Bayesian Analysis of Markov Point Processes
Recently Møller, Pettitt, Berthelsen and Reeves  introduced a new MCMC methodology for drawing samples from a posterior distribution when the likelihood function is only specified up to a normalising constant. We illustrate the method in the setting of Bayesian inference for Markov point processes; more specifically we consider a likelihood function given by a Strauss point process with priors imposed on the unknown parameters. The method relies on introducing an auxiliary variable specified by a normalised density which approximates the likelihood well. For the Strauss point process we use a partially ordered Markov point process as the auxiliary variable. As the method requires simulation from the “unknown” likelihood, perfect simulation algorithms for spatial point processes become useful.
Key wordsBayesian inference Markov chain Monte Carlo Markov point process Partially ordered Markov point process Perfect simulation Spatial point process Strauss process
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