Gibbs sampling for parameters estimation and change-points detection in inverse problems. Application to electromagnetic imaging

In the framework of Bayesian inverse problems, we investigate the use of suitable prior probabilities for modeling the presence of abrupt changes in the distribution of the non-observed data sequence. We adopt a Gibbs-type sampling method for estimating the posterior distribution of this sequence. In the second part, we apply recent results on stochastic versions of the well-known EM algorithm with averaging and acceleration techniques, to estimate some parameters of the model. A numerical example for the magnetotelluric inverse problem is proposed.