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Multivariate type G Matérn stochastic partial differential equation random fields

For many applications with multivariate data, random field models capturing departures from Gaussianity within realisations 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 Matérn type. We consider four increasingly flexible constructions of the noise, where the first two are similar to existing copula-based models. In contrast to these, the latter 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 suggested models is illustrated by numerical examples and two statistical applications.