Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method

C. P. Robert, T. Rydén, D. M. Titterington

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2000 · Volume 62 · Issue 1

Abstract

Hidden Markov models form an extension of mixture models which provides a flexible class of models exhibiting dependence and a possibly large degree of variability. We show how reversible jump Markov chain Monte Carlo techniques can be used to estimate the parameters as well as the number of components of a hidden Markov model in a Bayesian framework. We employ a mixture of zero-mean normal distributions as our main example and apply this model to three sets of data from finance, meteorology and geomagnetism.

Keywords

Bayesian inference, Hidden Markov model, Markov chain Monte Carlo methods, Model selection

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