Matérn cross-covariance functions for multivariate random fields. (English) Zbl 1390.62194

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


62M40 Random fields; image analysis
62H12 Estimation in multivariate analysis
62M15 Inference from stochastic processes and spectral analysis
62M30 Inference from spatial processes
86A32 Geostatistics
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