Spatial Poisson models for areal count data use nonstationary "intrinsic autoregressions," also often referred to as "conditionally autoregressive" (CAR) models. Bayesian inference for these models has generally involved using single parameter updating Markov chain Monte Carlo algorithms, which often exhibit slow mixing (i.e., poor convergence) properties. These spatial models are richly parameterized and lend themselves to the structured Markov chain Monte Carlo (SMCMC) algorithms. SMCMC provides a simple, general, and flexible framework for accelerating convergence in an MCMC sampler by providing a systematic way to block groups of similar parameters while taking full advantage of the posterior correlation structure induced by the model and data. Among the SMCMC strategies considered here are blocking using different size blocks (grouping by geographical region), reparameterization, updating jointly with and without model hyperparameters, "oversampling" some of the model parameters, and "pilot adaptation" versus continuous tuning techniques for the proposal density. We apply the techniques presented here to datasets on cancer mortality and late detection in the state of Minnesota. We find that, compared to univariate sampling procedures, our techniques will typically lead to more accurate posterior estimates, and they are sometimes also far more efficient in terms of the number of effective samples generated per second.
Bibliographical noteFunding Information:
The Ž rst and third authors were supported in part by NIAID grant R01-AI41966 and NSF/EPA grant SES 99-78238,while the second author wasupsportedin parbytthe MinnestaoOl HealthraClinilcResaeCentaerr, ch NIH/NIDR grant P30-DE09737.
- Convergence acceleration
- Disease mapping
- Gibbs sampling
- Hierarchical centering
- Hierarchical model
- Metropolis-Hastings algorithm