Bayesian Statistics The Fun Way - Python Solutions # CHAPTER 13.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import scipy.stats\n",
    "from scipy.stats import beta\n",
    "from scipy.stats import binom\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "\n",
    "# this will make plots a little bit prettier\n",
    "sns.set(style='darkgrid')\n",
    "sns.set_context('talk')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TOOLS OF PARAMETER ESTIMATION: THE PDF, CDF AND QUANTILE FUNCTION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Estimating the Conversion Rate for Email Signup List\n",
    "a = 300\n",
    "b = 39700"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = beta.rvs(a, b, size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x170513ceee0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1680x840 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# few style changes to make plot prettier\n",
    "plt.figure(figsize=(12,6), dpi=140)\n",
    "sns.distplot(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability of the actual rate being lower than 0.0065"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007978686170177607"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [0, 0.0065]\n",
    "lowb= beta.sf(x, a, b)[0] - beta.sf(x, a, b)[1] \n",
    "lowb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability of conversion rate being higher than expected (0.0085 or higher)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01248151030012834"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [0.0085, 1]\n",
    "highb = beta.sf(x, a, b)[0] - beta.sf(x, a, b)[1] \n",
    "highb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5643565912870714"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratio = highb/lowb\n",
    "ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Code shown in the book as \"Using the CDF in R\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00797868617017764"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta.cdf(0.0065, 300, 39700)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01248151030012834"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta.cdf(1, 300, 39700) - beta.cdf(0.0085, 300, 39700)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating Quantiles in <s>R</s> Python :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008903462119414618"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta.ppf(0.999, 300, 39700)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finding 95% CI "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "lower_bound = beta.ppf(0.025, 300, 39700)\n",
    "upper_bound = beta.ppf(0.975, 300, 39700)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0066780740444127165"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lower_bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008368562363876286"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "upper_bound"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Using the code example for plotting the PDF on page 127, plot the CDF and quantile functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**CDF BETA (300, 39700)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.arange(0.005, 0.01, 0.00001)\n",
    "Y = beta.cdf(X, 300, 39700)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x170536dc5b0>"
      ]
     },
     "execution_count": 100,
     "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": [
    "sns.lineplot(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quantile of Beta (300, 39700)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.arange(0.001, 0.99, 0.001)\n",
    "Y = beta.ppf(X, 300, 39700)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x17054b05550>"
      ]
     },
     "execution_count": 117,
     "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": [
    "sns.lineplot(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Returning to the task of measuring snowfall from Chapter 10, say you have the following measurements (in inches) of snowfall:\n",
    "### 7.8, 9.4, 10.0, 7.9, 9.4, 7.0, 7.0, 7.1, 8.9, 7.4\n",
    "### What is your 99.9 percent confidence interval for the true value of snowfall?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "vals = np.array([7.8, 9.4, 10.0, 7.9, 9.4, 7.0, 7.0, 7.1, 8.9, 7.4])\n",
    "mu = vals.mean()\n",
    "sigma = vals.std(ddof=1)   # this argument is required to achieve same results as in R, since we are calculating sd for samples\n",
    "                           # and not for the population - by default ddof is 0 and it is calculating sd for population"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "lower = norm.ppf(0.0005, loc=mu, scale=sigma)\n",
    "upper = norm.ppf(0.9995, loc=mu, scale=sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.456061591417175"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.923938408582863"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "upper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. A child is going door to door selling candy bars. So far she has visited 30 houses and sold 10 candy bars. She will visit 40 more houses today. What is the 95 percent confidence interval for how many candy bars she will sell the rest of the day? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 10\n",
    "b = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "upper = beta.ppf(0.975, a, b)\n",
    "lower = beta.ppf(0.025, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.17938364923511183"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.50832335380999"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "upper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.0"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# extreme values for binomial distribution given that probability of selling a candy bar is 1/3\n",
    "binom.ppf(0.975, 40, 0.333)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.0"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# extreme values for binomial distribution given that probability of selling a candy bar is 1/3\n",
    "binom.ppf(0.025, 40, 0.333)"
   ]
  }
 ],
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