Determinantal point process models and statistical inference : Extended version

TL;DR

This paper explores determinantal point processes (DPPs) as efficient models for spatial data with repulsion, offering tractable likelihoods, fast simulations, and practical inference methods, with accompanying software.

Contribution

It introduces parametric DPP models for spatial data, enabling easier likelihood evaluation and simulation compared to traditional Gibbs models.

Findings

DPPs effectively model repulsive spatial patterns.

Likelihood and moments for DPPs are computationally tractable.

Software for DPP simulation and inference is provided.

Abstract

Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop parametric models, where the likelihood and moment expressions can be easily evaluated and realizations can be quickly simulated. We discuss how statistical inference is conducted using the likelihood or moment properties of DPP models, and we provide freely available software for simulation and statistical inference.