solutions/chap09soln.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Think Bayes: Chapter 9\n",
    "\n",
    "This notebook presents code and exercises from Think Bayes, second edition.\n",
    "\n",
    "Copyright 2016 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "% matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import math\n",
    "import numpy as np\n",
    "\n",
    "from thinkbayes2 import Pmf, Cdf, Suite, Joint\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Improving Reading Ability\n",
    "\n",
    "From DASL(http://lib.stat.cmu.edu/DASL/Stories/ImprovingReadingAbility.html)\n",
    "\n",
    "> An educator conducted an experiment to test whether new directed reading activities in the classroom will help elementary school pupils improve some aspects of their reading ability. She arranged for a third grade class of 21 students to follow these activities for an 8-week period. A control classroom of 23 third graders followed the same curriculum without the activities. At the end of the 8 weeks, all students took a Degree of Reading Power (DRP) test, which measures the aspects of reading ability that the treatment is designed to improve.\n",
    "\n",
    "> Summary statistics on the two groups of children show that the average score of the treatment class was almost ten points higher than the average of the control class. A two-sample t-test is appropriate for testing whether this difference is statistically significant. The t-statistic is 2.31, which is significant at the .05 level.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll use Pandas to load the data into a DataFrame."
   ]
  },
  {
   "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>Treatment</th>\n",
       "      <th>Response</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Treated</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Treated</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Treated</td>\n",
       "      <td>58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Treated</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Treated</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Treatment  Response\n",
       "0   Treated        24\n",
       "1   Treated        43\n",
       "2   Treated        58\n",
       "3   Treated        71\n",
       "4   Treated        43"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv('../data/drp_scores.csv', skiprows=21, delimiter='\\t')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And use `groupby` to compute the means for the two groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Control 41.52173913043478\n",
      "Treated 51.476190476190474\n"
     ]
    }
   ],
   "source": [
    "grouped = df.groupby('Treatment')\n",
    "for name, group in grouped:\n",
    "    print(name, group.Response.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Normal` class provides a `Likelihood` function that computes the likelihood of a sample from a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "from thinkbayes2 import EvalNormalPdf\n",
    "\n",
    "class Normal(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"\n",
    "        \n",
    "        data: sequence of test scores\n",
    "        hypo: mu, sigma\n",
    "        \"\"\"\n",
    "        mu, sigma = hypo\n",
    "        likes = EvalNormalPdf(data, mu, sigma)\n",
    "        return np.prod(likes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prior distributions for `mu` and `sigma` are uniform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "mus = np.linspace(20, 80, 101)\n",
    "sigmas = np.linspace(5, 30, 101)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I use `itertools.product` to enumerate all pairs of `mu` and `sigma`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7918831921507665e-44"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from itertools import product\n",
    "\n",
    "control = Normal(product(mus, sigmas))\n",
    "data = df[df.Treatment=='Control'].Response\n",
    "control.Update(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the update, we can plot the probability of each `mu`-`sigma` pair as a contour plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Contour(control, pcolor=True)\n",
    "thinkplot.Config(xlabel='mu', ylabel='sigma')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then we can extract the marginal distribution of `mu`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_mu0 = control.Marginal(0)\n",
    "thinkplot.Pdf(pmf_mu0)\n",
    "thinkplot.Config(xlabel='mu', ylabel='Pmf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the marginal distribution of `sigma`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_sigma0 = control.Marginal(1)\n",
    "thinkplot.Pdf(pmf_sigma0)\n",
    "thinkplot.Config(xlabel='sigma', ylabel='Pmf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Run this analysis again for the control group.  What is the distribution of the difference between the groups?  What is the probability that the average \"reading power\" for the treatment group is higher?  What is the probability that the variance of the treatment group is higher?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.528569095615916e-37"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "treated = Normal(product(mus, sigmas))\n",
    "data = df[df.Treatment=='Treated'].Response\n",
    "treated.Update(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/downey/anaconda3/envs/ThinkBayes2/lib/python3.7/site-packages/matplotlib/contour.py:1004: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n",
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's the posterior joint distribution for the treated group\n",
    "\n",
    "thinkplot.Contour(treated, pcolor=True)\n",
    "thinkplot.Config(xlabel='mu', ylabel='Pmf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The marginal distribution of mu\n",
    "\n",
    "pmf_mu1 = treated.Marginal(0)\n",
    "thinkplot.Pdf(pmf_mu1)\n",
    "thinkplot.Config(xlabel='mu', ylabel='Pmf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The marginal distribution of sigma\n",
    "\n",
    "pmf_sigma1 = treated.Marginal(1)\n",
    "thinkplot.Pdf(pmf_sigma1)\n",
    "thinkplot.Config(xlabel='sigma', ylabel='Pmf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9.95441308894086, 9.0)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Now we can compute the distribution of the difference between groups\n",
    "\n",
    "pmf_diff = pmf_mu1 - pmf_mu0\n",
    "pmf_diff.Mean(), pmf_diff.MAP()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.019520974812674143"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# And CDF_diff(0), which is the probability that the difference is <= 0\n",
    "\n",
    "pmf_diff = pmf_mu1 - pmf_mu0\n",
    "cdf_diff = pmf_diff.MakeCdf()\n",
    "thinkplot.Cdf(cdf_diff)\n",
    "cdf_diff[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9804790251873251"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Or we could directly compute the probability that mu is\n",
    "# greater than mu2\n",
    "\n",
    "pmf_mu1.ProbGreater(pmf_mu0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.026887481110575564"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Finally, here's the probability that the standard deviation\n",
    "# in the treatment group is higher.\n",
    "\n",
    "pmf_sigma1.ProbGreater(pmf_sigma0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# It looks like there is a high probability that the mean of\n",
    "# the treatment group is higher, and the most likely size of\n",
    "# the effect is 9-10 points.\n",
    "\n",
    "# It looks like the variance of the treated group is substantially\n",
    "# smaller, which suggests that the treatment might be helping\n",
    "# low scorers more than high scorers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Paintball"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you are playing paintball in an indoor arena 30 feet\n",
    "wide and 50 feet long.  You are standing near one of the 30 foot\n",
    "walls, and you suspect that one of your opponents has taken cover\n",
    "nearby.  Along the wall, you see several paint spatters, all the same\n",
    "color, that you think your opponent fired recently.\n",
    "\n",
    "The spatters are at 15, 16, 18, and 21 feet, measured from the\n",
    "lower-left corner of the room.  Based on these data, where do you\n",
    "think your opponent is hiding?\n",
    "\n",
    "Here's the Suite that does the update.  It uses `MakeLocationPmf`,\n",
    "defined below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Paintball(Suite, Joint):\n",
    "    \"\"\"Represents hypotheses about the location of an opponent.\"\"\"\n",
    "\n",
    "    def __init__(self, alphas, betas, locations):\n",
    "        \"\"\"Makes a joint suite of parameters alpha and beta.\n",
    "\n",
    "        Enumerates all pairs of alpha and beta.\n",
    "        Stores locations for use in Likelihood.\n",
    "\n",
    "        alphas: possible values for alpha\n",
    "        betas: possible values for beta\n",
    "        locations: possible locations along the wall\n",
    "        \"\"\"\n",
    "        self.locations = locations\n",
    "        pairs = [(alpha, beta) \n",
    "                 for alpha in alphas \n",
    "                 for beta in betas]\n",
    "        Suite.__init__(self, pairs)\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: pair of alpha, beta\n",
    "        data: location of a hit\n",
    "\n",
    "        Returns: float likelihood\n",
    "        \"\"\"\n",
    "        alpha, beta = hypo\n",
    "        x = data\n",
    "        pmf = MakeLocationPmf(alpha, beta, self.locations)\n",
    "        like = pmf.Prob(x)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeLocationPmf(alpha, beta, locations):\n",
    "    \"\"\"Computes the Pmf of the locations, given alpha and beta. \n",
    "\n",
    "    Given that the shooter is at coordinates (alpha, beta),\n",
    "    the probability of hitting any spot is inversely proportionate\n",
    "    to the strafe speed.\n",
    "\n",
    "    alpha: x position\n",
    "    beta: y position\n",
    "    locations: x locations where the pmf is evaluated\n",
    "\n",
    "    Returns: Pmf object\n",
    "    \"\"\"\n",
    "    pmf = Pmf()\n",
    "    for x in locations:\n",
    "        prob = 1.0 / StrafingSpeed(alpha, beta, x)\n",
    "        pmf.Set(x, prob)\n",
    "    pmf.Normalize()\n",
    "    return pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def StrafingSpeed(alpha, beta, x):\n",
    "    \"\"\"Computes strafing speed, given location of shooter and impact.\n",
    "\n",
    "    alpha: x location of shooter\n",
    "    beta: y location of shooter\n",
    "    x: location of impact\n",
    "\n",
    "    Returns: derivative of x with respect to theta\n",
    "    \"\"\"\n",
    "    theta = math.atan2(x - alpha, beta)\n",
    "    speed = beta / math.cos(theta)**2\n",
    "    return speed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prior probabilities for `alpha` and `beta` are uniform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9032915958109017e-06"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphas = range(0, 31)\n",
    "betas = range(1, 51)\n",
    "locations = range(0, 31)\n",
    "\n",
    "suite = Paintball(alphas, betas, locations)\n",
    "suite.UpdateSet([15, 16, 18, 21])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize the joint posterior, I take slices for a few values of `beta` and plot the conditional distributions of `alpha`.  If the shooter is close to the wall, we can be somewhat confident of his position.  The farther away he is, the less certain we are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "locations = range(0, 31)\n",
    "alpha = 10\n",
    "betas = [10, 20, 40]\n",
    "thinkplot.PrePlot(num=len(betas))\n",
    "\n",
    "for beta in betas:\n",
    "    pmf = MakeLocationPmf(alpha, beta, locations)\n",
    "    pmf.label = 'beta = %d' % beta\n",
    "    thinkplot.Pdf(pmf)\n",
    "\n",
    "thinkplot.Config(xlabel='Distance',\n",
    "                ylabel='Prob')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the marginal posterior distributions for `alpha` and `beta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha CI (14, 21)\n",
      "beta CI (5, 31)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "marginal_alpha = suite.Marginal(0, label='alpha')\n",
    "marginal_beta = suite.Marginal(1, label='beta')\n",
    "\n",
    "print('alpha CI', marginal_alpha.CredibleInterval(50))\n",
    "print('beta CI', marginal_beta.CredibleInterval(50))\n",
    "\n",
    "thinkplot.PrePlot(num=2)\n",
    "    \n",
    "thinkplot.Cdf(Cdf(marginal_alpha))\n",
    "thinkplot.Cdf(Cdf(marginal_beta))\n",
    "    \n",
    "thinkplot.Config(xlabel='Distance',\n",
    "                ylabel='Prob')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize the joint posterior, I take slices for a few values of `beta` and plot the conditional distributions of `alpha`.  If the shooter is close to the wall, we can be somewhat confident of his position.  The farther away he is, the less certain we are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "betas = [10, 20, 40]\n",
    "thinkplot.PrePlot(num=len(betas))\n",
    "\n",
    "for beta in betas:\n",
    "    cond = suite.Conditional(0, 1, beta)\n",
    "    cond.label = 'beta = %d' % beta\n",
    "    thinkplot.Pdf(cond)\n",
    "\n",
    "thinkplot.Config(xlabel='Distance',\n",
    "                ylabel='Prob')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to visualize the posterio distribution: a pseudocolor plot of probability as a function of `alpha` and `beta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Contour(suite.GetDict(), contour=False, pcolor=True)\n",
    "\n",
    "thinkplot.Config(xlabel='alpha',\n",
    "                ylabel='beta',\n",
    "                axis=[0, 30, 0, 20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's another visualization that shows posterior credible regions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = dict((pair, 0) for pair in suite.Values())\n",
    "\n",
    "percentages = [75, 50, 25]\n",
    "for p in percentages:\n",
    "    interval = suite.MaxLikeInterval(p)\n",
    "    for pair in interval:\n",
    "        d[pair] += 1\n",
    "\n",
    "thinkplot.Contour(d, contour=False, pcolor=True)\n",
    "thinkplot.Text(17, 4, '25', color='white')\n",
    "thinkplot.Text(17, 15, '50', color='white')\n",
    "thinkplot.Text(17, 30, '75')\n",
    "\n",
    "thinkplot.Config(xlabel='alpha',\n",
    "                   ylabel='beta',\n",
    "                   legend=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** From [John D. Cook](http://www.johndcook.com/blog/2010/07/13/lincoln-index/)\n",
    "\n",
    "\"Suppose you have a tester who finds 20 bugs in your program. You want to estimate how many bugs are really in the program. You know there are at least 20 bugs, and if you have supreme confidence in your tester, you may suppose there are around 20 bugs. But maybe your tester isn't very good. Maybe there are hundreds of bugs. How can you have any idea how many bugs there are? There’s no way to know with one tester. But if you have two testers, you can get a good idea, even if you don’t know how skilled the testers are.\n",
    "\n",
    "Suppose two testers independently search for bugs. Let k1 be the number of errors the first tester finds and k2 the number of errors the second tester finds. Let c be the number of errors both testers find.  The Lincoln Index estimates the total number of errors as k1 k2 / c [I changed his notation to be consistent with mine].\"\n",
    "\n",
    "So if the first tester finds 20 bugs, the second finds 15, and they find 3 in common, we estimate that there are about 100 bugs.  What is the Bayesian estimate of the number of errors based on this data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "from scipy.special import binom as choose\n",
    "\n",
    "def binom(k, n, p):\n",
    "    \"\"\"Computes the rest of the binomial PMF.\n",
    "\n",
    "    k: number of hits\n",
    "    n: number of attempts\n",
    "    p: probability of a hit\n",
    "    \"\"\"\n",
    "    return p**k * (1-p)**(n-k)\n",
    "\n",
    "\n",
    "class Lincoln(Suite, Joint):\n",
    "    \"\"\"Represents hypotheses about the number of errors.\"\"\"\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: n, p1, p2\n",
    "        data: k1, k2, c\n",
    "        \"\"\"\n",
    "        n, p1, p2 = hypo\n",
    "        k1, k2, c = data\n",
    "\n",
    "        part1 = choose(n, k1) * binom(k1, n, p1)\n",
    "        part2 = choose(k1, c) * choose(n-k1, k2-c) * binom(k2, n, p2)\n",
    "        return part1 * part2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.754332814652822e-06"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "data = 20, 15, 3\n",
    "probs = np.linspace(0, 1, 31)\n",
    "hypos = []\n",
    "for n in range(32, 350):\n",
    "    for p1 in probs:\n",
    "        for p2 in probs:\n",
    "            hypos.append((n, p1, p2))\n",
    "\n",
    "suite = Lincoln(hypos)\n",
    "suite.Update(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "n_marginal = suite.Marginal(0)\n",
    "thinkplot.Pmf(n_marginal, label='n')\n",
    "thinkplot.Config(xlabel='number of bugs',\n",
    "                   ylabel='PMF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "post mean n 105.45742662709635\n",
      "MAP n 72\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "print('post mean n', n_marginal.Mean())\n",
    "print('MAP n', n_marginal.MAP())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** The GPS problem.  According to [Wikipedia]()\n",
    "\n",
    "￼\n",
    "> GPS included a (currently disabled) feature called Selective Availability (SA) that adds intentional, time varying errors of up to 100 meters (328 ft) to the publicly available navigation signals. This was intended to deny an enemy the use of civilian GPS receivers for precision weapon guidance.\n",
    "> [...]\n",
    "> Before it was turned off on May 2, 2000, typical SA errors were about 50 m (164 ft) horizontally and about 100 m (328 ft) vertically.[10] Because SA affects every GPS receiver in a given area almost equally, a fixed station with an accurately known position can measure the SA error values and transmit them to the local GPS receivers so they may correct their position fixes. This is called Differential GPS or DGPS. DGPS also corrects for several other important sources of GPS errors, particularly ionospheric delay, so it continues to be widely used even though SA has been turned off. The ineffectiveness of SA in the face of widely available DGPS was a common argument for turning off SA, and this was finally done by order of President Clinton in 2000.\n",
    "\n",
    "Suppose it is 1 May 2000, and you are standing in a field that is 200m square.  You are holding a GPS unit that indicates that your location is 51m north and 15m west of a known reference point in the middle of the field.\n",
    "\n",
    "However, you know that each of these coordinates has been perturbed by a \"feature\" that adds random errors with mean 0 and standard deviation 30m.\n",
    "\n",
    "1) After taking one measurement, what should you believe about your position?\n",
    "\n",
    "Note: Since the intentional errors are independent, you could solve this problem independently for X and Y.  But we'll treat it as a two-dimensional problem, partly for practice and partly to see how we could extend the solution to handle dependent errors.\n",
    "\n",
    "You can start with the code in gps.py.\n",
    "\n",
    "2) Suppose that after one second the GPS updates your position and reports coordinates (48, 90).  What should you believe now?\n",
    "\n",
    "3) Suppose you take 8 more measurements and get:\n",
    "\n",
    "    (11.903060613102866, 19.79168669735705)\n",
    "    (77.10743601503178, 39.87062906535289)\n",
    "    (80.16596823095534, -12.797927542984425)\n",
    "    (67.38157493119053, 83.52841028148538)\n",
    "    (89.43965206875271, 20.52141889230797)\n",
    "    (58.794021026248245, 30.23054016065644)\n",
    "    (2.5844401241265302, 51.012041625783766)\n",
    "    (45.58108994142448, 3.5718287379754585)\n",
    "\n",
    "At this point, how certain are you about your location?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "from thinkbayes2 import EvalNormalPdf\n",
    "\n",
    "class Gps(Suite, Joint):\n",
    "    \"\"\"Represents hypotheses about your location in the field.\"\"\"\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: \n",
    "        data: \n",
    "        \"\"\"\n",
    "        std = 30\n",
    "        meanx, meany = hypo\n",
    "        x, y = data\n",
    "        like = EvalNormalPdf(x, meanx, std)\n",
    "        like *= EvalNormalPdf(y, meany, std)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3287325820864567e-05"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "from itertools import product\n",
    "\n",
    "coords = np.linspace(-100, 100, 101)\n",
    "joint = Gps(product(coords, coords))\n",
    "joint.Update((51, -15))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.30241013197118e-06"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "joint.Update((48, 90))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1118148191216707e-34"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pairs = [(11.903060613102866, 19.79168669735705),\n",
    "         (77.10743601503178, 39.87062906535289),\n",
    "         (80.16596823095534, -12.797927542984425),\n",
    "         (67.38157493119053, 83.52841028148538),\n",
    "         (89.43965206875271, 20.52141889230797),\n",
    "         (58.794021026248245, 30.23054016065644),\n",
    "         (2.5844401241265302, 51.012041625783766),\n",
    "         (45.58108994142448, 3.5718287379754585)]\n",
    "\n",
    "joint.UpdateSet(pairs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "thinkplot.PrePlot(2)\n",
    "pdfx = joint.Marginal(0)\n",
    "pdfy = joint.Marginal(1)\n",
    "thinkplot.Pdf(pdfx, label='posterior x')\n",
    "thinkplot.Pdf(pdfy, label='posterior y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "53.195713209440854 9.486804947986958\n",
      "31.072862791788 9.486832980484914\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "print(pdfx.Mean(), pdfx.Std())\n",
    "print(pdfy.Mean(), pdfy.Std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** [The Flea Beetle problem from DASL](http://lib.stat.cmu.edu/DASL/Datafiles/FleaBeetles.html)\n",
    "\n",
    "Datafile Name: Flea Beetles\n",
    "\n",
    "Datafile Subjects: Biology\n",
    "\n",
    "Story Names: Flea Beetles\n",
    "\n",
    "Reference: Lubischew, A.A. (1962) On the use of discriminant functions in taxonomy. Biometrics, 18, 455-477. Also found in: Hand, D.J., et al. (1994) A Handbook of Small Data Sets, London: Chapman & Hall, 254-255.\n",
    "\n",
    "Authorization: Contact Authors\n",
    "\n",
    "Description: Data were collected on the genus of flea beetle Chaetocnema, which contains three species: concinna (Con), heikertingeri (Hei), and heptapotamica (Hep). Measurements were made on the width and angle of the aedeagus of each beetle. The goal of the original study was to form a classification rule to distinguish the three species.\n",
    "\n",
    "Number of cases: 74\n",
    "\n",
    "Variable Names:\n",
    "\n",
    "Width: The maximal width of aedeagus in the forpart (in microns)\n",
    "\n",
    "Angle: The front angle of the aedeagus (1 unit = 7.5 degrees)\n",
    "\n",
    "Species: Species of flea beetle from the genus Chaetocnema\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suggestions: \n",
    "\n",
    "1. Plot CDFs for the width and angle data, broken down by species, to get a visual sense of whether the normal distribution is a good model.\n",
    "\n",
    "2. Use the data to estimate the mean and standard deviation for each variable, broken down by species.\n",
    "\n",
    "3. Given a joint posterior distribution for `mu` and `sigma`, what is the likelihood of a given datum?\n",
    "\n",
    "4. Write a function that takes a measured width and angle and returns a posterior PMF of species.\n",
    "\n",
    "5. Use the function to classify each of the specimens in the table and see how many you get right.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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>Width</th>\n",
       "      <th>Angle</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>150</td>\n",
       "      <td>15</td>\n",
       "      <td>Con</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>147</td>\n",
       "      <td>13</td>\n",
       "      <td>Con</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>144</td>\n",
       "      <td>14</td>\n",
       "      <td>Con</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>144</td>\n",
       "      <td>16</td>\n",
       "      <td>Con</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>153</td>\n",
       "      <td>13</td>\n",
       "      <td>Con</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Width  Angle Species\n",
       "0    150     15     Con\n",
       "1    147     13     Con\n",
       "2    144     14     Con\n",
       "3    144     16     Con\n",
       "4    153     13     Con"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv('../data/flea_beetles.csv', delimiter='\\t')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_cdfs(df, col):\n",
    "    for name, group in df.groupby('Species'):\n",
    "        cdf = Cdf(group[col], label=name)\n",
    "        thinkplot.Cdf(cdf)\n",
    "    \n",
    "    thinkplot.Config(xlabel=col, legend=True, loc='lower right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cdfs(df, 'Width')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cdfs(df, 'Angle')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from thinkbayes2 import EvalNormalPdf\n",
    "\n",
    "class Beetle(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"\n",
    "        data: sequence of measurements\n",
    "        hypo: mu, sigma\n",
    "        \"\"\"\n",
    "        mu, sigma = hypo\n",
    "        likes = EvalNormalPdf(data, mu, sigma)\n",
    "        return np.prod(likes)\n",
    "    \n",
    "    def PredictiveProb(self, data):\n",
    "        \"\"\"Compute the posterior total probability of a datum.\n",
    "        \n",
    "        data: sequence of measurements\n",
    "        \"\"\"\n",
    "        total = 0\n",
    "        for (mu, sigma), prob in self.Items():\n",
    "            likes = norm.pdf(data, mu, sigma)\n",
    "            total += prob * np.prod(likes)\n",
    "        return total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "\n",
    "def MakeWidthSuite(data):\n",
    "    mus = np.linspace(115, 160, 51)\n",
    "    sigmas = np.linspace(1, 10, 51)\n",
    "    suite = Beetle(product(mus, sigmas))\n",
    "    suite.Update(data)\n",
    "    return suite"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "groups = df.groupby('Species')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/downey/anaconda3/envs/ThinkBayes2/lib/python3.7/site-packages/matplotlib/contour.py:1004: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Con 0.02008635228219648\n",
      "Hei 0.003680972113740979\n",
      "Hep 0.08677915567168913\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for name, group in groups:\n",
    "    suite = MakeWidthSuite(group.Width)\n",
    "    thinkplot.Contour(suite)\n",
    "    print(name, suite.PredictiveProb(137))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeAngleSuite(data):\n",
    "    mus = np.linspace(8, 16, 101)\n",
    "    sigmas = np.linspace(0.1, 2, 101)\n",
    "    suite = Beetle(product(mus, sigmas))\n",
    "    suite.Update(data)\n",
    "    return suite"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/downey/anaconda3/envs/ThinkBayes2/lib/python3.7/site-packages/matplotlib/contour.py:1004: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Con 0.20957983350995815\n",
      "Hei 0.18132754844057228\n",
      "Hep 0.01060175716818402\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for name, group in groups:\n",
    "    suite = MakeAngleSuite(group.Angle)\n",
    "    thinkplot.Contour(suite)\n",
    "    print(name, suite.PredictiveProb(13))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Species:\n",
    "    \n",
    "    def __init__(self, name, suite_width, suite_angle):\n",
    "        self.name = name\n",
    "        self.suite_width = suite_width\n",
    "        self.suite_angle = suite_angle\n",
    "        \n",
    "    def __str__(self):\n",
    "        return self.name\n",
    "        \n",
    "    def Likelihood(self, data):\n",
    "        width, angle = data\n",
    "        like1 = self.suite_width.PredictiveProb(width)\n",
    "        like2 = self.suite_angle.PredictiveProb(angle)\n",
    "        return like1 * like2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "species = {}\n",
    "\n",
    "for name, group in groups:\n",
    "    suite_width = MakeWidthSuite(group.Width)\n",
    "    suite_angle = MakeAngleSuite(group.Angle)\n",
    "    species[name] = Species(name, suite_width, suite_angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02739036224187184"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "species['Con'].Likelihood((145, 14))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Classifier(Suite):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        return hypo.Likelihood(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Con 0.3333333333333333\n",
      "Hei 0.3333333333333333\n",
      "Hep 0.3333333333333333\n"
     ]
    }
   ],
   "source": [
    "suite = Classifier(species.values())\n",
    "for hypo, prob in suite.Items():\n",
    "    print(hypo, prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Con 0.9981416141357145\n",
      "Hei 0.0006899413683764533\n",
      "Hep 0.0011684444959091246\n"
     ]
    }
   ],
   "source": [
    "suite.Update((145, 14))\n",
    "for hypo, prob in suite.Items():\n",
    "    print(hypo, prob)"
   ]
  },
  {
   "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}