On parameter estimation for doubly inhomogeneous cluster point processes

Abstract

Nowadays, spatial inhomogeneity and clustering are two important features frequently observed in point patterns. These features often reveal heterogeneity of processes/factors involved in the point pattern formation and interaction determining the relative locations of points. Thus, inhomogeneous cluster point processes can be viewed as flexible and relevant models for describing point patterns observed in biology, forestry and economics for example. In this article, we consider cluster point processes with double inhomogeneity in which locations of cluster centers are drawn under an inhomogeneous parametric intensity function and the distribution of clusters is spatially inhomogeneous and depends on a given parametric function. We propose a Bayesian estimation procedure based on an MCMC algorithm to simultaneously estimate inhomogeneity parameters, cluster parameters and cluster centers.This modeling and estimation framework was applied to a toy case study dealing with the small-scale dispersal of spores of a fungal pathogen infecting plants.