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arXiv · 2210.09376

Vecchia Approximations and Optimization for Multivariate Mat\'ern Models

Youssef Fahmy·Joseph Guinness
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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.

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Youssef Fahmy, Joseph Guinness. 2022-10-17. Vecchia Approximations and Optimization for Multivariate Mat\'ern Models. https://arxiv.org/abs/2210.09376

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