Modeling episodes of extreme events on graphs

Extreme value theory provides an asymptotic and probabilistic framework for modeling and simulating extreme events. For dependent extreme events, an interesting approach consists of modeling events for which a risk functional exceeds a high threshold. The resulting models are known as r-Pareto processes. These processes have been studied for georeferenced data but still remain little explored in the multivariate case for most of the risk functionals of interest. An important field of application for these methods concerns extreme climatic events occurring simultaneously in several geographical areas or in several variables. Objective of this project is to develop estimation and simulation methods for multivariate models, with a particular emphasis on models based on Markovian Gaussian fields for which a graph describes the interactions between variables. The proposed approaches will be applied to climate data in order to study the concomitance of extreme events in different geographic areas, such as French regions or certain watersheds, or between different climate variables, such as temperatures, precipitation and wind speeds. .