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Statistical inference for random T-tessellations models. Application to agricultural landscape modeling

Author

Listed:
  • Katarzyna Adamczyk-Chauvat

    (Université Paris-Saclay, INRAE, MaIAGE)

  • Mouna Kassa

    (INSA)

  • Julien Papaïx

    (INRAE, BioSP)

  • Kiên Kiêu

    (Université Paris-Saclay, INRAE, MaIAGE)

  • Radu S. Stoica

    (Université de Lorraine, CNRS, Institut Elie Cartan de Lorraine, Inria)

Abstract

The Gibbsian T-tessellation models allow the representation of a wide range of spatial patterns. This paper proposes an integrated approach for statistical inference. Model parameters are estimated via Monte Carlo maximum likelihood. The simulations needed for likelihood computation are produced using an adapted Metropolis-Hastings-Green dynamics. In order to reduce the computational costs, a pseudolikelihood estimate is derived and then used for the initialization of the likelihood optimization. Model assessment is based on global envelope tests applied to the set of functional statistics of tessellation. Finally, a real data application is presented. This application analyzes three French agricultural landscapes. The Gibbs T-tessellation models simultaneously provide a morphological and statistical characterization of these data.

Suggested Citation

  • Katarzyna Adamczyk-Chauvat & Mouna Kassa & Julien Papaïx & Kiên Kiêu & Radu S. Stoica, 2024. "Statistical inference for random T-tessellations models. Application to agricultural landscape modeling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(3), pages 447-479, June.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:3:d:10.1007_s10463-023-00893-3
    DOI: 10.1007/s10463-023-00893-3
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    References listed on IDEAS

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    1. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Le Ber, F. & Lavigne, C. & Adamczyk, K. & Angevin, F. & Colbach, N. & Mari, J.-F. & Monod, H., 2009. "Neutral modelling of agricultural landscapes by tessellation methods—Application for gene flow simulation," Ecological Modelling, Elsevier, vol. 220(24), pages 3536-3545.
    3. Gaucherel, C., 2008. "Neutral models for polygonal landscapes with linear networks," Ecological Modelling, Elsevier, vol. 219(1), pages 39-48.
    4. 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.
    5. Tomasz Schreiber & Marie‐Colette Van Lieshout, 2010. "Disagreement Loop and Path Creation/Annihilation Algorithms for Binary Planar Markov Fields with Applications to Image Segmentation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 264-285, June.
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