The Optimal Bayes Decision Rule

This chapter begins with a result from probability known as Bayes Theorem. This result shows how to switch the order of events in a conditional probability, and this is exactly the tool that allows us to compute the needed posterior probabilities. The resulting decision rule is called Bayes decision rule. The chapter argues that this is the optimal decision rule in the sense that no other rule can have a smaller probability of error. It ends with a discussion of Bayes Theorem and Bayes decision rule in the case of densities. Controlled Vocabulary Terms Bayes' theorem; posterior probability