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arXiv · 1105.2640

Bayesian analysis of variable-order, reversible Markov chains

Sergio Bacallado
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Abstract

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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Sergio Bacallado. 2011-05-13. Bayesian analysis of variable-order, reversible Markov chains. https://doi.org/10.1214/10-aos857

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