{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Chapter 6 - Inferring a Binomial Probability via Exact Mathematical Analysis" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.stats import beta\n", "from scipy.special import beta as beta_func\n", "\n", "plt.style.use('seaborn-white')\n", "color = '#87ceeb'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set up\n", "Here, we create a vector of values that theta can take on. This vector is **for plotting only**. We are calculating exact solutions here, so we will have priors, likelihoods, and posteriors for essentially all of the infinite number of number of values that theta can take on. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "n_theta_vals = 1001\n", "\n", "theta = np.linspace(0, 1, n_theta_vals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prior\n", "We will use a beta distribution to describe our prior beliefs about the values of $\\theta$. The use of a beta distribution to represent our prior belief about theta is critical here, because the beta distribution is the conjugate prior probability distribution for the Bernoulli likelihood that we used in chapter 5 and will reuse below.\n", "\n", "In addition, the beta distribution is flexible enough to permit several different patterns including:\n", "\n", "- $\\alpha=1, \\beta=1$ yields a uniform prior\n", "- $\\alpha=3, \\beta=3$ yields a prior peaked at $\\theta=0.5$ (a bit like the truncated normal we used in chapter 5)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "a = 3\n", "b = 3\n", "\n", "p_theta = 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": 12, "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", "Note that we are using the vector of theta values here this is because we want to plot the likelihood function below we **do not** need these lines of code in order to arrive at the posterior (as we will see)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# Compute the likelihood of the data:\n", "p_data_given_theta = theta**n_heads * (1-theta)**(n_tails)\n", "\n", "# calculate the evidence (P(D), the prior probability of the data)\n", "p_data = beta_func(n_heads + a, n_tails + b)/beta_func(a, b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Inference\n", "Here is the magic of using priors that are conjugate with our likelihood. Because we are using a beta prior, we can straightforwardly determine the posterior by adding the number of heads/tails to the $\\alpha$ and $\\beta$ parameters we used to construct our prior." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "post_a = n_heads + a\n", "post_b = n_tails + b\n", "\n", "# Compute the posterior for our values of theta for later visualization\n", "p_theta_given_data = beta.pdf(theta, post_a, post_b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize\n", "Plot the prior, the likelihood, and the posterior." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(9, 12))\n", "fig.tight_layout()\n", "plt.subplots_adjust(hspace = .4)\n", "\n", "# Plot the prior, the likelihood, and the posterior:\n", "for i,dist in enumerate([p_theta, p_data_given_theta, p_theta_given_data]):\n", " plt.subplot(3, 1, i+1)\n", " plt.plot(theta, dist)\n", " plt.xlim(0, 1)\n", " plt.xlabel('$\\\\theta$', size=16)\n", "\n", "# horizontal location of text labels\n", "locx = 0.1\n", "\n", "# prior\n", "plt.axes(fig.axes[0])\n", "plt.title('Prior', weight='bold', size=16)\n", "plt.xlim(0, 1)\n", "plt.ylim(0, np.max(p_theta)*1.2)\n", "plt.ylabel(r'$P(\\theta)$', size=16)\n", "plt.text(locx, np.max(p_theta)/2, r'beta(%s,%s)' % (a, b), size=16)\n", "\n", "# likelihood\n", "plt.axes(fig.axes[1])\n", "plt.title('Likelihood', weight='bold', size=16)\n", "plt.ylabel('$P(D|\\\\theta)$', size=16)\n", "plt.text(locx, np.max(p_data_given_theta)/2, 'D = %sH,%sT' % (n_heads, n_tails), size=16)\n", "\n", "# posterior\n", "plt.axes(fig.axes[2])\n", "plt.title('Posterior', weight='bold', size=16)\n", "plt.ylabel('$P(\\\\theta|D)$', size=16)\n", "locy = np.linspace(0, np.max(p_theta_given_data), 5)\n", "plt.text(locx, locy[1], r'beta(%s,%s)' % (post_a, post_b), size=16)\n", "plt.text(locx, locy[2], 'P(D) = %.2f' % p_data, size=16);" ] } ], "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": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 4 }