Bayesian regression

Objectives

The course will present the theory of Bayesian inference. Examples and exercises will be developed during the course.

At the end of the course, students should be able to :

.calculate the à-posteriori distribution for conjugate models, construct a Bayesian estimator, construct Bayesian hypothesis tests and confidence regions ;

. understand the difference between frequentist and Bayesian inference procedures

. implement a Bayesian inference procedure on a computer ;

.solve exercises based on concepts learned during the course.

Course outline

-Bayesian principles, exchangeability, likelihood principle.

-Determination of a priori laws

-Bayesian inference: point estimation, confidence regions, hypothesis testing.

-Asymptotic properties of Bayesian approaches.

-Model selection and comparison.

Prerequisites

Inferential statistics and computational statistics course.