Multivariate Spatial Modeling for Geostatistical Data Using Convolved Covariance Functions
 Anandamayee Majumdar,
 Alan E. Gelfand
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Get AccessSoil pollution data collection typically studies multivariate measurements at sampling locations, e.g., lead, zinc, copper or cadmium levels. With increased collection of such multivariate geostatistical spatial data, there arises the need for flexible explanatory stochastic models. Here, we propose a general constructive approach for building suitable models based upon convolution of covariance functions. We begin with a general theorem which asserts that, under weak conditions, cross convolution of covariance functions provides a valid cross covariance function. We also obtain a result on dependence induced by such convolution. Since, in general, convolution does not provide closedform integration, we discuss efficient computation.
We then suggest introducing such specification through a Gaussian process to model multivariate spatial random effects within a hierarchical model. We note that modeling spatial random effects in this way is parsimonious relative to say, the linear model of coregionalization. Through a limited simulation, we informally demonstrate that performance for these two specifications appears to be indistinguishable, encouraging the parsimonious choice. Finally, we use the convolved covariance model to analyze a trivariate pollution dataset from California.
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 Title
 Multivariate Spatial Modeling for Geostatistical Data Using Convolved Covariance Functions
 Journal

Mathematical Geology
Volume 39, Issue 2 , pp 225245
 Cover Date
 20070201
 DOI
 10.1007/s1100400690726
 Print ISSN
 08828121
 Online ISSN
 15738868
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 convolution
 coregionalization
 Fourier transforms
 Gaussian spatial process
 hierarchical model
 Markov chain Monte Carlo
 spectral density
 Industry Sectors
 Authors

 Anandamayee Majumdar ^{(1)}
 Alan E. Gelfand ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona, AZ, 852871804
 2. Institute of Statistics and Decision Sciences, Duke University, Durham, Duke, NC, 277080251