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 $m\ll d$ 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.
翻译:有条件的极端框架允许对依赖性极端进行基于事件的随机建模,并且最近已经扩展到空间和空间-时空环境。在对边际分布进行标准化和适用适当的线性正常化之后,某些非静止高斯进程可以用作固定参考地点和时间以临界超值为条件的流程的零星驱动模型。在这项工作中,我们调整现有的有条件极端模型,以便处理大型空间数据集。这包括以潜值$m\ll dd dispio-demode 高斯模型的方式指定美元地点的空间观测模型,其结构由高斯马可夫随机字段标定。我们用综合的拉比近定位或国家空间和空间时空时超值模型对包含数千个观察地点的数据集进行巴耶斯推论。我们解释了由于调节机制而导致的空间和空间-时空高值高值流程的制约如何通过潜在变量方法实施,而不会失去可计算方便的马尔科夫空间- 维度分布模型模型的结构。我们通过观察的海平面空间-海平面分布模型工具,通过观测的海面模型进行对比。