Nick Wilson 04-11-14 Segment 33.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem 1"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**How many distinct m by n contingency tables are there that have exactly N total events?**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I used a resource (slide 58 of http://www.math.binghamton.edu/dikran/447/combinatorics.pdf) that I shamelessly stole from Ellen's page.\n",
      "\n",
      "Let $k = m \\times n$ be the number of cells in the contingency table. Then the number of distinct contingency tables with $N$ total events is:\n",
      "\n",
      "$$\n",
      "\\binom{N + k - 1}{k - 1} = \\binom{N + k - 1}{N}\n",
      "$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem 2"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**For every distinct 2 by 2 contingency table containing exactly 14 elements, compute its chi-square statistic, and also its Wald statistic. Display your results as a scatter plot of one statistic versus the other.**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats\n",
      "import itertools\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define functions for the statistics:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def chi_square(counts):\n",
      "    expected = scipy.stats.contingency.expected_freq(counts)\n",
      "    return np.sum((counts - expected)**2 / expected)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def wald_2x2(counts):\n",
      "    m, n = counts[0, 0], counts[0, 1]\n",
      "    M, N = counts.sum(axis=0)\n",
      "\n",
      "    p1_hat = m / float(M)\n",
      "    p2_hat = n / float(N)\n",
      "    p_hat = (m + n) / float(M + N)\n",
      "\n",
      "    numerator = p1_hat - p2_hat\n",
      "    denominator = np.sqrt(p_hat * (1 - p_hat) * ((1.0 / M) + (1.0 / N)))\n",
      "    return numerator / denominator\n",
      "\n",
      "arr = np.array([[1, 2], [3, 4]])\n",
      "print 'wald', wald_2x2(arr)\n",
      "print 'chi-square', chi_square(arr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "wald -0.28171808491\n",
        "chi-square 0.0793650793651\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define the method to iterate over all possible contingency tables.\n",
      "\n",
      "I use the intuition from the linked slides (see problem 1) to generate all possible 2x2 contingency tables containing 14 elements for problem 2. To do this, I first create a list of $N + k - 1 = 17$ numbers:\n",
      "\n",
      "`0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16`\n",
      "\n",
      "I then use Python's `itertools.combinations` method to get all combinations of $k - 1 = 3$ numbers from this list. Those 3 numbers represent the position of the separators, and the $N$ remaining numbers represent elements in the table. For example, the 3 numbers `2 9 16` partition the list into 4 sets:\n",
      "\n",
      "`0 1 | 3 4 5 6 7 8 | 10 11 12 13 14 15 |`\n",
      "\n",
      "Which give counts of 2, 6, 6, and 0 for each of the 4 cells.\n",
      "\n",
      "Note that while I only use this for 2x2 tables, it is general enough to work on tables of any size!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def iter_contingency_tables_counts(m, n, N):\n",
      "    num_separators = m * n - 1\n",
      "    num_positions = N + num_separators\n",
      "\n",
      "    for separators in itertools.combinations(xrange(num_positions), num_separators):\n",
      "        counts = []\n",
      "        accumulator = 0\n",
      "        for pos in xrange(num_positions):\n",
      "            if pos in separators:\n",
      "                counts.append(accumulator)\n",
      "                accumulator = 0\n",
      "            else:\n",
      "                accumulator += 1\n",
      "        counts.append(accumulator)\n",
      "\n",
      "        assert len(counts) == m * n\n",
      "        assert sum(counts) == N\n",
      "\n",
      "        yield np.asarray(counts).reshape((m, n))\n",
      "\n",
      "\n",
      "# Sanity check for a small example: verify there are not duplicate count\n",
      "# matrices.\n",
      "counts = [tuple(c.flatten()) for c in iter_contingency_tables_counts(2, 2, 8)]\n",
      "assert len(set(counts)) == len(counts)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, create a scatter plot of chi-square and Wald statistics."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "chi_squares = []\n",
      "walds = []\n",
      "for counts in iter_contingency_tables_counts(2, 2, 14):\n",
      "    if np.any(counts.sum(axis=0) == 0) or np.any(counts.sum(axis=1) == 0):\n",
      "        # Skip those with 0 marginals.\n",
      "        continue\n",
      "    chi_squares.append(chi_square(counts))\n",
      "    walds.append(wald_2x2(counts))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(chi_squares, walds)\n",
      "plt.xlabel('chi-square')\n",
      "plt.ylabel('wald')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.text.Text at 0xa7e330c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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Iw63u8Lgtr776Ko0apQJtCDahuZbbbrs6XuVKkvSznOGWlFCaN2/Pd981INhA5i3gW+Ab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\ncEuSJEkxZOGWJEmSYsjCLUmSJMXQ/wfS4soAxcaNoAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa7cfb2c>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Alternatively, use the absolute value of the Wald statistic:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(chi_squares, np.abs(walds))\n",
      "plt.xlabel('chi-square')\n",
      "plt.ylabel('abs(wald)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.text.Text at 0xa7e3f2c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rrF69ulxDxcXFHfe3jrFjxzJmzBgAhgwZwoIFC1i3bl3x8x9++CHDhg1j8eLF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\nYYSGhhoZGRlG3759jQkTJpgdyXKSk5ONXr16mR3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       "text": [
        "<matplotlib.figure.Figure at 0xa66502c>"
       ]
      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}