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

TL;DR

This paper develops models for spatial point patterns that exhibit large-scale aggregation and small-scale regularity through dependent thinning, with methods for simulation and inference, extending previous work on interrupted point processes.

Contribution

It introduces parametric models for dependent thinning to achieve desired spatial properties and discusses inference procedures based on observed data.

Findings

Models successfully produce large-scale aggregation and small-scale regularity.

Simulation methods are developed for the proposed models.

Inference procedures are outlined for observed point patterns.

Abstract

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.