On Two-Stage Bayes Selection Procedures.

Abstract : Let Pi sub 1,..,Pi sub K be normal populations with unknown means and a common known variance. The goal is to find the population with the largest mean. Two-stage procedures with screening at the first stage are studied in a Bayesian approach. They are based on k samples of common size n sub 1 drawn at Stage 1, and on samples of common size n sub 2 drawn at Stage 2 from all those populations which have not been screened out at Stage 1. If only one population is selected at Stage 1, the procedure stops at Stage 1. Under the assumption of a specific loss function which includes costs of sampling, a Bayes procedure is derived with respect to i.i.d. normal priors. Its properties are discussed and several approximations are considered. The expected value of the maximum of k independent normals with known but distinct means and a common known variance plays a crucial rule in the determination of the Bayes procedure. (Author)