Spatial Modeling of Extremes and an Angular Component

Many environmental processes, such as rainfall, wind, or snowfall, are inherently spatial, and the modeling of extremes has to take into account that feature. In addition, such processes may be associated with a nonextremal feature, for example, wind speed and direction or extreme snowfall and time of occurrence in a year. This article proposes a Bayesian hierarchical model with a conditional independence assumption that aims at modeling simultaneously spatial extremes and an angular component. The proposed model relies on the extreme value theory as well as recent developments for handling directional statistics over a continuous domain. Working within a Bayesian setting, a Gibbs sampler is introduced whose performances are analysed through a simulation study. The paper ends with an application to extreme wind speed in France. Results show that extreme wind events in France are mainly coming from the West, apart from the Mediterranean part of France and the Alps.