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

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  • Dereudre, D.
  • Lavancier, F.

Abstract

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 detail.

Suggested Citation

  • Dereudre, D. & Lavancier, F., 2011. "Practical simulation and estimation for Gibbs Delaunay-Voronoi tessellations with geometric hardcore interaction," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 498-519, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:498-519
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    1. A. Baddeley & R. Turner & J. Møller & M. Hazelton, 2005. "Residual analysis for spatial point processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 617-666, November.
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    1. Löcherbach, Eva & Orlandi, Enza, 2011. "Neighborhood radius estimation for variable-neighborhood random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2151-2185, September.
    2. F. Seitl & L. Petrich & J. Staněk & C. E. Krill & V. Schmidt & V. Beneš, 2021. "Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 669-693, June.

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