Sensitivity of Bayes Procedures to the Prior Distribution

Abstract

In the statistical decision problem, let p 0 be a given prior probability distribution and d 0 be the Bayes decision function under p 0 . Our basic approach is to find the nearest distribution to p 0 for which the optimal decision function would lead to an expected saving of some fixed amount ϵ over using d 0 . Hence, for any prior distribution nearer to p 0 than this one, do is ϵ-Bayes. This sensitivity analysis is considered from two viewpoints, before and after performing the experiment. These results constitute a modification and extension of some recent results by Fishburn, Murphy, and Isaacs, and we make use of their basic approach and computing algorithm. Our modifications are applicable to their problem as well.