The Portrait Problem: Bayesian Inference with Joint Likelihood

Abstract

Chapter 7 discusses the “Portrait Problem,” which concerns the dispute about whether a portrait frequently associated with Thomas Bayes (and used, in fact, as the cover of this book!) is actually a picture of him. In doing so, the chapter highlights the fact that multiple pieces of information can be used in a Bayesian analysis. A key concept in this chapter is that multiple sources of data can be combined in a Bayesian inference framework. The main take-home point is that Bayesian analysis can be very, very flexible. A Bayesian analysis is possible as long as the likelihood of observing the data under each hypothesis can be computed. The chapter also discusses the concepts of joint likelihood and independence.