Bayésien non-paramétrique, convergence et forme limite de lois a posteriori
Ismaël Castillo · HAL (Le Centre pour la Communication Scientifique Directe) · 2014
This manuscript presents a synthesis of my research work over the last few years. It discusses my contributions to the study of the Bayes posterior distribution in statistical models with many or infinitely many parameters, such as nonparametric and semiparametric models. We follow a three-part outline. The first two chapters are a synthesis of the obtained results on convergence rates of posterior distributions. The third chapter considers limiting shape results. The Bernstein-von Mises theorem is established in infinite dimensions, in both semiparametric and nonparametric frameworks.