Bayesian statistics

Crédit : 4 ECTS
Langue du cours : anglais

Volume horaire

• CM : 24 h
• Volume horaire global (hors stage) : 24 h

Compétences 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.

Description 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

Bibliographie, lectures recommandées

Bayesian choice, C.P. Robert The fundamentals of Bayesian nonparametrics, S. Ghosal and A. van der Vaart

Enseignant responsable

JUDITH ROUSSEAU