Vecchia Approximations and Optimization for Multivariate Matérn Models

Fahmy, Youssef; Guinness, Joseph

doi:10.6339/22-JDS1074

Journal of Data Science

Vecchia Approximations and Optimization for Multivariate Matérn Models

Volume 20, Issue 4 (2022): Special Issue: Large-Scale Spatial Data Science, pp. 475–492

Youssef Fahmy Joseph Guinness

https://doi.org/10.6339/22-JDS1074

Pub. online: 14 October 2022 Type: Computing In Data Science

Open Access

Received
1 August 2022

Accepted
11 October 2022

Published
14 October 2022

Abstract

We describe our implementation of the multivariate Matérn model for multivariate spatial datasets, using Vecchia’s approximation and a Fisher scoring optimization algorithm. We consider various pararameterizations for the multivariate Matérn 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.

Supplementary material

Supplementary Material

The datasets and code used for this project can be found at https://github.com/yf297/GpGp_multi_paper.

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2022 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.

Open access article under the CC BY license.

Keywords

Gaussian process Fisher scoring software

Funding

This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562. This work is supported by the National Science Foundation Division of Mathematical Sciences under grant numbers 1916208 and 1953088.

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