The use of Previous Experience in Reaching Statistical Decisions

Abstract

Instead of minimizing the maximum risk it is proposed to restrict attention to decision procedures whose maximum risk does not exceed the minimax risk by more than a given amount. Subject to this restriction one may wish to minimize the average risk with respect to some guessed a priori distribution suggested by previous experience. It is shown how Wald's minimax theory can be modified to yield analogous results concerning such restricted Bayes solutions. A number of examples are discussed, and some extensions of the above criterion are briefly considered.