Spatial modeling of extremes and an angular component

Abstract: Many environmental processes such as rainfall, wind or snowfall are inherently spatial and the modelling of extremes has to take into account that feature. In addition, environmental processes are often attached with an angle, e.g., wind speed and direction or extreme snowfall and time of occurrence in year. This article proposes a Bayesian hierarchical model with a conditional independence assumption that aims at modelling 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 on extreme wind speed in France. Results show that extreme wind events in France are mainly coming from West apart from the Mediterranean part of France and the Alps.