Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models
Article first published online: 21 AUG 2000
Copyright © 2000 John Wiley & Sons, Ltd.
Statistics in Medicine
Special Issue: Disease Mapping with a Focus on Evaluation
Volume 19, Issue 17-18, pages 2279–2294, 15 - 30 September 2000
How to Cite
Eberly, L. E. and Carlin, B. P. (2000), Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models. Statist. Med., 19: 2279–2294. doi: 10.1002/1097-0258(20000915/30)19:17/18<2279::AID-SIM569>3.0.CO;2-R
- Issue published online: 21 AUG 2000
- Article first published online: 21 AUG 2000
- NIAID. Grant Numbers: 5-U01-AI42170-07, R01-AI41966
- NIEHS. Grant Number: 1-R01-ES07750
The marked increase in popularity of Bayesian methods in statistical practice over the last decade owes much to the simultaneous development of Markov chain Monte Carlo (MCMC) methods for the evaluation of requisite posterior distributions. However, along with this increase in computing power has come the temptation to fit models larger than the data can readily support, meaning that often the propriety of the posterior distributions for certain parameters depends on the propriety of the associated prior distributions. An important example arises in spatial modelling, wherein separate random effects for capturing unstructured heterogeneity and spatial clustering are of substantive interest, even though only their sum is well identified by the data. Increasing the informative content of the associated prior distributions offers an obvious remedy, but one that hampers parameter interpretability and may also significantly slow the convergence of the MCMC algorithm. In this paper we investigate the relationship among identifiability, Bayesian learning and MCMC convergence rates for a common class of spatial models, in order to provide guidance for piror selection and algorithm tuning. We are able to elucidate the key issues with relatively simple examples, and also illustrate the varying impacts of covariates, outliers and algorithm starting values on the resulting algorithms and posterior distributions. Copyright © 2000 John Wiley & Sons, Ltd.