Markovian & Gaussian processes

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 This course is mainly devoted to Gaussian process regression. This tool, also known as kriging and historically introduced for modeling and forecasting spatial quantities such as global surface temperature, is now widely used to model complex numerical experiments. We will present the model, parameter inference using frequentist and Bayesian methods, model prediction and its use in the context of uncertainty quantification.

1/ Introduction to uncertainty quantification in complex numerical models 2/ Gaussian process regression model 3/ Introduction to Bayesian statistics - application to the Gaussian process regression model. 4/ Bayesian optimization and sensitivity analysis.