Fully Bayesian analysis of Hidden Markov models

In this paper, we present in an unified framework some applications of stochastic simulation techniques, the Markov chain Monte Carlo methods, to perform Bayesian inference for a very wide class of hidden Markov models. Efficient implementation of the Gibbs sampler based on finite dimensional optimal filters is described. An improved version of this algorithm is also presented. Two problems of great practical interest in signal processing are addressed: blind deconvolution of Bernoulli-Gauss processes and blind equalization of a channel. In simulations, we obtain very satisfactory results.