Sensitivity of Bayes Procedures to the Prior Distribution

In the statistical decision problem, let p0 be a given prior probability distribution and d0 be the Bayes decision function under p0. Our basic approach is to find the nearest distribution to p0 for which the optimal decision function would lead to an expected saving of some fixed amount ϵ over using d0. Hence, for any prior distribution nearer to p0 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.