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March, 1978 On Finitely Additive Priors, Coherence, and Extended Admissibility
David Heath, William Sudderth
Ann. Statist. 6(2): 333-345 (March, 1978). DOI: 10.1214/aos/1176344128

Abstract

A decision maker is seen to be coherent in the sense of de Finetti if, and only if, his probabilities are computed in accordance with some finitely additive prior. If a bounded loss function is specified, then a decision rule is extended admissible (i.e., not uniformly dominated) if and only if it is Bayes for some finitely additive prior. However, if an improper countably additive prior is used, then decisions need not cohere and decision rules need not be extended admissible. Invariant, finitely additive priors are found and their posteriors calculated for a class of problems including translation parameter problems.

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David Heath. William Sudderth. "On Finitely Additive Priors, Coherence, and Extended Admissibility." Ann. Statist. 6 (2) 333 - 345, March, 1978. https://doi.org/10.1214/aos/1176344128

Information

Published: March, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0385.62005
MathSciNet: MR464450
Digital Object Identifier: 10.1214/aos/1176344128

Subjects:
Primary: 62C10
Secondary: 60A05

Keywords: Coherence , decision theory , extended admissibility , finite additivity , improper priors , invariant priors

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 2 • March, 1978
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