Matérn thinned Cox processes

Abstract A class of spatial point process models that combine short range repulsion with medium range clustering is introduced. The model is motivated by patterns of centres of non-overlapping spherical cells in biological tissue which tend to have a clustering behaviour. Such a combination of clustering and hard core behaviour can be achieved by applying a dependent Matern thinning to a Cox process. An exact formula for the intensity of a Matern thinned shot noise Cox process is derived from the Palm distribution. For the more general class of Matern thinned Cox processes, formulae for the intensity and second-order characteristics are established using the conditional Poisson assumption. These formulae include more complicated integrals for which approximations are suggested to simplify calculations. An example from pathology illustrates the applicability of the models.