ABSTRACT
Geographical referencing of environmental data is often achieved using a coordinate system such as longitude-latitude or some planar projections. Each variable of interest is measured at a point whose coordinates are assumed to be fixed. Such data are referred to as point-referenced data. This is to be contrasted with areally-referenced spatial data which arise as aggregates or summaries over regions or areas such as states, counties, zip-codes, census tracts and so on. This chapter focuses upon some key elements in constructing spatial processes. One can extend stationary correlation functions from isotropy, where association depends only upon distance, to anisotropy where association depends upon direction also. One particularly simple example is the class where separate the coordinates of the separation vector and assign a possibly different correlation function to each coordinate. The variogram appears in classical kriging where one seeks the best linear unbiased predictor (BLUP). The variogram and its variants have been the subject of much research in classical geostatistics.
