phewson/GibbsChangepoint.ipynb

## GibbsChangepoint.ipynb
{
 "metadata": {
  "name": "Gibbs Changepoint Coal"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Changepoint problem - Gibbs Sampler\n===================================\n\nThis is based on Example 5.1 (pages 143-5) \u2013 Figures 5.1 (page 144) and 5.2 (page 146) of [Gamerman and Lopes (2006) ](http://www.dme.ufrj.br/mcmc/) which in turn is based on an example of [Carlin, Gelfand and Smith (1992)](http://www.jstor.org/stable/2347570)\n\n# Poisson data with change point and conditionally conjugate Gamma priors:\n\nEssentially we consider count data where:\n$$Y_i ~ Poisson(\\lambda_i)$$\nsubject to \n\n$\\lambda_i =  \\lambda_b$ if year $<$ changepoint, and $\\lambda_i = \\lambda_a$ otherwise.   Assume $\\lambda_b ~ Gamma(\\alpha, \\beta)$ and $\\lambda_a ~ Gamma(\\gamma, \\delta)$.   I think we have discrete uniform prior on $Pr[Change = Year]$.   The posterior density is given by:\n\n$$f(\\lambda_b, \\lambda_a, changepoint) \\propto f(y_1, \\ldots, y_n | \\lambda_b, \\lambda_a, changepoint)p(\\lambda_b, \\lambda_a, changepoint)$.\n\nSetting the two sufficient statistics $s_b=\\sum_{i=1}^{changepoint} y_i$ and $s_a = sum_{changepoint+1}^n y_i$ we have the posterior as:\n\n$$f(\\lambda_b, \\lambda_a, changepoint) \\propto \\lambda_b^{\\alpha + s_m - 1} e^{-(\\beta+changepoint)\\lambda_b} \\lambda_a^{\\gamma+s_a-1} e^{-(\\delta s_a+n-changepoint)\\lambda_a}$$\n\nThis has three simple conditional densities which are specified later. \n\n\nIn total, there are 112 observations of $y_i$ from 1851 to 1962.\n\n\n\n\n\n\n\n"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "from numpy import array\n%load_ext rmagic ",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "First, load the data and plot it.   Note that we have years in actual years, and idx as a counter for years."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "disasters = ( 4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n                   3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n                   2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,\n                   1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n                   0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n                   3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n                   0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1)\nyears = range(1851,1962)\nlen(disasters)\nidx = range(111)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": "111"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%Rpush years disasters\n%R plot(years, disasters)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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Ll3WFQGhoKOLj4/HOO+/gypUrqFu3rv7TuK9iypQpCA8Px/79+/M8xoEDB3D58mVYW1tj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\nAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "Next, obtain cumulative totals.   Note that this is a slightly longwinded way of doing things, but we had an ulterior motive for wanting to use as much linear algebra as possible."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import numpy as np\nidxl = np.tril_indices(111)\nidxu = np.triu_indices(111)\n##create blank matrices of zeros\na=np.zeros(shape=(111,111))\nb=np.zeros(shape=(111,111))\n## Fill the upper triangle with ones\na[idxl] = 1\nb[idxu] = 1\n## Now get cumulative sums\ncumsumafter =  np.dot(b, disasters)\ncumsumbefore =  np.dot(a, disasters)\n## Now append zero at start/end as appropriate.\ncumsumafter = np.append(cumsumafter, 0)\ncumsumbefore = np.append(0, cumsumbefore)\n",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "Very simple plot of cumulative sums seems to show a change point."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%Rpush years cumsumbefore\n%R plot(years, cumsumbefore[-1])",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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JJ5+wbds2Xr58SUpKCrt27SIqKoq7d+8C0LNnTy5dusS8efNITEzEycmJuLg4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\nRJEAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "from scipy import random, exp\n\n#Provide values for the priors\nalphaprior = 0.001\nbetaprior = 0.001\ngammaprior = 0.001\ndeltaprior = 0.001\n\n\n",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## The last full conditional\n\nWe need to do the last thing first and define a function to calculate the messiest full conditional; namelt:\n\n$$f(changepoint) = \\frac{\\lambda_b^{\\alpha + s_m - 1} e^{-(\\beta+changepoint)\\lambda_b} \\lambda_a^{\\gamma+s_a-1} e^{-(\\delta s_a+n-changepoint)\\lambda_a}}{\\sum_{i=1}^n \\lambda_b^{\\alpha + s_m - 1} e^{-(\\beta+changepoint)\\lambda_b} \\lambda_a^{\\gamma+s_a-1} e^{-(\\delta s_a+n-changepoint)\\lambda_a}}$$\n\n* This ought perhaps be calculated as logs first (computational overflow looks like a risk here)\n* This is computed below by a loop which is inefficient\n* But first, a small function to calculate the numerator (and at least make sure this works OK)\n\nHaving computed these values, we can sample (random.choice in scipy) a changepoint value.\n\n"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "\ndef mprob(lb, la, ap, bp, gp, dp, m, sm, sl):\n        return (lb**(ap+sm-1))*(exp(-1*((bp)+m)*lb))*(la**(gp+sl-1))*(exp(-1*((dp)+(111-m))*la))",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "blah=np.zeros(111)\nfor i in range(111):\n    blah[i] = mprob(lambdabefore, lambdaafter, alphaprior, betaprior, gammaprior, deltaprior, i, cumsumbefore[i], cumsumafter[i]) \n    \ncondalpha =  blah / sum(blah)\nm=random.choice(range(111), size=1, replace = 0, p=condalpha)\n\n"
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "print lambdabefore\nprint lambdaafter"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "The easier full conditionals to simulate from are the two Poisson means.\n\n$$f(\\lambda_b) = Gamma(\\alpha + s_m, \\beta+changepoint)$$\nand\n$$f(\\lambda_b) = Gamma(\\gamma + s_l, \\delta + (n-changepoint))$$\n\nThis requires only the sufficient statistics $s_m$, $s_l$ and the current value of changepoint.\n\nThe Gibbs sampler proceeds in three stages:\n\n1. Simulate $\\lambda_b$ given current sufficient statistics and parameter value\n2. Simulate $\\lambda_a$ given current (updated) sufficient statistics and parameter values,\n3. Simulate $changepoint$ given current (updated) sufficient statistics and parameter values.\nRepeat."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "outlambdabefore=np.zeros(5000)\noutlambdaafter=np.zeros(5000)\noutm=np.zeros(5000)\n\noutlambdabefore[0]=12\noutlambdaafter[0]=3\noutm[0]=60\n\n\nfor iter in range(1,5000):\n    outlambdabefore[iter] = random.gamma(alphaprior+cumsumbefore[outm[iter-1]], 1.0/(betaprior+outm[iter-1])) \n    outlambdaafter[iter] = random.gamma(gammaprior+cumsumafter[outm[iter-1]], 1.0/(deltaprior+111-outm[iter-1])) \n\n    blah=np.zeros(111)\n    for i in range(111):\n        blah[i] = mprob(outlambdabefore[iter], outlambdaafter[iter], alphaprior, betaprior, gammaprior, deltaprior, i, cumsumbefore[i], cumsumafter[i]) \n    \n    condalpha =  blah / sum(blah)\n\n    outm[iter]=random.choice(range(0,111), size=1, replace = 0, p=condalpha)\n\n\n    ",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%Rpush outlambdabefore outlambdaafter outm\n%R plot(c(1:5000), outlambdabefore, type = \"l\")\n%R par(mfrow = c(2,2)); hist(outlambdabefore[c(1000:5000)], xlim = c(0,5)); hist(outlambdaafter[c(1000:5000)], xlim =c(0,5))\n%R plot(xtabs(~outm[c(1000:5000)]))\n%R acf(outlambdabefore[c(1000:5000)]) ; acf(outlambdaafter[c(1000:5000)])\n ",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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BAwBAnTp1MGHCBGzevNnricjIyMC0adPwyCOPYOPGjVi1ahWqVq2KGjVqYNiwYQzERERU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\n5F13pVKpEBYWhuvXr2P27Nn44osvsHr1agCW55Aj54k7lsWKigps3Lg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      },
      {
       "output_type": "display_data",
       "png": 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LE6aYV1dqaiopFAqNdqVSSRkZGVrX0TZGpZW+hKsmiouLtW5LpVJRSkpKuetU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\nbGyMTZs2YdKkSdi7dy8MDAzQsmVLDBs2DF999RU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      },
      {
       "output_type": "display_data",
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PP/yw+vTp48t8QKmUlBR16dLFdgwA8IhK3wMeOHCgGjZsqGPHjunee+9VRkaG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\nY4wxTzzxhElOTvZKBmMqfr4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      },
      {
       "output_type": "display_data",
       "png": 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AABZQwAAAWEABAwBgAQUMAIAFFDAAABZQwAAAWEABAwBgAQUMAIAFFDAAABZQ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\n5MKFCzbjXtbhw4dNzZo1zdmzZ40xxjz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      },
      {
       "output_type": "display_data",
       "png": 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BALCAAgYAwAIKGAAACyhgAAAsoIABALCAAgYAwAIKGAAACyhgAAAsoIABALCA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\nKGAAACyggAEAsOD/A/j5uxfkYU3NAAAAAElFTkSuQmCC\n"
      },
      {
       "output_type": "pyout",
       "prompt_number": 32,
       "text": "array([<rpy2.rinterface.SexpVector - Python:0x109ad4480 / R:0x7fe03ab56dd0>,\n       <rpy2.rinterface.SexpVector - Python:0x109ad4468 / R:0x7fe03d209a88>,\n       <rpy2.rinterface.SexpVector - Python:0x109ad4228 / R:0x7fe03d209a58>,\n       <rpy2.rinterface.SexpVector - Python:0x109ad4558 / R:0x7fe03ab56f20>,\n       <rpy2.rinterface.SexpVector - Python:0x109ad4570 / R:0x7fe03d209a28>,\n       rpy2.rinterface.NULL], dtype=object)"
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "* Note we are throwing away the first 1000 values as a burn in when plotting the posterior simulations\n* Note also that the change point is defined in terms of the index rather than years.   Add 1851 to these values (the posterior mode should be around 1890)"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "# Conclusions and to-do\n\nThis was a quick sketch of a Gibbs sampler for a rather famous change point problem.   The first thing to note is that analytic values are available and so the answers can be checked.\n\nAs a programming exercise there is still a little work: the way the posterior value for the change point is calculated currently uses a for loop which could be vectorised.   There are a few other efficiency tweaks that should be made.   But it appears that on the whole this works.\n"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}