Lectures/Lecture6/3dasm_Lecture6.ipynb

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    "<img src=../figures/Brown_logo.svg width=50%>\n",
    "\n",
    "## Data-Driven Design & Analyses of Structures & Materials (3dasm)\n",
    "\n",
    "## Lecture 6\n",
    "\n",
    "### Miguel A. Bessa | <a href = \"mailto: miguel_bessa@brown.edu\">miguel_bessa@brown.edu</a>  | Associate Professor"
   ]
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    "**What:** A lecture of the \"3dasm\" course\n",
    "\n",
    "**Where:** This notebook comes from this [repository](https://github.com/bessagroup/3dasm_course)\n",
    "\n",
    "**Reference for entire course:** Murphy, Kevin P. *Probabilistic machine learning: an introduction*. MIT press, 2022. Available online [here](https://probml.github.io/pml-book/book1.html)\n",
    "\n",
    "**How:** We try to follow Murphy's book closely, but the sequence of Chapters and Sections is different. The intention is to use notebooks as an introduction to the topic and Murphy's book as a resource.\n",
    "* If working offline: Go through this notebook and read the book.\n",
    "* If attending class in person: listen to me (!) but also go through the notebook in your laptop at the same time. Read the book.\n",
    "* If attending lectures remotely: listen to me (!) via Zoom and (ideally) use two screens where you have the notebook open in 1 screen and you see the lectures on the other. Read the book."
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    "**Optional reference (the \"bible\" by the \"bishop\"... pun intended 😆) :** Bishop, Christopher M. *Pattern recognition and machine learning*. Springer Verlag, 2006.\n",
    "\n",
    "**References/resources to create this notebook:**\n",
    "* [Car figure](https://korkortonline.se/en/theory/reaction-braking-stopping/)\n",
    "\n",
    "Apologies in advance if I missed some reference used in this notebook. Please contact me if that is the case, and I will gladly include it here."
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    "## **OPTION 1**. Run this notebook **locally in your computer**:\n",
    "1. Confirm that you have the '3dasm' mamba (or conda) environment (see Lecture 1).\n",
    "2. Go to the 3dasm_course folder in your computer and pull the last updates of the [repository](https://github.com/bessagroup/3dasm_course):\n",
    "```\n",
    "git pull\n",
    "```\n",
    "    - Note: if you can't pull the repo due to conflicts (and you can't handle these conflicts), use this command (with **caution**!) and your repo becomes the same as the one online:\n",
    "        ```\n",
    "        git reset --hard origin/main\n",
    "        ```\n",
    "3. Open command window and load jupyter notebook (it will open in your internet browser):\n",
    "```\n",
    "jupyter notebook\n",
    "```\n",
    "5. Open notebook of this Lecture and choose the '3dasm' kernel."
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    "## **OPTION 2**. Use **Google's Colab** (no installation required, but times out if idle):\n",
    "\n",
    "1. go to https://colab.research.google.com\n",
    "2. login\n",
    "3. File > Open notebook\n",
    "4. click on Github (no need to login or authorize anything)\n",
    "5. paste the git link: https://github.com/bessagroup/3dasm_course\n",
    "6. click search and then click on the notebook for this Lecture."
   ]
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    "# Basic plotting tools needed in Python.\n",
    "\n",
    "import matplotlib.pyplot as plt # import plotting tools to create figures\n",
    "import numpy as np # import numpy to handle a lot of things!\n",
    "from IPython.display import display, Math # to print with Latex math\n",
    "\n",
    "%config InlineBackend.figure_format = \"retina\" # render higher resolution images in the notebook\n",
    "plt.rcParams[\"figure.figsize\"] = (8,4) # rescale figure size appropriately for slides"
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    "## Outline for today\n",
    "\n",
    "* Continuation of previous lecture: Bayesian inference for one hidden rv\n",
    "    - Prior\n",
    "    - Likelihood\n",
    "    - Marginal likelihood\n",
    "    - Posterior\n",
    "    - Gaussian pdf's product\n",
    "\n",
    "**Reading material**: This notebook + Chapter 3"
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    "## Recap of Lecture 5: car stopping distance with known $x$\n",
    "\n",
    "We focused on the car stopping distance problem under the following conditions:\n",
    "* We kept $x=75$ m/s.\n",
    "* But the distribution of the rv $z$ is not known: $p(z)=?$\n",
    "\n",
    "Under these conditions, recall the \"true\" model by observing the following plot, including some data observations."
   ]
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    "# This cell is hidden during presentation. It's just to define a function to plot the governing model of\n",
    "# the car stopping distance problem. Defining a function that creates a plot allows to repeatedly run\n",
    "# this function on cells used in this notebook.\n",
    "def car_fig(ax):\n",
    "    x = np.linspace(3, 83, 1000)\n",
    "    mu_z = 1.5; sigma_z = 0.5;  # parameters of the \"true\" p(z)\n",
    "    mu_y = mu_z*x + 0.1*x**2 # From Homework of Lecture 4\n",
    "    sigma_y = np.sqrt( (x*sigma_z)**2 ) # From Homework of Lecture 4\n",
    "    ax.set_xlabel(\"x (m/s)\", fontsize=20) # create x-axis label with font size 20\n",
    "    ax.set_ylabel(\"y (m)\", fontsize=20) # create y-axis label with font size 20\n",
    "    ax.set_title(\"Car stopping distance problem\", fontsize=20); # create title with font size 20\n",
    "    ax.plot(x, mu_y, 'k:', label=\"Governing model $\\mu_y$\")\n",
    "    ax.fill_between(x, mu_y - 1.9600 * sigma_y,\n",
    "                    mu_y + 1.9600 * sigma_y,\n",
    "                    color='k', alpha=0.2,\n",
    "                    label='95% confidence interval ($\\mu_y \\pm 1.96\\sigma_y$)') # plot 95% credence interval\n",
    "    ax.legend(fontsize=15)"
   ]
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    "# This cell is also hidden during presentation.\n",
    "from scipy.stats import norm # import the normal dist, as we learned before!\n",
    "def samples_y(N_samples,x): # observations/measurements/samples for car stop. dist. prob.\n",
    "    mu_z = 1.5; sigma_z = 0.5;\n",
    "    samples_z = norm.rvs(mu_z, sigma_z, size=N_samples) # randomly draw samples from the normal dist.\n",
    "    samples_y = samples_z*x + 0.1*x**2 # compute the stopping distance for samples of z\n",
    "    return samples_y # return samples of y"
   ]
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     "text": [
      "Empirical mean[y] is 651.907517548372 (real mean[y]=675)\n",
      "Empirical std[y] is 14.50873859076062 (real std[y]=37.5)\n"
     ]
    },
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      "text/plain": [
       "<Figure size 1800x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 348,
       "width": 1459
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# vvvvvvvvvvv this is just a trick so that we can run this cell multiple times vvvvvvvvvvv\n",
    "fig_car_new, ax_car_new = plt.subplots(1,2); plt.close() # create figure and close it\n",
    "if fig_car_new.get_axes():\n",
    "    del ax_car_new; del fig_car_new # delete figure and axes if they exist\n",
    "    fig_car_new, ax_car_new = plt.subplots(1,2) # create them again\n",
    "# ^^^^^^^^^^^ end of the trick ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
    "N_samples = 3 # CHANGE THIS NUMBER AND RE-RUN THE CELL\n",
    "x = 75; empirical_y = samples_y(N_samples, x); # Empirical measurements of N_samples at x=75\n",
    "empirical_mu_y = np.mean(empirical_y); empirical_sigma_y = np.std(empirical_y); # empirical mean and std\n",
    "car_fig(ax_car_new[0]) # a function I created to include the background plot of the governing model\n",
    "for i in range(2): # create two plots (one is zooming in on the error bar)\n",
    "    ax_car_new[i].errorbar(x , empirical_mu_y,yerr=1.96*empirical_sigma_y, fmt='m*', markersize=15);\n",
    "    ax_car_new[i].scatter(x*np.ones_like(empirical_y),empirical_y, s=40,\n",
    "                          facecolors='none', edgecolors='k', linewidths=2.0)\n",
    "print(\"Empirical mean[y] is\",empirical_mu_y, \"(real mean[y]=675)\")\n",
    "print(\"Empirical std[y] is\",empirical_sigma_y,\"(real std[y]=37.5)\")\n",
    "fig_car_new.set_size_inches(25, 5) # scale figure to be wider (since there are 2 subplots)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Recap of Lecture 5: Summary of our model\n",
    "\n",
    "1. The **observation distribution**:\n",
    "\n",
    "$$\n",
    "p(y|z) = \\mathcal{N}\\left(y | \\mu_{y|z}=w z+b, \\sigma_{y|z}^2\\right) = \\frac{1}{C_{y|z}} \\exp\\left[ -\\frac{1}{2\\sigma_{y|z}^2}(y-\\mu_{y|z})^2\\right]\n",
    "$$\n",
    "\n",
    "where $C_{y|z} = \\sqrt{2\\pi \\sigma_{y|z}^2}$ is the **normalization constant** of the Gaussian pdf, and where $\\mu_{y|z}=w z+b$, with $w$, $b$ and $\\sigma_{y|z}^2$ being constants.\n",
    "\n",
    "2. and the **prior distribution**: $p(z) = \\frac{1}{C_z}$\n",
    "\n",
    "where $C_z = z_{max}-z_{min}$ is the **normalization constant** of the Uniform pdf, i.e. the value that guarantees that $p(z)$ integrates to one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Recap of Lecture 5: Data\n",
    "\n",
    "* Since we usually don't know the true process, we can only observe/collect data $y=\\mathcal{D}_y$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example of N=3 data points for y at x=75.0 m/s with : [676.34340551 726.27176696 699.9940938 ]\n"
     ]
    }
   ],
   "source": [
    "print(\"Example of N=%1i data points for y at x=%1.1f m/s with :\" % (N_samples,x), empirical_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Recap of Lecture 5: Posterior from Bayes' rule applied to data\n",
    "\n",
    "Use Bayes' rule applied to data to determine the <font color='green'>posterior</font>:\n",
    "\n",
    "$\\require{color}$\n",
    "$$\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} = \\frac{ {\\color{blue}p(y=\\mathcal{D}_y|z)}{\\color{red}p(z)} } {p(y=\\mathcal{D}_y)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "That requires calculating the <font color='blue'>likelihood</font> (here, it results from a product of Gaussian densities):\n",
    "\n",
    "$$\n",
    "{\\color{blue}p(y=\\mathcal{D}_y | z)} = \\frac{1}{|w|^N} \\cdot C \\cdot \\frac{1}{\\sqrt{2\\pi \\sigma^2}} \\exp\\left[ -\\frac{1}{2\\sigma^2}(z-\\mu)^2\\right]\n",
    "$$\n",
    "\n",
    "where $\\mu = \\frac{w^2\\sigma^2}{\\sigma_{y|z}^2} \\sum_{i=1}^N \\mu_i$\n",
    "\n",
    "$\\sigma^2 = \\frac{\\sigma_{y|z}^2}{w^2 N}$, and\n",
    "\n",
    "$C = \\frac{1}{2\\pi^{(N-1)/2}} \\sqrt{\\frac{\\sigma^2}{\\left( \\frac{\\sigma_{y|z}^2}{w^2}\\right)^N}}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "After calculating the likelihood, we determined the marginal likelihood:\n",
    "\n",
    "$$\n",
    "p(y=\\mathcal{D}_y) = \\frac{C}{|w|^N C_z}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "From which we got the <font color='green'>posterior</font>:\n",
    "\n",
    "$$\\require{color}\\begin{align}\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} &= \\frac{ p(y=\\mathcal{D}_y|z)p(z) } {p(y=\\mathcal{D}_y)} \\\\\n",
    "&= \\frac{1}{p(y=\\mathcal{D}_y)} \\cdot \\frac{1}{|w|^N} C \\cdot \\mathcal{N}(z|\\mu,\\sigma^2) \\cdot \\frac{1}{C_z} \\\\\n",
    "&= \\mathcal{N}(z|\\mu, \\sigma^2)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "which is a **normalized** Gaussian pdf in $z$ with mean and variance as shown in the previous cell."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Determining the Posterior Predictive Distribution (<a title=\"Posterior Predictive Distribution\">PPD</a>) from the posterior\n",
    "\n",
    "However, as we mentioned, Bayes' rule is just a way to calculate the posterior:\n",
    "\n",
    "$$\n",
    "p(z|y=\\mathcal{D}_y) = \\frac{ p(y=\\mathcal{D}_y|z)p(z) } {p(y=\\mathcal{D}_y)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "What we really want is the <font color='orange'>Posterior Predictive Distribution (<a title=\"Posterior Predictive Distribution\">PPD</a>)</font> . This comes after calculating the posterior given some data $\\mathcal{D}_y$:\n",
    "\n",
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|y=\\mathcal{D}_y)} = \\int p(y^*|z) p(z|y=\\mathcal{D}_y) dz\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "which is often written in simpler notation: $p(y^*|\\mathcal{D}_y) = \\int p(y^*|z) p(z|\\mathcal{D}_y) dz$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\int \\underbrace{p(y^*|z)}_{\\text{observation}\\\\ \\text{distribution}} \\overbrace{p(z|y=\\mathcal{D}_y)}^{\\text{posterior}} dz\n",
    "$$\n",
    "\n",
    "Considering the terms we found before, we get:\n",
    "\n",
    "$$\\begin{align}\n",
    "p(y^*|\\mathcal{D}_y) &= \\int \\underbrace{\\frac{1}{|w|}\\frac{1}{\\sqrt{2\\pi \\left(\\frac{\\sigma_{y|z}}{w}\\right)^2}} \\exp\\left\\{ -\\frac{1}{2\\left(\\frac{\\sigma_{y|z}}{w}\\right)^2}\\left[z-\\left(\\frac{y^*-b}{w}\\right)\\right]^2\\right\\} }_{\\text{observation}\\\\ \\text{distribution}} \\overbrace{\\mathcal{N}(z|\\mu, \\sigma^2)}^{\\text{posterior}} dz\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\frac{1}{|w|} \\int {\\color{blue}\\frac{1}{\\sqrt{2\\pi \\left(\\frac{\\sigma_{y|z}}{w}\\right)^2}} \\exp\\left\\{ -\\frac{1}{2\\left(\\frac{\\sigma_{y|z}}{w}\\right)^2}\\left[z-\\left(\\frac{y^*-b}{w}\\right)\\right]^2\\right\\}} \\mathcal{N}(z|\\mu, \\sigma^2) dz\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\frac{1}{|w|} \\int \\mathcal{N}\\left(z\\left|\\frac{y^*-b}{w}, \\left(\\frac{\\sigma_{y|z}}{w}\\right)^2\\right.\\right) \\mathcal{N}(z|\\mu, \\sigma^2) dz\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This is (again!) the product of two Gaussians!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In Lecture 5 (and the Homework!) you saw (and will demonstrate!) that the product of two or more univariate (and multivariate!) Gaussians is...\n",
    "\n",
    "* Another Gaussian! Although it needs to be scaled by a constant..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "So, we conclude that the <a title=\"Posterior Predictive Distribution\">PPD</a> is an integral of a Gaussian:\n",
    "\n",
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\frac{1}{|w|} \\int  C^* \\mathcal{N}\\left(z|\\mu^*, \\left(\\sigma^*\\right)^2\\right) dz\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "where $\\mu^* = \\left(\\sigma^* \\right)^2 \\left( \\frac{\\mu}{\\sigma^2} + \\frac{(y^*-b)/w}{\\left(\\frac{\\sigma_{y|z}}{w}\\right)^2} \\right) = \\left(\\sigma^* \\right)^2 \\left( \\frac{\\mu}{\\sigma^2} + \\frac{(y^*-b)\\cdot w}{\\sigma_{y|z}^2} \\right)$\n",
    "\n",
    "$\\left( \\sigma^* \\right)^2 = \\frac{1}{\\frac{1}{\\sigma^2}+\\frac{1}{\\left( \\frac{\\sigma_{y|z}}{w}\\right)^2}}= \\frac{1}{\\frac{1}{\\sigma^2}+\\frac{w^2}{\\sigma_{y|z}^2}}$\n",
    "\n",
    "$C^* = \\frac{1}{\\sqrt{2\\pi \\left( \\sigma^2 + \\frac{\\sigma_{y|z}^2}{w^2} \\right)}}\\exp\\left[ - \\frac{\\left(\\mu - \\frac{y^*-b}{w}\\right)^2}{2\\left( \\sigma^2+\\frac{\\sigma_{y|z}^2}{w^2}\\right)}\\right]$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This integral is simple to solve!\n",
    "\n",
    "$$\\require{color}\n",
    "\\begin{align}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} &= \\frac{1}{|w|} \\int  C^* \\mathcal{N}\\left(z|\\mu^*, \\left(\\sigma^*\\right)^2\\right) dz \\\\\n",
    "&= \\frac{C^*}{|w|} \\int   {\\color{blue}\\mathcal{N}\\left(z|\\mu^*, \\left(\\sigma^*\\right)^2\\right)} dz\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "What's the result of integrating the <font color='blue'>blue</font> term?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\frac{C^*}{|w|}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## In Homework 3 (exercise 2)\n",
    "\n",
    "Rewrite the <a title=\"Posterior Predictive Distribution\">PPD</a> to show that it becomes:\n",
    "\n",
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\mathcal{N}\\left(y^*| b+\\mu w, w^2\\sigma^2+\\sigma_{y|z}^2 \\right)\n",
    "$$\n",
    "\n",
    "a normalized univariate Gaussian!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A long way to show that the <a title=\"Posterior Predictive Distribution\">PPD</a> is a simple Gaussian...\n",
    "\n",
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\mathcal{N}\\left(y^*| b+\\mu w, w^2\\sigma^2+\\sigma_{y|z}^2 \\right)\n",
    "$$\n",
    "\n",
    "where we recall that each constant is:\n",
    "\n",
    "$b = 0.1x^2 = 562.5$\n",
    "\n",
    "$w = x = 75$\n",
    "\n",
    "$\\sigma_{y|z}^2 = s^2 = 80^2$\n",
    "\n",
    "$\\sigma^2 = \\frac{\\sigma_{y|z}^2}{w^2 N} = \\frac{s^2}{w^2 N} $\n",
    "\n",
    "$\\mu = \\frac{w^2 \\sigma^2}{\\sigma_{y|z}^2} \\sum_{i=1}^{N} \\mu_i = \\cdots = \\frac{\\sum_{i=1}^N y_i}{w N}-\\frac{b}{w}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "#### Note on algebra to determine $\\mu$ parameter:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mu &= \\frac{w^2 \\sigma^2}{\\sigma_{y|z}^2} \\sum_{i=1}^{N} \\mu_i \\\\\n",
    "&= \\frac{\\sum_{i=1}^{N} \\mu_i}{N} = \\frac{1}{N} \\sum_{i=1}^{N} \\left(\\frac{y_i-b}{w}\\right) \\\\\n",
    "&= \\frac{1}{w N} \\sum_{i=1}^N\\left( y_i-b\\right) \\\\\n",
    "&= \\frac{1}{w N} \\left( \\sum_{i=1}^N y_i-N b\\right) \\\\\n",
    "& = \\frac{\\sum_{i=1}^N y_i}{w N}-\\frac{b}{w}\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A long way to show that the <a title=\"Posterior Predictive Distribution\">PPD</a> is a simple Gaussian...\n",
    "\n",
    "$$\\require{color}\n",
    "\\begin{align}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} &= \\mathcal{N}\\left(y^*| b+\\mu w, w^2\\sigma^2+\\sigma_{y|z}^2 \\right) \\\\\n",
    "&= \\mathcal{N}\\left(y^* \\left| \\left(\\sum_{i=1}^N \\frac{y_i}{N}\\right), \\sigma_{y|z}^2 \\left(\\frac{1}{N} + 1 \\right) \\right. \\right)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $y_i$ are each of the $N$ data points of the observed data $\\mathcal{D}_y$, and $\\sigma_{y|z}^2 = s^2 = 80^2$ is the **variance we assumed** because we were not sure about the governing equation for $y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* **Very Important Questions (VIQs)**: What does this result tell us? Did you expect this predicted distribution for $y^*$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PPD & empirical mean[y] tend to the same value: 675.1441878349008 (real mean[y]=675)\n",
      "PPD std[y] we predict is 92.37604307034012 & empirical std[y] is 6.625878282988706 (real std[y]=37.5)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 348,
       "width": 1459
      },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_car_PPD, ax_car_PPD = plt.subplots(1,2); plt.close() # create figure and close it\n",
    "if fig_car_new.get_axes():\n",
    "    del ax_car_PPD; del fig_car_PPD; fig_car_PPD, ax_car_PPD = plt.subplots(1,2) # delete fig & axes & create them\n",
    "N_samples = 3 # CHANGE THIS NUMBER AND RE-RUN THE CELL\n",
    "x = 75; empirical_y = samples_y(N_samples, x); # Empirical measurements of N_samples at x=75\n",
    "empirical_mu_y = np.mean(empirical_y); empirical_sigma_y = np.std(empirical_y); # empirical mean and std\n",
    "# Calculate PPD mean and standard deviation:\n",
    "PPD_mu_y = np.mean(empirical_y); sigma_yGIVENz = 80; PPD_sigma_y = np.sqrt( sigma_yGIVENz**2*(1/N_samples + 1) )\n",
    "car_fig(ax_car_PPD[0]) # a function I created to include the background plot of the governing model\n",
    "for i in range(2): # create two plots (one is zooming in on the error bar)\n",
    "    ax_car_PPD[i].errorbar(x , empirical_mu_y,yerr=1.96*empirical_sigma_y, fmt='m*', markersize=15, elinewidth=6);\n",
    "    ax_car_PPD[i].errorbar(x , PPD_mu_y,yerr=1.96*PPD_sigma_y, color='#F39C12', fmt='*', markersize=5, elinewidth=3);\n",
    "    ax_car_PPD[i].scatter(x*np.ones_like(empirical_y),empirical_y, s=100,facecolors='none', edgecolors='k', linewidths=2.0)\n",
    "print(\"PPD & empirical mean[y] tend to the same value:\",empirical_mu_y, \"(real mean[y]=675)\")\n",
    "print(\"PPD std[y] we predict is\",PPD_sigma_y, \"& empirical std[y] is\",empirical_sigma_y,\"(real std[y]=37.5)\")\n",
    "fig_car_PPD.set_size_inches(25, 5) # scale figure to be wider (since there are 2 subplots)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "### Reflection on what we are observing\n",
    "\n",
    "1. Generally speaking, our PPD is quite reasonable and the result should be intuitive!\n",
    "    * For few data points, the variance of the PPD is a bit larger than the variance we assumed for the conditional pdf $p(y|z)$, i.e. $\\sigma_{y|z}^2=s^2=80^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "2. As the number of data points increases (see PPD as $N\\rightarrow \\infty$ or play with the figure above by increasing $N$), then the variance of the PPD $\\sigma_{y}^2 \\rightarrow s^2=80^2$ tends to the variance we assumed for our model: $\\sigma_{y|z}^2=s^2=80^2$.\n",
    "    * This results from our choice of likelihood and prior... Our model was incorrect in both:\n",
    "        * The hidden rv $z$ is actually a Gaussian distribution, instead of a noninformative Uniform distribution\n",
    "        * The real conditional pdf is the Dirac \"distribution\" around value $y = zx + 0.1 x^2$, instead of the Gaussian distribution with a mean of $\\mu_{y|z}= zx + 0.1 x^2$ and a variance of $\\sigma_{y|z} = s^2 = 80^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Please keep this in your head:\n",
    "* (Bayesian) ML is not magic. Every modeling choice you make affects the predictions you get.\n",
    "* Of course, there are ways of getting \"closer\" to the truth! We'll take steps in that direction in the remainder of the course. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Next lecture we will redo everything but for a different prior distribution\n",
    "\n",
    "Consider the same problem, but now starting from a different model:\n",
    "\n",
    "1. Same **observation distribution** as before:\n",
    "\n",
    "$$\n",
    "p(y|z) = \\mathcal{N}\\left(y | \\mu_{y|z}=w z+b, \\sigma_{y|z}^2\\right) = \\frac{1}{C_{y|z}} \\exp\\left[ -\\frac{1}{2\\sigma_{y|z}^2}(y-\\mu_{y|z})^2\\right]\n",
    "$$\n",
    "\n",
    "2. <font color='blue'>but now assuming a different **prior distribution**</font>: $p(z) = \\mathcal{N}\\left(z| \\overset{\\scriptscriptstyle <}{\\mu}_z=3, \\overset{\\scriptscriptstyle <}{\\sigma}_z^2=2^2\n",
    "\\right)$\n",
    "\n",
    "In my notation, the superscript $\\overset{\\scriptscriptstyle <}{(\\cdot)}$ indicates a parameter of the prior distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Notes about the prior distribution we are assuming\n",
    "\n",
    "* We would have to be very lucky if our \"belief\" coincided with the \"true\" distribution of $z$.\n",
    "    * Usually, we have beliefs but they are not really true (this is not a comment about religion...).\n",
    "        - Our hope is that our beliefs are at least reasonable!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* When defining a prior we are making a decision about two things:\n",
    "    1. The distribution.\n",
    "        * For example, in this exercise we are assuming that the prior is Gaussian (before we had assumed a \"noninformative\" Uniform prior). In this case we hit the jackpot! But remember that we are cheating here because we already know the actual distribution of $z$ is a Gaussian!\n",
    "    2. The parameters of the distribution.\n",
    "        * For example, in this exercise we are assuming values that are not the true ones! This is normal! As I said, usually we don't know the truth about the \"hidden\" variable. Most times we don't even know how  many hidden variables we have..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### See you next class\n",
    "\n",
    "Have fun!"
   ]
  }
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