If you recall from Chapter 4, Probability, the Bayesian interpretation of probability views probability as our degree of belief in a claim or hypothesis, and Bayesian inference tells us how to update that belief in the light of new evidence. In that chapter, we used Bayesian inference to determine the probability that employees of Daisy Girl, Inc. were using an illegal drug. We saw how the incorporation of prior beliefs saved two employees from being falsely accused and helped another employee get the help she needed even though her drug screen was falsely negative.
In a general sense, Bayesian methods tell us how to dole out credibility to different hypotheses, given prior belief in those hypotheses and new evidence. In the drug example, the hypothesis suite was discrete: drug user or not drug user. More commonly, though, when we perform Bayesian analysis, our hypothesis concerns a continuous parameter, or many parameters. Our posterior (or updated beliefs...