On the Risk Performance of Bays Empirical Bayes Procedures for Classification Between N(‐1,l) and N(1,1)

Summary In empirical Bayes decision making, the Bayes empirical Bayes approach is diccussed by Gilliland and Boyer (1979). In the finite state component case, the Bayes empirical Bayes procedures are shown to have optimal properties in a fairly general setting and believed to have small sample advantage over the classical rules. The flexibility of making desirable adjustments for these decision procedures by choice of prior enables one to set a proper strategy when dealing with actual problems. The applications of Bayes empirical Bayes procedures, however, create some interesting theoretical and computational problems as they are fairly complicated in structure. This paper gives a brief introduction into the Bayes empirical Bayes approach, and, to illustrate it, explicit results are given for testing H 0 : N(‐1,1) against H 1 : N(1,1).