Vecchia Approximations and Optimization for Multivariate Mat\'ern Models
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.
Cite
@article{arxiv.2210.09376,
title = {Vecchia Approximations and Optimization for Multivariate Mat\'ern Models},
author = {Youssef Fahmy and Joseph Guinness},
journal= {arXiv preprint arXiv:2210.09376},
year = {2022}
}