Bayesian analysis of Markov point processes

Kasper Klitgaard Berthelsen, Jesper Møller

Research output: Contribution to book/anthology/report/conference proceedingBook chapterEducation

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.
Original languageEnglish
Title of host publicationCase Studies in Spatial Point Process Modeling
EditorsAdrian Baddeley, Pablo Gregori, Jorge Mateu, Radu Stoica, Dietrich Stoyan
Number of pages13
Place of PublicationUSA
PublisherSpringer
Publication date2006
Pages85-97
ISBN (Print)0387283110
Publication statusPublished - 2006
SeriesLecture Notes in Statistics
Number185

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