Berthelsen, Kasper Klitgaard

Johansen, Per Michael

Møller, Jesper

With reference to a specific data set, 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 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 using a Metropolis-Hastings algorithm in the &quot;conventional&quot; way involves evaluating ratios of unknown normalising constants. We avoid this problem by applying a new auxiliary variable technique introduced by Møller, Pettitt, Reeves &amp; Berthelsen (2006). In the present setting the auxiliary variable used is an example of a partially ordered Markov point process model.With reference to a specific data set, 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 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 using a Metropolis-Hastings algorithm in the "conventional" way involves evaluating ratios of unknown normalising constants. We avoid this problem by applying a new auxiliary variable technique introduced by Møller, Pettitt, Reeves &amp; Berthelsen (2006). In the present setting the auxiliary variable used is an example of a partially ordered Markov point process model.</p

Non-parametric Bayesian inference for inhomogeneous Markov point processes

http://vbn.aau.dk/files/7722862/R-2007-09.pdf

Non-parametric Bayesian inference for inhomogeneous Markov point processes

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