Gibbsian T-tessellation model for agricultural landscape characterization

Katarzyna Adamczyk-Chauvat (1, 2) , Mouna Kassa (3) , Kiên Kiêu (1, 2) , Julien Papaïx (4) , Radu S. Stoica (5, 6)

1 MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas]
2 Université Paris-Saclay
3 INSA Rennes - Institut National des Sciences Appliquées - Rennes
4 BioSP - Biostatistique et Processus Spatiaux
5 IECL - Institut Élie Cartan de Lorraine
6 PASTA - Processus aléatoires spatio-temporels et leurs applications

A new class of planar tessellations, named T-tessellations, was introduced in ([10]). A model was proposed to be considered as a completely random T-tessellation model (CRTT) and its Gibbsian variants were discussed. A general simulation algorithm of Metropolis-Hastings-Green type was derived for model simulation, involving three local transformations of T-tessellations. The current paper focuses on statistical inference for Gibbs models of T-tessellations. Statistical methods originated from point pattern analysis are implemented on the example of three agricultural landscapes approximated by T-tessellations. The choice of model statistics is guided by their capacity to highlight the differences between the landscape patterns. Model parameters are estimated by Monte Carlo Maximum Likelihood method, yielding a baseline for landscapes comparison. In the last part of the paper a global envelope test based on the empty-space function is proposed for assessing the goodness-of-fit of the model.

Mots clés: Gibbsian T-tessellation model; Agricultural landscape; Monte Carlo Maximum Like- lihood estimation; Empty-space function

Domaines: Applications [stat.AP]

Katarzyna Adamczyk-Chauvat, Mouna Kassa, Kiên Kiêu, Julien Papaïx, Radu S. Stoica. Gibbsian T-tessellation model for agricultural landscape characterization. 2020. ⟨hal-02905984⟩