Local Clustering in Spatio-Temporal Point Patterns

Abstract

A wide range of contributions in the context of spatio-temporal point patterns have been recently developed in many scientific fields, such as environmental sciences, engineering, physics or biology. We consider here the problem of detecting local clusters in spatio-temporal point patterns. Local indicators of spatial association (LISA) have been used as exploratory data analytic tools to examine individual points in a point pattern in terms of how they relate to their neighbouring points. These tools are based on local second-order characteristics of spatial point processes. We extend the notion of spatial dependence to spatio-temporal structures defining LISTA functions derived from spatio-temporal product densities. We derive theoretical properties, and propose unbiased edge-corrected estimators of these new functions.