Vecchia Approximations and Optimization for Multivariate Mat\'ern Models

TL;DR

This paper presents an implementation of multivariate Matérn models using Vecchia's approximation and Fisher scoring, analyzing parameterizations and their effects on real-world spatial datasets.

Contribution

It introduces a flexible implementation of multivariate Matérn models with various parameterizations and studies their impact on model validity and performance.

Findings

Allowing cross-component nugget correlation improves model fit.

Ordering and conditioning choices significantly affect approximation accuracy.

Unconstrained parameterization offers more flexibility in modeling.

Abstract

We describe our implementation of the multivariate Mat\'ern model for multivariate spatial datasets, using Vecchia's approximation and a Fisher scoring optimization algorithm. We consider various pararameterizations for the multivariate Mat\'ern that have been proposed in the literature for ensuring model validity, as well as an unconstrained model. A strength of our study is that the code is tested on many real-world multivariate spatial datasets. We use it to study the effect of ordering and conditioning in Vecchia's approximation and the restrictions imposed by the various parameterizations. We also consider a model in which co-located nuggets are correlated across components and find that forcing this cross-component nugget correlation to be zero can have a serious impact on the other model parameters, so we suggest allowing cross-component correlation in co-located nugget terms.