Research on Bayesian nonparametric methods has received a growing interest for the past twenty years, especially since the development of powerful simulation algorithms which makes the implementation of complex Bayesian methods possible. From that point it is necessary to understand from a theoretical point of view the behaviour of Bayesian nonparametric methods. This thesis presents various contributions to the study of frequentist properties of Bayesian nonparametric procedures. Although studying these methods from an asymptotic angle may seems restrictive, it allows to grasp the operation of the Bayesian machinery in extremely complex models. Furthermore, this approach is particularly useful to detect the characteristics of the prior that are strongly influential in the inference. Many general results have been proposed in the literature in this setting, however the more complex and realistic the models the further they get from the usual assumptions. Thus many models that are of great interest in practice are not covered by the general theory. If the study of a model that does not fall under the general theory has an interest on its owns, it also allows for a better understanding of the behaviour of Bayesian nonparametric methods in a general setting.
Bayesian Statistics, Nonparametric Statistics, Semiparametric Statistics, Bayesian testing, Inverse problems, adaptation.
Information (theme 2)
L'université Paris-Dauphine
Algorithms and Complexity

Salomond, J.B. (2014, October 6). Propriétés fréquentistes des méthodes Bayésiennes semi-paramétriques et non-paramétriques = Frequentist properties of Bayesian semiparametric and nonparametric procedures..