HAL : hal-00402029, version 2

arXiv : 1005.5620

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v1 (07-07-2009)

v2 (31-05-2010)

Practical simulation and estimation for Gibbs Delaunay-Voronoi tessellations with geometric hardcore interaction.

David Dereudre 1, Frédéric Lavancier 2

(21/04/2010)

General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed as extensions of Ord's process, are considered. The interaction may occur on each cell of the tessellation and between neighbour cells. The tessellation may also be subjected to a geometric hardcore interaction, forcing the cells not to be too large, too small, or too flat. This setting, natural for applications, introduces some theoretical difficulties since the interaction is not necessarily hereditary. Mathematical results available for studying these models are reviewed and further outcomes are provided. They concern the existence, the simulation and the estimation of such tessellations. Based on these results, tools to handle these objects in practice are presented: how to simulate them, estimate their parameters and validate the fitted model. Some examples of simulated tessellations are studied in details.

1 :	Laboratoire de Mathématiques et leurs Applications de Valenciennes, EA 45 (LAMAV)
	Université de Valenciennes et du Hainaut-Cambresis – CNRS : FRE2956
2 :	Laboratoire de Mathématiques Jean Leray (LMJL)
	CNRS : UMR6629 – Université de Nantes – École Centrale de Nantes

Domaine

:

Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : Gibbs point process – random tessellations – stochastic geometry – pseudo-likelihood estimator – spatial statistics.

hal-00402029, version 2

http://hal.archives-ouvertes.fr/hal-00402029

oai:hal.archives-ouvertes.fr:hal-00402029

Contributeur : Frédéric Lavancier <>

Soumis le : Mercredi 21 Avril 2010, 12:55:18

Dernière modification le : Lundi 31 Mai 2010, 10:40:01