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, environmental extremes are often attached with an angle, e.g., wind gusts and direction or extreme snowfall and time of occurrence. This article proposes a Bayesian hierarchical model with a conditional independence assumption that aims at modeling simultaneously spatial extremes and angles. The proposed model relies on the extreme value theory as well a recent development for handling directional statistics over a continuous domain. Starting with sketches of the necessary elements of extreme value theory and directional statistics, the model is motivated. Working within a Bayesian setting, a Gibbs sampler is introduced and whose performances are analyzed through a simulation study. The paper ends with an application on extreme snowfalls in the French Alps. Results show that, the most severe events tend to occur later in the snowfall season for high elevation regions than for lower altitudes.

翻译：许多环境过程，如降雨、风或降雪，本质上是空间性的，极值建模必须考虑这一特征。此外，环境极值常伴有角度属性，例如阵风及其方向，或极端降雪及其发生时间。本文提出了一种基于条件独立性假设的贝叶斯层次模型，旨在同时建模空间极值及其角度。该模型依赖于极值理论以及连续域上方向统计的最新发展。首先概述了极值理论和方向统计的必要基础，进而引出模型构建。在贝叶斯框架下，引入吉布斯采样器并通过模拟研究分析其性能。最后，将该模型应用于法国阿尔卑斯山地区的极端降雪实例。结果表明，高海拔地区最严重事件往往在降雪季节后期发生，而低海拔地区则更早出现。