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 cluster centres 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, interaction parameters and cluster centres. We applied this modelling and estimation framework to investigate the small-scale dispersal of spores of a fungal pathogen. This procedure and an additional test of independent dispersal show that spores are dispersed as groups of spores whereas most dispersal models assume independent dispersal.
Joint work with Samuel Soubeyrand.

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