Bayesian statistics
Enseignant responsable :
Volume horaire : 24Description du contenu de l'enseignement :
This course will cover the foundations of Bayesian statistics: including Bayesian decision theory, Bayesian tests and model selection, credible measures and will cover also the fundamental results of Bayesian asymptotics: Posterior contraction and consistency, parametric Bernstein von Mises theorem, BIC formula and Laplace approximation
Pré-requis obligatoires :
Probability theory: conditional distributions, limit theorems, measures Statistics: likelihood, estimators, confidence regions
Compétence à acquérir :
The aim of this course is to introduce the foundations of Bayesian statistics , mostly from a theoretical perspective. The students should then be fluent in Bayesian decision theory and understand the mechanisms underlying Bayesian asymptotic theory; with its implications and its limitations.
Bibliographie, lectures recommandées
Bayesian choice, C.P. Robert The fundamentals of Bayesian nonparametrics, S. Ghosal and A. van der Vaart