Nonstationary Multivariate Process Modeling through Spatially Varying Coregionalization

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 provide such models. A critical specification in developing these models is the cross covariance function. An attractive, constructive approach for creating rich computationally manageable classes of such functions is the linear model of coregionalization (LMC). We begin with a fully Bayesian development of the LMC including the posterior distribution of the component ranges. We offer clarification of the connection between joint and conditional approaches to fitting such models including prior speci-fications. However, to substantially enhance the usefulness of such modeling we propose the notion of a spatially varying LMC (SVLMC) providing a 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 models are developed for income from and selling price of the property. KEY WORDS: Cross-covariance function; linear model of coregionalization; matric-variate Wishart spatial process; prior parametrization; spatial range; spatially varying process model.