On the problem of selecting good populations

The problem of selecting good populations out of k normal populations is considered in a Bayesian framework under exchangeable normal priors and additive loss functions. Some basic approximations to the Bayes rules are discussed. These approximations suggest that some well-known classical rules are "approximate" Bayes rules. Especially, it is shown that Gupta-type rules are extended Bayes with respect to a family of the exchangeable normal priors for any bounded and additive loss function. Furthermore, for a simple loss function, the results of a Monte Carlo comparison of Gupta-type rules and Seal-type rules are presented. They indicate that, in general, Gupta-type rules perform better than Seal-type rules