Consistency of likelihood estimation for Gibbs point processes

David Dereudre (1) , Frédéric Lavancier (2, 3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 SERPICO - Space-timE RePresentation, Imaging and cellular dynamics of molecular COmplexes

Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general and includes pairwise pair potentials, finite and infinite multibody interactions and geometrical interactions, where the range can be finite or infinite. The Gibbs interaction may depend linearly or non-linearly on the parameters, a particular case being hardcore parameters and interaction range parameters. As important examples, we deduce the consistency of the MLE for all parameters of the Strauss model, the hardcore Strauss model, the Lennard-Jones model and the area-interaction model.

Mots clés: Parametric estimation; Variational principle; Strauss model; Lennard-Jones model; Area-interaction model

Domaines: Théorie [stat.TH]

David Dereudre, Frédéric Lavancier. Consistency of likelihood estimation for Gibbs point processes. 2015. ⟨hal-01144877v1⟩