Advances in Modeling and Inference for Environmental Processes with Nonstationary Spatial Covariance

Modeling of the spatial dependence structure of environmental processes is fundamental to almost all statistical analyses of data that are sampled spatially. These analyses address tasks such as spatial estimation (kriging) and monitoring network design, as well as the basic scientific characterization of the second order properties of these processes. Prior to 1990, the lack of general models for the spatial covariance function led to almost exclusive reliance on stationary models of the form cov(Z(x), Z(y)) = C(x-y) where Z (x): ∈ D denotes a process defined over a spatial domain D ⊂ R d . However, it is now widely recognized that most, if not all, spatia-temporal environmental processes (and many spatial processes without a temporal aspect) manifest spatially nonstationary or heterogeneous covariance structure when considered over a sufficiently large spatial range.