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

Katarzyna Adamczyk-Chauvat (), Mouna Kassa, Julien Papaïx, Kiên Kiêu and Radu S. Stoica
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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

Annals of the Institute of Statistical Mathematics, 2024, vol. 76, issue 3, No 4, 447-479

Abstract: 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.

Keywords: Gibbsian T-tessellation; Monte Carlo Maximum Likelihood estimation; Pseudolikelihood; Global envelope test; Agricultural landscape (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10463-023-00893-3

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