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September, 1992 A Statistical Diptych: Admissible Inferences--Recurrence of Symmetric Markov Chains
Morris L. Eaton
Ann. Statist. 20(3): 1147-1179 (September, 1992). DOI: 10.1214/aos/1176348764


Given a parametric model and an improper prior distribution, the formal posterior distribution induces decision rules in any decision problem. The results here provide conditions under which this formal Bayes method produces admissible decision rules for all quadratically regular decision problems. The conditions derived are shown to be equivalent to the recurrence of a natural symmetric Markov chain (on the parameter space) generated by the model and the improper prior. The results are also used to give conditions under which formal predictive distributions are admissible decision rules in certain prediction problems.


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Morris L. Eaton. "A Statistical Diptych: Admissible Inferences--Recurrence of Symmetric Markov Chains." Ann. Statist. 20 (3) 1147 - 1179, September, 1992.


Published: September, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0767.62002
MathSciNet: MR1186245
Digital Object Identifier: 10.1214/aos/1176348764

Primary: 62C05
Secondary: 62C10 , 62C15

Keywords: almost admissibility , formal Bayes rules , formal posterior distributions , Improper prior distributions , prediction , predictive distributions , recurrence of symmetric Markov chains

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 3 • September, 1992
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