ABSTRACT
Suppose that a spatially distributed variable is of interest, which in theory is defined at every point over a bounded study region of interest, D ⊂ Rd , where d = 2 or 3. We suppose further that this variable has been observed (possibly with error) at each of n distinct points in D, and that from these observations we wish to make inferences about the process that governs how this variable is distributed spatially and about values of the variable at locations where it was not observed. The geostatistical approach for achieving these objectives is to assume that the observed data are a sample (at the n data locations) of one realization of a continuously indexed spatial stochastic process (random field) Y(·) ≡ {Y(s) : s ∈ D}. Chapter 2 reviewed some probabilistic theory for such processes. In this chapter, we are concerned with how to use the sampled realization to make statistical inferences about the process. In particular, we discuss a body of spatial statistical methodology that has come to be known as “classical geostatistics.” Classical geostatistical methods focus on estimating the first-order (large-scale or global trend) structure and especially the second-order (smallscale or local) structure of Y(·), and on predicting or interpolating (kriging) values of Y(·) at unsampled locations using linear combinations of the observations and evaluating the performance of these predictions by their (unconditional) mean squared errors. However, if the process Y is sufficiently non-Gaussian, methods based on considering just the first two moments of Y may be misleading. Furthermore, some common practices in classical geostatistics are problematic even for Gaussian processes, as we shall note herein.
