{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Statistics Seminar\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from thinkbayes2 import Suite\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian bandits\n",
    "\n",
    "\n",
    "Here's a definition for `Bandit`, which extends `Suite` and defines a likelihood function that computes the probability of the data (win or lose) for a given value of `x` (the probability of win).\n",
    "\n",
    "Note that `hypo` is in the range 0 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Bandit(Suite):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\" \n",
    "        hypo is the prob of win (0-100)\n",
    "        data is a string, either 'W' or 'L'\n",
    "        \"\"\"\n",
    "        x = hypo / 100\n",
    "        if data == 'W':\n",
    "            return x\n",
    "        else:\n",
    "            return 1-x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start with a uniform distribution from 0 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TBo4kqQkDR5LUhIEjSWrCwJEkNWHgSJKaMHAkSU0YOJKkJgwcSVITBo4kqQkDR5LUhIEj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\nMeViAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f115c57d4d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit = Bandit(range(101))\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can update with a single loss:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ULCKl53xmNpO/WM7XCzZQ8F9Vp+ua8lRqMvVrV/OtNyldChYPChaR0rdp+34m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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f112b30e950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit.Update('L')\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another loss:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GAA8RCrEn3f1+MxtH6Mjl8XCfScAIQhNe3uzuS8LtzwPZQBMgD7jX3Z82s8bA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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f112b006fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit.Update('L')\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a win:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mQkRJEySXeP+dhWdtsEPAQWC+95gpxIr1Ozh+8gwA1auUtyVcTMSpX6sKt1/b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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f112af29290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit.Update('W')\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting over, here's what it looks like after 1 win and 9 losses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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H10xDmvvGqjRG45xrquImFkV6t98CJgDPAs8Al5hZQjPvmxqfdd8wUy4fSfWN\n1xVrt7Oj9EBa43HONT1xE0vQ+z3XzHaZ2ZzgsbsRYksJn3XfML275zP2/IHR8tzXfcKkc+50id4K\nWy7p4pRG0kh81n3DXX/lJ6LPX1u8nrLyijRG45xrahJNLOOBdyVtkvR+sCjk+6kMLFUOlR2LPs/v\n4Jt8nY3zh/RhQO8uAJyoPMkr7/iqx865GokmlsnAucBE4AbgU8GfzUpV1SmOhr5dd2jrE/zOhiQ+\nVVjTavn7mx9QVXUqjRE555qSeGuFtZb0L8C3iMxdKQkWlNxmZtsaJcIkKiuviK790r5tq+j6V+7M\nXX7RkOjM+30Hyli0yrcuds5FxPuf9UlgLLAKmAr8MOURpVD4NlhHX46kQfJyc5gc2qvlr0U+9Ng5\nFxEvsYwwsy8GExo/C1zeCDGlzOFQYunQ3vtXGmryJ0dGW33rt+xm3eZmO1jQOZdE8RJLZfUTM2v2\nWwceKjsefZ7f3lssDdUlvx1XjB0SLT//6so0RuOcayriJZYLJR0OHkeAC6qfB/u0NCtHQomlo7dY\nkmLaxFHR50s/2OoTJp1zcfdjyQ72Y6nekyUn9LxR9mNJpsNHQ0ONPbEkRf9enbloRAEQ2RRnzoL3\n0huQcy7tMmpY1OFQi8X3EkmeaZNqls8vWrLhtBWknXOZJ6MSy+mTIz2xJMuIQb0ZUhDZHbqq6hRz\nX/cRYs5lsoxKLKeNCmvnt8KSRdJpfS3z3lod3f7ZOZd5Miyx+KiwVBl/wUB6dYt0u5UfP8G8t1an\nOSLnXLqkPLFImiJpnaQNwTbCtdV5VFKxpJWSRoeO/1pSaey6ZJLul7Qj2FUyvLNkvQ77qLCUycrK\n4tNXR//qmPPa+1ScqKznDOdcS5XSxCIpC3iMyFpjI4FbJQ2PqTMVGGRmQ4A7gV+Efvzb4NzaPGJm\nY4LHvHixmBmHj4YTi7dYkq3w4qF07RTZ4+Zw2TFeXuiLUzqXiVLdYhkHFAdri1UCs4FpMXWmAU8B\nmNkiIF9Sz6D8FlDXxAjVcbxW5cdPcOpUZKHEVnm55OWeya7MLhE5OdmntVqef3UllZVVaYzIOZcO\nqU4sfYHtofKO4Fh9dUpqqVOb6cGtsyck5cerfOhIeA6Lt1ZSZdKE4XTqENnn5sDhcl5bvD7NETnn\nGltz/dr+c+C7ZmaSHgAeAb5aW8UZM2YAkRV49+44Rfd+Q30OSwrl5eZw48QLeeqFdwB49uUVTBw/\njJyc7DTKOBikAAAU40lEQVRH5pyrS1FREUVFRUm7XqoTSwkwIFTuFxyLrdM/Tp3TmNneUPFXwIt1\n1a1OLItXbeWhJyJdMb7BV2pNvmwEz768nLLyCvYeOMIbS4uZOGF4/BOdc2lRWFhIYWFhtDxz5swG\nXS/Vt8KWAIMlFUjKA24B5sTUmQPcBiBpAnDQzEpDPxcx/SmSeoWKNwNxN14/ElrOxUeEpVbrVrnc\ncFXNbPw/v7SMkye9r8W5TJHSxGJmVcB0YD6wGphtZmsl3SnpjqDOXGCLpI3ALODr1edL+gOwEBgq\n6UNJXwl+9HCwRfJK4ErgX+PFcuhIaESY3wpLuesuP5/2bVsBsGf/ERYs8r4W5zJFyvtYgqHAw2KO\nzYopT6/j3M/Xcfy2M40jPOvehxqnXts2eXz66tE8PeddINJqKRw31EfjOZcBMmbm/SFPLI1u6uUj\no/1Z+w8dZf7ba9IckXOuMWRMYjly1GfdN7ZWebl85pox0fIzL6/geIXPxneupcuYxHL67pGeWBrL\ntZeOOG02/tw34o6zcM41cxmTWI74XixpkZubzWevvShafu6VFae1Hp1zLU/GJJbT9mLxFkujmjh+\n2GkrHz/78oo0R+ScS6WMSCwVJyo5UXkSgOzsLNq0zk1zRJklJyebL9wwPlr+2xurKP3ocBojcs6l\nUkYklnD/Ssd2rZHOaP1KlwSXXHjuabtM/uFvi9MckXMuVTIisRw+4rPu000St990abT81rKNbNy2\nJ40ROedSJTMSy1EfEdYUDD+3F+MvOCdafmrOu5hZGiNyzqVCRiSW8CikDj45Mq2+cMN4soJbkas3\n7mTxqq3pDcg5l3QZkVhOHxHmiSWd+vboxLWXjYiWf/vswujACudcy5ARicX7WJqWW667OLpA5d4D\nR3j+1ZVpjsg5l0wZkVhiR4W59OrQrjWfv35ctPzsyyvYu/9IGiNyziVTRiQWXyes6bnm0vMY2Lcb\nAJUnq3jyhXfTHJFzLlkyIrH4ysZNT1ZWFl/7zGXR8jsrN7FqQ70bhzrnmomMSCzeYmmazhvUm09e\nNDha/uWf3vCOfOdagJQnFklTJK2TtEHSvXXUeVRSsaSVkkaHjv9aUqmk92Pqd5Y0X9J6SS9Jyq8v\nhkNHfFRYU/XlaZfQpnUeADv3HuIZX0fMuWYvpYlFUhbwGDAZGAncKml4TJ2pwCAzGwLcCfwi9OPf\nBufGug94xcyGAQuAb9cVw8mTVZQfPxF5LYiORnJNQ5f8dnzxUzXriD33ygo+3LU/jRE55xoq1S2W\ncUCxmW0zs0pgNjAtps404CkAM1sE5EvqGZTfAg7Uct1pwJPB8yeBm+oKIDzrvn271mRlZcTdv2Zl\n8idHMOycXkBkHbHH//iGz8h3rhlL9f+yfYHtofKO4Fh9dUpqqROrh5mVApjZbqBHXRWP+HIuTZ4k\n7vzcFdGkv37Lbt/G2LlmLCfdASRJnV9vH/r+91izeAMAbS6e0GgBuTNT0KcLn540imdeXg5E1hEb\nPWIAPbp0SHNkzrV8RUVFFBUVJe16qU4sJcCAULlfcCy2Tv84dWKVSuppZqWSegF1LpN729emU5o1\nH4CRIwsSjdulwWcnj+GdlZvYufcQxysq+dkfXmPGXTf4NgfOpVhhYSGFhYXR8syZMxt0vVTfClsC\nDJZUICkPuAWYE1NnDnAbgKQJwMHq21wBBY/Yc24Pnn8ZeKGuAI4eq4g+b++z7pu0vNwc/vmLE6N/\n2R8U72TuGx+kNSbn3JlLaWIxsypgOjAfWA3MNrO1ku6UdEdQZy6wRdJGYBbw9erzJf0BWAgMlfSh\npK8EP3oIuEbSemAS8GBdMZSVn4g+b9/GR4Q1dUMH9uTTV0dHnPP0nHcp2XMwjRE5585UyvtYzGwe\nMCzm2KyY8vQ6zv18Hcf3A1cn8vpHy2taLO3a5iVyikuzz00Zy9LV2/hw134qT1bx098t4Ht330R2\nto/oc645aPH/UsvCicVbLM1Cbm42d39pYjSRFG/bwx//vjTNUTnnEtXyE0u4j8UnRzYbA/t245ap\nF0fLz768nPfW70hjRM65RLX4xHL6rTBPLM3JTZMu5BNDI1OaDPjJ069y8Eh5eoNyzsXV4hNL+FZY\nB08szUpWVhZ3f2lSdOHQQ0eO8ejTC3xWvnNNXItPLOHhxt5iaX46d2zL3V+aGC2/t34Hf35pWRoj\ncs7F0+ITS3hJF+9jaZ5GDe/PpyeNipb/9PelLF29LY0ROefq0+ITS/kxn8fSEtxy3cWMHNwHiPS3\n/PipV31+i3NNVItPLKeC+/F5uTnk5GSnORp3tnJysvm326+hW+f2ABw7foKHfjXvtC8OzrmmocUn\nlmp+G6z5y+/Qhnu/Opnc4AtCyZ6D/OTpVzl16lSaI3POhXlicc3Kuf278/Vbr4yWl67exm+eXegj\nxZxrQjyxuGbnirFDuSnUmf/3Nz/gxaL36znDOdeYMiax+HIuLcsXbxjPJaMGRctPPv8Ob6/YlMaI\nnHPVMiexeIulRZHEN754FcPP7RU99ujvFrBqQ7ytfJxzqZYxicWHGrc8ebk53Pe1KfTpng/AyZNV\nfP9X81i3eXeaI3Mus2VMYvEl81umDu1a83//6Xq65LcDoOJEJQ/MmsumD/emOTLnMlfGJJYOvntk\ni9Wza0dmTL8huqbYseMn+O4v/sq2nR+lOTLnMlPKE4ukKZLWSdog6d466jwqqVjSSkmj4p0r6X5J\nOyQtDx5T4sXht8Jatr49OjHjrk9FB2mUlVfwH4/OYeO2PWmOzLnMk9LEIikLeAyYDIwEbpU0PKbO\nVGCQmQ0B7gQeT/DcR8xsTPCYFy8W77xv+Qr6dOU//+l62rSO3PY8eqyC+3/2Iqs37kxzZM5lllS3\nWMYBxWa2zcwqgdnAtJg604CnAMxsEZAvqWcC5+pMAvF5LJlhcEEPZt51Q/Tv+3hFJf/1i7+xfM2H\naY7MucyR6sTSF9geKu8IjiVSJ96504NbZ09Iyo8XiLdYMsegAd35r29Mo1OHtgBUBqPFXn13bZoj\ncy4z5KQ7gFok0hL5OfBdMzNJDwCPAF+treKad/8KwE9/tJ0pk6+hsLAwWXG6JmxA7y48cPc0Zvzs\nRfYdKOPUqVP8/H9ep3TfEW69/mKkM2rwOteiFRUVUVRUlLTrKZVrLEmaAMwwsylB+T7AzOyhUJ3H\ngdfM7I9BeR1wJXBOvHOD4wXAi2Z2QS2vbzd/4xcA/PGH/9tXN85AHx0s479/OY+tJfuixy4bM5jp\nny8kL7cpfq9yLv0kYWZn/e0r1bfClgCDJRVIygNuAebE1JkD3AbRRHTQzErrO1dSr9D5NwMf1BdE\nq7xcTyoZqmun9jzwjRsZM2JA9Njbyzfy7R89z+59h9MYmXMtV0oTi5lVAdOB+cBqYLaZrZV0p6Q7\ngjpzgS2SNgKzgK/Xd25w6YclvS9pJZHWzb/WF0d7nxyZ0dq0zuO+r01h8mUjo8e2luzjWz/4C8t8\nJ0rnki6lt8LSrfpW2IDeXfjRfZ9LdzguzcyMlxeu5Yln3qKqKrKHi4CbJo3ilusu9latc4Gmfius\nSfChxg4i/1iuvWwE37t7Gl07RZaAMeC5V1dy34+eY0fpgfQG6FwL4YnFZZwhBT35wTc/ywVD+0WP\nbdmxj28+/Bf+9voq35HSuQbKkMTi64S50+V3aMN/fv16br/pUrKzI/8MKk9W8Ztn3+Y7P37e1xlz\nrgEyJLF4i8V9nCRuuOoCfvDNz9C/d5fo8eJte/jmD57hd3Pe5XhFZRojdK55yojE4rPuXX0K+nTl\nB//2Gf5hykXR1supU6d47tWVTH/gf3ht0Xpa8iAX55ItIxKLr2zs4snNzeaWqRfzw3//h9N2pTxw\nuJzH/vAa//7DZ3lv/Q5PMM4lIDMSi7dYXIL69+rMA9+Yxl23FkbXGgPYvH0v3/35X/m/j77g2x87\nF0dGrGnRto1PkHSJk8TECcO5dPQgnntlBS8seI/Kk1UArNu8mxk/e5Fh5/Ri2sQLufj8ArKyMuL7\nmXMJy4gJkg/e82mGFPRMdziumdp3oIxnXl7Oq++ui06srNarW0c+VXgBV44d6l9gXIvR0AmSGZFY\nfvp/bqFPj07pDsc1c3v2H+EvLy2jaMmGjyWYvNwcPjlmMNdedh6DB/Tw1ZNds+aJpR7VieW33/ty\ndD905xrqo4Nl/P2ND3jp7TWUHz/xsZ/37dGJT140mMsvGkLv7nG3CnKuyfHEUo/qxPKnR+6IDiN1\nLlmOV1SyYNE65i9cy/Zd+2utc27/7oz7xEDGfWIgA3p38ZaMaxY8sdRDkn3+W0/w+4dr3QPMuaQw\nMzZsLWX+wrW8s3IzFSdqn1TZvXMHRp3XjwuH9ecTQ/v6aEXXZHliqYcku+P+p5k144vpDsVliIoT\nlSxZtY03lxWzfO32OtcdE1DQtxsjBvXivEG9GX5OL7rkt2vcYJ2rgyeWekiyex76Mz/898+mOxSX\ngY4eq2DFmu28+/4WVqz9MO7yMJ07tmXwgB6c278bA/t2Y2DfrnTv3N5vn7lG1+QTi6QpwI+JTMb8\ndezWwkGdR4GpwFHgdjNbWd+5kjoDfwQKgK3A58zsUC3Xtf/86QvMnH5jKt6acwk7ebKK9VtLeW/d\nDlau287m7XtJ5F9e61a59OvZmT498unbszO9u+fTq2tHenbr6LfSXMo06cQiKQvYAEwCdhLZbvgW\nM1sXqjMVmG5m10saD/zEzCbUd66kh4CPzOxhSfcCnc3svlpe3x5+Yh7f+urklL3H5qKoqIjCwsJ0\nh9EkNIXP4uixCtZvKWXtpl2s3bybzTv21dk3U5e2rfPo2rk93Tq1o1vn9nTu2I7OHdvSqWNbOnVo\nQ8f2bchv35rWrXLrbPU0hc+iqfDPokZDE0uqZ96PA4rNbBuApNnANGBdqM404CkAM1skKV9ST+Cc\nes6dRmRLYoAngSLgY4kFoK2vEwb4P5qwpvBZtGvTijEjBjBmxAAgsujl9t0H2fThHrbu/IhtOz9i\na8lHlJVX1HmN8uMnKN+1v84RadVycrLp0LYV7du2on3b1rRtnUebNrm0a92Kec/9jr0VHWjTKpc2\nrXNplZtLXl4OrfJyaJWbQ15uNrm5OeTmZJObkxX8mU12duR5S7pN1xR+L1qKVCeWvsD2UHkHkWQT\nr07fOOf2NLNSADPbLalHXQH47QLXHGRlZVHQpwsFfWqW7zczDhwuZ+eeg5SUHmTnnkPs3neI0o8O\ns3vf4egyM/GcPFnFgcPlHDhc/rGfrd28m9lzl5x13AKyc7LJzsoiJzuL7OwssrNEVpbIUhbZ2SJL\nIisrCynyTTgrK4usLCEgK0vR9w9E6iCq85UU85yaRBY+Hi5/LMZ6kl/4em8uLea/Z/39zD8E9zFN\nca2ws/kKVOf9PF8y3zVXkuiS344u+e04f0jf035mZhwuO86+A2XsO1jGRwfLOHj4GPsPH+Xg4XIO\nHjnG4bJjHC47nnACOhtGJHGdpIq621bNw869h1i2Zlu6w2gZzCxlD2ACMC9Uvg+4N6bO48D/CpXX\nAT3rOxdYS6TVAtALWFvH65s//OEPf/jjzB8N+b8/1S2WJcBgSQXALuAW4NaYOnOAu4A/SpoAHDSz\nUkn76jl3DnA78BDwZeCF2l68IZ1Pzjnnzk5KE4uZVUmaDsynZsjwWkl3Rn5svzSzuZKuk7SRyHDj\nr9R3bnDph4A/SfpHYBvwuVS+D+ecc4lr0RMknXPONb4WuTKjpCmS1knaEMxzyRiS+klaIGm1pFWS\nvhEc7yxpvqT1kl6SlDHL7krKkrRc0pygnJGfRTCU/8+S1ga/H+Mz+LP4V0kfSHpf0u8l5WXKZyHp\n15JKJb0fOlbne5f0bUnFwe/NtYm8RotLLMHEyseAycBI4FZJw9MbVaM6CdxjZiOBS4C7gvd/H/CK\nmQ0DFgDfTmOMje1uYE2onKmfxU+AuWZ2HnAhkYEyGfdZSOoD/DMwxswuINIlcCuZ81n8lsj/j2G1\nvndJI4h0NZxHZHWUnyuByUstLrEQmpRpZpVA9cTKjGBmu6uXxDGzMiIj6PoR+QyeDKo9CdyUnggb\nl6R+wHXAE6HDGfdZSOoIXG5mvwUws5PBMkgZ91kEsoF2knKANkAJGfJZmNlbwIGYw3W99xuB2cHv\ny1agmI/PRfyYlphY6ppwmXEkDQRGAe8SM6kUqHNSaQvzI+BbRIZQVsvEz+IcYJ+k3wa3BX8pqS0Z\n+FmY2U7gh8CHRBLKITN7hQz8LEJ61PHeY/8/LSGB/09bYmJxgKT2wF+Au4OWS+wojRY/akPS9UBp\n0IKrr/ne4j8LIrd7xgA/M7MxREZg3kdm/l50IvINvQDoQ6Tl8gUy8LOoR4Pee0tMLCXAgFC5X3As\nYwTN+78AT5tZ9Ryf0mANNiT1AvakK75GdBlwo6TNwP8AEyU9DezOwM9iB7DdzJYG5WeIJJpM/L24\nGthsZvvNrAp4DriUzPwsqtX13kuA/qF6Cf1/2hITS3RSpqQ8IhMr56Q5psb2G2CNmf0kdKx6UinU\nM6m0JTGz75jZADM7l8jvwQIz+xLwIpn3WZQC2yUNDQ5NAlaTgb8XRG6BTZDUOuiInkRkcEcmfRbi\n9FZ8Xe99DnBLMGruHGAwsDjuxVviPBZF9nH5CTUTKx9Mc0iNRtJlwBvAKmqWZ/gOkV+GPxH59rGN\nyB42B9MVZ2OTdCXwb2Z2o6QuZOBnIelCIoMYcoHNRCYjZ5OZn8X9RL5sVAIrgK8BHciAz0LSH4BC\noCtQCtwPPA/8mVreu6RvA18l8lndbWbz475GS0wszjnn0qcl3gpzzjmXRp5YnHPOJZUnFuecc0nl\nicU551xSeWJxzjmXVJ5YnHPOJZUnFuecc0nlicU551xSeWJxrhFJGivpvWCJjHbBZlMj0h2Xc8nk\nM++da2SSvktkD5A2RBaGfCjNITmXVJ5YnGtkknKJLJZ6DLjU/B+ha2H8Vphzja8b0J7Iooet0xyL\nc0nnLRbnGpmkF4jsD3MO0MfM/jnNITmXVDnpDsC5TCLpS8AJM5stKQt4W1KhmRWlOTTnksZbLM45\n55LK+1icc84llScW55xzSeWJxTnnXFJ5YnHOOZdUnlicc84llScW55xzSeWJxTnnXFJ5YnHOOZdU\n/w+y6Slh3TwqjgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f115c57d350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit = Bandit(range(101))\n",
    "\n",
    "for outcome in 'LLWLLLLLLL':\n",
    "    bandit.Update(outcome)\n",
    "\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')\n",
    "bandit.MaximumLikelihood()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior mean is about 17%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.68194469884906"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bandit.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most likely value is the observed proportion 1/10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bandit.MaximumLikelihood()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior credible interval has a 90% chance of containing the true value (provided that the prior distribution truly represents our background knowledge)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 36)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bandit.CredibleInterval(90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian A/B testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose we have several bandits and we want to decide which one to play."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example, suppose we have 4 machines with these probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "actual_probs = [10, 20, 30, 40]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function simulates playing one machine once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from random import random\n",
    "from collections import Counter\n",
    "\n",
    "counter = Counter()\n",
    "\n",
    "def flip(p):\n",
    "    \"\"\"Returns True with probablity `p`, False otherwise.\n",
    "    \n",
    "    p: float probability\n",
    "    \n",
    "    returns: boolean\n",
    "    \"\"\"\n",
    "    return random() < p\n",
    "\n",
    "def play(i):\n",
    "    \"\"\"Plays the `i`th machine and returns the outcome.\n",
    "    \n",
    "    i: integer index into `actual_probs`\n",
    "    \"\"\"\n",
    "    counter[i] += 1\n",
    "    p = actual_probs[i] / 100\n",
    "    if flip(p):\n",
    "        return 'W'\n",
    "    else:\n",
    "        return 'L'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a test, playing Machine 3 twenty times:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L L W L W L W W W L W L L W W L L L L L "
     ]
    }
   ],
   "source": [
    "for i in range(20):\n",
    "    result = play(3)\n",
    "    print(result, end=' ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 1** Create a `Bandit` object to represent your beliefs about Machine 3.  Write a loop that plays Machine 3 20 times and updates your beliefs based on the outcome.  Plot the posterior distribution of `x` and the 90% credible interval.  Does the CI contain the actual probability for Machine 3, which is 30%?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(21, 54)\n"
     ]
    },
    {
     "data": {
      "image/png": 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cFOh3OFBSZaOWTFQJqc/BP8w0J+jc5qDyhi6u/WwX558KMUYT5EiZ9TdEggnj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\nwRhjzE0sORhjjLmJJQdjjDE3+f9C6LdIUsZM/gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f112ae5c650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "mach3 = Bandit(range(101))\n",
    "for i in range(20):\n",
    "    result = play(3)\n",
    "    mach3.Update(result)\n",
    "    \n",
    "thinkplot.Pdf(mach3)\n",
    "print(mach3.CredibleInterval(90))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## STOP HERE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The strategy\n",
    "\n",
    "Now I'll make 4 `Bandit` objects to represent our beliefs about the 4 machines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "prior = range(101)\n",
    "beliefs = [Bandit(prior) for i in range(4)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The core of the Bayesian Bandits Strategy is this process for choosing which machine to play:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def choose(beliefs):\n",
    "    \"\"\"Chooses a machine in proportion to its probability of superiority.\n",
    "    \n",
    "    beliefs: list of Bandit objects.\n",
    "    \n",
    "    returns: integer index of the chosen machine.\n",
    "    \"\"\"\n",
    "    ps = [b.Random() for b in beliefs]\n",
    "    return np.argmax(ps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It chooses a random value from each posterior and returns the index of the machine with this highest generated value of `x`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "choose(beliefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function updates our beliefs about one of the machines based on one outcome."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def update(beliefs, i, outcome):\n",
    "    \"\"\"Updates Machine `i` based on `outcome`.\n",
    "    \n",
    "    beliefs: list of Bandit objects.\n",
    "    i: index integet into beliefs\n",
    "    outcome: string, either 'W' or 'L'\n",
    "    \"\"\"\n",
    "    beliefs[i].Update(outcome)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2**  Fill in this function to use `choose` to pick a machine, `play` to play it, and `update` to update our beliefs about the chosen machine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def choose_play_update(beliefs, verbose=False):\n",
    "    \"\"\"Chooses a machine, plays it, and updates `beliefs`.\n",
    "    \n",
    "    If `verbose`, print the index of the chosen machine, `i`,\n",
    "    and the `outcome`.\n",
    "    \n",
    "    beliefs: list of Bandit objects.\n",
    "    verbose: boolean\n",
    "    \"\"\"\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def choose_play_update(beliefs, verbose=False):\n",
    "    \"\"\"Chooses a machine, plays it, and updates `beliefs`.\n",
    "    \n",
    "    If `verbose`, print the index of the chosen machine, `i`,\n",
    "    and the `outcome`.\n",
    "    \n",
    "    beliefs: list of Bandit objects.\n",
    "    verbose: boolean\n",
    "    \"\"\"\n",
    "    i = choose(beliefs)\n",
    "    outcome = play(i)\n",
    "    update(beliefs, i, outcome)\n",
    "    if verbose:\n",
    "        print(i, outcome, beliefs[i].Mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test your method here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 L 33.0\n"
     ]
    }
   ],
   "source": [
    "counter = Counter()\n",
    "choose_play_update(beliefs, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing the bandit strategy\n",
    "\n",
    "Start with a fresh batch of `Bandit` objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "prior = range(101)\n",
    "beliefs = [Bandit(prior) for i in range(4)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And reset the counter that keeps track of how many times we play each machine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "counter = Counter()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function displays the four distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "options = dict(yticklabels='invisible')\n",
    "\n",
    "def plot(beliefs):\n",
    "    thinkplot.preplot(rows=2, cols=2)\n",
    "    for i, b in enumerate(beliefs):\n",
    "        thinkplot.subplot(i+1)\n",
    "        thinkplot.Pdf(b, label=i)\n",
    "        thinkplot.config(**options)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f112ac79750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(beliefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can play a few times and see how `beliefs` gets updated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qghQfaeZ5bfQRVrMR185NVdtbjrG4pBZoJkkCgHVXzlVvb91VybNwiCgkXLj1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\niIiIiG6CIYmIiIjoJhiSiIiIiG7i/wPnVuspavhMcQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f112a74f450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    choose_play_update(beliefs)\n",
    "    \n",
    "plot(beliefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we play 90 more times, the estimates get better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ADesK4sdnhzjlRrScaklSYb4L9dWlAIBwOIxzvaNqvRQRUU6TjyJVFTlhs6p2603LxnWJ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\n+DwuPNoftWX1qtPfK7mCwvuTy1hMZPD+W6/jxJNnICLYH/GjP+JH1O/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f112abbf590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(90):\n",
    "    choose_play_update(beliefs)\n",
    "    \n",
    "plot(beliefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can summarize `beliefs` by printing the posterior means and credible intervals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.0675787728 (0, 34)\n",
      "23.5293975696 (9, 42)\n",
      "13.8614072846 (0, 39)\n",
      "43.4210526316 (34, 53)\n"
     ]
    }
   ],
   "source": [
    "for i, b in enumerate(beliefs):\n",
    "    print(b.Mean(), b.CredibleInterval(90))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The credible intervals usually contain the true value, but the estimates are still rough, especially for the lower-probability machines.  But that's not the important part.  \n",
    "\n",
    "The goal is to play the high-probability machines most often.  Making the estimates more precise is a means to that end, but not an end itself.\n",
    "\n",
    "Let's see how often we played each machine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 6\n",
      "1 15\n",
      "2 5\n",
      "3 74\n"
     ]
    }
   ],
   "source": [
    "for machine, count in sorted(counter.items()):\n",
    "    print(machine, count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise 3** Run another 100 iterations.  How many times do we play the best machine?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 3\n",
      "2 3\n",
      "3 94\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "counter = Counter()\n",
    "for i in range(100):\n",
    "    choose_play_update(beliefs)\n",
    "\n",
    "for machine, count in sorted(counter.items()):\n",
    "    print(machine, count)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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