Descriptif

Syllabus :   For the past few years, statistical learning and optimization of complex dynamical systems with latent data have been applied to time series analysis across a wide range of applied science and engineering domains such as signal processing, target tracking, enhancement and segmentation of speech and audio signals, inference of ecological networks, etc.

Solving Bayesian nonlinear filtering and smoothing problems, i.e. computing the posterior distributions of some hidden states given a record of observations, and computing the posterior distributions of the parameters is crucial to perform maximum likelihood estimation and prediction of future states of partially observed models. Estimators of these posterior distributions may be obtained for instance with Sequential Monte Carlo (SMC), also known as particle filtering and smoothing, and Markov Chain Monte Carlo (MCMC) methods.

This course sets the focus on MCMC algorithms and provides an overview of such approaches: introduction to standard procedures, convergence properties of a few algorithms and practical extensions (with simulations based on Python Notebooks) to more complex solutions.

Numerus Clausus: 30

Grading – 3 ECTS

Quiz

Project based on a research article

Topics covered
Markovian models (specific focus on observation-driven models).
Introduction to Markov chain Monte Carlo algorithms.
Some convergence results of Markov chain Monte Carlo algorithms.
Pseudo-Marginal MCMC and applications.
Hamiltonian Monte Carlo algorithms and variants.

Introduction to variational methods.