Modeling Multivariate Spatial Processes for Large Data

Large multivariate spatial data sets are common in environmental and climate sciences. This article proposes a flexible multivariate spatial statistical model for such data. Built upon Ma and Kang (2020), we model multivariate spatial processes in an additive form with two components to induce spatial dependence and a relationship between distinct variables: One component is of a low-rank format, and the other component is built in a conditional way with multivariate spatial conditional autoregressive (CAR) models. By combining these two components, the resulting model not only allows for efficient computation of parameter estimation and spatial prediction, but is also flexible to describe spatial covariance and cross-covariance structures that can potentially be nonstationary or asymmetric. The performance of the proposed model that we call the multivariate fused Gaussian process (MFGP) is investigated through an extensive simulation study and a real-data example. The results show that MFGP, by borrowing information from complementary data, provides substantially improved spatial predictions compared to the univariate models. We also demonstrate that MFGP outperforms the multivariate model with the low-rank component solely or with a multivariate CAR model with a separable covariance matrix.