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Multivariate spatial covariance models: a conditional approach

Journal Article


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Abstract


  • Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of 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 must be nonnegative-definite. In this article, we develop a conditional approach for spatial-model construction whose validity conditions are easy to check. We start with bivariate spatial covariance models and go on to demonstrate the approach's connection to multivariate models defined by networks of spatial variables. In some circumstances, such as modelling respiratory illness conditional on air pollution, the direction of conditional dependence is clear. When it is not, the two directional models can be compared. More generally, the graph structure of the network reduces the number of possible models to compare. Model selection then amounts to finding possible causative links in the network. We demonstrate our conditional approach on surface temperature and pressure data, where the role of the two variables is seen to be asymmetric.

Publication Date


  • 2016

Citation


  • Cressie, N. & Zammit-Mangion, A. (2016). Multivariate spatial covariance models: a conditional approach. Biometrika, 103 (4), 915-935.

Scopus Eid


  • 2-s2.0-85020491041

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7570&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6540

Has Global Citation Frequency


Number Of Pages


  • 20

Start Page


  • 915

End Page


  • 935

Volume


  • 103

Issue


  • 4

Place Of Publication


  • United Kingdom

Abstract


  • Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of 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 must be nonnegative-definite. In this article, we develop a conditional approach for spatial-model construction whose validity conditions are easy to check. We start with bivariate spatial covariance models and go on to demonstrate the approach's connection to multivariate models defined by networks of spatial variables. In some circumstances, such as modelling respiratory illness conditional on air pollution, the direction of conditional dependence is clear. When it is not, the two directional models can be compared. More generally, the graph structure of the network reduces the number of possible models to compare. Model selection then amounts to finding possible causative links in the network. We demonstrate our conditional approach on surface temperature and pressure data, where the role of the two variables is seen to be asymmetric.

Publication Date


  • 2016

Citation


  • Cressie, N. & Zammit-Mangion, A. (2016). Multivariate spatial covariance models: a conditional approach. Biometrika, 103 (4), 915-935.

Scopus Eid


  • 2-s2.0-85020491041

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7570&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6540

Has Global Citation Frequency


Number Of Pages


  • 20

Start Page


  • 915

End Page


  • 935

Volume


  • 103

Issue


  • 4

Place Of Publication


  • United Kingdom