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

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