Modelling aggregation on the large scale and regularity on the small scale in spatial point pattern datasets

Frédéric Lavancier (1, 2) , Jesper Møller (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 SERPICO - Space-timE RePresentation, Imaging and cellular dynamics of molecular COmplexes
3 Department of Mathematical Sciences [Aalborg]

We consider a dependent thinning of a regular point process with the aim of obtaining aggregation on the large scale and regularity on the small scale in the resulting target point process of retained points. Various parametric models for the underlying processes are suggested and the properties of the target point process are studied. Simulation and inference procedures are discussed when a realization of the target point process is observed , depending on whether the thinned points are observed or not. The paper extends previous work by Dietrich Stoyan on interrupted point processes.

Mots clés: pair correlation function; dependent thinning; Boolean model; chi-square process; determinantal point process; interrupted point process

Domaines: Statistiques [stat]; Méthodologie [stat.ME]

Frédéric Lavancier, Jesper Møller. Modelling aggregation on the large scale and regularity on the small scale in spatial point pattern datasets. Scandinavian Journal of Statistics, 2016, 43 (2), pp.587-609. ⟨hal-01155646⟩