Spatial Scan Statistics: Models, Calculations, and Applications

Abstract

A common problem in spatial statistics is whether a set of points are randomly distributed or if they show signs of clusters or clustering. When the locations of clusters are of interest, it is natural to use a spatial scan statistic. Different spatial scan statistics have been proposed. These are discussed and presented in a general framework that incorporates two-dimensional scan statistics on the plane or on a sphere, as well as three-dimensional scan statistics in space or in space—time. Computational issues are then looked at, presenting efficient algorithms that can be used for different scan statistics in connection with Monte Carlo-based hypothesis testing. It is shown that the computational requirements are reasonable even for very large data sets. Which scan statistic to use will depend on the application at hand, which is discussed in terms of past as well as possible future practical applications in areas such as epidemiology, medical imaging, astronomy, archaeology, urban and regional planning, and reconnaissance.