Spatial cluster point processes related to Poisson–Voronoi tessellations

Abstract

We discuss how to construct models for cluster point processes within ‘territories’ modelled by $$d$$ -dimensional Voronoi cells whose nuclei are generated by a latent Poisson process (where the planar case $$d=2$$ is of our primary interest). Conditional on the territories/cells, the clusters are independent Poisson processes whose points may be aggregated around or away from the nuclei and along or away from the boundaries of the cells. Observing the superposition of clusters within a bounded region, we discuss how to account for edge effects. Bayesian inference for a particular flexible model is discussed in connection to a botanical example.