmEK8McUGIAKsGAODCDG34+pvr5c\n7ONDuVYU2aDYqqnGBErhUAptMqGVCUftKLtWimqlyFSKjAYj4tr1vcLHBGazCbNSmE0KswKzSWFS\nCmVSmACTcn4CoOr+dZ6KwrnN1eyG/9Yd1wwnOl5ei4TbAlp+aqtPQ5ibm0vojxtauxrRCZRYswnd\nd7S9myE6iBJrNqEHvGekqjQ0nPyYOPJj4iiIiSM/phdHo7qjG+bltuCRGwVE+Sl6BpiIDTDRM8BE\nT4uJGIsJPwm4uyy/2Gj8Lr8QLr8QrTW23Hwqd+yhcsceatKzsGblYS8uPfWFALTGUVGFo8I5H7j1\nmN0mILL2qyuQ1yLhtt+MafGpngTgWUBCg3Kv2m2N9OnTh+Ux9fmNw4cPZ8SIER5UKzqraamp9JC+\nIdzkbf2lB9CnyT1GzDSl4ZhElErgJGngooGnn36aYoebwWhHFR0A0cOxnDccmbPEM952bxHeIzU1\ntVHaSVBQUIuv1eJZUJRSZmA3zocwc4D1wNVa650tbo0QQgghhBCdXItHwLXWdqXU74H/UT8NoQTf\nQgghhBBCnESrL8QjhBBCCCGEqGfYPFVKqSlKqV1KqT1KqXtPcMxipdRepVSqUkoSrLqoU/UVpdRs\npdSW2q9VSqmh7dFO4R3cubfUHjdGKWVVSs1oy/YJ7+Hm69A5SqlflFLblVLft3Ubhfdw47UoVCn1\nWW3Msk0pdWM7NFN4AaXUa0qpPKXU1pMc06wY15AAvMGiPBcCg4GrlVIDjjnmIqCP1rofMBd4yYi6\nRcfiTl8B9gNna62HA48CS9u2lcJbuNlf6o57Evi6bVsovIWbr0NhwD+BS7TWQ4Ar27yhwiu4eW+5\nHdihtR4BnAssUkq1+uxxwiu9jrOvNKklMa5RI+CuRXm01lagblGehqYBbwFordcBYUqpaIPqFx3H\nKfuK1nqt1rpufrm1OOecF12TO/cWgPnAMuBwWzZOeBV3+sps4COtdRaA1rqgjdsovIc7/UUDIbXf\nhwCFWmvPFwgQHY7WehVwsrkpmx3jGhWAN7Uoz7FB07HHZDVxjOj83OkrDd0CLG/VFglvdsr+opSK\nBaZrrV/kxGtriM7PnXtLfyBSKfW9UmqDUuq6Nmud8Dbu9Jcl/P/27jw+qupu/PjnzGRfSMhGSEgC\nhH1fEkQiiyCbG1R4WkTrVhd+WqqoVWt/rbW/Pra0WJeidX3EDRSBghsq+igQlJ0AIltYQ0ISEkJC\n9mXO74+b3EyAkEkymUyS7/v1yst77rn3zpl4uHNy5nu/BwYopTKA3cCDLmqbaHsaPcaVr1KE21JK\nXQ3cCVzV2m0Rbu15wD5+Uwbhoj4ewAhgIuAP/KCU+kFrnXr500QHNRXYpbWeqJSKB9YppYZorQtb\nu2Gi7XPWANyRRXnSgZgGjhHtn0MLOCmlhgCvAdO01rIkWcflSH9JAD5QSikgDJiulKrQWn/sojYK\n9+BIXzkF5GitS4FSpdQGYCggA/COx5H+cifwVwCt9RGl1DGgH7DdJS0UbUmjx7jOCkHZBvRSSsUp\npbyAOcCFH34fA7cBKKVGA+e01llOen3RdjTYV5RSscBK4Jda6yOt0EbhPhrsL1rrntU/PTDiwO+X\nwXeH5Mjn0BrgKqWUVSnlB1wByPoVHZMj/eUEcA1AdTxvH4wkAaJjUtT/DWujx7hOmQGvb1EepdR9\nRrV+TWv9uVLqWqVUKlCE8Zel6GAc6SvAH4AQ4OXqWc0KrfWo1mu1aC0O9pc6p7i8kcItOPg5dEAp\n9SWwB6gCXtNa/9SKzRatxMF7y1+AJXap5x7TWp9tpSaLVqSUWgpMAEKVUieBpwAvmjHGlYV4hBBC\nCCGEcKEGQ1CUUt2UUv+rlNpXnYj+N9X7OyulvlJKHVRKfVmdX1UIIYQQQghxGQ3OgCulIoFIrXWK\nUioA2IGR7/BOjJyYf69eQaqz1vqJFm+xEEIIIYQQbViDM+Ba60ytdUr1diHGAyvdMAbhb1cf9jYw\ns6UaKYQQQgghRHvRqBhwpVR34DtgEJCmte5sV3dWax3i5PYJIYQQQgjRrjichrA6/GQF8GD1TPiF\nI3d5mlMIIYQQQogGOJSGUCnlgTH4fldrvaZ6d5ZSqovWOqs6Tjz7UueOGTNGBwQEEBkZCYC/vz+9\nevVi2LBhAKSkpABIWcqsWLGCXr16uU17pOzeZekvUna0nJqayuzZs92mPVJ277L0FynXV05NTaWo\nqAiAzMxM4uPj+fe//92k1ZcdCkFRSr2DsXrYw3b7FgJntdYLL/cQ5pQpU/SHH37YlLaJDub+++/n\n5Zdfbu1miDZC+otwlPQV0RjSX4SjHnzwQd55550mDcAbnAFXSiUBtwB7lVK7MEJNngQWAsuVUndh\nrBb180udXzPzLURDYmNjGz5IiGrSX4SjpK+IxpD+IlyhwQG41noTYK2n+hrnNkcIIYQQQoj2zeGH\nMJvK39+/pV9CtBNBQbKWk3Cc9BfhKOkrojGkvwhHDR06tMnntvgAvOYhKSEaMnjw4NZugmhDpL8I\nR0lfEY0h/UU4quYBzaZoVB7wpvjmm2/0iBEjWvQ1hBBCtB9nvt3M2U07iZg2ls4JMhgSbVdhYSH5\n+fko1aTn9IQbsFqtREREXPL/4c6dO5k0aVLLPIQphBBCuErOd1vYcbORcOvY4vcIu/oKej36K4JG\nDGTT8XzyyyqJCfIhNtibYF/PVm6tEPXLzc0FICoqSgbgbVhxcTHZ2dl06dLFqddt8QF4SkoKMgMu\nHJGcnMxVV13V2s0QbYT0l/anLDuXPb/+c519Od9uIefbLVQkDOejkZPIjOlh1nXythIT7ENssA/T\n+4bSL+LSzxxJXxGN4az+UlZWRlRUlBNaJFqTn58f586dc/p1WzwGXAghhGiIttnYM//PlOfkAWD1\n8wFL7ayh5/ZdzH11Edcvex2PinIACsqq2JdVxNqDuTyxNpW84opWabsQQjRWiw/AmxOgLjoWmaES\njSH9pX059vJSctdvMwpK0f+ZRxj53rOET70Kbff1fZ99KUze8g1e1rpf6RdX2Fi2O+uS15a+IhpD\n+otwBZkBF0II0arO7dzH4b+9apa73XIDnRMH4xcXxdl597DkN3/g4KDhZv2gzRtYPDWWf1zXi1uG\n18ZlfrY/h6zz5S5tuxBtWWhoKH/84x/N8uLFi/n73//u8PlhYWFMmDCB8ePHc+utt5r7T548yeTJ\nk0lMTOTuu++msrLSrHviiSdISEhg3Lhx7N271zlvpA1q8QF4SkpKS7+EaCeSk5NbuwmiDZH+0j5U\nFBSye95T6MoqAAIH9CLuHmNh5eJKG28eLiIvvAuf//wuysLCAKg6V0D+f74k1M+TifGdiQ/1Na5l\n07y36/RFryF9RTRGR+ov3t7efPrpp+Tl5TXpfD8/P7777jvWr1/Pe++9Z+7/05/+xAMPPMC2bdsI\nCgoy69atW8exY8fYvn07//znP3n44Yed8j7aIpkBF0II0Sq01ux77O+UnMwAwOrvS7+nf4PFw8gP\n8MGxEs6WG6lyA7ysRMyaZp6b89YKdFUVSilmDw439687fJaT50pd+C6EaLs8PDy4/fbbefnll516\n3Y0bN3LjjTcCMGfOHD777DMA1q5dyy9+8QsAEhISKCgoIDs726mv3VZIDLhwGxJ3JxpD+kvbl7F8\nLZmrvzbLvZ+4D5+oCACOna/ks1O1A+nZMV6ETR+HJdDIdFJx6jQFX20EoG+4PwO7GPttGt7ZUXcW\nXPqKaIyO1l9+9atf8dFHH3H+/Pk6+1esWMH48eOZMGFCnZ8777zTPKasrIyJEycydepUPv/8cwDO\nnj1LcHAwFosxxIyKiuL0aePf5OnTp4mOjjbPt6/raCQPuBBCCJfTNhupi940y11uuJrwiaMBsGnN\nK4eKsFXX9Q20kBjigVKK4OsncXbZxwDkvPkhnaaNRynFTYPC2ZdVBMCGY+c4nFNM7zA/l74nIdqi\ngIAA5syZw6uvvoqPj4+5f/bs2cyePfuy5+7evZvIyEhOnDjBjBkzGDhwIIGBgbT0Io/tgcSAC7fR\nkeLuRPNJf2nb8rbspiTNmPnyCPQn/qE7zLqvT5dxqMB4aMuqYE6cj7mQSdCN16A8jQV4SvYepHj7\nHgB6hPgyMjrQvMZb2zPMbekrojE6Yn+ZN28e7733HiUlJea+mhnwC3/sZ8AjIyMBiIuLIykpiT17\n9hASEkJBQQE2m/EndEZGBl27dgWga9eupKenm+fb13U0EgMuhBDC5dKXrzW3w68Zg9XHGzAevHz3\nSLFZN6WLJ5E+tR9VHp2DCLxmjFnOeXO5uT1zUDg1yQm3nzrPntOFLdR6IdqX4OBgZs6cybvvvmvu\nmz17NuvXr7/o56233gIgPz+f8nIj61Bubi5bt26lb9++gBHGs3r1agA++OADrr32WgCmT5/Ohx9+\nCMC2bdvo1KkTERERLnuf7qTBAbhS6k2lVJZSao/dvqeUUqeUUjurf6bVd77EgAtHdbS4O9E80l/a\nrqriUjI/+V+zHDF9nLn9/ZlyCiuNr69DvRTTorwuOr/zTbUfOee//YHSIycAiO7kzZi4ILPure0Z\naK2lr4hG6aj95YEHHiAvL8/8tqkhBw8eZOLEiYwfP56ZM2eyYMEC+vTpA8BTTz3Fyy+/TGJiInl5\neWaKwsmTJxMXF8fIkSN5+OGHWbRoUYu9H3fnSAz4W8C/gHcu2P9PrfU/nd8kIYQQ7VnWlxuoKjRm\nuX1iIgkc0Mus25BZZm6Pj/DEy3LxYMArJgr/0cMp2rwLgNy3PiL6L48CMGNgGJtP5lOlYV9WEVvT\nCrgiNuiiawghjHzdNcLDw0lLS3P43FGjRtUbrhMXF8fXX399ybrG5BlvzxqcAddaJwOXShDp0J9I\nEgMuHNUR4+5E00l/absyln9hbneZPt6cccstq+LHc0bstwISQ+qfI+o8e7q5fW71OirOnAUgzN+L\nCfGdzbpVP56RviIaRfqLcIXmxID/WimVopR6Qykl0wtCCCEaVJqVQ876rWY5Ymrt1/3JWeXU5E7o\nHWAh2Kv+jyifgX3w6RcPgK6o4Ox7/zHrpvcNNbd3nz5PYVnlRecLIURramoawpeBP2uttVLqL8A/\ngV9d6sDU1FTuv/9+YmNjAQgKCmLw4MFmjFXNX5pSlvJVV13lVu2RsnuXpb+0zfLp1V8TWJ0d4UTP\nMDzSj3NlpLGQzoqNmykosdEpfhijQj3ZkbIDgJHDRgLUKSulOD4inrM/7WGAxZ+zyz7m+MheWLw8\nSRw9hl6hvuzc+gMAVUk3uM37l3LHKefn5xMVFYVoH5KTk9m7dy/5+fmAEb6TkJDApEmTmnQ95Uiu\nRqVUHPCJ1npIY+oAvvnmGz1ixIgmNU4IIUT7obVm09W/pPDAUQD6PDmPLtdNACCtqJLfbDU+2KwK\n/j7UHz+Py0c66iobx+/8LZXZOQDEvfoMgROMXOLrDp9lWUoWAMOjAlh4be+WeEtC1CsjI0MG4O1E\nff8vd+7cyaRJkxx7avUCjoagKOxivpVSkXZ1NwE/1neixIALR9XMHgjhCOkvbc/5fYfNwbfF24vQ\nCVeYdRuzys3twUHWBgffAMpqIXDcKLOcX70yJkBCt0DzQ2tjcjJ5JRXNbL3oKOTeIlzBkTSES4Hv\ngT5KqZNKqTuBvyul9iilUoDxwIIWbqcQQog2Lv2j2tzfoeMS8fD3BYyZ8Q1ZtdlPRoV6OnxN/6SR\n5vb5bzahK6sA6OzrSe8w4/o2DZuO5zer7UII4UweDR2gtZ57id1vOfoCkgdcOKombk4IR0h/aVts\nlZWcXvmVWe5il/v7YEElWaVGXLivFQYFWR2+rk/fnlhDg6nKPUfVuQKKtu8hYPRwABJjOnEop4RO\n8cNYfzSP6/uHOendiPZM7i3CFWQlTCGEEC0u59stlOcYGW09Q4MJThhs1tnPfg8P9sDzErm/66Ms\nFgLG1M6CF6yrDUMZGV0bhrI3s5C8YglDEaJGamoq48ePJy4ujtdff50HHniAZ555ptXa89xzz/HQ\nQw+12uu7WosPwCUGXDhK4u5EY0h/aVsyPrLL/T11LMpqfPxU2jSbsmvjv0eFNvjF7EUCkhLM7YJ1\nyejqLCvBvp70DvOj4EgKNg3Jx881tfmiA+ko95YXX3yRsWPHcuLECe65555GnXvjjTfy3nvvObU9\nCxYs4Pnnn3fqNd2ZzIALIYRoURX558n+snZm2n7p+d15FRRUGNm4gjwVvQMdDz+p4Tu4L5ZAfwAq\ns3Io2XvQrEuMCTS3NxyTAbgQNdLS0ujXr19rNwOAqqqqVjm3NbX4AFxiwIWjJO5ONIb0l7Yj67Pv\nsJUZs9z+fbrj3zPGrLMPP0kM8cCiGp/RS1mtBFxZm+62oE42lE4ExRufQ3tOF3JWwlBEAzrCvWXm\nzJkkJyfz2GOPERsby9GjR+vU5+fnc/PNN9OnTx/i4+O5+eabOX36NAD//d//zQ8//MDjjz9ObGws\nTzzxxEXXT0tLIzQ0lLfffpuBAwcycOBAFi9ebNYvXLiQO+64g3nz5tG9e3eWLVvGwoULmTdvnnnM\n2rVrGTNmDD179mTGjBkcOnTIrBs2bJg5gx8TE4Ot+luvtqTx3/UJIYQQjZD12XfmdsSU2sFNSaVm\ny5nmhZ/U8E9KMAfeBes20uXRe1BKEeTjQd9wPw6cKUZjhKHcOCC8ya8jhLNMeWOX06711d3DG3X8\n6tWrufHGG/n5z3/OrbfeelG9zWbjlltuYcmSJVRWVjJ//nwee+wx3n33XX7/+9+zZcuWes+1t2nT\nJnbs2MHRo0eZOXMmQ4YMYdw44xuwL774giVLlvDKK69QWlrKCy+8gKr+Azw1NZV7772X999/n6Sk\nJF566SXmzp3L5s2b8fAw7hOrVq1i+fLlhISEYLG0vYAOiQEXbqOjxN0J55D+0jZUFhaRs3G7WQ4b\nX5u3e2tOOWXVE1eRPopuvk3/SPIbPgDl6wNA+Yl0yg4dM+uCcveb2+uPShiKuDy5t0Dnzp25/vrr\n8fb2xt/fnwULFvD99983+jqPP/44Pj4+DBgwgLlz57Jy5UqzLjExkWnTpgHg4+NT57zVq1czZcoU\nxo0bh9VqZf78+ZSUlLB161bzmPvuu4+uXbvi7e3dxHfZutrenwxCCCHajDPfbEaXG2Ef/vGx+ERF\nmHUb7XN/h3ias19NYfHywn/UULNsn8eNTsgAAB/OSURBVA2lb7i/mQ3lx8xCciUMRYjLKikpYcGC\nBQwdOpTu3btz/fXXk5+fjyOrp9dQStVZPTImJobMzEyzHB0dXe+5mZmZxMTUhqoppYiOjjbDYIA2\nv8poi4egSAy4cFRHiLsTziP9pW3IWrve3A6dUDv7XVRpY3de7UA4oRnhJzUCkkZSuH4LYMSBR/z6\ndgAmjBvL1u9O1IahHDvHjIEShiIuzVX3lsaGjbjS4sWLOXr0KN988w1hYWH8+OOPTJgwAa01SimH\n/ljWWpOenk6vXr0AOHXqFJGRtQupX+4akZGR7N+/v86+9PT0OoPu5vzB7g5kBlwIIUSLsJWVc+br\n2q+tw8Ylmts7ciuorJ5Mi/G1EO7d/I8j/4QhKE9jFc3Sg0cpO5Fu1iXGdDK31x/La/ZrCdGeFRUV\n4ePjQ2BgIHl5eSxcuLBOfXh4OCdOnGjwOosWLaKkpIT9+/ezdOlSbrrpJodef+bMmaxbt46NGzdS\nWVnJv/71L3x8fEhMTGz45DZCYsCF25C4O9EY0l/cX27yDqoKiwHwiYrALz7WrPvB7uHL4Z2d82Ws\nxc8XvxEDzXJNGMq2zd/XWZRnX2YROUXll7iCEB3n3nK5GeR58+ZRUlJC7969mTZtGtdcc02d+vvu\nu481a9YQHx/P7373u3qvM2bMGBISEpg1axbz589n/PjxDrWtV69evPLKKzz22GP07t2bdevWsXTp\nUvMBzLY++w2SBUUIIUQLqRN+Mi7R/NAsq9LszHX+ABwg4KpEirYYEz8F65IJv3sOAJ18POgX4cf+\nbCMMZdPxfAlDER3amjVr6pRfeuklczsyMpKPP/64Tv3tt99ubicmJtZ5IPJSlFLceuut3HbbbRfV\nPf744w3uu/baa7n22msvee1du5yXQaa1SB5w4TYkplc0hvQX96arqsj+ovZByFC78JNdZ8spt8t+\nEtmM7CcX8h89DKpTkpWk/ERF1hkSR48BjJzgNTadkGwo4tLk3uIcjXlgsyOSGHAhhBBOd27HPspz\njFhrz86d6DSoj1lnH34yzImz3wDWwAB8h/Y3ywVfb6p9ragAc3vP6UIKSiud+tpCiFrtIUykJTU4\nAFdKvamUylJK7bHb11kp9ZVS6qBS6kulVFB950sMuHBUR4m7E84h/cW9ZX1eG34SclUCymp83FTY\nNNtzarOfDA92fiRkQNJIc7vgyw1s22w8CNrZ15P4UF8AbBo2n8x3+muLtk/uLc0XExNDTk5Om1wg\nx1Uc+c28BUy9YN8TwNda677A/wL1R+ALIYToULTWdeK/w8bXhp/szauguMr4ajrUSxHj5/wP6IAr\nR0L17FvR9j1UFRSZdSOiA83t5OMShiKEaB0N3vm01snAhTmbZgBvV2+/Dcys73yJAReOkrg70RjS\nX9xX4f4jlJzIAMDq50PwyEFm3YXhJy3xNbVHaDA+/eONQpWNvgW1oSb2A/Ad6ecpqahy+uuLtk3u\nLcIVmjr1EKG1zgLQWmcCEQ0cL4QQooOwDz/pPHoYFi8jN3eV1mzNsct+0gLhJzUCkhLMbftVMbsE\neNEtyFi6uqJKsy2toMXaIIQQ9XHW3a/eR11feOEF/P39iY018r8GBQUxePBg8y/MmlgrKUvZPu7O\nHdojZfcuS39x37L6YgMAP9mKiI0JpuaRyA/Xb+FUahGd4ofRyUNxNnUX55Ri5DAjZntHyg4Ap5QD\nkhLY8OqbRns2rKdbYRE7f9wNwIjo3pzKL6PgSArLSo4wbv5st/r9Sbl1yzX7mnu9/Pz8Nr9cuqiV\nnJzM3r17yc83nh05efIkCQkJTJo0qUnXU46kiVFKxQGfaK2HVJf3AxO01llKqUjgW611/0ud++yz\nz+q77rqrSY0THUtycrJ54xKiIdJf3FPxiQw2XGEMaJWnB6M/ew0Pfz8A3jhcxGenSgEYG+7B3Dif\nFm3LyQf+SNmRE/xkK2LKc88QfL3xQZl2rpSn1h0DwM/TwvJbB+NllYfFhMFZ95aMjAwZgLcT9f2/\n3LlzJ5MmTWpSHJ2jdxxV/VPjY+CO6u3bgTUXnlBDYsCFo2QwJRpD+ot7yq6e/QYIHjnIHHzbtGZz\nC6x+eTk12VAGWPwp+Ko2DKVbkDfh/kZYTHGFjZSM8y3eFtF2dJR7y7Bhw9iwYcMl6zZv3swVV1zh\n0vYsW7as3oV3muK5557joYcectr1nM2RNIRLge+BPkqpk0qpO4G/AZOVUgeBSdVlIYQQHVzd7Cej\nzO3U85Xklhmr7/hZoU+AtcXb4m8XB35+w1ZspWWAkZ94pN3DmJuOSzpCIeyNHj2aLVu2uPx1nflQ\n9oIFC3j++eeddj1ncyQLylytdZTW2ltrHau1fktrnae1vkZr3VdrPUVrXW8uJ8kDLhxlH38nREOk\nv7if0qwc8rbuNQpKETK2Nh+3/ez3kGAPrJaWX6TDOy4az5iu/GQrQpeUUpi8zayzz4by/Yl8qmyy\nap8wyL2l7auqanp2o+ac2xgS9CaEEMIpMld/DTZjljtoaD+8OhtrtOlWCD+pUScbil0YSs9QX4J8\njFn4/NJK9mUVXXSuEO3dzp07ufLKK4mPj2f+/PmUlxv/Tjdt2sSgQbXpQ1944QVGjhxJbGwsY8aM\n4bPPPjPrjh07xg033ED37t3p06cPd999t1l36NAhbrrpJuLj47niiitYvXq1WZeXl8fcuXOJi4tj\n8uTJHDt2rN52pqWlERoayttvv83AgQMZOHAgixcvNusXLlzIHXfcwbx58+jevTvLli1j4cKFzJs3\nzzxm7dq1jBkzhp49ezJjxgwOHTpk1g0bNowXX3yRsWPHEhMTg636PtaSWvwuKDHgwlEdJe5OOIf0\nF/eTsfIrczti6lhz+2RRFadLjA80bwv079Ty4Sc1ApJGMuCDTwAo+PYHbOUVWLw8sSjF8KhAvjtq\nfIG76cQ5hnQNuNylRAfhqnvLF5FjnHataZnfN+m8FStWsGrVKvz8/JgzZw6LFi3iySefBOqGg/To\n0YO1a9cSERHB6tWrmTdvHjt27CAiIoJnnnmGiRMn8sknn1BeXs6uXbsAKC4uZtasWfz+979n5cqV\n7Nu3j5/97GcMGDCAPn368Oijj+Lr68vBgwc5duwYs2fPpnv37pdt76ZNm9ixYwdHjx5l5syZDBky\nhHHjxgHwxRdfsGTJEl555RVKS0t54YUXzPeQmprKvffey/vvv09SUhIvvfQSc+fOZfPmzXh4GEPh\nVatWsXz5ckJCQlyygqfMgAshhGi2wsPHKdhzADCyn4RdXfsA18as2tnvQUFWPF0QflLDu1d3PCLC\nALAVFFK0tTYscmQ3+zjwcziSFUyI9uSee+6ha9euBAUF8fDDD7Nq1apLHnfjjTcSEWEs+TJz5kx6\n9uzJzp07AfD09CQtLY2MjAy8vLzMhze//PJL4uLimDNnDkopBg0axA033MCaNWuw2Wx8+umnPPnk\nk/j4+NC/f39uvvnmBtv7+OOP4+Pjw4ABA5g7dy4rV6406xITE5k2bRoAPj51MyytXr2aKVOmMG7c\nOKxWK/Pnz6ekpIStW7eax9x333107doVb2/vRvwGm67FB+ASAy4cJXF3ojGkv7iX06tqZ79DxgzH\nI9AfMBbf+S6rzKxLCPF0abuUUhzt3cUs24eh9A33x8/T+BjMLqwgNbfEpW0T7qkj3VvsU+vFxMSQ\nmZl5yeM++OADxo8fT48ePejRowcHDhwgNzcXgKeffhqbzcbkyZNJSkri/fffB4ywke3bt9OzZ096\n9uxJjx49WLFiBWfOnCEnJ4fKyso6r9+tW7fLtlUpddn2RkdH13tuZmYmMTExda4VHR3N6dOnL/m7\ncAXXBeIJIYRol7TWZNgNwCOm1Iaf7M2rMLOfBHjA4CDXhZ/U8B3UFzbtA6Dg62SinnoQZbXiYVEM\njQrkhxNGFpTk4+foHebn8vaJjqmpYSPOlJ6ebm6npaURGRl50TGnTp1iwYIFrFmzhlGjjMxG48eP\nN78xCg8PN7ONbN68mZtuuomkpCSio6NJSkqqM0tdw2az4enpSXp6Or169bqoLZeita5z/KlTp+q0\n93IZVCIjI9m/f/9F791+0O3MDCyOaPEZcIkBF46SmF7RGNJf3Me5HT9SciIDAKu/HyFX1t73v82s\nnf0eFeKa7CcXuvLGG7BWPxBalXuO4l37zDr7dITJxyQMRXSse8ubb75JRkYGeXl5PPfcc/zsZz+7\n6JiioiIsFguhoaHYbDbef//9OoPZNWvWkJFh/PsPCgrCYrFgsViYOnUqR44cYfny5VRWVlJRUcGu\nXbs4fPgwFouF66+/noULF1JSUsKBAwdYtmxZg+1dtGgRJSUl7N+/n6VLl3LTTTc59D5nzpzJunXr\n2LhxI5WVlfzrX//Cx8eHxMREB39Tzicx4EIIIZrltN3Dl2FXX4HF2wuAokpbnewnV4a5NvykhrJa\nCBgzwiwXfFm7+MjALv54W40/CtLyyzhwptjl7ROiNSilmD17NrNmzWLkyJH07NmTRx555KLj+vbt\ny/3338+UKVPo168fBw4cYPTo0Wb9rl27mDx5MrGxsfzyl7/kr3/9K7GxsQQEBLBy5UpWrVrFgAED\nGDBgAH/+85/NTCsLFy6ksLCQ/v37M3/+fG655ZYG2zxmzBgSEhKYNWsW8+fPZ/z48Q691169evHK\nK6/w2GOP0bt3b9atW8fSpUvNBzBdPfsNDi5F3xyyFL1wlCwtLhpD+ot7sFVU8u3QG6k4a2QTGfzi\nHwgeORCArzJK+fdBI71fN18Lvx/YOuEdO1J20M/mTcaT/wDAs2sEfb5dZn7o/s+2DJKrF+OZ3jeU\nBWNjW6Wdwj3IUvTuJy0tjeHDh5Odne2SDCUXas2l6IUQQoiL5Hy3xRx8e4WHEDS8v1n37ena8JPR\nYa37yJHfkH5YAow/ACpOZ1NSnbEFYFyPYHP7u6N5lFS4ZiEOIYTj2lt4mMSAC7chs5miMaS/uAf7\n7CcRk5NQ1bNT6cVVHCioBIwPmsSQ1huAjxw2EuXhgf+VtWEoeR/VLiQSH+pL10AjbKakwsaGY/Uu\n7iw6ALm3uKfWCBNpSTIDLoQQokkqi4rJ/qI2rV/4lNqBi/3Dl4OCrHTybL2Pm9eWvA5A0LTaeNFz\nn/4vVecLAeODfazdLPjaA7mubaAQ4rJiYmLIyclplfCTliJ5wIXb6Ei5V0XzSX9pfdlrN1BVUgqA\nX/do/HsZsdNVWvOd3QC8tR6+rPH6O28A4DOgN17djVzDuqSUc6trZ+/HxAVR/SwmP2UXcTKv1OXt\nFO5B7i3CFdrPnxJCCCFc6sKl52u+IrbP/e3vYcyAuwOlFEHXTzTLZ5d9YsaVdvLxYFhUbUrCLw7J\nLLgQouU0awCulDqulNqtlNqllNp6qWMkBlw4SuLuRGNIf2ldZWfOkrO+9rYfPiXJ3L4w97dHK+T+\nrk+niWNQvsYy1WVHTlC8bY9ZZx+Gsu7wWSqqbC5vn2h9zrq3eHt7k5ub2+4eHuxoiouLsVqdP4nQ\n3KdibMAErXWeMxojhBCibTi95muwGQPUTkP64hMZDrhP7u/6WPx86TTxSvI/+xaAs8s+xn/UUAAG\nRfrT2deDvJJK8ksr2XKygKvsBuVCNEZoaCiFhYVkZGS0uwcIOxKr1UpERITTr9vcAbiigVn0lJQU\nRowYcblDhAAkr7NoHOkvrcdWWcnJNz4yyxFTa5ee35RdTnn1xHG0r4UYP/cIP7EXdN1EcwBesG4j\nlTln8QgLwaIUSd2D+HS/EX7yxaFcGYB3QM68twQEBBAQEOCUa4n2pbkx4BpYp5TappS6xxkNEkII\n4d5O/2cdxcfTAbAG+BE+eYxZZ5/7+8pWzv1d47op19Ype/eMxad/LwB0RSV5K78w6+zDULafKuBM\nUTlCCOFszR2AJ2mtRwDXAg8opS76k1FiwIWjZDZTNIb0l9ahq6o48vzbZjn6F9fh4W8scLPvXIXb\n5P6296cnnrpoX9B1dg9jfvgJuspYfCfc34v+Ecb7sWn46tBZ1zRSuA25twhXaNbdUWt9uvq/Z5RS\n/wFGAXXy96xYsYI33niD2FgjPVVQUBCDBw82O3hNuh8pS1nKUpay+5dzNm7D58hJAA54VaF6RxCH\nsUrdos83UVBcRaf4YSSGeHB43y7AWAgHjCXh3aUcMC6R7xa/gi4uYUB6FoUbt3HAx4idGdtjIPuz\niyk4ksL7p/dx87BbsCjlFr9/KUtZyq1X3rt3L/n5+QCcPHmShIQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figsize(12.5, 15)\n", + "\n", + "p = 0.6\n", + "beta1_params = np.array([1.,1.])\n", + "beta2_params = np.array([2,10])\n", + "beta = stats.beta\n", + "\n", + "x = np.linspace(0.00, 1, 125)\n", + "data = stats.bernoulli.rvs(p, size=500)\n", + "\n", + "plt.figure()\n", + "for i,N in enumerate([0,4,8, 32,64, 128, 500]):\n", + " s = data[:N].sum() \n", + " plt.subplot(8,1,i+1)\n", + " params1 = beta1_params + np.array([s, N-s])\n", + " params2 = beta2_params + np.array([s, N-s])\n", + " y1,y2 = beta.pdf(x, *params1), beta.pdf( x, *params2)\n", + " plt.plot(x,y1, label = r\"flat prior\", lw =3)\n", + " plt.plot(x, y2, label = \"biased prior\", lw= 3)\n", + " plt.fill_between(x, 0, y1, color =\"#348ABD\", alpha = 0.15) \n", + " plt.fill_between(x, 0, y2, color =\"#A60628\", alpha = 0.15) \n", + " plt.legend(title = \"N=%d\" % N)\n", + " plt.vlines(p, 0.0, 7.5, linestyles = \"--\", linewidth=1)\n", + " #plt.ylim( 0, 10)#\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind, not all posteriors will \"forget\" the prior this quickly. This example was just to show that *eventually* the prior is forgotten. The \"forgetfulness\" of the prior as we become awash in more and more data is the reason why Bayesian and Frequentist inference eventually converge as well." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Bayesian perspective of Penalized Linear Regressions\n", + "\n", + "There is a very interesting relationship between a penalized least-squares regression and Bayesian priors. A penalized linear regression is a optimization problem of the form:\n", + "\n", + "$$ \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + f(\\beta)$$\n", + "\n", + "for some function $f$ (typically a norm like $|| \\cdot ||_p^p$). \n", + "\n", + "We will first describe the probabilistic interpretation of least-squares linear regression. Denote our response variable $Y$, and features are contained in the data matrix $X$. The standard linear model is:\n", + "\n", + "\\begin{equation}\n", + "Y = X\\beta + \\epsilon\n", + "\\end{equation}\n", + "\n", + "where $\\epsilon \\sim \\text{Normal}( {\\bf 0}, \\sigma{\\bf I })$. Simply, the observed $Y$ is a linear function of $X$ (with coefficients $\\beta$) plus some noise term. Our unknown to be determined is $\\beta$. We use the following property of Normal random variables:\n", + "\n", + "$$ \\mu' + \\text{Normal}( \\mu, \\sigma ) \\sim \\text{Normal}( \\mu' + \\mu , \\sigma ) $$\n", + "\n", + "to rewrite the above linear model as:\n", + "\n", + "\\begin{align}\n", + "& Y = X\\beta + \\text{Normal}( {\\bf 0}, \\sigma{\\bf I }) \\\\\\\\\n", + "& Y = \\text{Normal}( X\\beta , \\sigma{\\bf I }) \\\\\\\\\n", + "\\end{align}\n", + "\n", + "In probabilistic notation, denote $f_Y(y \\; | \\; \\beta )$ the probability distribution of $Y$, and recalling the density function for a Normal random variable (see [here](http://en.wikipedia.org/wiki/Normal_distribution) ):\n", + "\n", + "$$ f_Y( Y \\; |\\; \\beta, X) = L(\\beta|\\; X,Y)= \\frac{1}{\\sqrt{ 2\\pi\\sigma} } \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) $$\n", + "\n", + "This is the likelihood function for $\\beta$. Taking the $\\log$:\n", + "\n", + "$$ \\ell(\\beta) = K - c(Y - X\\beta)^T(Y - X\\beta) $$\n", + "\n", + "where $K$ and $c>0$ are constants. Maximum likelihood techniques wish to maximize this for $\\beta$, \n", + "\n", + "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; - (Y - X\\beta)^T(Y - X\\beta) $$\n", + "\n", + "Equivalently we can *minimize the negative* of the above:\n", + "\n", + "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) $$\n", + "\n", + "This is the familiar least-squares linear regression equation. Therefore we showed that the solution to a linear least-squares is the same as the maximum likelihood assuming Normal noise. Next we extend this to show how we can arrive at penalized linear regression by a suitable choice of prior on $\\beta$. \n", + "\n", + "#### Penalized least-squares\n", + "\n", + "In the above, once we have the likelihood, we can include a prior distribution on $\\beta$ to derive to the equation for the posterior distribution:\n", + "\n", + "$$P( \\beta | Y, X ) = L(\\beta|\\;X,Y)p( \\beta )$$\n", + "\n", + "where $p(\\beta)$ is a prior on the elements of $\\beta$. What are some interesting priors? \n", + "\n", + "1\\. If we include *no explicit* prior term, we are actually including an uninformative prior, $P( \\beta ) \\propto 1$, think of it as uniform over all numbers. \n", + "\n", + "2\\. If we have reason to believe the elements of $\\beta$ are not too large, we can suppose that *a priori*:\n", + "\n", + "$$ \\beta \\sim \\text{Normal}({\\bf 0 }, \\lambda {\\bf I } ) $$\n", + "\n", + "The resulting posterior density function for $\\beta$ is *proportional to*:\n", + "\n", + "$$ \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) \\exp \\left( \\frac{1}{2\\lambda^2} \\beta^T\\beta \\right) $$\n", + "\n", + "and taking the $\\log$ of this, and combining and redefining constants, we arrive at:\n", + "\n", + "$$ \\ell(\\beta) \\propto K - (Y - X\\beta)^T(Y - X\\beta) - \\alpha \\beta^T\\beta $$\n", + "\n", + "we arrive at the function we wish to maximize (recall the point that maximizes the posterior distribution is the MAP, or *maximum a posterior*):\n", + "\n", + "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; -(Y - X\\beta)^T(Y - X\\beta) - \\alpha \\;\\beta^T\\beta $$\n", + "\n", + "Equivalently, we can minimize the negative of the above, and rewriting $\\beta^T \\beta = ||\\beta||_2^2$:\n", + "\n", + "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_2^2$$\n", + "\n", + "This above term is exactly Ridge Regression. Thus we can see that ridge regression corresponds to the MAP of a linear model with Normal errors and a Normal prior on $\\beta$.\n", + "\n", + "3\\. Similarly, if we assume a *Laplace* prior on $\\beta$, ie. \n", + "\n", + "$$ f_\\beta( \\beta) \\propto \\exp \\left(- \\lambda ||\\beta||_1 \\right)$$\n", + "\n", + "and following the same steps as above, we recover:\n", + "\n", + "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_1$$\n", + "\n", + "which is LASSO regression. Some important notes about this equivalence. The sparsity that is a result of using a LASSO regularization is not a result of the prior assigning high probability to sparsity. Quite the opposite actually. It is the combination of the $|| \\cdot ||_1$ function and using the MAP that creates sparsity on $\\beta$: [purely a geometric argument](http://camdp.com/blogs/least-squares-regression-l1-penalty). The prior does contribute to an overall shrinking of the coefficients towards 0 though. An interesting discussion of this can be found in [2].\n", + "\n", + "For an example of Bayesian linear regression, see Chapter 4's example on financial losses." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### References\n", + "\n", + "1. Macro, . \"What is the relationship between sample size and the influence of prior on posterior?.\" 13 Jun 2013. StackOverflow, Online Posting to Cross-Validated. Web. 25 Apr. 2013.\n", + "\n", + "2. Starck, J.-L., , et al. \"Sparsity and the Bayesian Perspective.\" Astronomy & Astrophysics. (2013): n. page. Print.\n", + "\n", + "3. Kuleshov, Volodymyr, and Doina Precup. \"Algorithms for the multi-armed bandit problem.\" Journal of Machine Learning Research. (2000): 1-49. Print.\n", + "\n", + "4. Gelman, Andrew. \"Prior distributions for variance parameters in hierarchical models.\" Bayesian Analysis. 1.3 (2006): 515-533. Print.\n", + "\n", + "5. Gelman, Andrew, and Cosma R. Shalizi. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 17 Apr. 2013.\n", + "\n", + "6. http://jmlr.csail.mit.edu/proceedings/papers/v22/kaufmann12/kaufmann12.pdf\n", + "\n", + "7. James, Neufeld. \"Reddit's \"best\" comment scoring algorithm as a multi-armed bandit task.\" Simple ML Hacks. Blogger, 09 Apr 2013. Web. 25 Apr. 2013.\n", + "\n", + "8. Oakley, J. E., Daneshkhah, A. and O’Hagan, A. Nonparametric elicitation using the roulette method. Submitted to Bayesian Analysis.\n", + "\n", + "9. \"Eliciting priors from experts.\" 19 Jul 2010. StackOverflow, Online Posting to Cross-Validated. Web. 1 May. 2013. .\n", + "\n", + "10. Taleb, Nassim Nicholas (2007), The Black Swan: The Impact of the Highly Improbable, Random House, ISBN 978-1400063512" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.core.display import HTML\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [conda env:bayes]", + "language": "python", + "name": "conda-env-bayes-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Chapter6_Priorities/other_strats.py b/Chapter6_Priorities/other_strats.py index 430c08d7..f13fa1e8 100644 --- a/Chapter6_Priorities/other_strats.py +++ b/Chapter6_Priorities/other_strats.py @@ -3,13 +3,12 @@ import scipy.stats as stats import numpy as np -from pymc import rbeta rand = np.random.rand beta = stats.beta -class GeneralBanditStrat( object ): +class GeneralBanditStrat(object): """ Implements a online, learning strategy to solve @@ -32,72 +31,72 @@ class GeneralBanditStrat( object ): def __init__(self, bandits, choice_function): self.bandits = bandits - n_bandits = len( self.bandits ) - self.wins = np.zeros( n_bandits ) - self.trials = np.zeros(n_bandits ) + n_bandits = len(self.bandits) + self.wins = np.zeros(n_bandits) + self.trials = np.zeros(n_bandits) self.N = 0 self.choices = [] self.score = [] self.choice_function = choice_function - def sample_bandits( self, n=1 ): + def sample_bandits(self, n=1): - score = np.zeros( n ) - choices = np.zeros( n ) + score = np.zeros(n) + choices = np.zeros(n) for k in range(n): #sample from the bandits's priors, and select the largest sample choice = self.choice_function(self) #sample the chosen bandit - result = self.bandits.pull( choice ) + result = self.bandits.pull(choice) #update priors and score - self.wins[ choice ] += result - self.trials[ choice ] += 1 - score[ k ] = result + self.wins[choice] += result + self.trials[choice] += 1 + score[k] = result self.N += 1 - choices[ k ] = choice + choices[k] = choice - self.score = np.r_[ self.score, score ] - self.choices = np.r_[ self.choices, choices ] + self.score = np.r_[self.score, score] + self.choices = np.r_[self.choices, choices] return def bayesian_bandit_choice(self): - return np.argmax( rbeta( 1 + self.wins, 1 + self.trials - self.wins) ) + return np.argmax(np.random.beta(1 + self.wins, 1 + self.trials - self.wins)) -def max_mean( self ): +def max_mean(self): """pick the bandit with the current best observed proportion of winning """ - return np.argmax( self.wins / ( self.trials +1 ) ) + return np.argmax(self.wins / (self.trials +1)) def lower_credible_choice( self ): """pick the bandit with the best LOWER BOUND. See chapter 5""" def lb(a,b): - return a/(a+b) - 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1) ) ) + return a/(a+b) - 1.65*np.sqrt((a*b)/( (a+b)**2*(a+b+1))) a = self.wins + 1 b = self.trials - self.wins + 1 - return np.argmax( lb(a,b) ) + return np.argmax(lb(a,b)) -def upper_credible_choice( self ): +def upper_credible_choice(self): """pick the bandit with the best LOWER BOUND. See chapter 5""" def lb(a,b): - return a/(a+b) + 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1) ) ) + return a/(a+b) + 1.65*np.sqrt((a*b)/((a+b)**2*(a+b+1))) a = self.wins + 1 b = self.trials - self.wins + 1 - return np.argmax( lb(a,b) ) + return np.argmax(lb(a,b)) -def random_choice( self): - return np.random.randint( 0, len( self.wins ) ) +def random_choice(self): + return np.random.randint(0, len(self.wins)) -def ucb_bayes( self ): +def ucb_bayes(self): C = 0 n = 10000 - alpha =1 - 1./( (self.N+1) ) - return np.argmax( beta.ppf( alpha, + alpha =1 - 1./((self.N+1)) + return np.argmax(beta.ppf(alpha, 1 + self.wins, - 1 + self.trials - self.wins ) ) + 1 + self.trials - self.wins)) @@ -117,7 +116,7 @@ def __init__(self, p_array): self.p = p_array self.optimal = np.argmax(p_array) - def pull( self, i ): + def pull(self, i): #i is which arm to pull return rand() < self.p[i]