Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is a strong limitation when modeling extremes over large geographical domains, and yet it has been mostly overlooked in the literature. We here develop a more realistic Bayesian framework based on a novel Gaussian scale mixture model, with the Gaussian process component defined by a stochastic partial differential equation yielding a sparse precision matrix, and the random scale component modeled as a low-rank Pareto-tailed or Weibull-tailed spatial process determined by compactly-supported basis functions. We show that our proposed model is approximately tail-stationary and that it can capture a wide range of extremal dependence structures. Its inherently sparse structure allows fast Bayesian computations in high spatial dimensions based on a customized Markov chain Monte Carlo algorithm prioritizing calibration in the tail. We fit our model to analyze heavy monsoon rainfall data in Bangladesh. Our study shows that our model outperforms natural competitors and that it fits precipitation extremes well. We finally use the fitted model to draw inference on long-term return levels for marginal precipitation and spatial aggregates.

翻译：各种自然现象在短空间距离上表现出空间极值依赖性。然而，现有空间极值文献中提出的模型通常假设极值依赖性在整个区域内持续存在。这在建模大地理区域的极值时是一个严重局限，但文献中却大多对此忽略。我们在此基于一种新颖的高斯尺度混合模型开发了更符合实际的贝叶斯框架，其中高斯过程分量由随机偏微分方程定义，产生稀疏精度矩阵，而随机尺度分量则建模为由紧支撑基函数确定的低秩帕累托尾或威布尔尾空间过程。我们表明，所提出的模型近似尾部平稳，并且能够捕获广泛的极值依赖结构。其固有的稀疏结构使得基于定制的优先校准尾部的马尔可夫链蒙特卡洛算法，能够在高维空间中进行快速贝叶斯计算。我们将模型拟合用于分析孟加拉国暴雨降雨数据。我们的研究表明，我们的模型优于自然竞争模型，并且能够很好地拟合降水极值。最后，我们使用拟合模型推断边际降水和空间聚集的长期重现水平。