Bayesian Statistics The Fun Way - Python Solutions # CHAPTER 19.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "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",
    "import random\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": [
    "# FROM HYPOTHESIS TESTING TO PARAMETER ESTIMATION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is the Carnival Game Really Fair?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = 0.5\n",
    "k = 24\n",
    "n = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.050013106514625e-08"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binom.cdf(k=k, n=n, p=p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dx = 0.01\n",
    "htess = np.arange(start=0, stop=1.01, step=dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "h_bottom = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bayes_factor(h_top, h_bottom):\n",
    "    ratio = ((h_top**24) * (1-h_top)**76) / ((h_bottom**24) * (1-h_bottom)**76)\n",
    "    return ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "bfs = []\n",
    "for val in htess:\n",
    "    bfs.append(bayes_factor(val, h_bottom))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x13d49687790>"
      ]
     },
     "execution_count": 9,
     "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(htess, bfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1478775.9567598568"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(bfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfs.index(max(bfs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "htess[bfs.index(max(bfs))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding Priors to Our Likelihood Ratios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "priors = []\n",
    "for val in htess:\n",
    "    if val <= 0.3 and val >= 0.2:\n",
    "        prior = 0.001\n",
    "    else:\n",
    "        prior = 1\n",
    "    priors.append(prior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x13d4b79f310>"
      ]
     },
     "execution_count": 14,
     "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(htess, priors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "priors = np.array(priors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "posteriors = priors * bfs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x13d4c7ceeb0>"
      ]
     },
     "execution_count": 17,
     "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(htess, posteriors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3140687.468075799"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(posteriors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalizing posteriors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_posteriors = posteriors/sum(posteriors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x13d4c8010a0>"
      ]
     },
     "execution_count": 20,
     "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(htess, p_posteriors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "filtr = np.where(htess < 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999995179170433"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(p_posteriors[filtr])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24027039578371676"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(p_posteriors * htess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "max_filtr = np.where(max(p_posteriors))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21924146853825416"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(p_posteriors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "likely = np.where(p_posteriors == max(p_posteriors))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.19])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "htess[likely]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the Bayes Factor to Parameter Estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_of_trials = 1000   # number of times we will simulate an event\n",
    "a = 24\n",
    "b = 76\n",
    "r = beta.rvs(a, b, size=num_of_trials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1)"
      ]
     },
     "execution_count": 29,
     "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": [
    "plt.figure(figsize=(12,6), dpi=140)\n",
    "\n",
    "ax = sns.distplot(r)\n",
    "ax.set_xlim(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_of_trials = 1000   # number of times we will simulate an event\n",
    "a = 24\n",
    "b = 76\n",
    "r = beta.rvs(a + 1, b + 1, size=num_of_trials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1)"
      ]
     },
     "execution_count": 31,
     "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": [
    "plt.figure(figsize=(12,6), dpi=140)\n",
    "\n",
    "ax = sns.distplot(r)\n",
    "ax.set_xlim(0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Our Bayes factor assumed that we were looking at H1: P(prize) = 0.5. This allowed us to derive a version of the beta distribution with an alpha of 1 and a beta of 1. Would it matter if we chose a different probability for H1 ? Assume H1 is P(prize) = 0.24 , then see if the resulting distribution, once normalized to sum to 1, is any different than the original hypothesis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x13d4c801130>"
      ]
     },
     "execution_count": 32,
     "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": [
    "dx = 0.01\n",
    "h_bottom = 0.24\n",
    "htess = np.arange(start=0, stop=1.01, step=dx)\n",
    "bfs = []\n",
    "for val in htess:\n",
    "    bfs.append(bayes_factor(val, h_bottom))\n",
    "\n",
    "sns.lineplot(htess, bfs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Write a prior for the distribution in which each hypothesis is 1.05 times more likely than the previous hypothesis (assume our dx remains the same)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(bfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "vals = [1]\n",
    "for i in range(len(bfs) - 1):\n",
    "    vals.append(1.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "priors = np.cumprod(vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x13d4c97f190>"
      ]
     },
     "execution_count": 36,
     "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": [
    "posteriors = bfs * priors\n",
    "p_posteriors = posteriors/sum(posteriors)\n",
    "sns.lineplot(htess, p_posteriors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Suppose you observed another duck game that included 34 ducks with prizes and 66 ducks without prizes. How would you set up a test to determine “What is the probability that you have a better chance of winning a prize in this game than in the game we used in our example?” Implementing this requires a bit more sophistication than the R used in this book, but see if you can learn this on your own to kick off your adventures in more advanced Bayesian statistics!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Old game\n",
    "num_of_trials = 100000   # number of times we will simulate an event\n",
    "a = 24\n",
    "b = 76\n",
    "A = beta.rvs(a + 1, b + 1, size=num_of_trials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# New game\n",
    "a2 = 34\n",
    "b2 = 66\n",
    "B = beta.rvs(a2 + 1, b2 + 1, size=num_of_trials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.93807"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(B > A)/num_of_trials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ecdf(data):\n",
    "    \"\"\" Compute ECDF \"\"\"\n",
    "    x = np.sort(data)\n",
    "    n = x.size\n",
    "    y = np.arange(1, n+1) / n\n",
    "    return(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "ratios = B/A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y = ecdf(ratios)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x13d4cdcab80>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mdht8uNVz8nfiyH7Y4qJMrkhE2kMBIB32+dcnOeU4B8CNY9NMrkZE2ksBIB22pnHo56iBPenXM97kakSkvRQA0iH245V8fcgBeIZ+ikjwUABIh/zvtkMA9OvZjSsze5hcjYhcCgWAXDbnuXo+230cgG9/K00XfokEGQWAXLbNXx6jzuUmJsrKxBF9zS5HRC5RuwNg1apV3HTTTYwaNYr8/HxWrlzZ5vPdbjfPP/88N9xwA6NGjeKWW27hvffe63DBEhgMw2D9F4cBmDA8hbiYSJMrEpFL1a6/2qKiIgoKCpg9ezZ5eXmsXbuWefPmERsby/Tp01td59e//jVvvvkmDz30EEOHDuW9997j3/7t37DZbFx33XWd+iHE/74+5OBoeTWALvwSCVLtCoDFixeTn5/PggULAMjLy8PhcLBkyZJWA8But/Pqq6/yn//5n9x+++0ATJgwgYMHD/LRRx8pAELAhsat/6y+CWT2TTC5GhG5HD4DoKysDLvdzkMPPeTVPm3aNIqKiigrKyM93Xv439q1a4mNjWXmzJle7a+88konlCxmc56r5+97TwIwebS2/kWClc9zAMXFxQBkZ3vf2DszMxOAkpKSFuvs27eP7OxsNm/ezK233sqwYcOYOnUq77//fmfULCbb/NUxXA2ek7/jr9SsnyLByuceQGVlJQA2m82rPT7ec8VnVVVVi3UqKio4evQoCxYs4F//9V9JS0tjxYoVPPjggyQnJ3PNNddccqEWCyQmxl3yesEgMtIKBMfnMwyDj3YeBeDa0f1J6R1ch3+Cqa+DmfrZf9rqa18js30GgGEYjS9kabU9IqLlTkR9fT0VFRW88MILXH/99YDnHEBxcTHPPffcZQWABIa9pac5dMIT+lNzMkyuRkQ6wmcAJCR4tvAu3NJ3Op1ey88XHx+P1WolNze3uc1isTBx4kTeeuutyyrUMMDhqLmsdQNdU3IHw+db+1kp4LnlY8/46KCo+XzB1NfBTP3sP231dc+etjb3AnyeA2g69m+3273aS0tLvZafLzMzE7fbjcvl8mqvr6/X1aJBrN7l5u97Pbd8nDAsxeRqRKSjfAZAZmYmaWlprF692qt9zZo1ZGVlkZqa2mKdvLw8DMOgqKiouc3lcvHRRx8xZsyYTihbzLBj/ymc51xEWCzkDNeVvyLBrl3XAcydO5fCwkISExOZPHky69ato6ioiKeeegrwnPS12+0MGjQIm83GhAkTuO666/jVr35FdXU1WVlZvPbaaxw+fJgnn3yySz+QdJ2Pv/Sc/B0xIJnE+GiTqxGRjmpXAMyaNYu6ujqWLVvGihUrSE9PZ+HChcyYMQOA9evXU1hYyPLly8nJyQHgmWeeYcmSJbz44os4HA6GDRvGsmXLGDFiRNd9GukyDmcdXxVXADBpZD+TqxGRzmAxmobzBDi326C8vOWQ01AQDCfMPthi5811+4mPjWTx/ZOIigzOeQSDoa9DgfrZf3ydBI6IuPh51+D8Kxa/MgyDTY2Hf8ZfmRK0X/4i4k1/yeKT/XgVh056hv1OHKmTvyKhQgEgPm36yrP1369nNwb0625yNSLSWRQA0iZXg5tPd3nu+jVxRF9dxyESQhQA0qYvD5RTVVOPBZigsf8iIUUBIG3a9NUxAIZl9SC5e6zJ1YhIZ1IAyEVV1dSzY/8pAHI19l8k5CgA5KI+232cBrdBbLSV0YN7m12OiHQyBYBcVNPUD+OG9iEmympyNSLS2RQA0qrDJ6soPea5GZAO/4iEJgWAtKrp5G/vpFiuSEs0uRoR6QoKAGmhwe3mk8YAyB3RT2P/RUKUAkBa2FVyGoezDvBc/CUioUkBIC1sbpz6YWhGEr2SdFNvkVClABAv1efq2f4Pz9j/iSN08lcklCkAxMuWPSdwNbiJjopgzBCN/RcJZQoA8bJ5l+fk75jBfYiLadcN40QkSCkApNkpRw37DzkAnfwVCQcKAGn2970nAOjeLYqhmUkmVyMiXU0BIM0+2+2Z93/s0D5YI/SrIRLq9FcuABwtd2I/XgVAzrAUk6sREX9QAAjwzdZ/cvcYBvbX1A8i4UABIBiGwaeNAZBzZQoRmvpBJCwoAITio2c5cboGgGt020eRsKEAELbs9oz+6d8rnvQ+NpOrERF/UQCEObfbYMvexsM/OvkrElYUAGFur/00jirPzJ/jFQAiYaXdAbBq1SpuuukmRo0aRX5+PitXrmz3mxw9epQxY8bwm9/85rKKlK7TdPJ3YP/u9NHMnyJhpV0BUFRUREFBAbm5uSxdupTx48czb948Vq9e7XNdwzBYsGABVVVVHS5WOle9q4Ft+zzH/3Ou1Na/SLhp12xfixcvJj8/nwULFgCQl5eHw+FgyZIlTJ8+vc11X3vtNYqLizteqXS6HfvLqaltIMJiYbwCQCTs+NwDKCsrw263M3XqVK/2adOmUVxcTFlZWZvrLlq0iP/6r//qeKXS6T5pnPlzeHYy3eOjTa5GRPzN5x5A09Z7dna2V3tmZiYAJSUlpKent1jP7XYzf/588vPzufbaaztcqMUCiYmheYw6MtIK+PfzVdXU82VxBQDfHpsesn17ITP6Ohypn/2nrb72dU2nzwCorKwEwGbzHh8eHx8PcNFj+3/84x8pKyvjhRde8PUWYoJPvjyKq8FNbLSV8cN1+EckHPkMAMMwALBcECVN7RGtzBpZXFzM008/zTPPPENCQkJn1IlhgMNR0ymvFWiaktufn+9vWz2H7q6+ohe1NfXU1tT77b3NZEZfhyP1s/+01dc9e9ra3AvweQ6g6Qv8wi19p9PptbxJQ0MD8+fPZ/r06eTm5uJyuXC5XIDnsFDTYzHPqTM17Cs7A8A1wzT1g0i48hkATcf+7Xa7V3tpaanX8iZHjx5lx44drFy5kuHDhzf/D+DZZ59tfizmaRr7nxgfzfDsHiZXIyJm8XkIKDMzk7S0NFavXs2NN97Y3L5mzRqysrJITU31en6fPn146623WrzO9773Pe68806++93vdkLZ0hFb9njG/o+7Ujd+EQln7boOYO7cuRQWFpKYmMjkyZNZt24dRUVFPPXUUwBUVFRgt9sZNGgQNpuNkSNHtvo6ffr0uegy8Y+j5U4OnfQcztPYf5Hw1q7Nv1mzZvHII4/w8ccfM3fuXLZs2cLChQuZMWMGAOvXr+eOO+5g165dXVqsdFzT1n/P7jEMTO1ucjUiYiaL0TScJ8C53Qbl5aE5nYS/RkwYhsEvfvcZxyqqmT4+g+9/e1CXvl8g0ugU/1A/+4+vUUARERcfBqQDwGHk4LFKjlVUA5r6WUQUAGHlk688Uz+k9oonI0U3fhEJdwqAMOFqcDcP/5w4om+LC/tEJPwoAMLEVyUVVNXUYwEm6L6/IoICIGx82jjz59DMHvRIiDG5GhEJBAqAMFBT6+KLr08BOvkrIt9QAISBz78+SZ3LTaTVwtghvc0uR0QChAIgDHy6y3Py96qBvegWG2VyNSISKBQAIc7hrGP3wdMAXKN5/0XkPAqAEPf3PcdxGwZxMZGMGtjT7HJEJIAoAEJc09j/sUN6E9V46zgREVAAhLTjp6spPnIWgGs0+kdELqAACGGfNZ78TbJFMyRDN34REW8KgBBlGAafNB7+GX9lSpszAopIeFIAhKgDh89yvHHmz4kjNPWDiLSkAAhRH395FICMFBsZKQkmVyMigUgBEIJq6xr4bI/n8E/uyH4mVyMigUoBEIK2/eMEtXUNRFotmvlTRC5KARCCNjfe+OWqQb2wxWnqBxFpnQIgxJyurGVP49QPuSN0+EdELk4BEGI+2XUMA7DFRTFiQLLZ5YhIAFMAhBDDMNjUOPonZ1gKkVb95xWRi9M3RAgpPnqWo+Wesf+TNPpHRHxQAISQDV8cASC9j43Mvhr7LyJtUwCEiOpzLrY0jv2/7upUk6sRkWCgAAgRn+0+Rl29m+ioCK4ZprH/IuJbuwNg1apV3HTTTYwaNYr8/HxWrlzZ5vNPnjzJww8/zPXXX8/o0aOZNWsWRUVFHS5YWjIMg407PCd/xw3tQ7fYSJMrEpFg0K5viqKiIgoKCpg9ezZ5eXmsXbuWefPmERsby/Tp01s8v66ujnvvvZfKykoeeOAB+vTpwwcffMDPfvYzGhoauPnmmzv9g4SzA0fOUnq8EoDrru5vcjUiEizaFQCLFy8mPz+fBQsWAJCXl4fD4WDJkiWtBsDGjRvZu3cvK1asYNSoUQDk5uZy5MgRfve73ykAOtn/bjsEQGZKAgNTu5tcjYgEC5+HgMrKyrDb7UydOtWrfdq0aRQXF1NWVtZinfj4eO644w5Gjhzp1T5gwADsdnsHS5bznamqZeveEwDcMCYNi0Xz/otI+/jcAyguLgYgOzvbqz0zMxOAkpIS0tPTvZZNmDCBCRMmeLXV19ezYcMGrrjiig4VLN7+tv0wDW4DW1wUOcP6mF2OiAQRnwFQWek5tmyz2bza4+PjAaiqqmrXGy1atIiDBw+ydOnSS60RAIsFEhPjLmvdQBfZeLP2S/189a4GNu70jP2fmpNBr542H2vI5fa1XBr1s/+01de+Dgj4DADDMBpfyNJqe0RE20eRDMPgiSee4OWXX+aee+5hypQpvt5S2mnTzqM4quqwRliYfk2W2eWISJDxGQAJCZ4rSi/c0nc6nV7LW1NXV8f8+fN57733uOeee/j5z39+2YUaBjgcNZe9fiBrSu5L+XyGYfCX9fsBGDOkN5EYIds/nely+lounfrZf9rq6549bW3uBfgMgKZj/3a7nSFDhjS3l5aWei2/UFVVFXPmzGH79u0sWLCAf/7nf/b1VnIJdh2s4NBJTwhPz8kwuRoRCUY+RwFlZmaSlpbG6tWrvdrXrFlDVlYWqaktpx1oaGjgxz/+MTt27GDx4sX68u8Cqz/zjKYampFEVl8N/RSRS9eu6wDmzp1LYWEhiYmJTJ48mXXr1lFUVMRTTz0FQEVFBXa7nUGDBmGz2XjjjTfYsmULd9xxB/369eOLL75ofi2LxcJVV13VNZ8mTBw6WcXuxpu+aOtfRC5XuwJg1qxZ1NXVsWzZMlasWEF6ejoLFy5kxowZAKxfv57CwkKWL19OTk4OH3zwAQBvvvkmb775ptdrWa1Wdu/e3ckfI7x8+HfPtRcpyd0YMaCnydWISLCyGE3DeQKc221QXt6+IafB5lJOmJ111lHwm824GtzcPXUw138rravLCyk6Oekf6mf/8XUSOCLi4meBNRtokPnb54dxNbiJj41kou75KyIdoAAIIvWuBtZt98z7M3l0f2KirSZXJCLBTAEQRD7ZdZzK6nqsERa+rUM/ItJBCoAg4TYMihqHfuYMS6FHQozJFYlIsFMABIkte45zvMJzw/d8Df0UkU6gAAgCDW43Kz8qATzTPvTvrUnfRKTjFABB4NNdxzlxugYLMDNvgNnliEiIUAAEOFeDm1WbDwIwflgK/XvFm1uQiIQMBUCA2/DFEY6frsFigZsnZpldjoiEEAVAAKs+5+Kdjz3H/q+9KlVb/yLSqRQAAeyvm0qoqqknJsrKzEmtT7stInK5FAABqvRYJR9u9Uz6NmNCJok2jfsXkc6lAAhAhmHwypp9GAak9orXuH8R6RIKgAC0cccRDhw5C8DdUwcTadV/JhHpfPpmCTBnqmr5898OAHDN8BSGZPQwuSIRCVUKgADiNgx+/94eampd2OKiuPOGK8wuSURCmAIggKzZUsaukgoAZk8bQkK3aJMrEpFQpgAIEF+XneF/NngO/Vx7VSpjh/YxuSIRCXUKgADgPFfP4te30+A26Nezmw79iIhftOum8NJ1Gtxunnvjc06criE6MoKfzByhO32JiF9oD8BEhmHwx9X72L7vJAB33ThYUz2LiN8oAEz01voDfLzzKACzJg/k2qtSTa5IRMKJAsAkRZ+VNt/iccq4dO6aOsTkikQk3OgcgJ+5DYP3Nh/kL013+Brcm/tmjsRisZhcmYiEGwWAHznP1fPSu7vZcaAcgCsze3DfrcOxRujLX0T8TwHgJ/bjlSz9y5ecPHMOgMlXp3LnlMFEReoonIiYQwHQxdxugw1fHOaNdfupd7mJioxg9rQh5I7sZ3ZpIhLm2h0Aq1at4vnnn04d4rYAAAikSURBVKesrIz+/fszZ84cZs6cedHnO51OFi1axJo1a6iurmbs2LH84he/ICsrqzPqDniGYbDjQDlvbyjm0MkqAHonxTL3tpFkpCSYXJ2ISDsDoKioiIKCAmbPnk1eXh5r165l3rx5xMbGMn369FbXefDBB/nyyy/5+c9/Tnx8PM899xyzZ8/mvffeIyEhdL8AG9xudh4op+hTO/sPO5rbJ47oy51TriA+NsrE6kREvtGuAFi8eDH5+fksWLAAgLy8PBwOB0uWLGk1ALZu3cqGDRv43e9+x7XXXgvA2LFjueGGG3j99de57777OvEjmM95rp599jPsPljB1n0nOeusa142IjuZ264dQHa/7iZWKCLSks8AKCsrw26389BDD3m1T5s2jaKiIsrKykhPT/datmnTJuLj48nNzW1uS05OZty4cWzcuDHoAsDtNqiqqedMVS1nnXU4nHWcqarl+Okayo5XYT9RiWF883wLMCw7mZsnZGo+fxEJWD4DoLi4GIDsbO+bkmdmZgJQUlLSIgCKi4vJzMzEavWe0yYjI4OioqLLKtRigcTEuEtez1FVyyur91Jxtha3YeB2GxiG0fzYbdD408A473FdfQPn6hqorWugtr7B5/tEWi1ckd6Dbw3pzaSrUunTo1u7a4yM9PTT5Xw+uTTqa/9QP/tPW33t6/IinwFQWVkJgM3mPUdNfHw8AFVVVS3WqaqqavH8pnVae35X2rn/FOu2Heq017NGWEi0xZBki6ZPcjcyUhIYnNGDYVnJmsRNRIKKzwAwGo9tXHilalN7RETLcezG+cdDLtDa89vDMMDhqLnk9YakJfL96wdRWV1HRIQFi8VChAUiLBYsEec9tlgal3v+HRUZQUyUlZhoKzFRVhLioki0RRMfF0VEK7F6rqaOc5deHvBNcl/O55NLo772D/Wz/7TV1z172trcC/AZAE0jdi7ccnc6nV7Lz2ez2Th0qOVWt9PpbHXPoCvFRFmZnpPh1/cUEQkGPjfHm4792+12r/bS0lKv5ReuU1ZW1mJPoLS0tNXni4iI//kMgMzMTNLS0li9erVX+5o1a8jKyiI1teUUxpMmTeLs2bNs3ry5ua2iooKtW7cyceLETihbREQ6ql3XAcydO5fCwkISExOZPHky69ato6ioiKeeegrwfLnb7XYGDRqEzWZj3LhxjB8/noceeoiCggKSkpJ49tlnSUhI4M477+zSDyQiIu1jMdo6Y3ueN954g2XLlnH06FHS09O57777mqeCePvttyksLGT58uXk5OQA4HA4eOyxx1i7di1ut5sxY8Ywf/58BgwYcFmFut0G5eX+HUHkLzph5j/qa/9QP/uPr5PAEW3MNtzuADCbAkA6g/raP9TP/tORANBcxCIiYSpo9gCMxit1Q1HTON1Q/XyBRH3tH+pn/2mrry2WltdweS0PlgAQEZHOpUNAIiJhSgEgIhKmFAAiImFKASAiEqYUACIiYUoBICISphQAIiJhSgEgIhKmFAAiImFKASAiEqYUACIiYUoBICISphQAAWLPnj0MHz6cY8eOmV1KSHK73bz++uvccsstjB49milTpvDoo49SVRWa95gwi2EYvPzyy0ybNo1Ro0Zx66238u6775pdVsi7//77ufHGGy95vXbdElK6VnFxMXPmzMHlcpldSsh66aWXePrpp7nnnnuYMGECJSUlPPPMM+zfv5/f//73ZpcXMn7729/yzDPP8NOf/pSrr76ajRs3UlBQgNVqZcaMGWaXF5LeeecdPvzwQzIyMi55XU0HbSKXy8Wbb77Jk08+SVRUFGfOnGHDhg307dvX7NJCimEY5OTkcNNNN/Hv//7vze3vv/8+Dz74ICtXruTKK680scLQUF9fT25uLrfccgu//OUvm9vvvvtuGhoaeO2110ysLjQdP36cW265hbi4OKKjo/nwww8vaX3tAZho27ZtLFq0iHvuuYeUlBQefvhhs0sKSU6nk1tvvZX8/Hyv9qb7U9vtdgVAJ7BarfzpT38iKSnJqz0qKorq6mqTqgptDz/8MLm5ucTExLBt27ZLXl/nAEw0cOBA1q5dy/3334/VajW7nJBls9l4+OGHGTNmjFf72rVrARg0aJAZZYWciIgIhgwZQkpKCoZhcOrUKV588UU2b97MHXfcYXZ5IWfFihXs2rXLa2/rUmkPwES9evUyu4SwtWPHDl588UWmTJnCwIEDzS4n5KxZs4YHHngAgMmTJ3PrrbeaXFFoOXz4MI8++iiPPvooycnJl/062gOQsLNt2zbuvfde0tLS+NWvfmV2OSFp2LBhvPLKK/zyl79k+/bt3HfffWaXFDIMw2DBggVcd911TJs2rUOvpT0ACSvvv/8+8+fPJysri5deeokePXqYXVJISk9PJz09nXHjxmGz2Zg3bx6ff/45o0ePNru0oPfqq6+yb98+3n333eaRg01jeVwuF1artc0bwZ9PASBh4w9/+AMLFy5k/PjxLF26lISEBLNLCilnzpxh/fr1TJgwgZSUlOb2YcOGAZ4RK9JxH3zwAadPn2bSpEktlg0fPpxHH32UWbNmteu1FAASFlasWMFjjz3GjBkzWLhwIdHR0WaXFHLcbjfz58/nJz/5SfPxf4BNmzYBMHjwYLNKCymPPPIITqfTq23p0qXs2bOH5557jrS0tHa/lgJAQl55eTn//d//Tf/+/fnBD37A7t27vZZnZGR06ESaeCQnJ3PXXXfx4osvEhsby8iRI9m2bRu//e1vuf3225uH3UrHtNaPSUlJREdHM3LkyEt6LQWAhLyPPvqImpoaDh8+zA9+8IMWyx9//HG+853vmFBZ6CksLKRfv3689dZbPPvss/Tt25ef/vSn3HvvvWaXJq3QlcAiImFKw0BFRMKUAkBEJEwpAEREwpQCQEQkTCkARETClAJARCRMKQBERMKUAkBEJEwpAEREwtT/B+63ijvjzsXZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(x, y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x13d4ee95b50>"
      ]
     },
     "execution_count": 52,
     "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": [
    "plt.figure(figsize=(12,6), dpi=140)\n",
    "sns.distplot(ratios, kde=False, bins=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The author said that to solve this problem you will need to use a different approach than the one presented in the A/B testing chapter, although I am not sure why. I might be missing something, but I consider this problem to be very similar to what we have seen with e-mail conversion rates in chapter 15."
   ]
  }
 ],
 "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": "3.8.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}