Bayesian Prediction under Relative Entropy Regret

• Activity Number: 166
• Type: Invited
• Date/Time: Monday, August 8, 2005 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Trevor J. Sweeting*+
• Companies: University College London
• Keywords: Bayesian prediction ; Relative entropy regret ; Robustness ; Minimaxity

Abstract

In this paper, we investigate the performance of Bayesian prediction under a relative entropy regret criterion. Since the underlying logarithmic scoring rule is proper, Bayesian prediction will be optimal whenever prior specifications are complete and well-calibrated. In such cases, there is no need to go beyond the Bayesian paradigm. However, if our prior specifications are partial or not properly formulated, performance considerations become important. Particular cases include the extremes of vague, unspecified prior knowledge and substantive but incomplete prior specification---for example, when only a few quantiles have been elicited. In either case, an inappropriate specification of the prior may lead to poor predictive performance. The predictive criterion used here is based on Aitchison (1975), and can be viewed as a predictive version of the relative entropy regret considered by Bernardo (1979), Clarke and Barron (1994), and others. However, the focus here is on predictive performance with respect to some unspecified prior distribution as opposed to performance in repeated sampling. Within this framework, this talk explores Bayesian predictive robustness and minimaxity.