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

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

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,

ISSN 0281-1944

Hidden Markov models form an extension of mixture models providing a flexible class of models exhibiting dependence and a possibly large degree of variability. In this paper 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, respectively.
Key words:
Hidden Markov model, Bayesian inference, model selection, Markov chain Monte Carlo