Multivariate type G Mat\'ern stochastic partial differential equation random fields

TL;DR

This paper introduces a new class of multivariate non-Gaussian spatial models based on stochastic partial differential equations with type G noise, enabling flexible modeling of complex spatial data.

Contribution

It develops novel non-Gaussian multivariate models using SPDEs with type G noise, extending existing copula-based approaches and allowing for non-Gaussian data without replicates.

Findings

Models effectively capture non-Gaussian spatial dependence.

Proposed methods enable efficient likelihood-based inference.

Numerical examples demonstrate model flexibility and applicability.

Abstract

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 Mat\'ern 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.