ABSTRACT
Observing spatial data entails the recording of an attribute of interest the attributeand location. Parting with notation used earlier we denote the attribute of interest being measured by and the location at which we observe this attribute as . A spatial observation is then de- s noted as , the observation of attribute at location . The bold-faced vector notation s s s is used to emphasize that typically contains multidimensional coordinates. The case we wills consider throughout this chapter is where is a point in , two-dimensional Euclidean spaces and the elements of represent longitude and latitude in the plane. As an example considers yield monitoring a corn field which may give rise to spatially referenced observations. The data consist of s s s s , where denotes the corn yield at location . Should we think of these observations as a (random) sample of wheat yields of size ? First we note that the sample locations were not chosen at random since the combine collects samples at systematic intervals. Second, it is (fairly) obvious that the ob- servations cannot possibly be independent as a random sample would imply. If you were given the information that is bushels per acre, how surprised would you be to find s out that the next observation, , collected only a few feet from , was bushels s s per acre? We would not be surprised at all. In fact we would be surprised if s bushels per acre. This phenomenon is sometimes referred to as Tobler's law of geography: “Everything is related to everything else, but near things are more related than distant things.” Tobler's law of geography (Tobler 1970) instructs that we should expect relationships between spatially distributed quantities and that the strength of the relationships is a function of their spatial separation. In the sequel we will define and model numerous mathematical forms of this sentiment. But there is a deeper issue to be considered here.
