Markov processes and Gaussian processes for modelling temporal and spatial phenomena

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.