Spatial Statistics

Abstract

Spatial statistics (SS)—statistics that address and account for the correlations among georeferenced observations arising from their relative locations in geographic space (i.e., spatial autocorrelation [SA])—has a formal history dating to the mid-1900s, although conceptual awareness of it dates back to the very early 1900s. It is a special case of correlated data. It arises from a relaxation of the independent observations assumption of classical statistics. Its development emphasized the following three themes: point pattern analysis, spatial autoregression, and geostatistics. Point pattern analysis was a precursor to spatial autoregression, whereas these latter two themes evolved in parallel, with little cross-fertilization during most of their first 40 years of development, primarily because spatial autoregression was the preferred interest of English-speaking scholars, whereas geostatistics was the preferred interest of French-speaking scholars. Much of the early work treated point patterns; spatial autoregression and geostatistics began eclipsing this emphasis around 1990. SS is best understood after completion of a course in multivariate statistical analysis. Spatial Autocorrelation, the book by Cliff and Ord in 1973 initiated a popularizing of SS in the early 1970s; later, Spatial Econometrics, by Paelinck and Klaassen in 1979, extended it to spatial econometrics. The important message is that accounting for SA in georeferenced data really matters in the environmental sciences.