Spatial Poisson models using intrinsic autoregressions are commonly used in Bayesian modeling of areal data. Inference for such models is generally carried out via Markov chain Monte Carlo methods, which often exhibit slow mixing. Although several techniques have been proposed that produce better samplers with some success, one still has to worry about the usual MCMC convergence and mixing diagnostics when selecting a sampler that appears to provide the most accurate results. In our work, we propose a method for producing independent samples from the posterior distribution. We exploit the low dimensionality of the precision components to provide a systematic method for producing heavy tailed proposal distributions that can be used in rejection sampling and perfect simulation schemes for these models. The perfect sampling algorithm used is along the lines of the method described in Moller and Nicholls (1999), and uses a combination of Coupling from the Past (C.F.T.P.) and simulated tempering ideas. We describe the application of our methods to several data sets. We find that our methods are easy to use and produce i.i.d. draws fairly efficiently.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.