Bayesian computation

Objectifs

This course is an introduction to Bayesian statistics and the numerical methods classically used within this framework. First, the foundations of this non-frequentist approach will be presented, along with the computational techniques derived from it. Secondly, the Markov chain Monte Carlo method will be studied. This is a class of algorithms for sampling probability distributions based on the construction of an ergodic Markov chain. These algorithms are commonly used in Bayesian statistics, but also for the evaluation of multiple integrals. At the end of this course, students should be able to solve inferential statistics problems using a Bayesian approach, and to implement classical Markov chain Monte Carlo algorithms.

Plan

A priori and a posteriori distributions. Bayes estimator. Choice of a priori distribution.
Random number generator (pseudo-random numbers, inversion of distribution function, acceptance-rejection).
Monte-Carlo method and MCMC (Metropolis-Hastings, Gibbs).

Prérequis

Probability, SEM, Markov chains, Inferential statistics