## ABSTRACT

The beta-binomial is used when making inferences about a proportion or a probability. Suppose a forensic accountant wants to estimate the proportion of fraudulent claims filed with an insurance company by an automobile repair chain. Formally, one would have to assume that an infinite number of claims have been filed, and that the forensic accountant is sampling this population of claims at random. For another mock case study that illustrates several facets of Bayesian reasoning, suppose that a hospital review system flags a nurse who has had an unusually large number of his patients die during his shift. The police are consulted, and the district attorney wants to determine how improbable that observed number of deaths might be. Conjugacy is sometimes helpful, but most realistic applications are more complex. Modern Bayesian analysis can address essentially any question that frequentist methods do, but there are some areas where the Bayesian perspective is especially elegant.