Tests of Spatial Randomness Adjusted for an Inhomogeneity

Abstract

In many applications, it is of interest to test whether a spatial point pattern is randomly generated after adjusting for an underlying spatial inhomogeneity. A great variety of different test statistics have been proposed for this purpose by scientists in different fields; these are reviewed in this article. Despite apparent dissimilarities in terms of their original formulations, most of these statistics can be placed into one general framework of which they are special cases. This makes it easier to see exactly how they relate to one another and also to determine which test to use for a particular application. The general framework can also be used for proposing new tests by combining properties of existing tests, for developing theoretical foundations for these types of test statistics, for doing structured comparative evaluations, and for software development.