Bayesian analysis for reversible Markov chains

Details Bayesian analysis for reversible Markov chains Bayesian analysis for reversible Markov chains

2006-05-22

arxiv.org/abs/math/0605582v2

Annals of Statistics 2006, Vol. 34, No. 3, 1270-1292

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000290 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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 P\'{o}lya'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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