Bayesian statistical methods for complex numerical models

This course focuses on the modeling of time- and space-dependent random phenomena. The first part of the course is mainly devoted to Gaussian process regression. This tool, also known as kriging and historically introduced for modeling and forecasting spatial quantities, is now widely used to model complex numerical experiments. Uncertainty quantification and metamodel-based optimization techniques will also be presented, along with an introduction to Bayesian statistics. The second part is devoted to Markov processes, which are used to model temporal phenomena.

1/ Kriging model on spatialized data 2/ Frequentist estimation 3/ Estimation using a Bayesian approach 4/ Using kriging to approximate expensive numerical models: Bayesian optimization and uncertainty quantification. 5/ Continuous-time Markov chains 6/ Continuous-time Markov processes