A Bivariate Asymmetric Spatial Covariance Model with Consistent Marginals

Thomas M. Menino Convention & Exhibition Center 

We develop a bivariate asymmetric spatial covariance model using the conditional approach of Cressie and Zammit-Mangion (2016). Our construction includes both a simple pointwise dependence interaction and an asymmetric dependence interaction, while ensuring that both marginal covariance functions are from the same family such as the Matérn class. Unlike the conditional formulation in Cressie and Zammit-Mangion (2016), in which the same covariance family is imposed on only one marginal and a conditional component, our approach preserves the same marginals for both observed variables, aiding interpretation, comparison with familiar univariate spatial models, and model specification in practice. We derive sufficient conditions under which the resulting bivariate covariance function is positive definite. Through simulation studies with cokriging, we compare the proposed models with existing symmetric and asymmetric Matérn-based alternatives and assess predictive performance. We further illustrate the superior performance of the proposed models with a spatial temperature-pressure dataset.

Geostatistics

Asymmetry

Matérn covariance

Cross-covariance

Conditional approach 

Section on Statistics and the Environment