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.
|Original language||English (US)|
|Number of pages||25|
|Journal||Journal of the Royal Statistical Society. Series B: Statistical Methodology|
|State||Published - Dec 17 2019|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work has been supported by the Swedish Research Council under grant 2016-04187 and the Knut and Alice Wallenberg Foundation (grant KAW 20012.0067). The authors thank Holger Rootzén, the Joint Editor, Associate Editor and the reviewers for valuable comments on the manuscript. We also thank Mikael Kuusela for helping with the Argo data.