Preference-Order Recursion for Finding Relevant Pure, Admissible and Optimal Statistical Decision Functions

Abstract

A preference-order recursion algorithm for obtaining a relevant subset of pure, admissible (non-dominated, efficient) decision functions which converges towards an optimal solution in statistical decision problems is proposed. The procedure permits a decision maker to interactively express strong binary preferences for partial decision functions at each stage of the recursion, from which an imprecise probability and/or utility function is imputed and used as one of several pruning mechanisms to obtain a reduced relevant subset of admissible decision functions or to converge on an optimal one. The computational and measurement burden is thereby mitigated significantly, for example, by not requiring explicit or full probability and utility information from the decision maker. The algorithm is applicable to both linear and nonlinear utility functions. The results of behavioral and computational experimentation show that the approach is viable, efficient, and robust.