Attendance Problem.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Attendance Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets see how we can use bayes to solve an actual problem\n",
    "\n",
    "*I have a list of 7 events with attendance and registered people for each event, Can we guess what will be the attendance of the event given that the number of people registered are 100?*\n",
    "\n",
    "so given the data of the 7 events we want to predict how many people will attend the 8th event given that there are 100 registrations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from thinkbayes2 import Suite\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from scipy.stats import binom, beta\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# import the dataset\n",
    "data = pd.read_csv('attendance.csv', index_col='Event')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>attended</th>\n",
       "      <th>registered</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Event</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>17</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>20</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>36</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>34</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>29</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>34</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>51</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       attended  registered\n",
       "Event                      \n",
       "A            17          88\n",
       "B            20          47\n",
       "C            36          75\n",
       "D            34          65\n",
       "E            29          60\n",
       "F            34          90\n",
       "G            51          38"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head(7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class AttendanceModel(Suite):\n",
    "    def Likelihood(self, data, hypo):\n",
    "        x = hypo / 100\n",
    "        if data == 1:\n",
    "            return x\n",
    "        else:\n",
    "            return 1 - x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Beta Distributions\n",
    "\n",
    "The beta distributions, is controlled by 2 shape parameters aplpha(a) and beta(b). Its generally used when we need to add more information to the prior. In our problem, lets say I have a prior belief that I am 60% sure that 40% people would attend the events, to add the information I assign alpha 4  and beta 6. So in other words alpha is controlling the position and beta is controlling the spread of the curve\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12f545bf0f0>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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bKHykIed+389FJDT1fohIoil8pKF582DhQo33kPSw995w2WXq/RCRxFH4SEMT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\nUur/AxA/OqBccLyCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12f54562e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Play around a bit with the beta distribution\n",
    "plt.plot(beta.pdf(range(101), a=4, b=6, scale=100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AC4EfAO9LKZVmwJxHlt1y64zDfaJwnFqOK7WchcUaV6z5Uen6Fet+jCxakPOZScpbQxNO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\nJEm5+v9jng6rzISK5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12f558133c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "attendance = AttendanceModel(range(101))\n",
    "# Feel free to change this to represent your own belief. \n",
    "prior = beta.pdf(range(101), a=4, b=6, loc=0, scale=100)\n",
    "for index in range(101):\n",
    "    attendance[index] = prior[index]\n",
    "attendance.Normalize()\n",
    "thinkplot.Pmf(attendance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9AZiklnCPhTTDDA/vN1RIahmDhTTD7B7cWzdUdLTPZX7HvEmuSNJsYrCQZomO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\nre7h8wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12f557a8eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for attended, registered in zip(data.attended.tolist(), data.registered.tolist()):\n",
    "    attendance.UpdateSet([1] * attended + [0] * (registered - attended))\n",
    "attendance.Normalize()\n",
    "thinkplot.Pmf(attendance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "46.296296296296283"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Discribe the posterior\n",
    "attendance.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(42, 51)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "attendance.CredibleInterval(95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To predict the number of people who show up for the next event, we can generate a **predictive distribution** by drawing samples from the posterior that we just calculated, and then drawing samples from a Binomial distribution with parameters x and n, where n is the number of people who signed up and x is the probability of them showing up."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binomial Distribution\n",
    "\n",
    "The binomial distribution is defined by 2 params *n* and *p*, where *n* is the number of trials and *p* is the probability of success. I want to predict the number of people coming to the event given that there are 110 registrations, thus\n",
    "            \n",
    "                n = 110\n",
    "\n",
    "and *p* the probability of success in this term, probability of people coming can be generated by sampling 110 people and taking the mean of the sample as p\n",
    "\n",
    "                p = Mean of Sample from our posterior from the attendance model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "number_of_registered = 110\n",
    "p = attendance.Sample(number_of_registered).mean() / 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "predictive_prior = binom(number_of_registered, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12f557b05f8>]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eGE3Ya02m9Ub8sd7WEu91TooGjLW1taqtrZ3076tXr9a3vvUtbd++PaqvVViY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\niETh/wFsKGZ1LhX6pgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12f5593de48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(predictive_prior.pmf(range(101)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'There will be around 40.0 to 61.0 people attending the event.'"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'There will be around {0} to {1} people attending the event.'.format(*predictive_prior.interval(0.95))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving the same problem in the frequentist paradigm, how should we approach ? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets do a simple regression to compare our results and see the differences in the insights gained from the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12f55802518>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5ouvVw3X5soX08UnoioSeSJCNOoiIiBaIbduIxpMwy9UArDMA00kYhOdZ9Qq2IFzXxVgs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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12f557c4da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(data.attended, data.registered)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg = LinearRegression()\n",
    "reg.fit(X=data.registered.values.reshape(7,1), y=data.attended.values.reshape(7,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 23.79428044]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.predict(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q: If you had to bet on the result, which one would you bet the range that we got above or the result from regression ?"
   ]
  }
 ],
 "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": 1
}