Determinantal point process models and statistical inference
Résumé
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 data sets 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 by using the likelihood or moment properties of DPP models, and we provide freely
available software for simulation and statistical inference.