MPS-RR 2004-23
October 2004

Bayesian Analysis of Markov Point Processes

by: Kasper K. Berthelsen , Jesper Møller

Abstract

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.

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