{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian Statistics Made Simple\n",
    "\n",
    "Code and exercises from my workshop on Bayesian statistics in Python.\n",
    "\n",
    "Copyright 2019 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 distribution import Pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you have two urns full of marbles:\n",
    "\n",
    "* Urn 1 has 20 blue and 10 red marbles\n",
    "\n",
    "* Urn 2 has 10 blue and 20 red marbles.\n",
    "\n",
    "You choose an urn at random and draw two marbles.  They are both blue.  What is the probability that you chose Urn 1?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<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>Urn 1</th>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Urn 2</th>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Urn 1    0.8\n",
       "Urn 2    0.2\n",
       "dtype: float64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf = Pmf.from_seq(['Urn 1', 'Urn 2'])\n",
    "pmf['Urn 1'] *= (2/3)**2\n",
    "pmf['Urn 2'] *= (1/3)**2\n",
    "pmf.normalize()\n",
    "pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<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>Urn 1</th>\n",
       "      <td>0.808511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Urn 2</th>\n",
       "      <td>0.191489</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Urn 1    0.808511\n",
       "Urn 2    0.191489\n",
       "dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf = Pmf.from_seq(['Urn 1', 'Urn 2'])\n",
    "pmf['Urn 1'] *= 20/30 * 19/29\n",
    "pmf['Urn 2'] *= 10/30 * 9/29\n",
    "pmf.normalize()\n",
    "pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose I have a box of dice with one each of 4-sided, 6-sided, 8-sided, 10-sided, 12-sided, and 20-sided dice.\n",
    "\n",
    "I choose a die at random, roll it, and get a 9.  What is the probability that I chose the 12-sided die?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<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>10</th>\n",
       "      <td>0.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.357143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.214286</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "10    0.428571\n",
       "12    0.357143\n",
       "20    0.214286\n",
       "dtype: float64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice = Pmf.from_seq([10,12,20])\n",
    "dice[10] /= 10\n",
    "dice[12] /= 12\n",
    "dice[20] /= 20\n",
    "dice.normalize()\n",
    "dice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a few lines of code that use the Pmf class to compute the answer to the following question.\n",
    "\n",
    "Suppose I roll two six-sided dice and tell you (honestly) that the sum is not 7.\n",
    "\n",
    "What is the probability that the sum is 2 or 12?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<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>2</th>\n",
       "      <td>0.033333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.066667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.133333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.133333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.066667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.033333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "2     0.033333\n",
       "3     0.066667\n",
       "4     0.100000\n",
       "5     0.133333\n",
       "6     0.166667\n",
       "7     0.000000\n",
       "8     0.166667\n",
       "9     0.133333\n",
       "10    0.100000\n",
       "11    0.066667\n",
       "12    0.033333\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d6 = Pmf.from_seq([1,2,3,4,5,6])\n",
    "twice = d6 + d6\n",
    "twice[7] = 0\n",
    "twice.normalize()\n",
    "twice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.06666666666666667"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "twice[2] + twice[12]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose I flip the same coin twice and tell you only whether the outcomes are the same or different.\n",
    "\n",
    "Write a likelihood function that takes data and hypo and returns the probability of the data under the hypothesis, where:\n",
    "\n",
    "1. data is a string, either 'S' for the same outcome or 'D' for different, and\n",
    "\n",
    "2. hypo is the hypothetical probability of heads, from 0-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood_flip(data, hypo):\n",
    "    \"\"\" Likelihood function for the Euro problem.\n",
    "    \n",
    "    data: string, either 'S' or 'D'\n",
    "    hypo: prob of heads (0-1)\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    x = hypo\n",
    "    if data == 'S':\n",
    "        return x*x + (1-x)*(1-x)\n",
    "    else:\n",
    "        return 2 * x * (1-x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decorate_flip(title):\n",
    "    \"\"\"Labels the axes.\n",
    "    \n",
    "    title: string\n",
    "    \"\"\"\n",
    "    plt.xlabel('Probability of heads')\n",
    "    plt.ylabel('PMF')\n",
    "    plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "same = Pmf.from_seq(np.linspace(0, 1))\n",
    "same.update(likelihood_flip, 'S')\n",
    "same.plot()\n",
    "decorate_flip('Same outcome')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "diff = Pmf.from_seq(np.linspace(0, 1))\n",
    "diff.update(likelihood_flip, 'D')\n",
    "diff.plot()\n",
    "decorate_flip('Different outcome')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you have a fixed but unknown probability, `p`, of answering a question on this quiz correctly.\n",
    "\n",
    "Out of six questions, the number you get correct, `k`, is well modeled by the binomial distribution with parameters `n` and `p`, where `n` is the number of questions.\n",
    "\n",
    "Write a likelihood function that takes `data` and `hypo` and returns the probability of the data under the hypothesis, where:\n",
    "\n",
    "1. `data` is a list of two values, `k` and `n`\n",
    "\n",
    "2. `hypo` is your probability of getting a question right, `p`, from 0-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import binom\n",
    "\n",
    "def likelihood_quiz(data, hypo):\n",
    "    \"\"\" Likelihood function for the Euro problem.\n",
    "    \n",
    "    data: k, n\n",
    "    hypo: p\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    k, n = data\n",
    "    p = hypo\n",
    "    \n",
    "    return binom.pmf(k, n, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decorate_quiz(title):\n",
    "    \"\"\"Labels the axes.\n",
    "    \n",
    "    title: string\n",
    "    \"\"\"\n",
    "    plt.xlabel('Probability of correct')\n",
    "    plt.ylabel('PMF')\n",
    "    plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": [
    "quiz = Pmf.from_seq(np.linspace(0, 1))\n",
    "quiz.update(likelihood_quiz, (7, 9))\n",
    "quiz.plot()\n",
    "decorate_quiz('7 out of 9')"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}