Open Access
June 2006 Bayesian analysis for reversible Markov chains
Persi Diaconis, Silke W. W. Rolles
Ann. Statist. 34(3): 1270-1292 (June 2006). DOI: 10.1214/009053606000000290


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.


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Persi Diaconis. Silke W. W. Rolles. "Bayesian analysis for reversible Markov chains." Ann. Statist. 34 (3) 1270 - 1292, June 2006.


Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1118.62085
MathSciNet: MR2278358
Digital Object Identifier: 10.1214/009053606000000290

Primary: 62M02
Secondary: 62C10

Keywords: Bayesian analysis , conjugate priors , Hypothesis testing , reversible Markov chains

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 3 • June 2006
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