Module 18 Bayesian Data Analysis

by Patrick Boily and Ehssan Ghashim


Bayesian analysis is sometimes maligned by data analysts, due in part to the perceived element of arbitrariness associated with the selection of a meaningful prior distribution for a specific problem and the (former) difficulties involved with producing posterior distributions for all but the simplest situations.

On the other hand, we have heard it said that ``while classical data analysts need a large bag of clever tricks to unleash on their data, Bayesians only ever really need one.’’ With the advent of efficient numerical samplers, modern data analysts cannot shy away from adding the Bayesian arrow to their quiver.

In this module, we introduce the basic concepts underpinning Bayesian analysis, and we present a small number of examples that illustrate the strengths of the approach.

Contents

18.1 Plausible Reasoning
     18.1.1 Rules of Probability
     18.1.2 Bayes’ Theorem
     18.1.3 Bayesian Inference Basics
     18.1.4 Bayesian Data Analysis

18.2 Examples
     18.2.1 The Mysterious Coin
     18.2.2 The Salary Question
     18.2.3 Money (Dollar Bill Y’All)

18.3 Prior Distributions
     18.3.1 Conjugate Priors
     18.3.2 Uninformative Priors
     18.3.3 Informative Priors
     18.3.4 Maximum Entropy Priors

18.4 Posterior Distributions
     18.4.1 High-Density Intervals
     18.4.2 MCMC Methods
     18.4.3 The MH Algorithm

18.5 Additional Topics
     18.5.1 Uncertainty
     18.5.2 Bayesian A/B Testing

18.6 Exercises