Frequentist properties of semi-parametric and non-parametric Bayesian methods.

Summary Research on non-parametric Bayesian methods has grown considerably over the last twenty years, especially since the development of simulation algorithms that allow them to be put into practice. It is therefore necessary to understand, from a theoretical point of view, the behavior of these methods. This thesis presents different contributions to the analysis of the frequentist properties of non-parametric Bayesian methods. Although being placed in an asymptotic framework may seem restrictive at first sight, it nevertheless allows us to understand the functioning of Bayesian procedures in extremely complex models. In particular, it allows us to detect the aspects of the a priori that are particularly influential on the inference. Many general results have been obtained in this framework, but as the models become more and more complex and realistic, they deviate from the classical assumptions and are no longer covered by the existing theory. In addition to the intrinsic interest of studying a specific model that does not satisfy the classical assumptions, this also allows for a better understanding of the mechanisms that govern the operation of non-parametric Bayesian methods.