  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.
