A Bayesian MCMC method for point process models with intractable normalising constants

We present new methodology for drawing samples from a posterior distribution when the likelihood function is only specified up to a normalising constant. Our method is "on-line" as compared with alternative approaches to the problem which require "off-line" computations. Since it is needed to simulate from the "unknown distribution", perfect simulation algorithms become useful. We illustrate the method in cases whre the likelihood is given by a Markov point process model. Particularly, we consider semi-parametric Bayesian inference in connection to both inhomogeneous Markov point process models and pairwise interaction point processes.