Variance modeling for nonstationary spatial processes with temporal replications

Abstract

We have previously formulated a Bayesian approach to the Sampson and Guttorp model for the nonstationary correlation function r(x,x′) of a Gaussian spatial process [Damian et al., 2001]. This model assumes that the nonstationarity can be encoded through a bijective space deformation, ∫, that defines a new coordinate system in which the spatial correlation function can be considered isotropic, namely r(x,x′) = p(∥∫(x) - ∫(x′)∥), where ρ belongs to a known parametric family. We extend this model to incorporate spatial heterogeneity in site-specific temporal variances. In our Bayesian framework the variances are considered (hidden) realizations of another spatial process, which we model as log-Gaussian, with correlation structure expressed in terms of the same spatial deformation function underlying that of the observed process. We demonstrate the method in simulations and in an application. Copyright 2003 by the American Geophysical Union.