Unbiased estimating equation for spatial point processes ET CLT for Crossings of random trigonometric Polynomials

English

Séminaire Probabilités & Statistique

25/10/2012 - 14:00 Salle 1 - Tour IRMA

Rasmus WAAGEPETERSEN
Titre : Unbiased estimating equation for spatial point processes

Résumé : Spatial Gibbs and Cox processes differ in many respects. Gibbs point processes are most useful for modeling repulsive point processes while Cox processes are flexible models for clustering. From a theoretical point of view, Gibbs point processes are specified by the conditional intensity while Cox processes are specified by a random intensity function. For a Cox process the conditional intensity is intractable while the intensity is typically tractable and vice versa for Gibbs point processes. However, despite of the many differences it turns out that estimating functions based on respectively the conditional intensity (for Gibbs) or the intensity (for Cox) have a very common structure. We review such estimating functions and discuss some Monte Carlo versions which become useful when certain integrals in the estimating functions need to be approximated. We also briefly consider an optimal estimating function based on the intensity function and show how it is related to quasi-likelihood.

José LEON
Titre : CLT for Crossings of random trigonometric Polynomials

Résumé : voir fichier ci-joint