Determinantal point process models and statistical inference : Extended version

Frédéric Lavancier (1) , Jesper Møller (2) , Ege Rubak (2)

1 Probabilités, statistique et calcul scientifique
2 Department of Mathematical Sciences [Aalborg]

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.

Mots clés: maximum likelihood based inference; point process density; product densities; simulation; repulsiveness; spectral approach.; spectral approach

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Frédéric Lavancier, Jesper Møller, Ege Rubak. Determinantal point process models and statistical inference : Extended version. 2012. ⟨hal-00698958v4⟩