ABSTRACT
This chapter discusses the spatial models for exposures. The study of exposures to environmental hazards and their potential effects on health outcomes begins with understanding the underlying structure of, and variation in, the hazard over space and time. Techniques for modeling random spatial fields began in earnest in the 1950s, when the foundation of the subject of geostatistics was laid by Krige and Matheron. Spatial statistics has since become an extremely important topic within statistical science. The first stage of a spatial analysis is to investigate the distribution of the exposure of interest, for example concentrations of lead, in order to assess whether the assumptions necessary for applying subsequent methods are tenable. The covariance function and the semi-variogram are both functions that summarize the strength of association as a function of distance and, in the case of anisotropy, direction.
