The Annals of Statistics
- Ann. Statist.
- Volume 6, Number 2 (1978), 333-345.
On Finitely Additive Priors, Coherence, and Extended Admissibility
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.
Ann. Statist., Volume 6, Number 2 (1978), 333-345.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 60A05: Axioms; other general questions
Heath, David; Sudderth, William. On Finitely Additive Priors, Coherence, and Extended Admissibility. Ann. Statist. 6 (1978), no. 2, 333--345. doi:10.1214/aos/1176344128. https://projecteuclid.org/euclid.aos/1176344128