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We consider a dependent thinning of a regular point process with the aim ofobtaining aggregation on the large scale and regularity on the small scale inthe resulting target point process of retained points. Various parametricmodels for the underlying processes are suggested and the properties of thetarget point process are studied. Simulation and inference procedures arediscussed when a realization of the target point process is observed, dependingon whether the thinned points are observed or not. The paper extends previouswork by Dietrich Stoyan on interrupted point processes.

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