Bayesian analysis of variable-order, reversible Markov chains

Details Bayesian analysis of variable-order, reversible Markov chains Bayesian analysis of variable-order, reversible Markov chains

2011-05-13

arxiv.org/abs/1105.2640v1

Annals of Statistics 2011, Vol. 39, No. 2, 838-864

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/10-AOS857 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/10-AOS857

We define a conjugate prior for the reversible Markov chain of order $r$. The prior arises from a partially exchangeable reinforced random walk, in the same way that the Beta distribution arises from the exchangeable Poly\'{a} urn. An extension to variable-order Markov chains is also derived. We show the utility of this prior in testing the order and estimating the parameters of a reversible Markov model.

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