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：多种自然现象在短空间距离上表现出空间极值依赖性。然而，空间极值文献中提出的现有模型通常假设这种极值依赖性在整个区域内持续存在。在对大地理区域的极值进行建模时，这是一个很强的局限性，但文献中对此大多未予重视。本文基于一种新型高斯尺度混合模型，发展了一个更现实的贝叶斯框架：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；随机尺度分量则建模为低秩帕累托尾部或威布尔尾部的空间过程，由紧支撑基函数确定。我们证明，所提模型近似尾部平稳，并能捕捉广泛的极值依赖结构。其固有的稀疏结构允许基于定制的马尔可夫链蒙特卡洛算法在高维空间中进行快速贝叶斯计算，该算法优先校准尾部。我们将该模型应用于分析孟加拉国的重季风降雨数据。研究表明，本模型优于自然竞争模型，并能很好地拟合降水极值。最后，我们利用拟合模型对边际降水和空间聚合的长期重现水平进行推断。