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

David Dereudre (1) , Frédéric Lavancier (2)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 LMJL - Laboratoire de Mathématiques Jean Leray

We consider general models of Gibbs Delaunay-Voronoi tessellations, which can be viewed as an extension of the Ord's process. 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, implies some theoretical difficulties since the interaction is not necessarily hereditary. We review the mathematical results available for studying these models and provide further outcomes. They concern the existence, the simulation and the estimation of such tessellations. Based on these results, we present tools to handle these objects in practice : how to simulate them, estimate their parameters and validate the fitted model. Some examples of simulated tessellations are deeply studied.

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

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

David Dereudre, Frédéric Lavancier. Practical simulation and estimation for Gibbs Delaunay-Voronoi tessellations with geometric hardcore interaction.. 2009. ⟨hal-00402029v1⟩