Summary
Recently Møller, Pettitt, Berthelsen and Reeves [17] 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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Berthelsen, K.K., Møller, J. (2006). Bayesian Analysis of Markov Point Processes. In: Baddeley, A., Gregori, P., Mateu, J., Stoica, R., Stoyan, D. (eds) Case Studies in Spatial Point Process Modeling. Lecture Notes in Statistics, vol 185. Springer, New York, NY. https://doi.org/10.1007/0-387-31144-0_4
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DOI: https://doi.org/10.1007/0-387-31144-0_4
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