Sample Size Determination in Bayesian Analysis

The problem of sample size determination in the context of Bayesian analysis, decision theory and quality management is considered. For the familiar, and practically important, parameter of a binomial distribution with a beta prior, we present complete and exact solutions for determining the sample sizes when preset precision conditions are imposed on commonly used criteria such as posterior variance, Bayes risk and expected value of sample information. The results obtained here also permit a unifying treatment of several sample size problems of practical interest and an example shows how they can be used in a managerial situation. A computer program for a personal computer handles all computational complexities and is available upon request.