JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1074 10.6339/22-JDS1074 Computing in Data Science Vecchia Approximations and Optimization for Multivariate Matérn Models FahmyYoussef1 GuinnessJosephguinness@cornell.edu1∗ Department of Statistics and Data Science, Cornell University, Ithaca, NY, USA Corresponding author. Email: guinness@cornell.edu. 202214102022204475492 Supplementary Material

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

18202211102022 2022 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2022 Open access article under the CC BY license.

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.

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