Fully Bayesian analysis of conditionally linear Gaussian state space models

In this paper, we use the Gibbs sampler to carry out Bayesian inference on conditionally linear Gaussian state space models. In a Bayesian framework, the Gibbs sampler is a powerful iterative procedure which can be seen as a stochastic analogue of the EM algorithm. To use it, it is necessary to sample from complex multivariate densities. An efficient algorithm is derived. An application to Bernoulli-Gauss processes deconvolution is given for which very satisfactory results are obtained. For this example, the geometric convergence of the algorithm is established