High-dimensional modeling of spatial and spatio-temporal conditional extremes using INLA and Gaussian Markov random fields
High-dimensional modeling of spatial and spatio-temporal conditional extremes using INLA and Gaussian Markov random fields
复制标题
使用 INLA 和高斯马尔可夫随机场对空间和时空条件极值进行高维建模
作者：
Emma S. Simpson;T. Opitz;J. Wadsworth
The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatio-temporal settings. After standardizing the marginal distributions and applying an appropriate linear normalization, certain non-stationary Gaussian processes can be used as asymptotically-motivated models for the process conditioned on threshold exceedances at a fixed reference location and time. In this work, we adapt existing conditional extremes models to allow for the handling of large spatial datasets. This involves specifying the model for spatial observations at d locations in terms of a latent m≪d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m\ll d$$\end{document} dimensional Gaussian model, whose structure is specified by a Gaussian Markov random field. We perform Bayesian inference for such models for datasets containing thousands of observation locations using the integrated nested Laplace approximation, or INLA. We explain how constraints on the spatial and spatio-temporal Gaussian processes, arising from the conditioning mechanism, can be implemented through the latent variable approach without losing the computationally convenient Markov property. We discuss tools for the comparison of models via their posterior distributions, and illustrate the flexibility of the approach with gridded Red Sea surface temperature data at over 6,000 observed locations. Posterior sampling is exploited to study the probability distribution of cluster functionals of spatial and spatio-temporal extreme episodes.
The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatio-temporal settings. After standardizing the marginal distributions and applying an appropriate linear normalization, certain non-stationary Gaussian processes can be used as asymptotically-motivated models for the process conditioned on threshold exceedances at a fixed reference location and time. In this work, we adapt existing conditional extremes models to allow for the handling of large spatial datasets. This involves specifying the model for spatial observations at d locations in terms of a latent m≪d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m\ll d$$\end{document} dimensional Gaussian model, whose structure is specified by a Gaussian Markov random field. We perform Bayesian inference for such models for datasets containing thousands of observation locations using the integrated nested Laplace approximation, or INLA. We explain how constraints on the spatial and spatio-temporal Gaussian processes, arising from the conditioning mechanism, can be implemented through the latent variable approach without losing the computationally convenient Markov property. We discuss tools for the comparison of models via their posterior distributions, and illustrate the flexibility of the approach with gridded Red Sea surface temperature data at over 6,000 observed locations. Posterior sampling is exploited to study the probability distribution of cluster functionals of spatial and spatio-temporal extreme episodes.
DOI：
10.48550/arxiv.1912.06560
发表时间：
2019
期刊：
arXiv e-prints
影响因子：
--
作者：
Wadsworth Jennifer L.
通讯作者：
Wadsworth Jennifer L.
影响因子：
1.7
作者：
Richards J
通讯作者：
Richards J
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.