A new class of nonstationaryspatial models
Montserrat Fuentes, Richard L. Smith · 2001
Spatial processes are an important modeling tool for many problems of environmental monitoring. Classical geostatistics is based on processes which are stationary and isotropic, but it is widely recognized that real environmental processes are rarely stationary and isotropic. In this paper, a new class of nonstationary processes is proposed, based on a convolution of local stationary processes. This model has the advantage that the model is simultaneously defined everywhere, unlike \\moving window" approaches, but it retains the attractive property that locally in small regions, it behaves like a stationary spatial processes. We discuss model fitting through exact and approximate likelihood maximization, and propose a hierarchical Bayes approach to allow predictive inference when the parameters of the model are unknown. Applications include obtaining the total loading of sulfur dioxide concentrations over different geo-political boundaries.