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Multivariate type G Matern stochastic partial differential equation random fields

Journal article
Authors David Bolin
J. Wallin
Published in Journal of the Royal Statistical Society Series B-Statistical Methodology
Pages 25
ISSN 1369-7412
Publication year 2020
Published at Department of Mathematical Sciences
Pages 25
Language en
Keywords Matern covariances, Multivariate random fields, Non-Gaussian models, Spatial statistics, Stochastic partial differential equations, cross-covariance functions, vector random-fields, scoring rules, models, Mathematics
Subject categories Mathematics


For many applications with multivariate data, random-field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matern type. We consider four increasingly flexible constructions of the noise, where the first two are similar to existing copula-based models. In contrast with these, the last two constructions can model non-Gaussian spatial data without replicates. Computationally efficient methods for likelihood-based parameter estimation and probabilistic prediction are proposed, and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications.

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