{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## A Crash Course in Bayesian Statistics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayes Rule\n", "\n", "Recall that Bayes Rule is \n", "$$\n", "Prob(A|B) = \\frac{Prob(B|A)Prob(A)}{Prob(B)}\n", "$$ \n", "\n", "![conditional probability](../site_pics/conditional.png)\n", "\n", "Based on the definition of conditional probability, \n", "\n", "$$\n", "Pr(A | B) = \\frac{Pr(A \\cap B)}{Pr(B)}\n", "$$\n", "\n", "Since $Pr(A\\cap B) = Pr(B\\cap A)$, \n", "\n", "$$\n", "Pr(A|B)Pr(B) = Pr(B|A)Pr(A)\n", "$$\n", "giving us the Bayes Rule result:\n", "\n", "$$\n", "Pr(A|B) = \\frac{Pr(B|A)Pr(A)}{Pr(B)}\n", "$$\n", "\n", "#### The Monty Hall Problem\n", "\n", "The following example- one made famous for many university professors ridiculing a journalist for what they perceivied to be faulty reasoning (in fact, the journalist was correct [[see this link for some info on how often people get this wrong]](http://www.wired.com/2014/11/monty-hall-erdos-limited-minds/))- shows how we might apply Bayes Rule for cases where prior beliefs are updated with new information. It should be noted that expositions like this- of which there are many- don't really illuminate the econometric use of Bayes Rule very much, but help with understanding Bayes Rule.\n", "\n", "**The Problem**\n", "\n", ">Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, \"Do you want to pick door No. 2?\" Is it to your advantage to switch your choice? (Whitaker, 1990, as quoted by vos Savant 1990a)\n", "\n", "##### The probablility that the car is behind door 2\n", "Denote C,G as the value actually behind each door (a car and a goat respectively). Let Y and M represent Your and Monte's choices, respectively and the numbers 1,2,3 represent the 3 doors. We can solve this in a variety of ways (not necessarily involving Bayes Rule). Using Bayes Rule, let's consider that person 1 having chosen door 1 (Y1) and Monty having chosen door 3 (M3), that the probability that the car is actually behind door 2 (C2):\n", "$$\n", "Pr(C2|Y1,M3) = \\frac{Pr(M3|Y1,C2)Pr(C2|Y1)}{P(M3|Y1)}\n", "$$\n", "\n", "Let's start with the numerator:\n", "$$\n", "Pr(M3|Y1,C2)Pr(C2|Y1) = 1 \\times \\frac{1}{3} = \\frac{1}{3} \n", "$$\n", "\n", "Note that your **priors** when you choose Y=1 are:\n", "$$\n", "Pr(C1|Y1) = \\frac{1}{3} \\\\\n", "Pr(C2|Y1) = \\frac{1}{3} \\\\ \n", "Pr(C3|Y1) = \\frac{1}{3}\n", "$$\n", "Since your choice reveals no information about where the car is, your best guess about the probability that the car is behind any given door is $\\frac{1}{3}$ On the other hand, if the contestant having chosen door 1 and the car actually being behind door 2, means that Monte has to open door 3 with probability 1, since he will never reveal the actual location of the car until the contestant has had the opportunity to switch or not.\n", "\n", "The denominator, is\n", "$$\n", "P(M3|Y1) = P(M3 | Y1, C1) Pr(C1| Y1) + P(M3 | Y1, C2) Pr(C2| Y1) + P(M3 | Y1, C3) Pr(C3| Y1)\n", "$$\n", "which is equal to\n", "$$\n", "\\frac{1}{2} \\times \\frac{1}{3} + 1 \\times \\frac{1}{3} + 0 \\times \\frac{1}{3} = \\frac{1}{2} \n", "$$\n", "Note that the denominator \"integrates out\" all possible values of our parameter (where the car actually is), while holding constant Monte's choice and the contestant's initial choice.\n", "\n", "The expected probability that the car is behind door #2 from Bayes Rule is then\n", "$$\n", "\\frac{\\frac{1}{3}}{\\frac{1}{2}} = \\frac{2}{3}\n", "$$\n", "\n", "##### The probability that the car is behind door 1\n", "\n", "I'll let you solve for this, and the number you should get is $\\frac{1}{3}$. Therefore, you should always switch doors." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayes Rule for Econometric Analysis\n", "\n", "Replacing the generic A and B (or You and Monte) with data and parameters, starts us down the path of operationalizing Bayesian Econometrics:\n", "\n", "![bayes formula](../site_pics/bayesrule2.png)\n", "\n", "For example, in an OLS setting $\\theta$ is comprised of the parameters $(\\beta,\\sigma)$ and we have data (usually comprised of what we call $\\mathbf{y}$ and $\\mathbf{x}$).\n", "\n", "One can see from the Monte Hall Problem that you must \"integrate out\" all possible values for where the car might be. For statistical models like OLS, the denominator ($Pr(y)$) is calculated as\n", "\n", "$$\n", "Prob(\\mathbf{y}|\\mathbf{x}) = \\int_{\\theta} Pr(\\mathbf{y}|\\theta,\\mathbf{x})Pr(\\theta|\\mathbf{x})d\\theta\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How do we use this idea for econometric inference? A very good book on this topic is by John Geweke, \"Contemporary Bayesian Econometrics and Statistics\". Consider the following definitions for getting us started:\n", "\n", "- Parameters we are trying to estimate (like $\\beta$): $\\theta$\n", "- Prior distribution of parameters (what we believe a priori about model parameters): $Prob(\\theta)$. Note, the prior distribution depends on additional parameters that Geweke calls \"Hyper Parameters\". These are not parameters we try to estimate. \n", "- Sampling distribution of dependent variable $\\mathbf{y}$: $Prob(\\mathbf{y}|\\theta,\\mathbf{x})$. This is also called the likelihood function (exactly equivalent to what we did in MLE).\n", "- Marginal likelihood (the evidence):\n", "$$\n", "Prob(\\mathbf{y}|\\mathbf{x})=\\int_{\\theta}Prob(\\mathbf{y}|\\theta,\\mathbf{x})Prob(\\theta|\\mathbf{x})d\\theta = \\text{Normalizing Constant}\n", "$$\n", "- Posterior Distribution (this is the link to Bayes Rule): \n", "$$\n", "Prob(\\theta |\\mathbf{y}) = \\frac{Prob(\\mathbf{y}|\\theta,\\mathbf{x})Prob(\\theta|\\mathbf{x}))}{Prob(\\mathbf{y}|\\mathbf{x})} \\propto Prob(\\mathbf{y}|\\theta,\\mathbf{x})Prob(\\theta|\\mathbf{x}))\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__An example__\n", "\n", "Let's examine the posterior, $Prob(\\mathbf{y}|\\theta,\\mathbf{x})Prob(\\theta|\\mathbf{x}))$ and see how priors influence the posterior probabilities. Suppose we have an ultra-simple model: we have no independent variables (there is no $\\mathbf{x}$) and only have 1 observation on y (the number of ice-cream cones Rob consumed during a long hot summer): \n", "\n", "* You observe y=7 and know that Rob's standard deviation for y is 1.\n", "* You also have strong beliefs based on people similar to Rob, that people consume 5 ice-cream cones with a standard deviation of 2. Denote these beliefs (hyperparameters) as $\\mu_0$ and $\\sigma_0$.\n", "\n", "Letting both $Prob(\\mathbf{y}|\\theta,\\mathbf{x})$ and $Prob(\\theta|\\mathbf{x}))$ be normal pdf's, we have the likelihood:\n", "$$\n", "Prob(\\mathbf{y}|\\mu) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{-\\frac{(y - \\mu)^2}{2\\sigma^2}} = \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{(y - \\mu)^2}{2}}\n", "$$\n", "\n", "and the prior:\n", "$$\n", "P(\\mu) = \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} e^{-\\frac{(\\mu - \\mu_0)^2}{2 \\sigma_0^2}} = \\frac{1}{\\sqrt{2\\pi 4}} e^{-\\frac{(\\mu - 5)^2}{2 \\times 4}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from scipy.stats import norm,uniform\n", "import matplotlib.pyplot as plt\n", "import seaborn as sbn\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "sbn.set_style('white')\n", "sbn.set_context('talk')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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