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 adopt a Bayesian perspective by implementing estimation through the integrated nested Laplace approximation (INLA), allowing for novel and flexible semi-parametric specifications of the Gaussian mean function. By using Gauss-Markov approximations of the Mat\'ern covariance function (known as the Stochastic Partial Differential Equation approach) at a latent stage of the model, likelihood-based inference becomes feasible even with thousands of observed locations. 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模型潜在阶段以固定参考地点和时间临界超值为条件的进程的零星动力模型。在这项工作中,我们采用巴伊西亚观点,通过综合嵌巢拉普尔近距离(INLA)进行估算,允许对高斯平均函数进行新颖和灵活的半参数规格说明。在使用马特尔肯同异函数的高斯-马尔科夫近似值(称为“局部部分不同比例”方法)之后,可以在模型的潜伏阶段使用非静止高斯-马尔科夫进程作为以固定参考地点和时间设定临界值超值为条件的模型。我们通过调节机制对空间和空间-空间-时空高值的流程进行估计,可以通过隐性变量方法实施,而不会失去计算方便的马尔科夫平均功能的半参数。我们讨论在模型上观察的海平面分布工具,通过可观察到的海面模型进行对比。