TY - RPRT
T1 - Non-parametric Bayesian inference for inhomogeneous Markov point processes
AU - Berthelsen, Kasper Klitgaard
AU - Møller, Jesper
AU - Johansen, Per Michael
PY - 2007
Y1 - 2007
N2 - 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 & Berthelsen (2006). In the present setting the auxiliary variable used is an example of a partially ordered Markov point process model.
AB - 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 & Berthelsen (2006). In the present setting the auxiliary variable used is an example of a partially ordered Markov point process model.
M3 - Report
T3 - Research Report Series
BT - Non-parametric Bayesian inference for inhomogeneous Markov point processes
PB - Department of Mathematical Sciences, Aalborg University
ER -