02_dice_soln.ipynb

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   "source": [
    "Bayesian Statistics Made Simple\n",
    "===\n",
    "\n",
    "Code and exercises from my workshop on Bayesian statistics in Python.\n",
    "\n",
    "Copyright 2016 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_style('white')\n",
    "sns.set_context('talk')\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from empyrical_dist import Pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The dice problem\n",
    "\n",
    "Create a Suite to represent dice with different numbers of sides."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "4     0.25\n",
       "6     0.25\n",
       "8     0.25\n",
       "12    0.25\n",
       "dtype: float64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice = Pmf.from_seq([4, 6, 8, 12])\n",
    "dice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 1:** We'll solve this problem two ways.  First we'll do it \"by hand\", as we did with the cookie problem; that is, we'll multiply each hypothesis by the likelihood of the data, and then renormalize.\n",
    "\n",
    "In the space below, update `dice` based on the likelihood of the data (rolling a 6), then normalize and display the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.444444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.222222</td>\n",
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       "4     0.000000\n",
       "6     0.444444\n",
       "8     0.333333\n",
       "12    0.222222\n",
       "dtype: float64"
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   "source": [
    "# Solution\n",
    "\n",
    "dice[4] *= 0\n",
    "dice[6] *= 1/6\n",
    "dice[8] *= 1/8\n",
    "dice[12] *= 1/12\n",
    "\n",
    "dice.normalize()\n",
    "dice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2:**  Now let's do the same calculation using `Pmf.update`, which encodes the structure of a Bayesian update."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function called `likelihood_dice` that takes `data` and `hypo` and returns the probability of the data (the outcome of rolling the die) for a given hypothesis (number of sides on the die).\n",
    "\n",
    "Hint: What should you do if the outcome exceeds the hypothetical number of sides on the die?\n",
    "\n",
    "Here's an outline to get you started."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood_dice(data, hypo):\n",
    "    \"\"\"Likelihood function for the dice problem.\n",
    "    \n",
    "    data: outcome of the die roll\n",
    "    hypo: number of sides\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    # TODO: fill this in!\n",
    "    return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "    \n",
    "def likelihood_dice(data, hypo):\n",
    "    \"\"\"Likelihood function for the dice problem.\n",
    "    \n",
    "    data: outcome of the die roll\n",
    "    hypo: number of sides\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    if data > hypo:\n",
    "        return 0\n",
    "    else:\n",
    "        return 1 / hypo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can create a `Pmf` object and update it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.444444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "4     0.000000\n",
       "6     0.444444\n",
       "8     0.333333\n",
       "12    0.222222\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "dice = Pmf.from_seq([4, 6, 8, 12])\n",
    "dice.update(likelihood_dice, 6)\n",
    "dice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we get more data, we can perform more updates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "for roll in [8, 7, 7, 5, 4]:\n",
    "    dice.update(likelihood_dice, roll)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.919294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.080706</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "4     0.000000\n",
       "6     0.000000\n",
       "8     0.919294\n",
       "12    0.080706\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The German tank problem\n",
    "\n",
    "The German tank problem is actually identical to the dice problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood_tank(data, hypo):\n",
    "    \"\"\"Likelihood function for the tank problem.\n",
    "    \n",
    "    data: observed serial number\n",
    "    hypo: number of tanks\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    if data > hypo:\n",
    "        return 0\n",
    "    else:\n",
    "        return 1 / hypo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the update after seeing Tank #42."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "66.32784309363326"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tank = Pmf.from_seq(range(100))\n",
    "tank.update(likelihood_tank, 42)\n",
    "tank.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what the posterior distribution looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decorate_tank(title):\n",
    "    \"\"\"Labels the axes.\n",
    "    \n",
    "    title: string\n",
    "    \"\"\"\n",
    "    plt.xlabel('Number of tanks')\n",
    "    plt.ylabel('PMF')\n",
    "    plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tank.plot()\n",
    "decorate_tank('Distribution after one tank')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 3:**  Suppose we see another tank with serial number 17.  What effect does this have on the posterior probabilities?\n",
    "\n",
    "Update the `Pmf` with the new data and plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "62.25994473449364"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "tank.plot(color='0.7', label='prior')\n",
    "tank.update(likelihood_tank, 17)\n",
    "tank.plot(label='posterior')\n",
    "\n",
    "plt.legend()\n",
    "decorate_tank('Distribution after two tanks')\n",
    "\n",
    "tank.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}