Bayesian inference for spatially inhomogeneous pairwise interacting point processes

Abstract

Spatial point patterns are frequently modeled with pairwise interacting point processes. Unfortunately, inference in these models is complicated by the presence of an intractable function of the parameters in the likelihood. Because of the relative computational simplicity, frequentist inference in pairwise interacting point processes has dominated the literature. However, a Bayesian approach has not been computationally feasible until recently. Since the Metropolis–Hastings acceptance probability contains a ratio of two likelihoods evaluated at di2ering parameter values, the resulting intractable ratio complicates the required application of MCMC. In this article, we describe how to obtain Bayesian inferences without conditioning on the number of points in the pattern, allowing the modeling of spatial inhomogeneity in the density of points. After describing our importance sampling within MCMC algorithm, we analyze the well-known Irish drumlin data set using a hard-core Straussian model. c © 2004 Elsevier B.V. All rights reserved.

DOI: 10.1016/j.csda.2004.04.008

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Cite this paper

@article{Bognar2005BayesianIF, title={Bayesian inference for spatially inhomogeneous pairwise interacting point processes}, author={Matthew A. Bognar}, journal={Computational Statistics & Data Analysis}, year={2005}, volume={49}, pages={1-18} }