The Annals of Statistics

Bayesian analysis for reversible Markov chains

Persi Diaconis and Silke W. W. Rolles

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Abstract

We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Pólya’s urn. We give closed form normalizing constants, a simple method of simulation from the posterior and a characterization along the lines of W. E. Johnson’s characterization of the Dirichlet prior.

Article information

Source
Ann. Statist., Volume 34, Number 3 (2006), 1270-1292.

Dates
First available in Project Euclid: 10 July 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1152540749

Digital Object Identifier
doi:10.1214/009053606000000290

Mathematical Reviews number (MathSciNet)
MR2278358

Zentralblatt MATH identifier
1118.62085

Subjects
Primary: 62M02: Markov processes: hypothesis testing
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Bayesian analysis reversible Markov chains conjugate priors hypothesis testing

Citation

Diaconis, Persi; Rolles, Silke W. W. Bayesian analysis for reversible Markov chains. Ann. Statist. 34 (2006), no. 3, 1270--1292. doi:10.1214/009053606000000290. https://projecteuclid.org/euclid.aos/1152540749


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