Articulating Spatial Statistics and Spatial Optimization Relationships: Expanding the Relevance of Statistics

Abstract

Both historically and in terms of practiced academic organization, the anticipation should be that a flourishing synergistic interface exists between statistics and operations research in general, and between spatial statistics/econometrics and spatial optimization in particular. Unfortunately, for the most part, this expectation is false. The purpose of this paper is to address this existential missing link by focusing on the beneficial contributions of spatial statistics to spatial optimization, via spatial autocorrelation (i.e., dis/similar attribute values tend to cluster together on a map), in order to encourage considerably more future collaboration and interaction between contributors to their two parent bodies of knowledge. The key basic statistical concept in this pursuit is the median in its bivariate form, with special reference to the global and to sets of regional spatial medians. One-dimensional examples illustrate situations that the narrative then extends to two-dimensional illustrations, which, in turn, connects these treatments to the spatial statistics centrography theme. Because of computational time constraints (reported results include some for timing experiments), the summarized analysis restricts attention to problems involving one global and two or three regional spatial medians. The fundamental and foundational spatial, statistical, conceptual tool employed here is spatial autocorrelation: geographically informed sampling designs—which acknowledge a non-random mixture of geographic demand weight values that manifests itself as local, homogeneous, spatial clusters of these values—can help spatial optimization techniques determine the spatial optima, at least for location-allocation problems. A valuable discovery by this study is that existing but ignored spatial autocorrelation latent in georeferenced demand point weights undermines spatial optimization algorithms. All in all, this paper should help initiate a dissipation of the existing isolation between statistics and operations research, hopefully inspiring substantially more collaborative work by their professionals in the future.