The Annals of Statistics

Elements of Multi-Bayesian Decision Theory

S. Weerahandi and J. V. Zidek

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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.

Article information

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346319

Digital Object Identifier
doi:10.1214/aos/1176346319

Mathematical Reviews number (MathSciNet)
MR865343

Zentralblatt MATH identifier
0574.62001

JSTOR
links.jstor.org

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

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

Citation

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


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