ABSTRACT
Modeling of the spatial dependence structure of environmental processes is fundamental to almost all statistical analyses of data that are sampled spatially. The classical geostatistical model for a spatial process {Y(s) : s ∈ D} defined over the spatial domain D ⊂ Rd , specifies a decomposition into mean (or trend) and residual fields, Y(s) = μ(s) + e(s). The process is commonly assumed to be second order stationary, meaning that the spatial covariance function can be written C(s, s+h) = Cov(Y(s), Y(s+h)) = Cov(e(s), e(s+h)) = C(h), so that the covariance between any two locations depends only on the spatial lag vector connecting them. There is a long history of modeling the spatial covariance under an assumption of “intrinsic stationarity” in terms of the semivariogram, γ (h) = 12 var(Y(s+h)−Y(s)). However, it is now widely recognized that most, if not all, environmental processes manifest spatially nonstationary or heterogeneous covariance structure when considered over sufficiently large spatial scales.
