{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Problem 1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import pandas\n",
      "\n",
      "def get_num_false_discoveries(m, alpha):\n",
      "    \"\"\"Return the number of false discoveries when applying the Benjamini-Hochberg\n",
      "    prescription with `alpha` to `m` uniformly distributed p-values.\"\"\"\n",
      "    pvals = np.random.random(m)\n",
      "    pvals.sort()\n",
      "    k = np.arange(1, len(pvals) + 1)\n",
      "    thresholds = k * (alpha / m)\n",
      "    return np.sum(pvals <= thresholds)\n",
      "\n",
      "def estimate_probs(m=50, alpha=0.05, num_simulations=10**5):\n",
      "    \"\"\"Estimate the probability of getting N=0, 1, 2, and 3 false discoveries\n",
      "    when applying the Benjamini-Hochberg prescription with `alpha` to `m` uniformly\n",
      "    distributed p-values.\"\"\"\n",
      "    counts = np.zeros(4)\n",
      "    for _ in xrange(num_simulations):\n",
      "        num_discoveries = get_num_false_discoveries(m, alpha)\n",
      "        if num_discoveries < len(counts):\n",
      "            counts[num_discoveries] += 1\n",
      "\n",
      "    probs = counts / counts.sum()\n",
      "    return probs\n",
      "\n",
      "for count, prob in enumerate(estimate_probs()):\n",
      "    print 'P({0}) = {1}'.format(count, prob)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(0) = 0.94991\n",
        "P(1) = 0.04654\n",
        "P(2) = 0.00327\n",
        "P(3) = 0.00028\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Problem 2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def collect_results(ms, alphas):\n",
      "    \"\"\"Collect probabilities of false discoveries for every combination of ms and alphas.\"\"\"\n",
      "    results = []\n",
      "    for m in ms:\n",
      "        for alpha in alphas:\n",
      "            result = [m, alpha]\n",
      "            result.extend(estimate_probs(m=m, alpha=alpha))\n",
      "            results.append(result)\n",
      "\n",
      "    return pandas.DataFrame(results, columns=['m', 'alpha', 'p0', 'p1', 'p2', 'p3'])\n",
      "\n",
      "def plot_results(results, x_var, logx=True):\n",
      "    fig, axs = plt.subplots(2, 2, figsize=(6, 6))\n",
      "    for num_discoveries in xrange(4):\n",
      "        row = num_discoveries // 2\n",
      "        col = num_discoveries % 2\n",
      "        x_axis = results[x_var]\n",
      "        probs = results['p{0}'.format(num_discoveries)]\n",
      "        axs[row][col].plot(x_axis, probs, marker='o')\n",
      "        axs[row][col].set_xscale('log')\n",
      "        axs[row][col].set_title('p{0}'.format(num_discoveries))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Collect and plot results for varying values of alpha."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vary_alpha_results = collect_results([50], [0.0001, 0.001, 0.01, 0.1, 0.5])\n",
      "vary_alpha_results"
     ],
     "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>m</th>\n",
        "      <th>alpha</th>\n",
        "      <th>p0</th>\n",
        "      <th>p1</th>\n",
        "      <th>p2</th>\n",
        "      <th>p3</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 50</td>\n",
        "      <td> 0.0001</td>\n",
        "      <td> 0.999910</td>\n",
        "      <td> 0.000090</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 50</td>\n",
        "      <td> 0.0010</td>\n",
        "      <td> 0.999080</td>\n",
        "      <td> 0.000920</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 50</td>\n",
        "      <td> 0.0100</td>\n",
        "      <td> 0.990490</td>\n",
        "      <td> 0.009420</td>\n",
        "      <td> 0.000090</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 50</td>\n",
        "      <td> 0.1000</td>\n",
        "      <td> 0.898847</td>\n",
        "      <td> 0.087688</td>\n",
        "      <td> 0.011555</td>\n",
        "      <td> 0.001911</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 50</td>\n",
        "      <td> 0.5000</td>\n",
        "      <td> 0.571245</td>\n",
        "      <td> 0.232542</td>\n",
        "      <td> 0.123220</td>\n",
        "      <td> 0.072992</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 6 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "    m   alpha        p0        p1        p2        p3\n",
        "0  50  0.0001  0.999910  0.000090  0.000000  0.000000\n",
        "1  50  0.0010  0.999080  0.000920  0.000000  0.000000\n",
        "2  50  0.0100  0.990490  0.009420  0.000090  0.000000\n",
        "3  50  0.1000  0.898847  0.087688  0.011555  0.001911\n",
        "4  50  0.5000  0.571245  0.232542  0.123220  0.072992\n",
        "\n",
        "[5 rows x 6 columns]"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_results(vary_alpha_results, 'alpha')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AsrNXYsOGgzJFxV/1FWt9fHwwceJE/Yq1VavWLl++HPfv38ecOXMQGBiIfo9KoNV1LCHm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\nSNAXDIqE7gfAnPIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107aece10>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Collect and plot results for varying values of m."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vary_m_results = collect_results([5, 50, 500, 5000, 50000], [0.05])\n",
      "vary_m_results"
     ],
     "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>m</th>\n",
        "      <th>alpha</th>\n",
        "      <th>p0</th>\n",
        "      <th>p1</th>\n",
        "      <th>p2</th>\n",
        "      <th>p3</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>     5</td>\n",
        "      <td> 0.05</td>\n",
        "      <td> 0.949959</td>\n",
        "      <td> 0.047080</td>\n",
        "      <td> 0.00289</td>\n",
        "      <td> 0.00007</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>    50</td>\n",
        "      <td> 0.05</td>\n",
        "      <td> 0.949988</td>\n",
        "      <td> 0.046511</td>\n",
        "      <td> 0.00323</td>\n",
        "      <td> 0.00027</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>   500</td>\n",
        "      <td> 0.05</td>\n",
        "      <td> 0.950659</td>\n",
        "      <td> 0.045651</td>\n",
        "      <td> 0.00330</td>\n",
        "      <td> 0.00039</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>  5000</td>\n",
        "      <td> 0.05</td>\n",
        "      <td> 0.949107</td>\n",
        "      <td> 0.047523</td>\n",
        "      <td> 0.00308</td>\n",
        "      <td> 0.00029</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 50000</td>\n",
        "      <td> 0.05</td>\n",
        "      <td> 0.950880</td>\n",
        "      <td> 0.045400</td>\n",
        "      <td> 0.00342</td>\n",
        "      <td> 0.00030</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 6 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "       m  alpha        p0        p1       p2       p3\n",
        "0      5   0.05  0.949959  0.047080  0.00289  0.00007\n",
        "1     50   0.05  0.949988  0.046511  0.00323  0.00027\n",
        "2    500   0.05  0.950659  0.045651  0.00330  0.00039\n",
        "3   5000   0.05  0.949107  0.047523  0.00308  0.00029\n",
        "4  50000   0.05  0.950880  0.045400  0.00342  0.00030\n",
        "\n",
        "[5 rows x 6 columns]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_results(vary_m_results, 'm')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fH2QyGXJychqeDZ2IN98UFkZJpWJ7YpzBg4UZHWKPVRMJe2BY2sMwJ7arx2lY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\nnMUVDZu22dOw0WhEREQEALG/t9FotLAPs7E4R6vVIiEhAVu2DGwk5Q+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       "text": [
        "<matplotlib.figure.Figure at 0x107fc53d0>"
       ]
      }
     ],
     "prompt_number": 10
    }
   ],
   "metadata": {}
  }
 ]
}