MODELING NONSTATIONARY AND ASYMMETRIC MULTIVARIATE SPATIAL COVARIANCES VIA DEFORMATIONS

Multivariate spatial-statistical models are often used when modeling en-vironmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the cross-covariances, but these assumptions are rarely tenable in practice. In this ar-ticle, we introduce a new and highly flexible class of nonstationary and asymmetric multivariate spatial covariance models that are constructed by modeling the simpler and more familiar stationary and symmetric multivariate covariances on a warped domain. Inspired by recent developments in the univariate case, we propose model-ing the warping function as a composition of a number of simple injective warping functions in a deep-learning framework. Importantly, covariance-model validity is guaranteed by construction. We establish the types of warpings that allow for cross-covariance symmetry and asymmetry, and we use likelihood-based methods for inference that are computationally efficient. The utility of this new class of mod-els is shown through two data illustrations: a simulation study on nonstationary data, and an application to ocean temperatures at two different depths.

Automated summary

This article introduces a new class of nonstationary and asymmetric multivariate spatial covariance models by modeling the simpler and more familiar stationary and symmetric multivariate covariances on a warped domain. The warping function is modeled as a composition of several simple injective warping functions in a deep-learning framework. The validity of the covariance model is guaranteed by construction. The utility of this new class of models is demonstrated through two data illustrations.