Processus de Markov et Processus Gaussiens pour la modélisation de phénomènes temporels et spatiaux

This course is oriented towards the modeling of random phenomena depending on time or space. The first part will be devoted to Markovian processes, processes involved in the modeling of temporal phenomena. Both theoretical modeling tools and numerical aspects will be presented. Their use will be seen through models from ecology, the environment or finance. The second part will be mainly devoted to regression by Gaussian processes. This tool also known as kriging and historically introduced for the modeling and forecasting of spatial quantities, is now widely used to model complex numerical experiments. We will also present the techniques of uncertainty quantification and Bayesian optimization.

1/ Continuous Time Markov Chain 2/ MArkov processes in continuous time 3/ Kriging model for spatial data 4/ Kriging in the context of approximation of expensive codes: Bayesian optimization and uncertainty quantification.