Bayesian Estimation in Spatially Inhomogeneous Pairwise Interacting Point Processes

• Activity Number: 217
• Type: Topic Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Matthew Bognar*+
• Companies: University of Iowa
• Keywords: spatial point pattern ; reversible jump MCMC ; importance sampling ; pairwise interacting point process ; Bayesian inference ; Metropolis-Hastings algorithm

Abstract

Spatial point patterns are frequently modeled with pairwise interacting point processes. However, inference is complicated by the presence of an intractable function of the parameters in the likelihood. While various frequentist inferential techniques have been developed, Bognar and Cowles (2004) suggested the use of Bayesian methodology for inference. Because the Metropolis-Hastings acceptance probability contains a ratio of two likelihoods evaluated at differing parameter values, the resulting intractable ratio complicates the required application of MCMC. Within each iteration of the sampler, Bognar and Cowles estimate this intractable ratio with importance sampling. While the aforementioned inferential techniques have assumed spatial homogeneity in the density of points, we will examine a generalization of the Bayesian inferential framework of Bognar and Cowles which allows the modeling of spatial inhomogeneity in the density of points (the literature is absent of such an extension in a frequentist framework). We conclude with an analysis of a glacial drumlin dataset using an inhomogeneous Strauss point process.