{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 23: Beta distribution, Bayes' Billiards\n", "\n", "\n", "## Stat 110, Prof. Joe Blitzstein, Harvard University\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Beta Distribution\n", "\n", "The Beta distribution is characterized as $\\operatorname{Beta}(\\alpha, \\beta)$ where $\\alpha \\gt 0 \\text{, } \\beta \\gt 0$.\n", "\n", "The Beta distribution PDF is given by:\n", "\n", "\\begin{align}\n", " f(x) &= c \\, x^{\\alpha-1} \\, (1 - x)^{\\beta-1} \\quad \\text{where } 0 \\lt x \\lt 1 \n", "\\end{align}\n", "\n", "We will put aside the normalization constant $c$ for now (wait until lecture 25!).\n", "\n", "$\\operatorname{Beta}(\\alpha ,\\beta)$ distribution\n", "\n", "* is a flexible family of continuous distributions over $(0,1)$ (see graph below for some examples)\n", "* often used as a _prior_ for a parameter in range $(0,1)$\n", "* _conjugate prior_ for $\\operatorname{Binomial}$ distribution" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt0AAAIoCAYAAAC1aFdYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWIhx0c0YY4wxxliIcdHNGGOMMcZYiP0fXBQ+Hij1Y70AAAAASUVORK5CYII=\n", "text/plain": [ "<matplotlib.figure.Figure at 0x2005d78d4a8>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from matplotlib.ticker import (MultipleLocator, FormatStrFormatter,\n", " AutoMinorLocator)\n", "from scipy.stats import beta\n", "\n", "%matplotlib inline\n", "\n", "plt.xkcd()\n", "\n", "_, ax = plt.subplots(figsize=(12,8))\n", "\n", "x = np.linspace(0, 1.0, 500)\n", "\n", "# seme Beta parameters\n", "alphas = [0.5, 5, 1, 1, 2, 3]\n", "betas = [0.5, 3, 2, 1, 1, 5]\n", "params = map(list, zip(alphas, betas))\n", "\n", "# qualitative color scheme\n", "colors = ['#66c2a5', '#fc8d62', '#8da0cb', '#e78ac3', '#a6d854', '#ffd92f']\n", "\n", "for i,(a,b) in enumerate(params):\n", " y = beta.pdf(x, a, b)\n", " ax.plot(x, y, color=colors[i], lw=3.2, label=r'$\\alpha$={}, $\\beta$={}'.format(a,b))\n", "\n", "# legend styling\n", "legend = ax.legend()\n", "for label in legend.get_texts():\n", " label.set_fontsize('large')\n", "for label in legend.get_lines():\n", " label.set_linewidth(1.5)\n", "\n", "# y-axis\n", "ax.set_ylim([0.0, 5.0])\n", "ax.set_ylabel(r'$f(x)$')\n", "\n", "# x-axis\n", "ax.set_xlim([0, 1.0])\n", "ax.set_xlabel(r'$x$')\n", "\n", "# x-axis tick formatting\n", "majorLocator = MultipleLocator(.2)\n", "majorFormatter = FormatStrFormatter('%0.1f')\n", "minorLocator = MultipleLocator(.1)\n", "ax.xaxis.set_major_locator(majorLocator)\n", "ax.xaxis.set_major_formatter(majorFormatter)\n", "ax.xaxis.set_minor_locator(minorLocator)\n", "\n", "ax.grid(color='grey', linestyle='-', linewidth=0.3)\n", "\n", "plt.suptitle(r'Beta Distribution $f(x) = \\frac{x^{\\alpha-1} \\, (1-x)^{\\beta-1}}{B(\\alpha,\\beta)}$')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Conjugate prior to the Binomial\n", "\n", "Recall Laplace's Rule of Succession dealing with the problem of the sun rising: there, we probability $p$ that the sun will rise on any given day $X_k$, given a consecutive string of days $X_1,X_2, \\dots, X_{k-1}$, to be i.i.d. $\\operatorname{Bern}(p)$. \n", "\n", "We made an assumption that $p \\sim \\operatorname{Unif}(0,1)$.\n", "\n", "$\\operatorname{Beta}(1,1)$ is the same as $\\operatorname{Unif}(0,1)$, and so we will show how to generalize using the $\\operatorname{Beta}$ distribution.\n", "\n", "Given $X|p \\sim \\operatorname{Bin}(n,p)$. We get to observe $X$, but we do not know the true value of $p$. \n", "\n", "In such a case, we can assume that the _prior_ $p \\sim \\operatorname{Beta}(\\alpha, \\beta)$. After observing $n$ further trials, where perhaps $k$ are successes and $n-k$ are failures, we can use this information to update our beliefs on the nature of $p$ using Bayes Theorem.\n", "\n", "So we what we want is the _posterior_ $p|X$, since we will get to observe more values of $X$ and want to update our understanding of $p$.\n", "\n", "\\begin{align}\n", " f(p|X=k) &= \\frac{P(X=k|p) \\, f(p)}{P(X=k)} \\\\\n", " &= \\frac{\\binom{n}{k} \\, p^k \\, (1-p)^{n-k} \\, c \\, p^{\\alpha-1}(1-p)^{\\beta-1}}{P(X=k)} \\\\\n", " &\\propto p^{\\alpha + k - 1} (1-p)^{\\beta + n - k - 1} \\quad \\text{since }\\binom{n}{k} \\text{, }c \\text{ and }P(X=k) \\text{ do not depend on }p \\\\\n", " \\\\\n", " \\Rightarrow p|X &\\sim \\operatorname{Beta}(\\alpha + X, \\beta + n - X) \n", "\\end{align}\n", "\n", "_Conjugate_ refers to the fact that we are looking at an entire _family_ of $\\operatorname{Beta}$ distributions as the _prior_. We started off with $\\operatorname{Beta}(\\alpha, \\beta)$, and after an additional $n$ more observations of $X$ we end up with $\\operatorname{Beta}(\\alpha + X, \\beta + n - X)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayes' Billiards\n", "\n", "The $\\operatorname{Beta}(\\alpha, \\beta)$ distribution has PDF:\n", "\n", "\\begin{align}\n", " f(x) &= c \\, x^{\\alpha-1} \\, (1 - x)^{\\beta-1}\n", "\\end{align}\n", "\n", "Let's try to find the normalizing constant $c$ for the case where $\\alpha \\gt 0 \\text{, } \\beta \\gt 0$, and $\\alpha,\\beta \\in \\mathbb{Z}$\n", "\n", "In order to do that, we need to find out \n", "\n", "\\begin{align}\n", " \\int_0^1 x^k \\, (1 - x)^{n-k} \\, dx \\\\\n", " \\\\\n", " \\rightarrow \\int_0^1 \\binom{n}{k} x^k \\, (1 - x)^{n-k} \\, dx\n", "\\end{align}\n", "\n", "#### Story 1\n", "We have $n+1$ white billiard balls, and we paint one of them pink. Now we throw them down on the number line from 0 to 1.\n", "\n", "#### Story 2\n", "We throw our $n+1$ white billiard balls down on the number line from 0 to 1, and _then_ randomly select one of them to paint in pink. \n", "\n", "\n", "\n", "_Note that the image above could have resulted from either of the stories, so both stories are actually equivalent._\n", "\n", "#### Doing calculus without using calculus\n", "\n", "At this point, we know exactly how to the above integral _without using any calculus._\n", "\n", "Let $X = \\text{# balls to left of pink}$, so $X$ ranges from $0$ to $n$. If we condition on $p$ (pink billiard ball), we can consider this to be a binomial distribution problem, where \"success\" means being to the left of the pink ball.\n", "\n", "\\begin{align}\n", " P(X = k) &= \\int_0^1 P(X=k|p) \\, f(p) \\, dp &\\quad \\text{conditioning on } p \\\\\n", " &= \\int_0^1 \\binom{n}{k} p^k \\, (1-p)^{n-k} \\, dp &\\quad \\text{since } f(p) \\sim Unif(0,1) \\\\\n", " \\\\\n", " & &\\quad \\text{but from Story 2, } k \\text{ could be any value in } \\{0,n\\} \\\\\n", " \\\\\n", " &= \\boxed{ \\frac{1}{n+1} }\n", "\\end{align}\n", "\n", "And so now we have the normalizing constant when $\\alpha, \\beta$ are positive integers.\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "View [Lecture 23: Beta distribution | Statistics 110](http://bit.ly/2Nprujo) on YouTube." ] } ], "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }