The analysis of point data plays a fundamental role in the study of any system in which events of interest occur at discrete locations in space and time. Examples can most readily be found in epidemiology, in which such events might represent cases of disease (see Pfeiffer et al., 2008), but similar analysis has also been applied more recently in the context of crime, in which events correspond to offences (e.g. Johnson et al., 2007), and international conflict, in which events correspond to militarised disputes between countries (e.g. Braithwaite, 2010). In either case, the identification of patterns within such data can offer insight into the underlying generative process, while also suggesting possible courses of preventative action.
One of the primary phenomena of interest in point pattern analysis is that of clustering, whereby events tend to occur ‘close’ to each other, in some sense. This is most naturally seen as the disproportionate occurrence of events at some location in either time or space; that is, a density of points that is greater than would be expected if the distribution of risk was uniform. Clustering of this form may suggest that some property of those places or times is particularly conducive to the phenomenon in question. In terms of disease or crime, the presence of such clustering ...