Local statistical spatial analysis: Inventory and prospect

The past decade has witnessed extensive development of measures that examine characteristics of spatial subsets (local spaces) defined with respect to a complete data set (global space). Such procedures have evolved independently in fields such as geography, GIS, cartography, remote sensing, and landscape ecology. Collectively, we label these procedures as local spatial methods. We focus on those methods that share a common goal of identifying subsets whose characteristics are statistically 'significant' in some way. We propose the concept of local spatial statistical analysis (LoSSA) both as an integrative structure for existing methods and as a framework that facilitates the development of new local and global statistics. By formalizing what is involved when a particular local statistic is used, LoSSA helps to reveal the key features and limitations of the procedure. These include a consideration of the nature of the spatial subsets, their spatial relationship to the complete data set, and the relationship between a given global statistic and the corresponding local statistics computed for the data set.