Bayesian estimation of state-space models applied to deconvolution of Bernoulli-Gaussian processes

In this article, we use stochastic simulation techniques to estimate the a posteriori density of the hidden-state process and hyperparameters of conditionally linear Gaussian state-space models. The estimation method relies on Markov chains Monte Carlo methods and more especially the Gibbs sampler. We apply this algorithm to non-blind and blind Bayesian deconvolution of Bernoulli-Gaussian processes. Convergence of the algorithm is established. In simulations, very satisfactory results are obtained. (C) 1997 Elsevier Science B.V.