Matern Cross-Covariance Functions for Multivariate Random Fields

• Activity Number: 118
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Tilmann Gneiting*+ and William Kleiber and Martin Schlather
• Companies: Heidelberg University and University of Washington and University of Goettingen
• Keywords: spatial statistics ; covariance function ; weather forecasting ; random field

Abstract

We introduce a flexible parametric family of matrix-valued covariance functions for multivariate spatial random fields, where each constituent component is a Matern process. The model parameters are interpretable in terms of process variance, smoothness, correlation length, and co-located correlation coefficients, which can be positive or negative. Both the marginal and the cross covariance functions are of the Matern type. In a data example on error fields for numerical predictions of temperature and pressure over the Pacific Northwest, we compare the Matern model to the traditional linear model of coregionalization.