The Annals of Statistics

A Statistical Diptych: Admissible Inferences--Recurrence of Symmetric Markov Chains

Morris L. Eaton

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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.

Article information

Ann. Statist., Volume 20, Number 3 (1992), 1147-1179.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62C05: General considerations
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 62C15: Admissibility

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


Eaton, Morris L. A Statistical Diptych: Admissible Inferences--Recurrence of Symmetric Markov Chains. Ann. Statist. 20 (1992), no. 3, 1147--1179. doi:10.1214/aos/1176348764.

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