Bayesian inference for Hidden Markov Model

Abstract

� Hidden Markov Models can be considered an extension of mixture models, allowing for dependent observations. In a hierarchical Bayesian framework, we show how Reversible Jump Markov Chain Monte Carlo techniques can be used to estimate the parameters of a model, as well as the number of regimes. We consider a mixture of normal distributions characterized by different means and variances under each regime, extending the model proposed by Robert et al. (2000), based on a mixture of zero mean normal distributions.