{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.stats as sps\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "plt.rcParams.update({'figure.figsize': (10.0, 6.0), 'font.size': 18})\n", "t = np.linspace(-10,10,1000) # x-axis for our plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bayesian inference for Gaussian distribution\n", "\n", "\n", "Gaussian distribution parametrized by mean $\\mu$ and precision $\\lambda = \\frac{1}{\\sigma^2}$ rather than variance $\\sigma^2$\n", "$$\n", "\\DeclareMathOperator{\\NormalGamma}{NormalGamma}\n", "\\DeclareMathOperator{\\Norm}{\\mathcal{N}}\n", "\\DeclareMathOperator{\\Gam}{Gam}\n", "\\DeclareMathOperator{\\e}{exp}\n", "\\large\n", "p(x | \\mu, \\lambda) = \\Norm(x \\mid \\mu, \\lambda^{-1}) = \\frac{\\sqrt{\\lambda}}{\\sqrt{2\\pi}} \\e\\{ \\frac{-\\lambda(x - \\mu)^2}{2}\\}\n", "$$\n", "\n", "NormalGamma distribution can be used as the conjugate prior over the mean $\\mu$ and precision $\\lambda$ parameters of Gaussian distribution.\n", "\n", "$$\n", "\\large\n", "\\NormalGamma(\\mu,\\lambda|m,\\kappa,a,b) = \\Norm(\\mu|m,(\\kappa\\lambda)^{-1}) \\Gam(\\lambda|a,b)\n", "$$\n", "\n", "where gamma distribution\n", "\n", "$$\n", "\\large\n", "\\Gam(\\lambda \\mid a, b) = \\frac{1}{\\Gamma(a)} b^a \\lambda^{a - 1} \\e \\{ -b \\lambda\\}\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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bWJazPq116xyHfD3hwPrWlIpWLI0QMlmmTtScc/MA/hDAEoBPRsqcDuB0AFi/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\nH+HB3vvbl9O3RS+kuD2Afbz3m9tr5WzhnHseemMCNf8K4CIAfw7gOu/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mWpoC113VzyRhTAhxOdmKSAixZjlZCxX0ofyN/b2xMjiIv7ubKWsMw2jjW2fL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\nnc0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dgFpn/HAMdE8a3euiu9PokoOW4rLrL7rHFe6rlCaJQqoLZ1idPc3q/ElqC2eIw/YC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\nayX93kTme7xIOiLVOTenumurpNsl/X1Z3SW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def NormalGamma_pdf(mu, lmbd, m, kappa, a, b):\n", " # sps.norm.pdf takes mean and std (not variance), therefore 1.0/\n", " # sps.gamma.pdf takes shape and scale (not rate), therefore 1.0/b\n", " return sps.norm.pdf(mu, m, 1.0/np.sqrt(lmbd*kappa))* sps.gamma.pdf(lmbd, a, scale=1.0/b)\n", "\n", "def NormalGamma_rvs(m, kappa, a, b, N):\n", " # Sample from NormalGamma distribution\n", " lmbd = sps.gamma.rvs(a, scale=1.0/b, size=N)\n", " mu = sps.norm.rvs(m, 1.0/np.sqrt(lmbd*kappa), N)\n", " return mu, lmbd\n", "\n", "def NormalGamma_plot(m0, kappa0, a0, b0, limits):\n", " mu_vals, lmbd_vals = np.meshgrid(np.linspace(limits[0], limits[1], 500), np.linspace(limits[2], limits[3], 500))\n", " pdf = NormalGamma_pdf(mu_vals, lmbd_vals, m0, kappa0, a0, b0)\n", " plt.imshow(pdf, origin='lower', cmap='Greys', extent=limits)\n", " plt.xlabel('$\\mu$'); plt.ylabel('$\\lambda$')\n", "\n", "\n", "#Plot some example NormalGamma distribution\n", "m0, kappa0, a0, b0 = 0.0, 1.0, 1.0, 1.0\n", "plot_limits=[-6, 6, 0.01, 5]\n", "NormalGamma_plot(m0, kappa0, a0, b0, limits=plot_limits)\n", "\n", "# Obtain few samples from the prior distribution.\n", "mu_sampled, lmbd_sampled = NormalGamma_rvs(m0, kappa0, a0, b0, 50)\n", "plt.plot(mu_sampled, lmbd_sampled, '+'); plt.axis(plot_limits)\n", "\n", "# Each of these sample represents mean and precision. Plot the corresponding Gaussian distributions\n", "plt.figure()\n", "plt.plot(t, sps.norm.pdf(t[:,np.newaxis], mu_sampled, 1/np.sqrt(lmbd_sampled)));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given $N$ observations $\\mathbf{x}=[x_1, x_2, \\dots, x_N]$ from gaussian distribution $\\Norm(x \\mid \\mu, \\lambda^{-1})$ and given prior $p(\\mu, \\lambda^{-1}) = \\NormalGamma(\\mu,\\lambda|m_0,\\kappa_0,a_0,b_0)$ the poterior distribution over the Gaussian parameters is:\n", "\n", "$$\n", "\\large\n", "p(\\mu, \\lambda^{-1}|\\mathbf{x}) = \\NormalGamma(\\mu,\\lambda|m_N,\\kappa_N,a_N,b_N)\n", "$$, \n", "\n", "where\n", "\n", "\n", "$$\n", "\\large\n", "\\begin{align}\n", "m_N &= \\frac{\\kappa_0 m_0 + N \\bar{x}} {\\kappa_0 + N} \\\\\n", "\\kappa_N &= \\kappa_0 + N \\\\\n", "a_N &= a_0 + \\frac{N}{2} \\\\\n", "b_N &= b_0 + \\frac{N}{2} ( s + \\frac{\\kappa_0 (\\bar{x} - m_0)^2}{\\kappa_0 + N} ) \\\\\n", "\\bar{x} &= \\frac{1}{N} \\sum_i x_i \\\\\n", "s &= \\frac{1}{N} \\sum_i (x_i - \\bar{x})^2\n", "\\end{align}\n", "$$\n", "\n", "Note that the prior parameters can be interpreted as follows:\n", "* $2a_0$ - prior number of observation for precision (or variance)\n", "* $b_0/a_0$ - prior variance (around $m_0$)\n", "* $\\kappa_0$ - number of prior observations for mean\n", "* $m_0$ - prior mean" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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lQmt8j7rdA1SBTERBTUTmkCLdmKnjncJYaseB1EzPeGuocBmOcAJBvDyHP7Zy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\njWlm59P4M/iMmX0rb7JS5YIasB6NAel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2I/ECLocNXyUDWlPIRnD7HWzY00b/YvHWk7k8bOhisLdAfWEnmbydLa0jmNrG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def NormalGammaPosteriorParams(m0, kappa0, a0, b0, x):\n", " # given prior parameters m0, kappa0, a0, b0 and observations x\n", " # sufficient statistics N, mean, var calculate parameters of posterior\n", " N = len(x)\n", " mean = np.mean(x)\n", " var = np.var(x)\n", "\n", " kappaN = kappa0 + N\n", " mN = (kappa0*m0 + mean*N) / kappaN;\n", " aN = a0 + 0.5*N;\n", " bN = b0 + 0.5 * N * (var + kappa0*(mean-m0)**2/(kappa0 + N))\n", " return mN, kappaN, aN, bN\n", "\n", "def NormalGammaPosteriorParams2(m0, kappa0, a0, b0, x):\n", " # alternative more practical implementation, which does not crash for N=0\n", " N = len(x)\n", " f = np.sum(x)\n", " s = np.sum(x**2)\n", "\n", " kappaN = kappa0 + N\n", " mN = (kappa0*m0 + f) / kappaN;\n", " aN = a0 + 0.5*N;\n", " bN = b0 + 0.5 * (s + kappa0 * m0**2 - kappaN * mN**2);\n", " return mN, kappaN, aN, bN\n", "\n", "\n", "# Generate observation from agiven Gaussian distribution \n", "N = 5\n", "mu = 1.0 # mean\n", "sigma = 1 # standard deviation (std)\n", "x = sps.norm.rvs(mu, sigma, N)\n", "\n", "# Given NormalGamma prior and the observation, calculate and plot posterior distibution of the Gaussian parameters\n", "mN, kappaN, aN, bN = NormalGammaPosteriorParams2(m0, kappa0, a0, b0, x)\n", "NormalGamma_plot(mN, kappaN, aN, bN, limits=plot_limits)\n", "\n", "# Obtain few samples from the posterior distribution.\n", "mu_sampled, lmbd_sampled = NormalGamma_rvs(mN, kappaN, aN, bN, 50)\n", "plt.plot(mu_sampled, lmbd_sampled, '+'); plt.axis(plot_limits)\n", "\n", "# Each of these sample represents mean and precision. Plot the corresponding Gaussian distributions\n", "pdfs_sampled = sps.norm.pdf(t[:,np.newaxis], mu_sampled, 1/np.sqrt(lmbd_sampled))\n", "plt.figure()\n", "plt.plot(t, pdfs_sampled);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predictive probability\n", "\n", "For the Gaussian with NormalGamma prior, the posterior predictive distribution is the Student's t-distribution:\n", "\n", "$$\n", "\\large\n", "\\newcommand{\\diff}{\\mathop{}\\!d}\n", "\\DeclareMathOperator{\\St}{\\mathcal{St}}\n", "\\begin{align}\n", "p(x' \\mid \\mathbf{x}) \n", "&= \\int_{-\\infty}^{\\infty} p(x'|\\mu, \\lambda) p(\\mu, \\lambda \\mid \\mathbf{x}) \\diff \\mu \\diff \\lambda \\\\\n", "&= \\int_{-\\infty}^{\\infty} \\Norm(x'|\\mu, \\lambda) \\NormalGamma(\\mu,\\lambda|m_0,\\kappa_0,a_0,b_0) \\diff \\mu \\diff \\lambda \\\\ \n", "&= \\St(x' \\mid m_N, 2a_N, \\frac{a_N \\kappa_N}{b_N(\\kappa_N + 1)} )\n", "\\end{align}\n", "$$\n", "\n", "where:\n", "\n", "$$\n", "\\large\n", "\\St(x' \\mid \\mu, \\nu, \\gamma) = \\frac{\\Gamma(\\frac{\\nu}{2} + \\frac{1}{2})}{\\Gamma(\\frac{\\nu}{2})} \\Big( \\frac{\\gamma}{\\pi \\nu} \\Big)^{\\frac{1}{2}} \\Big[ 1 + \\frac{\\gamma (x - \\mu)^2}{\\nu} \\Big]^{-\\frac{\\nu}{2} - \\frac{1}{2}}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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mLWa2x8wWm1mv/6lpZiPN7Jtm9mrouhNmttnMHjOz4m7Ov8LMXA8/L57NHyki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\nDMPIIf4fzO5M+21ZFgIAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the distribution from which the observations were generated\n", "plt.plot(t, sps.norm.pdf(t, mu, sigma), 'r',lw=3)\n", "\n", "# Plot predictive distribution, which depends on the prior and the observations \n", "# (i.e. depends on the posterior distribution over the parameters \\mu and \\lambda)\n", "plt.plot(t, sps.t.pdf(t, loc=mN, df=2*aN, scale=np.sqrt(bN*(kappaN+1)/aN/kappaN)), 'k',lw=1)\n", "\n", "# Take all the sampled Gaussian distributions from the previous figure, average them and plot the resulting distribution\n", "# For large number of samples, this should be good approximation to the predictive distribution \n", "plt.plot(t, pdfs_sampled.mean(axis=1));" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }