The Annals of Statistics

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

Morris L. Eaton

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348764

Digital Object Identifier
doi:10.1214/aos/1176348764

Mathematical Reviews number (MathSciNet)
MR1186245

Zentralblatt MATH identifier
0767.62002

JSTOR
links.jstor.org

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1176348764


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