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With reference to a specific dataset, we consider how to perform a flexible non-parametric Bayesian analysis of an inhomogeneous point pattern modelled by a Markov point process, with a location-dependent first-order term and pairwise interaction only. A priori we assume that the first-order term is a shot noise process, and that the interaction function for a pair of points depends only on the distance between the two points and is a piecewise linear function modelled by a marked Poisson process. Simulation of the resulting posterior distribution using a Metropolis–Hastings algorithm in the ‘conventional’ way involves evaluating ratios of unknown normalizing constants. We avoid this problem by applying a recently introduced auxiliary variable technique. In the present setting, the auxiliary variable used is an example of a partially ordered Markov point process model.
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Keywords: Markov chain Monte Carlo; auxiliary variable method; hard core; pairwise interaction point process; partially ordered Markov point process; perfect simulation; shot noise process

Document Type: Research Article

Publication date: September 1, 2008

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