Monte Carlo algorithms for Bayesian estimation of hidden Markovian models. Application to radiation signal processing.

Summary Hidden Markovian models (CMMs) are used to model a large number of signals in various domains, including the field of nuclear measurement. Except for a few simple cases, Bayesian estimation problems for CMMs do not admit analytical solutions. This thesis is devoted to the algorithmic solution of a part of these problems by monte carlo methods and to the application of these algorithms to radiation signal processing. After having given some elements on the radiation signals and the associated mmc, the bayesian estimation problems are formulated. We then propose a synthesis of monte carlo algorithms for online Bayesian estimation of non-linear and non-Gaussian mmc and propose several original extensions of existing methods. In the following chapters, offline estimation methods based on markov chain monte carlo methods (mcmc) are presented. First, data augmentation and two original simulated annealing algorithms based on data augmentation are proposed and studied for the estimation of states of linear models with jumps. A simulated annealing algorithm based on data augmentation is then proposed and studied for the estimation of parameters in the sense of maximum a posteriori of finite state mcm. Then we propose mcmc algorithms for Bayesian estimation of arma models driven by a finite and/or continuous mixture of Gaussians of unknown parameters. The first algorithm is a gibbs sampler. This algorithm suffers from several shortcomings, a second more efficient algorithm based on the concept of partial conditioning is proposed. It is applied to the estimation of arma models with impulse excitation as well as to the blind deconvolution of bernoulli-gauss processes. Finally, we propose a mcmc algorithm for the Bayesian estimation of models with non-Gaussian observations. Two original procedures for simulating the hidden state process are proposed. This algorithm is applied to the estimation of the intensity of a doubly stochastic fish process from count data.