Vecchia Approximations and Optimization for Multivariate Matérn Models

Youssef Fahmy ； Joseph Guinness

《Journal of Data Science》 20卷4期 (2022/10) Pp. 475-492

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

摘要

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

關鍵字

Gaussian process ； Fisher scoring ； software