Title :

A completely random T-tessellation model and Gibbsian extensions

Author(s) :

Kiêu, Kiên [Auteur]
Unité de recherche Mathématiques et Informatique Appliquées [MIA]
Adamczyk-Chauvat, Katarzyna [Auteur]
Unité de recherche Mathématiques et Informatique Appliquées [MIA]
Monod, Hervé [Auteur]
Unité de recherche Mathématiques et Informatique Appliquées [MIA]
Stoica, Radu [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]

English keyword(s) :

Stochastic geometry
random tessellation
Gibbs model
simulation
Metropolis-Hastings algorithm

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]

English abstract : [en]

In their 1993 paper, Arak, Clifford and Surgailis discussed a new model of random planar graph. As a particular case, that model yields tessellations with only T-vertices (T-tessellations). Using a similar approach involving ...
Show more >In their 1993 paper, Arak, Clifford and Surgailis discussed a new model of random planar graph. As a particular case, that model yields tessellations with only T-vertices (T-tessellations). Using a similar approach involving Poisson lines, a new model of random T-tessellations is proposed. Campbell measures, Papangelou kernels and Georgii-Nguyen-Zessin formulae are translated from point process theory to random T-tessellations. It is shown that the new model shows properties similar to the Poisson point process and can therefore be considered as a completely random T-tessellation. Gibbs variants are introduced leading to models of random T-tessellations where selected features are controlled. Gibbs random T-tessellations are expected to better represent observed tessellations. As numerical experiments are a key tool for investigating Gibbs models, we derive a simulation algorithm of the Metropolis-Hastings-Green family.Show less >

Language :

Anglais

Comment :

A revised version of this paper has been published in Spatial Statistics, 2013, volume 6, pages 118- 138.

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL