Multivariate type G Matérn stochastic partial differential equation random fields

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 Matérn 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.