Numerical Specification of Discrete Least Favorable Prior Distributions

Abstract

A broad class of statistical decision problems are solved by minimax procedures which are Bayes with respect to discrete least favorable prior distributions. A general algorithm for specifying such distributions is presented which exploits the statistical properties of minimax procedures. The algorithm is demonstrated by characterizing the procedure which simultaneously minimizes a Bayes risk and a maximum risk under different loss functions in a simple multi-objective decision problem.