Hierarchical Bayesian Selection Procedures for the Best Binomial Population

Abstract : In this paper a hierarchical Bayesian model is adopted to derive selection procedures for selecting the best of k binomial parameters, say the probability of success corresponding to k different suppliers. This model facilitates the use of prior information in the analysis for both small and large sample sizes. In addition to computing posterior probabilities that the i to the th power supplier is best, this paper presents expressions for deciding how much better a given supplier is relative to the others. Prior information is assumed to begin with exchangeability and can be more informative if the experimenter has other knowledge about the suppliers as a group. A numerical example is given and the paper concludes with remarks about future work.