Bayesian statistics - WMM9AM22

Goal(s)

The course aims at providing an overview of Bayesian parametric and nonparametric statistics. Students will learn how to model statistical and machine learning problems from a Bayesian perspective and study theoretical properties of the models.

Content(s)

This course is in two parts covering fundamentals of Bayesian parametric and nonparametric inference, respectively. It focuses on the key probabilistic concepts and stochastic modelling tools at the basis of the most recent advances in the field.
Part 1

Foundations of Bayesian inference: exchangeability, de Finetti's representation theorem
Conjugacy in simple models (binomial, Poisson, Gaussian)
Some elements of posterior sampling, Markov chain Monte Carlo
Bayesian neural networks and their Gaussian process limit

Part 2

Clustering and Dirichlet process, random partitions
Models beyond the Dirichlet process, random measures, Indian buffet process
Some elements of Bayesian asymptotics