Efficient Modeling of Spatial Extremes over Large Geographical Domains
针对现有空间极值模型假设极端依赖在全域存在的局限，提出一种基于高斯尺度混合模型的贝叶斯框架，通过稀疏精度矩阵和低秩空间过程捕捉多种极端依赖结构，并应用于孟加拉国季风降雨数据分析，在计算效率和拟合效果上优于传统方法。
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 though 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 compactlysupported 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 probabilistic 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.