{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Hands On - MCMC methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the material of a Hands-On we had in the NeuroBiophysics research group of Institute of Physics of S\u00e3o Carlos (USP). As a part of a Journal Club, this followed the reading of the first chapter of classical textbook on Markov Chain Monte Carlo methods. For this reason, you may not find all the basic details of MCMC methods in here, as well as its derivation.\n", "\n", "We basically studied two separate cases. In *Part 1*, we are interested in drawing random samples from a given probability distribution so that we can perform a statistical inference. *Part 2* is then concerned with bayesian statistical inference using Markov Chains to draw samples from a posterior distribution, given a probabilistic model. In this later case, I have used the pymc package (currently in its version 2.2).\n", "\n", "\n", "I appreciate comments and suggestions.\n", "\n", "All the following python code and data is in WTFPL license (details in the end)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part 1 - Drawing from given distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's start with a simple Gibbs sampling process. The scenario can be the following. You have a very hard expression describing some probabilistic model over some variables (usually, way more than one). You cannot compute the marginal distributions, but can compute the conditionals. The objective is to construct a stationary Markov chain whose equilibrium distributions is exactly that hard distribution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import random, math\n", "from math import *\n", "import numpy as np\n", "import pylab as p\n", "import matplotlib.pyplot as plt\n", "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n", "\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 41 }, { "cell_type": "code", "collapsed": false, "input": [ "def gibbs(N=5000, thin=1000, outequilibrium=500):\n", " \n", " x0 = 0.\n", " y0 = 0.\n", " \n", " for i in range(outequilibrium):\n", " x0 = random.gammavariate(3, 1.0/( y0*y0 + 4 ) )\n", " y0 = random.gauss(1.0/( x0 + 1 ), 1.0/math.sqrt( 2*x0 + 2 ))\n", "\n", " x = np.array([x0])\n", " y = np.array([y0])\n", " \n", " xaux = x0\n", " yaux = y0\n", " \n", " for i in range(N):\n", " for j in range(thin):\n", " xaux = random.gammavariate(3, 1.0/( yaux*yaux + 4 ) )\n", " yaux = random.gauss(1.0/( xaux + 1 ), 1.0/math.sqrt( 2*xaux + 2 ))\n", " \n", " # Storing uncorrelated data\n", " x = np.append( x, xaux )\n", " y = np.append( y, yaux )\n", " \n", " return x,y" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 42 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's generate some observations" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x,y = gibbs(N=1000,thin=10)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now use them to evaluate some average values." ] }, { "cell_type": "code", "collapsed": false, "input": [ "m = np.mean(x)\n", "print ' = %f' %(m)\n", "\n", "m = np.mean(y)\n", "print ' = %f' %(m)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " = 0.649957\n", " = 0.638119\n" ] } ], "prompt_number": 44 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even some non-trivial average values..." ] }, { "cell_type": "code", "collapsed": false, "input": [ "n = x.shape[0]\n", "m = 0\n", "for j in range(n):\n", " m += x[j]*math.cos(y[j])\n", "m /= float(n)\n", "print '< X cos(Y) > = %f' %(m)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "< X cos(Y) > = 0.476095\n" ] } ], "prompt_number": 45 }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is very instructive to really see how the average values are evoling with the amount of monte carlo steps we are performing." ] }, { "cell_type": "code", "collapsed": false, "input": [ "Nmedias = 100\n", "Nj = 100\n", "\n", "avgX = np.array([])\n", "avgY = np.array([])\n", "x = np.array([])\n", "y = np.array([])\n", "\n", "for j in range(Nmedias):\n", " \n", " xn,yn = gibbs(N = Nj, thin = 50)\n", " \n", " x = np.append( x, xn )\n", " avgX = np.append( avgX, np.mean(x) )\n", " y = np.append( y, yn )\n", " avgY = np.append( avgY, np.mean(y) )\n", " \n", "\n", "plt.plot(avgX, '-r')\n", "plt.plot(avgY, '-b')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 49, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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hh/z9yM/nk9bhwxz4JeiLptCmAn9BAWBryz/2337j7lfNbdeu2rVoK6vaef6t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\n+KXGL4QQzccsAr/U+IUQovm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"text": [ "" ] } ], "prompt_number": 49 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, let's estimate the whole distribution from our observations" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Nbins = 30\n", "H, xedges, yedges = np.histogram2d(x, y, bins=( Nbins, Nbins) )\n", "extent = [yedges[0], yedges[-1], xedges[-1], xedges[0]]\n", "\n", "X, Y = np.meshgrid(xedges[0:Nbins], yedges[0:Nbins])\n", "\n", "fig = plt.figure()\n", "ax = fig.gca(projection='3d')\n", "ax = fig.add_subplot(111, projection='3d')\n", "surf = ax.plot_surface(X, Y, H, rstride=1, cstride=1, cmap=cm.coolwarm,\n", " linewidth=0, antialiased=False)\n", "\n", "#ax.set_zlim(-1.01, 1.01)\n", "ax.zaxis.set_major_locator(LinearLocator(10))\n", "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n", "\n", "fig.colorbar(surf, shrink=0.5, aspect=5)\n", "\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part 2 - Fitting from given distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I now move on to the second part and start to play with the pymc package. The main idea is to make an bayesian inference and find everything we can about a statistical mixture of a bimodal data set. As pointed out by *Brenno Barbosa*, this is indeed the subject of chapter 24 in the main reference I cited in the begin of this text (Gilks et al). In fact, you can check there for more information." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's start calling some important libraries" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%reset" ], "language": "python", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "stream": "stdout", "text": [ "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pylab\n", "\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 - Simple gaussian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To start understanding bayesian inference and how this can be implemented with pymc, we start with a simpler example: a normally distributed data set. See by yourself:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print 'Reading the data...'\n", "s = np.loadtxt('data/dados_nonmixture.data')\n", "\n", "\n", "print 'We have %d observations' %(s.shape[0])\n", "\n", "print 'Building histogram...'\n", "hist, bin_edges = np.histogram(s, density=True, bins=15)\n", "plt.bar(bin_edges[:-1], hist, width=0.2)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Reading the data...\n", "We have 2000 observations\n", "Building histogram...\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course we wouldn't need any bayesian inference to discover the average value and variance, but suppose we are not interested in these (even more, we are not frequentists, we are bayesians!). In fact what we want is to draw the distribution of both mean value and variance (i.e., they are not parameters anymore, they are random variable) given the data we have in our hands. We hope that the distribution has a small support and have a well defined bell shape, so that we can learn something about the mean and variance of the dataset." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We the following, we define a model in which the mean and variance (here given as precision = inverse of variance) are drawn from uniform distributions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Defining the model\n", "def mymodel():\n", " s = np.loadtxt('data/dados_nonmixture.data')\n", " mean = Uniform( 'mean', lower = s.min(), upper = s.max() )\n", " precision = Uniform('precision', lower = 0.0001, upper = 1.5)\n", " process = Normal('process', mu = mean, tau = precision, observed = True, value = s)\n", " return locals()\n", "\n", "\n", "# Model object\n", "model = MCMC( mymodel() )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To run the model, we just call the sample() method. The variable names are self-explanatory and match the names we have used in Part 1." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Sampling procedure\n", "model.sample( iter = 2000, thin = 10 , burn = 100)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 2000 of 2000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "model.stats()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 21, "text": [ "{'mean': {'95% HPD interval': array([-1.02737691, -0.95901627]),\n", " 'mc error': 0.0016671214231405488,\n", " 'mean': -0.98841406086924199,\n", " 'n': 190,\n", " 'quantiles': {2.5: -1.027376910881334,\n", " 25: -0.99926181151830407,\n", " 50: -0.98583565879817858,\n", " 75: -0.97672509856598488,\n", " 97.5: -0.95379519481852748},\n", " 'standard deviation': 0.017442049317452416},\n", " 'precision': {'95% HPD interval': array([ 1.49875542, 1.49959646]),\n", " 'mc error': 0.00045840846910202588,\n", " 'mean': 1.4986940543572966,\n", " 'n': 190,\n", " 'quantiles': {2.5: 1.4939545646260397,\n", " 25: 1.4987554173346109,\n", " 50: 1.4987554173346109,\n", " 75: 1.4994072196730017,\n", " 97.5: 1.4995964588047999},\n", " 'standard deviation': 0.003371510905781389}}" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check the mean and precision distributions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Checking the model variables\n", "Matplot.plot(model)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Plotting precision\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " mean\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Y81WHI19EREREJsTii4iIiMiEWHwRERER1cOeLyKSFTkd83LKhUhq7Pmqw5Ev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\nT09HVVUVZs+eDQBwd3fHiRMnGgfAngl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7ETtr/v7mqynlqkHlctbc6azxMKhOx5bH6tjR9HXt2gk5eSdPMqH0f/8H/OUv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\niExH02RtyZIlqKurw86dO7Fu3Tq0t7cHvH7rrbeiqakJn332GYqLi/H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"text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Please, draw your conclusions from the above distributions. Are both of them good enough? Are our priors good guesses? What needs to be changed? What can be changed?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also see a graphical representation of this model" ] }, { "cell_type": "code", "collapsed": false, "input": [ "graph = pymc.graph.graph(model)\n", "graph.write_png(\"graph_nomix.png\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 24, "text": [ "True" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 Simple statistical mixture" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Almost the same thing, but now with some interesting ingredient: we have a mixture of two gaussians. Our assumption now is that these observations are drawn from a gaussian with some average value with probability, say, p, and with some different average value with probability 1-p. We want to find out what are the mean values of each gaussian, variance and at what rate they are mixed.\n", "\n", "For the sake of simplicity, I'll assume both the gaussians have the same variance. This is far from being necessary. Now, you can start wondering how would you solve this problem without this assumption." ] }, { "cell_type": "code", "collapsed": false, "input": [ "print 'Reading the data...'\n", "s = np.loadtxt('data/dados_mixture.data')\n", "\n", "print 'We have %d observations' %(s.shape[0])\n", "\n", "print 'Building histogram...'\n", "hist, bin_edges = np.histogram(s, density=True, bins=15)\n", "plt.bar(bin_edges[:-1], hist, width=0.2)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Reading the data...\n", "We have 2000 observations\n", "Building histogram...\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 39 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our model will be as follows." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Definition of the model\n", "def hip():\n", " \n", " # This is the data\n", " s = np.loadtxt('data/dados_mixture.data')\n", " \n", " # The Bernoulli parameter\n", " theta = Uniform(\"theta\", lower = 0., upper = 1. )\n", " \n", " # Bernoulli process to mix the two distributions\n", " bern = Bernoulli(\"bern\", p = theta, size = s.shape[0])\n", " \n", " # Means and variances for the two gaussian distributions\n", " mean1 = Uniform('mean1', lower = s.min(), upper = s.max() )\n", " mean2 = Uniform('mean2', lower = s.min(), upper = s.max() )\n", " std_dev = Uniform('std_dev', lower = 0., upper = 5.)\n", " \n", " # Constructing the mean value for the mixed process\n", " @deterministic(plot = False)\n", " def mean(bern = bern, mean1 = mean1, mean2 = mean2):\n", " return bern * mean1 + (1 - bern) * mean2\n", " \n", " @deterministic(plot = False)\n", " def precision(std_dev = std_dev):\n", " return 1.0 / ( std_dev * std_dev )\n", " \n", " # The process itself \n", " process = Normal('process', mu = mean, tau = precision, value = s, \\\n", " observed = True) \n", " \n", " return locals()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "# Defining the model\n", "model = MCMC( hip() )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "# Steps\n", "MCstep = 200\n", "Nburns = 10000\n", "Nsteps = MCstep*200 + Nburns\n", "\n", "# Iteration process\n", "model.sample( iter = Nsteps, burn = Nburns, thin = MCstep )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 50000 of 50000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 29 }, { "cell_type": "code", "collapsed": false, "input": [ "model.stats( variables = ['mean1', 'mean2'] )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 38, "text": [ "{'mean1': {'95% HPD interval': array([-1.03187514, -0.3999318 ]),\n", " 'mc error': 0.022692637182771567,\n", " 'mean': -0.86364250126878428,\n", " 'n': 700,\n", " 'quantiles': {2.5: -1.0221344185334451,\n", " 25: -1.0084127363144639,\n", " 50: -0.99853025989043254,\n", " 75: -0.63354873573445469,\n", " 97.5: -0.29597917456679484},\n", " 'standard deviation': 0.23164490052596071},\n", " 'mean2': {'95% HPD interval': array([-0.63747047, 1.04457518]),\n", " 'mc error': 0.068787299351651399,\n", " 'mean': 0.55667255585550057,\n", " 'n': 700,\n", " 'quantiles': {2.5: -0.70568504677328225,\n", " 25: -0.43520448807601259,\n", " 50: 0.98332536793538394,\n", " 75: 1.0025922455921525,\n", " 97.5: 1.0299970299783643},\n", " 'standard deviation': 0.69400477536385885}}" ] } ], "prompt_number": 38 }, { "cell_type": "code", "collapsed": false, "input": [ "# Checking the dynamics of mean1 and mean2\n", "Matplot.plot( model.trace('mean1') )\n", "Matplot.plot( model.trace('mean2') )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Plotting mean1\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " mean2\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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YsMGyY8kXY/WLpS5HrEcPcq2MWfrGUYRYQwM5TKK4c4YoLibh5OOjLRxlR6x7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\ntXywRYza0Xsuld73j4iIAgcrYtSO3nOp9L5/REQUOFgRI6dgaikKpn2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1Fa6urhrb+fr6omXLlmjWrBns7e2RmZmp9z6efRYYNIiCodJSYPhw5WP1XTVp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\n6lrL4O11vs5Tc11ETkqW3b6+7l7r8nSu3mtdegCwRkzfE2vEAnnSfY2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"text": [ "" ] } ], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need more steps to reach convergence..." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Trying again with larger burn interval\n", "model.sample( iter = 800*MCstep, burn = 300*MCstep, thin = MCstep )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 160000 of 160000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 33 }, { "cell_type": "code", "collapsed": false, "input": [ "Matplot.plot( model.trace('mean1') )\n", "Matplot.plot( model.trace('mean2') )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Plotting mean1\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " mean2\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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LGre2Gq2WlcWa+BmSBbh43y+lWHOVuJnf8z17rLeJIAgiGPCTyKrawy0PdSXW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/w4ceAuTF5A8dAihyffas/7MdSeRUVASLL91+dA3k60Dn5jXs6CR+yInzuh4l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"text": [ "" ] } ], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now it seems that we have gone far enought to reach an equilibrium condition. Let's take a quick look into the other two variables." ] }, { "cell_type": "code", "collapsed": false, "input": [ "Matplot.plot( model.trace('theta') )\n", "Matplot.plot( model.trace('std_dev') )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Plotting theta\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " std_dev\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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uQkLEcvn+cJIDZiXA6NrJbhfdT05ywOTzkgWQXa7a//4HrF0r5pC0Wl81hZWV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u8fXZs2djx44duu3XrVuH8PBwHD9+HD179sT69estO8oPHK+8QgaM2lqge3eS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"text": [ "" ] } ], "prompt_number": 35 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Getting the status of the model starting after 300 monte carlo steps." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model.stats(start = 300)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 36, "text": [ "{'bern': {'95% HPD interval': array([[ 1., 1.],\n", " [ 1., 1.],\n", " [ 0., 0.],\n", " ..., \n", " [ 0., 0.],\n", " [ 0., 1.],\n", " [ 1., 1.]]),\n", " 'mc error': array([ 0. , 0. , 0. , ..., 0. ,\n", " 0.04277485, 0. ]),\n", " 'mean': array([ 1. , 1. , 0. , ..., 0. , 0.7375, 1. ]),\n", " 'n': 400,\n", " 'quantiles': {2.5: array([ 1., 1., 0., ..., 0., 0., 1.]),\n", " 25: array([ 1., 1., 0., ..., 0., 0., 1.]),\n", " 50: array([ 1., 1., 0., ..., 0., 1., 1.]),\n", " 75: array([ 1., 1., 0., ..., 0., 1., 1.]),\n", " 97.5: array([ 1., 1., 0., ..., 0., 1., 1.])},\n", " 'standard deviation': array([ 0. , 0. , 0. , ..., 0. , 0.4399929, 0. ])},\n", " 'mean': {'95% HPD interval': array([[-1.02325994, -0.9836972 ],\n", " [-1.02325994, -0.9836972 ],\n", " [ 0.95414825, 1.03166316],\n", " ..., \n", " [ 0.95414825, 1.03166316],\n", " [-1.02325994, 1.01421082],\n", " [-1.02325994, -0.9836972 ]]),\n", " 'mc error': array([ 0.00051406, 0.00051406, 0.00106816, ..., 0.00106816,\n", " 0.08540785, 0.00051406]),\n", " 'mean': array([-1.00347714, -1.00347714, 0.9961384 , ..., 0.9961384 ,\n", " -0.47916034, -1.00347714]),\n", " 'n': 400,\n", " 'quantiles': {2.5: array([-1.02325994, -1.02325994, 0.95482211, ..., 0.95482211,\n", " -1.02123343, -1.02325994]),\n", " 25: array([-1.01000676, -1.01000676, 0.98205589, ..., 0.98205589,\n", " -1.00770635, -1.01000676]),\n", " 50: array([-1.00361561, -1.00361561, 0.99725366, ..., 0.99725366,\n", " -0.99829576, -1.00361561]),\n", " 75: array([-0.99627449, -0.99627449, 1.01060757, ..., 1.01060757,\n", " 0.95750727, -0.99627449]),\n", " 97.5: array([-0.9836972 , -0.9836972 , 1.03394489, ..., 1.03394489,\n", " 1.01945825, -0.9836972 ])},\n", " 'standard deviation': array([ 0.01045394, 0.01045394, 0.02001978, ..., 0.02001978,\n", " 0.87833447, 0.01045394])},\n", " 'mean1': {'95% HPD interval': array([-1.02325994, -0.9836972 ]),\n", " 'mc error': 0.00051406400622172946,\n", " 'mean': -1.0034771428317881,\n", " 'n': 400,\n", " 'quantiles': {2.5: -1.0232599398349786,\n", " 25: -1.0100067619684092,\n", " 50: -1.0036156103530811,\n", " 75: -0.99627449437075899,\n", " 97.5: -0.98369719572723935},\n", " 'standard deviation': 0.010453936320626071},\n", " 'mean2': {'95% HPD interval': array([ 0.95414825, 1.03166316]),\n", " 'mc error': 0.0010681575460294817,\n", " 'mean': 0.99613840086734851,\n", " 'n': 400,\n", " 'quantiles': {2.5: 0.95482210920101107,\n", " 25: 0.98205588880816674,\n", " 50: 0.99725366267368132,\n", " 75: 1.0106075740696616,\n", " 97.5: 1.0339448861048506},\n", " 'standard deviation': 0.020019784690695663},\n", " 'precision': {'95% HPD interval': array([ 5.78728904, 6.57111383]),\n", " 'mc error': 0.010101309396832252,\n", " 'mean': 6.1729449300525649,\n", " 'n': 400,\n", " 'quantiles': {2.5: 5.762178465512406,\n", " 25: 6.0360094542061757,\n", " 50: 6.1802201331222504,\n", " 75: 6.3064494491035239,\n", " 97.5: 6.5606939643129909},\n", " 'standard deviation': 0.198547699951762},\n", " 'std_dev': {'95% HPD interval': array([ 0.39010409, 0.41568314]),\n", " 'mc error': 0.00033097829183626018,\n", " 'mean': 0.40264546302423981,\n", " 'n': 400,\n", " 'quantiles': {2.5: 0.39051092420533512,\n", " 25: 0.39820607128876617,\n", " 50: 0.40229082686851181,\n", " 75: 0.40707568062516614,\n", " 97.5: 0.41692774708686103},\n", " 'standard deviation': 0.0064948079945427494},\n", " 'theta': {'95% HPD interval': array([ 0.74323787, 0.77982117]),\n", " 'mc error': 0.00050010167963355145,\n", " 'mean': 0.75987424839119411,\n", " 'n': 400,\n", " 'quantiles': {2.5: 0.74115288756009057,\n", " 25: 0.75326977356496794,\n", " 50: 0.76036854609327098,\n", " 75: 0.76628608606936777,\n", " 97.5: 0.77816423924817746},\n", " 'standard deviation': 0.0096024160929834186}}" ] } ], "prompt_number": 36 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Saving a graphical representation of the model" ] }, { "cell_type": "code", "collapsed": false, "input": [ "graph = pymc.graph.graph(model)\n", "graph.write_png(\"graph_mix.png\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 37, "text": [ "True" ] } ], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, I have provided the file that I have used to generate this data ('scripts/twogaussiasn.py'). You can compare the values we have obtained here and see how good is our inference method.\n", "\n", "Moreover, it's important that you get your hands dirty. There are two things you could do in this sense:\n", "\n", "1. What could you change in this code to make it better? Rewrite it, think about the assumptions and the priors that I have used.\n", "\n", "2. Try another simple problem. I have supplied a Poisson process with a sudden change in its rate. Find out at which time this change happens." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## License" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
\n", " Version 2, December 2004 \n", "\n", " Copyright (C) 2004 Sam Hocevar \n", "\n", " Everyone is permitted to copy and distribute verbatim or modified
\n", " copies of this license document, and changing it is allowed as long
\n", " as the name is changed.
\n", "\n", " DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE \n", " TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION \n", "\n", " 0. You just DO WHAT THE FUCK YOU WANT TO.\n", "\n", "\n", "\n", "
\n", "tl;dr version: \"Copy it, use it, share it, don't expect anything, don't sue me.\"" ] } ], "metadata": {} } ] }