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

arXiv: https://arxiv.org/abs/1606.08298 · HTML: https://mlsanity.com/paper/1606.08298/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2016.

## Built on by (most cited first, 1 of 1)

- [Spatiotemporal Besov Priors for Bayesian Inverse Problems](https://mlsanity.com/paper/2306.16378/) (2023)

## Abstract (arXiv)

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.