Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns

Abstract

We develop methods for analysing the ‘interaction’ or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely non‐parametric study of interactions is possible using an analogue of the K ‐function. Alternatively one may assume a semi‐parametric model in which a (parametrically specified) homogeneous Markov point process is subjected to (non‐parametric) inhomogeneous independent thinning. The effectiveness of these approaches is tested on datasets representing the positions of trees in forests.