Efficient Modeling of Spatial Extremes over Large Geographical Domains
Efficient Modeling of Spatial Extremes over Large Geographical Domains
复制标题
大地理区域空间极值的有效建模
DOI：
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复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
D. Bolin
中科院分区：
文献类型：
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作者：
A. Hazra;Raphael Huser;D. Bolin
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，在空间极值文献中提出的现有模型通常假设极值依赖在整个域中持续存在。这是一个强大的限制时，在大的地理域建模极端，但它在文献中大多被忽视。在这里，我们开发了一个更现实的贝叶斯框架的基础上，一个新的高斯尺度混合模型，高斯过程组件定义的随机偏微分方程产生一个稀疏的精度矩阵，和随机尺度组件建模为一个低秩的帕累托尾或威布尔尾空间过程确定的紧支持的基函数。我们表明，我们提出的模型是近似尾平稳的，它可以捕捉到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罗算法在高空间维度上进行快速贝叶斯计算，该算法优先考虑尾部的校准。我们适合我们的模型来分析孟加拉国的季风降雨数据。我们的研究表明，我们的模型优于自然竞争对手，它适合降水极端。最后，我们使用拟合模型得出的推论，对长期回报水平的边际降水和空间聚集。
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.
DOI：
10.48550/arxiv.1912.06560
发表时间：
2019
期刊：
arXiv e-prints
影响因子：
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作者：
Wadsworth Jennifer L.
通讯作者：
Wadsworth Jennifer L.
用于对多位置数据集进行空间极值灵活建模的分层变换尺度混合
影响因子：
3.7
作者：
Zhang, Likun;Shaby, Benjamin A.;Wadsworth, Jennifer L.
通讯作者：
Wadsworth, Jennifer L.