Elements of Multi-Bayesian Decision Theory

Abstract

This work provides the elements of a framework for multi-Bayesian statistical decision theory. Solution concepts and criteria are presented. The relationship to Wald's theory is discussed. And two criteria for assessing group decision procedures are defined. One is based on the idea of subsampling the group, and it is found that among the proposed solution concepts only Nash's solution is optimal under subsampling as well. The other assumes the group is itself a sample from a superpopulation, and this yields an analogue of Wald's theory where the elicitation of the priors becomes part of the experimental process. Results on admissibility, minimaxity and so on found in Wald's classical theory become directly applicable in the new setting.