Non-parametric bayesian inference for inhomogeneous markov point processes

With reference to a specific dataset, we consider how to perform a flexible non-parametric Bayesian analysis of an inhomogeneous point pattern modelled by a Markov point process, with a location-dependent first-order term and pairwise interaction only. A priori we assume that the first-order term is a shot noise process, and that the interaction function for a pair of points depends only on the distance between the two points and is a piecewise linear function modelled by a marked Poisson process. Simulation of the resulting posterior distribution using a Metropolis-Hastings algorithm in the 'conventional' way involves evaluating ratios of unknown normalizing constants. We avoid this problem by applying a recently introduced auxiliary variable technique. In the present setting, the auxiliary variable used is an example of a partially ordered Markov point process model.