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Activity Number: 335 - Recent Advances in Spatial and Spatio-Temporal Modeling
Type: Contributed
Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics and the Environment
Abstract #322920
Title: Extremal Dependence of Type-G Mat\'Ern Stochastic Partial Differential Equation Random Fields
Author(s): Zhongwei Zhang* and David Bolin and Sebastian Engelke and Raphael Huser
Companies: King Abdullah University of Science and Technology and King Abdullah University of Science and Technology (KAUST) and Université de Genève and King Abdullah University of Science and Technology (KAUST)
Keywords: Non-Gaussian mode; SPDE Mat\'ern model; Spatial extremes
Abstract:

The type-G Mat\'ern stochastic partial differential equation (SPDE) random field is an important extension of the well-known SPDE-based formulation of Gaussian random fields to construct non-Gaussian random fields with good theoretical and computational properties. However, unlike Gaussian random fields, whose extremal dependence structure is known in the literature, the extremal dependence structure of the resulted non-Gaussian model has not been studied. Here we show that this exact non-Gaussian random field exhibits only asymptotic independence, whereas its finite element approximation can be both asymptotically independent and asymptotically dependent, depending on whether the closest mesh nodes of the two sites are the same. Moreover, the residual tail dependence coefficient can be computed explicitly in the asymptotic independence case. In terms of statistical modeling, the theoretical results imply that the extremal dependence structure depends on the chosen mesh for the finite element approximation. That is, more accurate approximations require finer meshes, but high-resolution meshes only capture asymptotic dependence at very short distances.


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