Comparing clustering of two inhomogeneous spatial point processes

Speaker: Peter Henrys (University of Lancaster)

Abstract

Modeling clustering in spatial point processes dates back as early as Bartlett (1964) and Ripley (1976) but only in 2000 did Badderley et al. develop cluster detection methods for processes with heterogeneous intensities. Recent literature has tested spatial point patterns for clustering whilst taking heterogeneous environments into account by using a control group, known to follow an inhomogeneous poisson process, to model the underlying intensity. Often in practice, however, both the cases and the control group are clustered, and the question of scientific interest is the amount of clustering of the cases relative to the controls. Therefore, we propose a method to test for significant differences in the levels of clustering between two processes whilst taking into account the first order heterogeneity that may exist. Existing methods are developed to allow for the control group itself to follow a clustered process whilst individual level covariates, observed at only event locations, can be taken into account to see the affect they have on clustering. Inference and diagnostics are based around the inhomogeneous K-function and methods developed are demonstrated using data from a large study of tropical trees in Sri Lanka.