The Annals of Statistics

Elements of Multi-Bayesian Decision Theory

S. Weerahandi and J. V. Zidek

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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.

Article information

Ann. Statist., Volume 11, Number 4 (1983), 1032-1046.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62A15
Secondary: 62C99: None of the above, but in this section

Bayes estimate Nash solution multivariate normal law statistical decision theory utility theory multi-person games bargaining games opinion pooling


Weerahandi, S.; Zidek, J. V. Elements of Multi-Bayesian Decision Theory. Ann. Statist. 11 (1983), no. 4, 1032--1046. doi:10.1214/aos/1176346319.

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