{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# MCMC: Metropolis-Hastings algorithm and diagnostics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Florent Leclercq,
\n", "Imperial Centre for Inference and Cosmology, Imperial College London,
\n", "florent.leclercq@polytechnique.org" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.stats import norm, binom, beta\n", "from matplotlib import pyplot as plt\n", "from cycler import cycler\n", "np.random.seed(123456)\n", "%matplotlib inline\n", "plt.rcParams.update({'lines.linewidth': 2})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we consider a Bernoulli experiment (a series of $N_{\\mathrm{trials}}$ independent experiments, each with its own boolean-valued outcome). The target parameter is the success rate $\\theta$. The likelihood for this problem is a [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution) and the [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) provides a family of conjuguate priors for Bayesian inference." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate data" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "33" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "groundtruth = 0.38\n", "Ntrials = 100\n", "Nsuccesses = binom(Ntrials, groundtruth).rvs()\n", "Nsuccesses" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analytic solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the likelihood is a binomial distribution with $N_{\\mathrm{successes}}$ for $N_{\\mathrm{trials}}$, and if the prior is a beta distribution with parameters ($\\alpha$, $\\beta$), then the posterior is a beta distribution with parameters\n", "\\begin{equation}\n", "\\alpha' = \\alpha+N_{\\mathrm{successes}}, \\quad \\beta' = \\beta + N_{\\mathrm{trials}} - N_{\\mathrm{successes}}\n", "\\end{equation}\n", "(see for example https://en.wikipedia.org/wiki/Conjugate_prior#When_likelihood_function_is_a_discrete_distribution)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def target_pdf(theta,Ntrials,Nsuccesses,lh,prior):\n", " if theta < 0 or theta > 1:\n", " return 0\n", " else:\n", " return lh(Ntrials,theta).pmf(Nsuccesses)*prior.pdf(theta)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "a = 10\n", "b = 10\n", "lh = binom\n", "prior = beta(a,b)\n", "posterior = beta(a+Nsuccesses, b+Ntrials-Nsuccesses)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "thetas = np.linspace(0, 1, 200)\n", "plt.figure(figsize=(10,6))\n", "plt.xlim([0,1])\n", "plt.ylim([0,1.05])\n", "plt.xlabel(\"$\\\\theta$\")\n", "plt.plot(thetas, prior.pdf(thetas)/prior.pdf(thetas).max(), label=\"prior\")\n", "plt.plot(thetas, lh(Ntrials,thetas).pmf(Nsuccesses)/lh(Ntrials,thetas).pmf(Nsuccesses).max(), label=\"likelihood\")\n", "plt.plot(thetas, posterior.pdf(thetas)/posterior.pdf(thetas).max(), label=\"posterior\")\n", "plt.plot([groundtruth,groundtruth],[0,1.05],color='black',linestyle='--',label=\"groundtruth\")\n", "plt.title(\"Analytic solution\")\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Metropolis-Hastings sampler" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def proposal_pdf(sigma):\n", " return norm(0,sigma)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def MH_sampler(Ntries,theta_start,Ntrials,Nsuccesses,lh,prior,proposal_sigma):\n", " Naccepted=0\n", " samples=np.zeros(Ntries+1)\n", " samples[0]=theta_start\n", " theta=theta_start\n", " for i in range(Ntries):\n", " theta_p = theta + proposal_pdf(proposal_sigma).rvs()\n", " # the Gaussian proposal pdf satisfies the detailed balance equation, so the\n", " # acceptance ratio simplifies to the Metropolis ratio\n", " a = min(1, target_pdf(theta_p,Ntrials,Nsuccesses,lh,prior)/target_pdf(theta,Ntrials,Nsuccesses,lh,prior))\n", " u = np.random.uniform()\n", " if u < a:\n", " Naccepted+=1\n", " theta=theta_p\n", " samples[i+1] = theta\n", " return Naccepted, samples" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "Ntries1=10000\n", "Nburnin=1000\n", "proposal_sigma=0.1\n", "theta_start=0.6\n", "Naccepted, samples = MH_sampler(Ntries1,theta_start,Ntrials,Nsuccesses,lh,prior,proposal_sigma)\n", "fraction_accepted=float(Naccepted)/Ntries1" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10,6))\n", "ax.set_xlim(0,Ntries1)\n", "ax.set_xlabel(\"sample number\")\n", "ax.set_title(\"Trace plot\")\n", "ax.set_ylabel(\"$\\\\theta$\")\n", "ax.plot(np.arange(Ntries1+1),samples,marker='.',color='C4')\n", "ymin, ymax = ax.get_ylim()\n", "ax.set_ylim([ymin,ymax])\n", "ax.plot([Nburnin,Nburnin],[ymin,ymax],color='black',linestyle=':')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4524" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fraction_accepted" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "burnedin_samples=samples[Nburnin:]\n", "plt.figure(figsize=(10,6))\n", "plt.xlim([0,1])\n", "plt.xlabel(\"$\\\\theta$\")\n", "plt.plot(thetas, prior.pdf(thetas), label=\"prior\")\n", "plt.hist(burnedin_samples, 40, histtype='step', density=True, color='C2', linewidth=2, label=\"MH posterior\")\n", "plt.plot(thetas, posterior.pdf(thetas), color='C2', linestyle='--', label=\"analytic posterior\")\n", "plt.title(\"Metropolis-Hastings sampling, acceptance ratio={:.3f}\".format(fraction_accepted))\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Markov Chain diagnostics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1- Step size" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "Ntries2=1000\n", "theta_start=0.6" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# Suitable step size\n", "proposal_sigma_1=0.1\n", "Naccepted_1, samples_1 = MH_sampler(Ntries2,theta_start,Ntrials,Nsuccesses,lh,prior,proposal_sigma_1)\n", "fraction_accepted_1=float(Naccepted_1)/Ntries2" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# Step size too large\n", "proposal_sigma_2=4\n", "Naccepted_2, samples_2 = MH_sampler(Ntries2,theta_start,Ntrials,Nsuccesses,lh,prior,proposal_sigma_2)\n", "fraction_accepted_2=float(Naccepted_2)/Ntries2" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# Step size too small\n", "proposal_sigma_3=0.003\n", "Naccepted_3, samples_3 = MH_sampler(Ntries2,theta_start,Ntrials,Nsuccesses,lh,prior,proposal_sigma_3)\n", "fraction_accepted_3=float(Naccepted_3)/Ntries2" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True, figsize=(15,5))\n", "ax1.set_xlim(0,Ntries2)\n", "ax1.set_xlabel(\"sample number\")\n", "ax1.set_ylabel(\"$\\\\theta$\")\n", "ax1.plot(np.arange(Ntries2+1),samples_1,marker='.',color='C4')\n", "ax1.set_title(\"sigma={}, acceptance ratio={:.3f}\".format(proposal_sigma_1,fraction_accepted_1))\n", "ax2.set_xlim(0,Ntries2)\n", "ax2.set_xlabel(\"sample number\")\n", "ax2.plot(np.arange(Ntries2+1),samples_2,marker='.',color='C4')\n", "ax2.set_title(\"sigma={}, acceptance ratio={:.3f}\".format(proposal_sigma_2,fraction_accepted_2))\n", "ax3.set_xlim(0,Ntries2)\n", "ax3.set_xlabel(\"sample number\")\n", "ax3.plot(np.arange(Ntries2+1),samples_3,marker='.',color='C4')\n", "ax3.set_title(\"sigma={}, acceptance ratio={:.3f}\".format(proposal_sigma_3,fraction_accepted_3))\n", "ymin, ymax = ax1.get_ylim()\n", "ax1.text(200,ymax-(ymax-ymin)/10., \"adequate step size\",fontsize=14)\n", "ax2.text(200,ymax-(ymax-ymin)/10., \"step size too large\",fontsize=14)\n", "ax3.text(200,ymax-(ymax-ymin)/10., \"step size too small\",fontsize=14)\n", "f.subplots_adjust(wspace=0.1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2- Multiple chains, different starting point" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "Ntries3=100\n", "proposal_sigma=0.05\n", "Nchains=5" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "# Run Nchains different chains starting at different positions in parameter space\n", "chains = [MH_sampler(Ntries3,theta_start,Ntrials,Nsuccesses,lh,prior,proposal_sigma)\n", " for theta_start in np.linspace(0.1,0.9,Nchains)]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10,6))\n", "ax.set_xlim(0,Ntries3)\n", "ax.set_xlabel(\"sample number\")\n", "ax.set_ylabel(\"$\\\\theta$\")\n", "ax.set_prop_cycle(cycler('color', [plt.cm.Set2(i) for i in np.linspace(0, 1., 8)]))\n", "for samples in chains:\n", " ax.plot(np.arange(Ntries3+1),samples[1],marker='.')\n", "plt.title(\"Trace plot for different chains\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3- Gelman-Rubin test" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gelman *et al.*, \"*Bayesian Data Analysis*\" (third edition), p. 284-285\n", "\n", "**Parameters**:\n", "* $m$: number of chains\n", "* $n$: length of chains\n", "\n", "**Definitions**:\n", "* \"between\" chains variance:\n", "\\begin{equation}\n", "B \\equiv \\frac{n}{m-1} \\sum_{j=1}^m \\left( \\bar{\\psi}_{. j} - \\bar{\\psi}_{..} \\right)^2 \\quad \\mathrm{where} \\quad \\bar{\\psi}_{. j} = \\frac{1}{n} \\sum_{i=1}^n \\psi_{ij} \\quad \\mathrm{and} \\quad \\bar{\\psi}_{..} = \\frac{1}{m} \\sum_{j=1}^m \\bar{\\psi}_{.j}\n", "\\end{equation}\n", "* \"within\" chains variance:\n", "\\begin{equation}\n", "W \\equiv \\frac{1}{m} \\sum_{j=1}^m s_j^2 \\quad \\mathrm{where} \\quad s_j^2 = \\frac{1}{n-1} \\sum_{i=1}^n \\left( \\psi_{ij} - \\bar{\\psi}_{.j} \\right)^2\n", "\\end{equation}\n", "\n", "**Estimators**:\n", "Estimators of the marginal posterior variance of the estimand:\n", "* $\\widehat{\\mathrm{var}}^- \\equiv W$: underestimates the variance\n", "* $\\widehat{\\mathrm{var}}^+ \\equiv \\frac{n}{n-1}W + \\frac{1}{n} B$: overestimates the variance\n", "\n", "**Test**:\n", "* Potential scale reduction factor: $\\widehat{R} \\equiv \\sqrt{\\frac{\\widehat{\\mathrm{var}}^+}{\\widehat{\\mathrm{var}}^-}}$\n", "* Test: $\\widehat{R} \\rightarrow 1$ as $n \\rightarrow \\infty$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.00040276881731590047" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "psi_j = np.array([np.mean(chains[j][1]) for j in range(Nchains)])\n", "psi = np.mean(psi_j)\n", "B = float(Nchains)/(Ntries3-1)*np.sum((psi_j-psi*np.ones(Nchains))**2)\n", "B" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.01067472484604469" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s_j = np.array([1./(Ntries3-1)*np.sum((chains[j][1]-psi_j[j])**2) for j in range(Nchains)])\n", "W = np.mean(s_j)\n", "W" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.01067472484604469, 0.01078657803771325)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var_minus=W\n", "var_plus=float(Ntries3)/(Ntries3-1)*W+1./Ntries3*B\n", "var_minus, var_plus" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0052255074490637" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R=np.sqrt(var_plus/var_minus)\n", "R" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }