KCBO Demonstration.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "KCBO"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### *Introducing a new Bayesian Data Analysis Toolkit*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "KCBO is a toolkit for anyone who wants to do Bayesian data analysis without worrying about all the implementation details for a certain test. \n",
      "\n",
      "Currently KCBO is very much alpha/pre-alpha software and only implements a three tests. [Here](https://github.com/HHammond/kcbo/blob/master/Objectives.md) is a list of future objectives for the project."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Installation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "KCBO is available through PyPI and on [Github here](https://github.com/HHammond/kcbo). The following commands will install KCBO:\n",
      "\n",
      "\n",
      "### From PyPI:\n",
      "\n",
      "```\n",
      "pip install kcbo\n",
      "```\n",
      "\n",
      "### From Source:\n",
      "\n",
      "```\n",
      "git clone https://github.com/HHammond/kcbo\n",
      "cd kcbo\n",
      "python setup.py sdist install\n",
      "```\n",
      "\n",
      "If any of this fails, you may need to install numpy (`pip install numpy`) in order to install some dependencies of KCBO, then retry installing it."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Usage"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are currently three tests implemented in the KCBO library:\n",
      "\n",
      "* Lognormal-Difference of medians: used to compare medians of log-normal distributed data with the same variance.\n",
      "\n",
      "* Bayesian t-Test: an implementation of Kruschke's t-Test.\n",
      "\n",
      "* Conversion Test: test of conversion to success using the Beta-Binomial model. Popular in A/B testing and estimation."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Examples:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from kcbo import lognormal_comparison_test, t_test, conversion_test"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import numpy as np\n",
      "from matplotlib import pyplot as plt\n",
      "import seaborn as sns\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Lognormal-Difference of Medians test"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note: Because this test uses an MC simulation on the lognormal distribution conjugate prior, it assumes that both distributions have the same variance."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Generate some data\n",
      "g1d = np.random.lognormal(mean=3, sigma=1, size=10000)\n",
      "g1l = ['A'] * g1d.shape[0]\n",
      "g2d = np.random.lognormal(mean=3.03, sigma=1, size=10000)\n",
      "g2l = ['B'] * g2d.shape[0]\n",
      "\n",
      "g1 = pd.DataFrame(data=g1d, columns=['value'])\n",
      "g1['group'] = g1l\n",
      "g2 = pd.DataFrame(data=g2d, columns=['value'])\n",
      "g2['group'] = g2l\n",
      "\n",
      "lognormal_data = pd.concat([g1, g2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "summary, data = lognormal_comparison_test(lognormal_data, samples=100000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print summary"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                        Lognormal Median Comparison Test                        \n",
        "\n",
        "Groups: A, B\n",
        "\n",
        "Estimates:\n",
        "\n",
        "| Group   |   Median |   95% CI Lower |   95% CI Upper |      Mu |   95% CI Lower |   95% CI Upper |\n",
        "|:--------|---------:|---------------:|---------------:|--------:|---------------:|---------------:|\n",
        "| A       |  19.7915 |        19.3976 |        20.1921 | 2.9852  |        2.96515 |        3.00529 |\n",
        "| B       |  20.3804 |        19.9753 |        20.7924 | 3.01452 |        2.9945  |        3.03459 |\n",
        "\n",
        "Comparisions:\n",
        "\n",
        "| Hypothesis   |   Difference of Medians |   P.Value |   95% CI Lower |   95% CI Upper |\n",
        "|:-------------|------------------------:|----------:|---------------:|---------------:|\n",
        "| A < B        |                 0.58924 |   0.97753 |      0.0129132 |        1.15935 |\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A,B = data['A']['median'], data['B']['median']\n",
      "diff = data[('A','B')]['diff_medians']\n",
      "\n",
      "f, axes = plt.subplots(1,2, figsize=(12, 7))\n",
      "sns.set(style=\"white\", palette=\"muted\")\n",
      "sns.despine(left=True)\n",
      "\n",
      "sns.distplot(A, ax=axes[0], label='Median Estimate Density for A')\n",
      "sns.distplot(B, ax=axes[0], label='Median Estimate Density for B')\n",
      "sns.distplot(diff, ax=axes[1], label='Difference of Densities (B-A)')\n",
      "\n",
      "axes[0].legend()\n",
      "axes[1].legend()\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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UVlZWx7Fjx35ORNSrV6+j69at+59ig4KCCtesWbNEKBQa9Xq9TCaTaYiIfH19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\nguL/A19b0gd5JeTvAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ed3de50>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Bayesian t-Test"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Kruschke's implementation of the Bayesian t-Test. Since the implementation of this test uses PyMC2 and HMCMC it can take a while for the sampler to converge."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n1,n2 = (140,200)\n",
      "\n",
      "group1 = np.random.normal(15,2,n1)\n",
      "group2 = np.random.normal(15.7,2,n2)\n",
      "\n",
      "A = zip(['A']*n1, group1)\n",
      "B = zip(['B']*n2, group2)\n",
      "\n",
      "df = pd.concat([pd.DataFrame(A), pd.DataFrame(B)])\n",
      "df.columns = 'group','value'\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>group</th>\n",
        "      <th>value</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> A</td>\n",
        "      <td> 12.755334</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> A</td>\n",
        "      <td> 17.371657</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> A</td>\n",
        "      <td> 15.678301</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> A</td>\n",
        "      <td> 13.358686</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> A</td>\n",
        "      <td> 10.424609</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "  group      value\n",
        "0     A  12.755334\n",
        "1     A  17.371657\n",
        "2     A  15.678301\n",
        "3     A  13.358686\n",
        "4     A  10.424609"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "description, data = t_test(df,groupcol='group',valuecol='value',  samples=60000, progress_bar=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 1119 of 60000 complete in 0.5 sec"
       ]
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      {
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        "\r",
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     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print description"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                                Bayesian t-Test                                 \n",
        "\n",
        " \n",
        "\n",
        "| Hypothesis   |   Difference of Means |   P.Value |   95% CI Lower |   95% CI Upper |\n",
        "|:-------------|----------------------:|----------:|---------------:|---------------:|\n",
        "| A < B        |               1.02472 |         1 |        0.60196 |        1.44501 |\n",
        "\n",
        "| Hypothesis   |   Difference of S.Dev |   P.Value |   95% CI Lower |   95% CI Upper |\n",
        "|:-------------|----------------------:|----------:|---------------:|---------------:|\n",
        "| A < B        |             0.0458748 |         1 |       -0.25691 |       0.339418 |\n",
        "\n",
        "| Hypothesis   |   Effect Size |   P.Value |   95% CI Lower |   95% CI Upper |\n",
        "|:-------------|--------------:|----------:|---------------:|---------------:|\n",
        "| A < B        |      0.546456 |         1 |          0.317 |       0.775599 |\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "diff = data[('A', 'B')]['diff_means']\n",
      "\n",
      "f, axes = plt.subplots(1,1, figsize=(12, 7))\n",
      "sns.despine(left=True)\n",
      "sns.distplot(diff, label='Difference of Means').legend()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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uGwQQHSgfAICwGZj3GJ/HlqtzZRiGJo1NVHevqYpKtl4BiA6UDwBA2FRU+ZTk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\n6MbLspWS5LQ7EhAzDMPQlbPTdcWsdLV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bb731UPaqRaarzV1/f3/RsmXLPozFYn7HcYzD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\nSgxOAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ed38950>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Beta-Binomial Conversion Rate Test"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A common test in A/B tests is comparing the conversion rate between two features. Here we take the number of successes and total trials (or tests) and use the beta-binomial model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A = {'group':'A', 'trials': 10000, 'successes':5000}\n",
      "B = {'group':'B', 'trials': 8000, 'successes':4090}\n",
      "\n",
      "df = pd.DataFrame([A,B])\n",
      "df"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>group</th>\n",
        "      <th>successes</th>\n",
        "      <th>trials</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> A</td>\n",
        "      <td> 5000</td>\n",
        "      <td> 10000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> B</td>\n",
        "      <td> 4090</td>\n",
        "      <td>  8000</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "  group  successes  trials\n",
        "0     A       5000   10000\n",
        "1     B       4090    8000"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "summary, data = conversion_test(df, groupcol='group',successcol='successes',totalcol='trials')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print summary"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                       Beta-Binomial Conversion Rate Test                       \n",
        "\n",
        "Groups: A, B\n",
        "\n",
        "Estimates:\n",
        "\n",
        "| Group   |   Estimate |   95% CI Lower |   95% CI Upper |\n",
        "|:--------|-----------:|---------------:|---------------:|\n",
        "| A       |   0.500016 |       0.490261 |       0.509824 |\n",
        "| B       |   0.511272 |       0.500279 |       0.522188 |\n",
        "\n",
        "Comparisions:\n",
        "\n",
        "| Hypothesis   |   Difference |   P.Value |   95% CI Lower |   95% CI Upper |\n",
        "|:-------------|-------------:|----------:|---------------:|---------------:|\n",
        "| A < B        |    0.0112787 |   0.93366 |    -0.00343106 |      0.0259026 |\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A = data['A']['distribution']\n",
      "B = data['B']['distribution']\n",
      "diff = data[('A','B')]['distribution']\n",
      "\n",
      "f, axes = plt.subplots(1,2, figsize=(12, 7))\n",
      "sns.set(style=\"white\", palette=\"muted\")\n",
      "sns.despine(left=True)\n",
      "\n",
      "sns.distplot(A, ax=axes[0], label='Density Estimate for A')\n",
      "sns.distplot(B, ax=axes[0], label='Density Estimate for B')\n",
      "sns.distplot(diff, ax=axes[1], label='Difference of Densities (B-A)')\n",
      "\n",
      "axes[0].legend()\n",
      "axes[1].legend()\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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w+vRIuWD79sGXWQAA/9xSHq+lEUUxECFKUMGQjHKHH1mpeuikC7fy7tXVCAD4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       "text": [
        "<matplotlib.figure.Figure at 0x10f747650>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}