Covariance Modeling for Multivariate Spatial Processes Based on Separable Approximations

Abstract

The computational treatment of high dimensionality problems is a challenge. In the context of geostatistics, analyzing multivariate data requires the specification of the cross-covariance function, which defines the dependence between the components of a response vector for all locations in the spatial domain. However, the computational cost to make inference and predictions can be prohibitive. As a result, the use of complex models might be unfeasible. In this paper, we consider a flexible nonseparable covariance model for multivariate spatiotemporal data and present a way to approximate the full covariance matrix from two separable matrices of minor dimensions. The method is applied only in the likelihood computation, keeping the interpretation of the original model. We present a simulation study comparing the inferential and predictive performance of our proposal and we see that the approximation provides important gains in computational efficiency without presenting substantial losses in predictive terms.