{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Chapter 7 - Markov Chain Monte Carlo" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.stats import beta\n", "\n", "plt.style.use('seaborn-white')\n", "color = '#87ceeb'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prior\n", "We will again use a beta distribution to describe our prior beliefs about the values of $\\theta$. However, it is now written as a function that takes values of $\\theta$ and returns probabilties. We will also do this for our likelihood and our posterior. This allows us to repeatedly call these for arbitrary parameter (i.e., $\\theta$) values as we wander the the parameter space during our MCMC sampling." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "a = 1\n", "b = 1\n", "\n", "def prior(theta):\n", " return beta.pdf(theta, a, b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data\n", "This constructs a set of flip outcomes. Specify the number of heads (i.e., `n_heads`) and the number of tails (i.e., `n_tails`). There are three scenarios prepared:\n", "\n", "1. 1 flip that comes up heads\n", "2. 4 flips, 1 of which comes up heads (25% heads)\n", "3. 40 flips, 10 of which come up heads (25% heads)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "# example 1\n", "n_heads = 1\n", "n_tails = 0\n", "\n", "# example 2\n", "#n_heads = 1\n", "#n_tails = 3\n", "\n", "# example 3\n", "n_heads = 10\n", "n_tails = 30\n", "\n", "data = np.repeat([1, 0], [n_heads, n_tails])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Likelihood\n", "Here again, we have rewritten our usual Bernoulli likelihood as a function that returns the likelihood for a given $\\theta$ and given set of data." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def likelihood(theta, n_flips, n_heads):\n", " return (theta**n_heads) * ( (1-theta)**(n_flips - n_heads) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exact Inference\n", "Here we calculate the posterior exactly. This will allow us to easily visualize how well our MCMC approximation is performing. Again, we have written this as a function." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "post_a = n_heads + a\n", "post_b = n_tails + b\n", "\n", "def posterior(theta):\n", " return beta.pdf(theta, post_a, post_b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Approximate Inference via MCMC\n", "Here we approximate the posterior using the Metropolis algorithm. This routine is **for illustrative purposes only**. It is written for clarity and is slow.\n", "\n", "Sampling parameters (number of samples, number of chains, width of the proposal distribution) are here to be tweaked. Note that the alternative values for the width of the proposal distribution are intended to yield poor sampling performance." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "# Metropolis parameters\n", "# number of draw\n", "n_draws = 5000\n", "n_chains = 2\n", "\n", "# width of proposal distribution\n", "sigma = 0.25\n", "# sigma = 0.01\n", "# sigma = 10\n", "\n", "# this will store our list of credible parameter values\n", "# that generated by the Metropolis algorithm\n", "theta_trace = np.zeros([n_chains, n_draws])\n", "theta_trace[:, 0] = np.random.uniform(size=n_chains)\n", "\n", "# let's keep track of how many proposed jumps we accept\n", "n_accept = 0\n", "\n", "for i in range(n_chains):\n", " for j in range(1, n_draws):\n", "\n", " # retrieve the current value of theta from our list\n", " current_theta = theta_trace[i, j - 1]\n", " # unnormalized posterior of the current value of theta\n", " theta_p = likelihood(current_theta, (n_heads + n_tails), n_heads) * prior(\n", " current_theta\n", " )\n", " # generate the proposal\n", " theta_star = current_theta + np.random.normal(0, sigma, 1)[0]\n", " # unnormalized posterior of the proposed value of theta\n", " theta_star_p = likelihood(theta_star, (n_heads + n_tails), n_heads) * prior(\n", " theta_star\n", " )\n", "\n", " # determine whether to accept proposal\n", " if (theta_star_p / theta_p) > np.random.uniform(size=1)[0]:\n", " theta_trace[i, j] = theta_star\n", " n_accept += 1\n", " else:\n", " theta_trace[i, j] = current_theta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ok, so now we have wandered around the parameter space a bit. Let's see how many of our proposals were accepted." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# of proposals:\t\t\t10000\n", "# of proposals accepted:\t3176\n", "% of proposals accepted:\t31.76\n" ] } ], "source": [ "print(f\"# of proposals:\\t\\t\\t{n_chains * n_draws}\")\n", "print(f\"# of proposals accepted:\\t{n_accept}\")\n", "print(f\"% of proposals accepted:\\t{100 * (n_accept / (n_chains * n_draws)):.2f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize\n", "Plot the prior, the likelihood, and the posterior." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(2, figsize=(9, 6))\n", "xs = np.linspace(0, 1, 1000)\n", "ax[0].plot(xs, prior(xs), label=\"Prior\")\n", "ax[0].plot(xs, posterior(xs), label=\"Posterior\")\n", "for i,c in zip(range(n_chains), [\"blue\", \"green\"]):\n", " ax[0].hist(\n", " theta_trace[i, :],\n", " alpha=0.3,\n", " bins=100,\n", " density=True,\n", " color=c,\n", " label=\"Posterior Samples (\" + str(i + 1) + \")\",\n", " )\n", "\n", "ax[0].text(0.35, np.max(posterior(xs)), \"D = %sH,%sT\" % (n_heads, n_tails), size=16)\n", "\n", "ax[0].set(xlabel=r\"$\\theta$\")\n", "ax[0].yaxis.set(ticks=())\n", "# ax[0].legend(['Prior', 'Posterior (exact)', 'Posterior Samples']);\n", "ax[0].legend()\n", "\n", "for i in range(n_chains):\n", " ax[1].plot(theta_trace[i, :], alpha=0.5, linewidth=0.5, label=\"Chain \" + str(i + 1))\n", "ax[1].set(xlabel=\"Step\", ylabel=r\"$\\theta$\", ylim=[0, 1])\n", "ax[1].legend()\n", "fig.tight_layout()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 4 }