Bayesian Estimation of a Potential Function in a Pairwise Interacting Point Process

• Activity Number: 282
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Matthew A. Bognar*+
• Companies: University of Iowa
• Keywords: Bayesian inference ; spatial point pattern ; pairwise interacting point process ; importance sampling ; Metropolis-Hastings algorithm

Abstract

In the past, inference in pairwise interacting point processes has been performed via frequentist methods. However, some frequentist methods can produce severely biased estimates when the data exhibit strong interaction. Furthermore, interval estimates are typically obtained by parametric bootstrap methods, but in the current setting, the behavior of such estimates is unclear. We propose Bayesian methods for inference in pairwise interacting point processes. The requisite application of Markov chain Monte Carlo (MCMC) techniques is complicated by the existence of an intractable function of the parameters in the likelihood. The acceptance probability in a Metropolis-Hastings algorithm involves the ratio of two likelihoods evaluated at differing parameter values. The intractable functions do not cancel, and hence an intractable ratio must be estimated within each iteration of a Metropolis-Hastings sampler. Our unique implementation involves the use of importance sampling techniques within an MCMC sampler to estimate this intractable ratio. Although computationally costly, the ability to obtain interpretable posterior distributions justifies our Bayesian model-fitting strategy.