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

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.