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.

翻译：许多环境过程，如降雨、风或降雪，本质上具有空间特性，因此在建立极端事件模型时必须考虑这一特征。此外，环境过程常与角度信息相关联，例如风速与风向、极端降雪与其在一年中的发生时间。本文提出了一种基于条件独立性假设的贝叶斯分层模型，旨在同时建模空间极端事件及其角度分量。该模型建立在极值理论以及处理连续域上方向统计学的最新进展基础之上。在贝叶斯框架下，本文引入了一种Gibbs采样器，并通过模拟研究分析了其性能。最后，文章将模型应用于法国极端风速数据的分析。结果表明，除法国地中海区域和阿尔卑斯山区外，法国的极端风事件主要来自西向。