Bayes’ Theorem

Abstract

This chapter focuses on Bayes’ Theorem. The chapter first gives a brief introduction to Thomas Bayes, who first formulated the theorem. It then builds on the content presented in Chapters 1 and 2 to derive Bayes’ Theorem and describes two ways to think about it. First, Bayes’ Theorem describes the relationship between two inverse conditional probabilities, P(A | B) and P(B | A). Second, Bayes’ Theorem can be used to express how a degree of belief for a given hypothesis can be updated in light of new evidence. This chapter focuses on the first interpretation. The chapter also discusses the concepts of joint probability and marginal probability.