Matérn Cross-Covariance Functions for Multivariate Random Fields

By Tilmann Gneiting, William Kleiber, Martin Schlather. 2010

460 citations recorded by the source corpus.

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.

Subfields: Environmental Engineering, Global and Planetary Change

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Citations in the corpus

Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere (2016, methodology): “In particular, we propose multivariate Matérn mappings (Gneiting, Kleiber, and Schlather 2010; Apanasovich, Genton, and Sun 2012) that have been proposed earlier in the framework of Euclidean distance only.”
Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes (2012, background): “Some of the multivariate spatial models currently of interest in the statistics community may also be useful to this end [Apanasovich and Genton, 2010; Gelfand et al., 2004; Gneiting et al., 2010].”
Non‐stationary Cross‐Covariance Models for Multivariate Processes on a Globe (2011, methodology): “1 Covariance models for multivariate spatial processes Linear model of coregionalization: Schmidt and Gelfand (2003), Gelfand et al.”
Basis-Function Models in Spatial Statistics (2021, methodology): “In contrast, the multivariate Matérn cross-covariance function requires special conditions on parameters in order for Equation 26 to be positivesemidefinite (Gneiting et al., 2010).”
The role of the range parameter for estimation and prediction in geostatistics (2011, background): “For example, Zhang & Wang (2010) find that fixingρ at arbitrary large values has little impact on predictive performance, and Gneiting et al. (2010) argue that specifying a singleρ for all variables in a multivariate model is not restrictive.”
A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components (2012, methodology): “At the same time, the special case of our model for only two components compares well with the criterion proposed in Gneiting et al. (2010).”
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (2011, background): “C.4, also reveal the possibility of multivariate fields, similar to Gneiting et al. (2010).”
Classes of compactly supported covariance functions for multivariate random fields (2015, background): “In the case of multivariate RFs, this has been encountered, for instance, for temperature and pressure observations and forecasts at 157 locations in the North American Pacific Northwest (Gneiting et al. 2010).”