A Stepwise Bayesian Procedure

Abstract

Ordinarily a Bayesian estimation procedure uses one prior distribution to obtain a unique estimation rule (its Bayes rule). From the decision theoretical point of view, this procedure can be regarded as a convenient way to obtain admissible decision rules. However, many intuitively appealing, admissible estimation rules cannot be obtained directly in this way. We propose a new mechanism, called the Stepwise Bayesian Procedure (SBP). When the parameter space contains only finitely-many points and the loss function is strictly convex, this SBP can be used to obtain every admissible estimation rule. A relationship between SBP and the limiting Bayes rules is given.