Bayesian inference for a random tessellation process

This article describes an inhomogeneous Poisson point process in the plane with an intensity function based on a Dirichlet tessellation process and a method for using observations on the point process to make fully Bayesian inferences about the underlying tessellation. The method is implemented using a Markov chain Monte Carlo approach. An application to modeling the territories of clans of badgers, Meles meles, is described.