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Nonstationary multivariate process modeling through spatially varying coregionalization

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Abstract

Models for the analysis of multivariate spatial data are receiving increased attention these days. In many applications it will be preferable to work with multivariate spatial processes to specify such models. A critical specification in providing these models is the cross covariance function. Constructive approaches for developing valid cross-covariance functions offer the most practical strategy for doing this. These approaches include separability, kernel convolution or moving average methods, and convolution of covariance functions. We review these approaches but take as our main focus the computationally manageable class referred to as the linear model of coregionalization (LMC). We introduce a fully Bayesian development of the LMC. We offer clarification of the connection between joint and conditional approaches to fitting such models including prior specifications. However, to substantially enhance the usefulness of such modelling we propose the notion of a spatially varying LMC (SVLMC) providing a very rich class of multivariate nonstationary processes with simple interpretation. We illustrate the use of our proposed SVLMC with application to more than 600 commercial property transactions in three quite different real estate markets, Chicago, Dallas and San Diego. Bivariate nonstationary process inodels are developed for income from and selling price of the property.

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Authors and Affiliations

  1. Institute of Statistics and Decision Sciences, Duke University, USA

    Alan E. Gelfand

  2. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brazil

    Alexandra M. Schmidt

  3. Division of Biostatistics, School of Public Health, University of Minnesota, USA

    Sudipto Banerjee

  4. Center for Real Estate and Urban Economic Studies, University of Connecticut, USA

    C. F. Sirmans

Authors
  1. Alan E. Gelfand
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  2. Alexandra M. Schmidt
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  3. Sudipto Banerjee
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  4. C. F. Sirmans
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Corresponding author

Correspondence to Alan E. Gelfand.

Additional information

The work of the first and second authors was supported in part by NIH grant R01ES07750-06.

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Gelfand, A.E., Schmidt, A.M., Banerjee, S. et al. Nonstationary multivariate process modeling through spatially varying coregionalization. Test 13, 263–312 (2004). https://doi.org/10.1007/BF02595775

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