Determinantal shot noise Cox processes

TL;DR

This paper introduces determinantal shot noise Cox processes (DSNCP), a new class of repulsive cluster point process models, with tractable estimation methods demonstrated through simulations and real data analysis.

Contribution

It proposes DSNCP models with determinantal cluster centers, providing new analytical tools and estimation techniques for modeling repulsive clustered point patterns.

Findings

DSNCP models require lower cluster center intensity than traditional shot noise Cox processes.

Moment results facilitate parameter estimation in specific Gaussian and Ginibre kernel cases.

Simulation and real data analysis validate the effectiveness of DSNCP models.

Abstract

We present a new class of cluster point process models, which we call determinantal shot noise Cox processes (DSNCP), with repulsion between cluster centres. They are the special case of generalized shot noise Cox processes where the cluster centres are determinantal point processes. We establish various moment results and describe how these can be used to easily estimate unknown parameters in two particularly tractable cases, namely when the offspring density is isotropic Gaussian and the kernel of the determinantal point process of cluster centres is Gaussian or like in a scaled Ginibre point process. Through a simulation study and the analysis of a real point pattern data set we see that when modelling clustered point patterns, a much lower intensity of cluster centres may be needed in DSNCP models as compared to shot noise Cox processes.