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Title: High-dimensional modeling of spatial and spatio-temporal conditional extremes using INLA and the SPDE approach Authors:  Thomas Opitz - BioSP-INRAE (France) [presenting]
Emma Simpson - University College London (United Kingdom)
Jenny Wadsworth - Lancaster University (United Kingdom)
Abstract: The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatiotemporal settings. After standardizing the marginal distributions and applying an appropriate linear normalization, certain nonstationary Gaussian processes can be used as asymptotically motivated models for the process conditioned on threshold exceedances at a fixed reference location. 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 Matern 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 spatiotemporal Gaussian processes, arising from the conditioning mechanism, can be implemented through the latent variable approach without losing the computationally convenient Markov property. We discuss model comparison and illustrate 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 spatiotemporal extreme episodes.