, Volume 13, Issue 2, pp 263–312

Nonstationary multivariate process modeling through spatially varying coregionalization

  • Alan E. Gelfand
  • Alexandra M. Schmidt
  • Sudipto Banerjee
  • C. F. Sirmans

DOI: 10.1007/BF02595775

Cite this article as:
Gelfand, A.E., Schmidt, A.M., Banerjee, S. et al. Test (2004) 13: 263. doi:10.1007/BF02595775


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.

Key Words

Cross-covariance functionlinear model of coregionalizationmatric-variate Wishart spatial processprior parametrizationspatial rangespatially varying process model

AMS subject classification


Copyright information

© Sociedad Española de Estadistica e Investigación Operativa 2004

Authors and Affiliations

  • Alan E. Gelfand
    • 1
  • Alexandra M. Schmidt
    • 2
  • Sudipto Banerjee
    • 3
  • C. F. Sirmans
    • 4
  1. 1.Institute of Statistics and Decision SciencesDuke UniversityUSA
  2. 2.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroBrazil
  3. 3.Division of Biostatistics, School of Public HealthUniversity of MinnesotaUSA
  4. 4.Center for Real Estate and Urban Economic StudiesUniversity of ConnecticutUSA