Building a bayesin AB test application.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": [
    "### Monte Carlo Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.95877"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_trials = 100000\n",
    "A = beta.rvs(39, 121, size = n_trials)\n",
    "B = beta.rvs(53, 107, size = n_trials)\n",
    "sum(B>A)/n_trials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\Miniconda\\envs\\datascience\\lib\\site-packages\\seaborn\\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting a histogram\n",
    "ratio = B/A\n",
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "sns.distplot(ratio,\n",
    "             ax=ax,\n",
    "             bins = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating an ecdf plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2eb68cbe160>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def ecdf(data):\n",
    "    x = np.sort(data)\n",
    "    n = x.size\n",
    "    y = np.arange(1, n+1)/n\n",
    "    return x, y\n",
    "\n",
    "x, y = ecdf(ratio)\n",
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "ax.plot(x,\n",
    "        y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q1. \n",
    "\n",
    "* Suppose a director of marketing with many years of experience tells you he believes very strongly that the variant without images (B) won’t perform any differently than the original variant. \n",
    "\n",
    "* How could you account for this in our model? Implement this change and see how your final conclusions change as well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.73708"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior_a = 300\n",
    "prior_b = 700\n",
    "A = beta.rvs(36 + prior_a, 114 + prior_b, size=n_trials)\n",
    "B = beta.rvs(50 +  prior_a, 100 +  prior_b, size=n_trials)\n",
    "sum(B>A)/n_trials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q2. \n",
    "\n",
    "* The lead designer sees your results and insists that there’s no way that variant B should perform better with no images. She feels that you should assume the conversion rate for variant B is closer to 20 percent than 30 percent. Implement a solution for this and again review the results of our analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.65523"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_prior_a = 30\n",
    "a_prior_b = 70\n",
    "\n",
    "b_prior_a = 20\n",
    "b_prior_b = 80\n",
    "\n",
    "A = beta.rvs(36 + a_prior_a, 114 + a_prior_b, size=n_trials)\n",
    "B = beta.rvs(50 + b_prior_a, 100 + b_prior_b, size=n_trials)\n",
    "sum(B>A)/n_trials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q3. \n",
    "\n",
    "* Assume that being 95 percent certain means that you’re more or less “convinced” of a hypothesis. Also assume that there’s no longer any limit to the number of emails you can send in your test. If the true conversion for A is 0.25 and for B is 0.3, explore how many samples it would take to convince the director of marketing that B was in fact superior. Explore the same for the lead designer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### `In case of director of marketing`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100\n",
      "200\n",
      "300\n",
      "400\n",
      "500\n",
      "600\n",
      "700\n",
      "800\n",
      "900\n",
      "1000\n",
      "1100\n",
      "1200\n",
      "1300\n",
      "1400\n",
      "1500\n",
      "1600\n",
      "1700\n",
      "1800\n",
      "1900\n"
     ]
    }
   ],
   "source": [
    "a_true_rate = 0.25\n",
    "b_true_rate = 0.3\n",
    "\n",
    "prior_a = 300\n",
    "prior_b = 700\n",
    "\n",
    "p_b_sup = 0\n",
    "n_samples = 0\n",
    "n_trials = 100000\n",
    "\n",
    "def b_supirior(B, A, n_trials):\n",
    "    return sum(B > A)/n_trials\n",
    "\n",
    "def draw_results(n_samples, rate):\n",
    "    results = []\n",
    "    for i in range(int(n_samples/2)):\n",
    "        draw = random.random()\n",
    "        results.append(draw)\n",
    "    results = np.array(results)\n",
    "    a = sum(results <= rate)\n",
    "    b = sum(results > rate)\n",
    "    return a, b\n",
    "\n",
    "while p_b_sup < 0.95:\n",
    "    n_samples += 100\n",
    "    a_samples_a, a_samples_b = draw_results(n_samples, a_true_rate)\n",
    "    b_samples_a, b_samples_b = draw_results(n_samples, b_true_rate)\n",
    "    a_samples = beta.rvs(a_samples_a + prior_a, a_samples_b + prior_b, size = n_trials)\n",
    "    b_samples = beta.rvs(b_samples_a + prior_a, b_samples_b + prior_b, size = n_trials)\n",
    "    p_b_sup = b_supirior(b_samples, a_samples, n_trials)\n",
    "    print(n_samples)\n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### `In case of lead designer`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100\n",
      "200\n",
      "300\n",
      "400\n",
      "500\n",
      "600\n",
      "700\n",
      "800\n",
      "900\n",
      "1000\n",
      "1100\n"
     ]
    }
   ],
   "source": [
    "a_true_rate = 0.2\n",
    "b_true_rate = 0.3\n",
    "\n",
    "prior_a = 300\n",
    "prior_b = 700\n",
    "\n",
    "p_b_sup = 0\n",
    "n_samples = 0\n",
    "n_trials = 100000\n",
    "\n",
    "def b_supirior(B, A, n_trials):\n",
    "    return sum(B > A)/n_trials\n",
    "\n",
    "def draw_results(n_samples, rate):\n",
    "    results = []\n",
    "    for i in range(int(n_samples/2)):\n",
    "        draw = random.random()\n",
    "        results.append(draw)\n",
    "    results = np.array(results)\n",
    "    a = sum(results <= rate)\n",
    "    b = sum(results > rate)\n",
    "    return a, b\n",
    "\n",
    "while p_b_sup < 0.95:\n",
    "    n_samples += 100\n",
    "    a_samples_a, a_samples_b = draw_results(n_samples, a_true_rate)\n",
    "    b_samples_a, b_samples_b = draw_results(n_samples, b_true_rate)\n",
    "    a_samples = beta.rvs(a_samples_a + prior_a, a_samples_b + prior_b, size = n_trials)\n",
    "    b_samples = beta.rvs(b_samples_a + prior_a, b_samples_b + prior_b, size = n_trials)\n",
    "    p_b_sup = b_supirior(b_samples, a_samples, n_trials)\n",
    "    print(n_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interactive A/B testing using ipywidget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from ipywidgets import interactive                        # widgets and interactivity\n",
    "from ipywidgets import widgets                            # widgets and interactivity\n",
    "import matplotlib; import matplotlib.pyplot as plt        # plotting\n",
    "from matplotlib.ticker import (MultipleLocator, AutoMinorLocator) # control of axes ticks\n",
    "plt.rc('axes', axisbelow=True)                  # set axes and grids in the background for all plots\n",
    "import numpy as np                                        # working with arrays\n",
    "from scipy.stats import triang                            # parametric distributions\n",
    "from scipy.stats import binom\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import beta, boxcox_normmax\n",
    "import seaborn as sns\n",
    "\n",
    "# Integer box for the model input\n",
    "\n",
    "A_converted = widgets.BoundedIntText(\n",
    "    value=39,\n",
    "    min=0,\n",
    "    max=10000,\n",
    "    step=1,\n",
    "    description='A_converted',\n",
    "    disabled=False\n",
    ")\n",
    "\n",
    "A_not_converted = widgets.BoundedIntText(\n",
    "    value=121,\n",
    "    min=0,\n",
    "    max=10000,\n",
    "    step=1,\n",
    "    description='A_not_converted',\n",
    "    disabled=False\n",
    ")\n",
    "\n",
    "B_converted = widgets.BoundedIntText(\n",
    "    value=53,\n",
    "    min=0,\n",
    "    max=10000,\n",
    "    step=1,\n",
    "    description='B_converted',\n",
    "    disabled=False\n",
    ")\n",
    "\n",
    "B_not_converted = widgets.BoundedIntText(\n",
    "    value=107,\n",
    "    min=0,\n",
    "    max=10000,\n",
    "    step=1,\n",
    "    description='B_not_converted',\n",
    "    disabled=False\n",
    ")\n",
    "\n",
    "Prior_a = widgets.BoundedIntText(\n",
    "    value=1,\n",
    "    min=0,\n",
    "    max=10000,\n",
    "    step=1,\n",
    "    description='Prior_A',\n",
    "    disabled=False\n",
    ")\n",
    "\n",
    "Prior_b = widgets.BoundedIntText(\n",
    "    value=1,\n",
    "    min=0,\n",
    "    max=10000,\n",
    "    step=1,\n",
    "    description='Prior_B',\n",
    "    disabled=False\n",
    ")\n",
    "\n",
    "\n",
    "ui = widgets.VBox([A_converted, A_not_converted, B_converted, B_not_converted, Prior_a, Prior_b],)\n",
    "\n",
    "def ecdf(data):\n",
    "    x = np.sort(data)\n",
    "    n = x.size\n",
    "    y = np.arange(1, n+1)/n\n",
    "    return x, y\n",
    "\n",
    "def f(A_converted, A_not_converted, B_converted, B_not_converted, Prior_a, Prior_b): \n",
    "\n",
    "    n_trials = 100000\n",
    "    A = beta.rvs(A_converted + Prior_a, A_not_converted + Prior_b, size = n_trials)\n",
    "    B = beta.rvs(B_converted + Prior_a, B_not_converted + Prior_b, size = n_trials)\n",
    "    # sum(B>A)/n_trials\n",
    "\n",
    "    ratio = B/A\n",
    "    fig, ax = plt.subplots(figsize=(7,4), nrows = 1, ncols = 2)\n",
    "    sns.distplot(ratio,\n",
    "                ax=ax[0],\n",
    "                bins = 20)\n",
    "    ax[0].set_title(\"Distribution of B/A\")\n",
    "\n",
    "    x, y = ecdf(ratio)\n",
    "    ax[1].plot(x,\n",
    "            y)\n",
    "    ax[1].set_title(\"ECDF of B/A\")\n",
    "\n",
    "interactive_plot = widgets.interactive_output(f, {'A_converted': A_converted,\n",
    "                                                  'A_not_converted': A_not_converted,\n",
    "                                                  'B_converted': B_converted,\n",
    "                                                  'B_not_converted': B_not_converted,\n",
    "                                                  'Prior_a': Prior_a, \n",
    "                                                  'Prior_b' : Prior_b})\n",
    "interactive_plot.clear_output(wait = True)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e23e233243484e4b9ad3907fd5377748",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(BoundedIntText(value=39, description='A_converted', max=10000), BoundedIntText(value=121, descr…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6c526d76a40842ff89dbe1639d52f3da",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output(outputs=({'name': 'stderr', 'text': 'd:\\\\Miniconda\\\\envs\\\\datascience\\\\lib\\\\site-packages\\\\seaborn\\\\dis…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(ui, interactive_plot) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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