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arXiv · 2004.08724

Modeling Nonstationary and Asymmetric Multivariate Spatial Covariances via Deformations

Quan Vu·Andrew Zammit-Mangion·Noel Cressie
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Abstract

Multivariate spatial-statistical models are often used when modeling environmental 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 article 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 modeling 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 models is shown through two data illustrations: a simulation study on nonstationary data and an application on ocean temperatures at two different depths.

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Quan Vu, Andrew Zammit-Mangion, Noel Cressie. 2020-04-18. Modeling Nonstationary and Asymmetric Multivariate Spatial Covariances via Deformations. https://doi.org/10.5705/ss.202020.0156

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