NOTEBOOK FOR SPATIAL DATA ANALYSIS Part II

Given the above model of stationary random spatial effects { ( ) : } s s R   , our ultimate objective is to apply these concepts to spatial models involving global trends, ( ) s  , i.e., to spatial stochastic models of the form, ( ) ( ) ( ) , Y s s s s R      . In continuous spatial data analysis, the most fully developed models of this type focus on spatial prediction, where values of spatial variables observed at certain locations are used to predict values at other locations. But it is important to emphasize here that many such models are in fact completely deterministic in nature [i.e., implicitly assume that ( ) 0 s   ]. Such models are typical referred to as spatial interpolation (or smoothing) models [so we reserve the term spatial prediction for stochastic models of this type, as discussed later]. Indeed the Inverse Distance Weighting (IDW) model used for the Sudan Rainfall example in Section 2.1 above is an interpolation model. Moreover, a variety of other such models are in common use, and indeed, are also available in ARCMAP. So before developing the spatial prediction models that are of central interest for our purposes, it is appropriate to begin with selected examples of these interpolation models. In Section 6 below, we shall then consider the simplest types of spatial prediction models in which the global trend is constant, i.e., with ( ) s    for all s R  . This will be followed in Section 7 with a development of more general prediction models in which the global trend, ( ) s  , is allowed to vary over space, and takes on a more important role.