Multivariate spatial covariance models: a conditional approach

Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables and their locations in a continuously indexed domain. Multivariate spatial covariance models need to be built with care, since any covariance matrix that is derived from such a model has to be nonnegative-definite. In this article, we develop a conditional approach for model construction. Starting with bivariate spatial covariance models, we demonstrate the approach’s generality, including its connection to regression and to multi variate models defined by spatial networks. We demonstrate the fitting of such models on a minimum-maximum temperature dataset.