Posterior distribution of hierarchical models using CAR(1) distributions

D Sun
1999 Biometrika  
We examine properties of the CAR1 model, which is commonly used to represent regional e ects in Bayesian analyses of mortality rates. We consider a Bayesian hierarchical linear mixed model where the xed e ects have a v ague prior such a s a constant prior and the random e ect follows a class of CAR1 models including those whose joint prior distribution of the regional e ects is improper. We give su cient conditions for the existence of the posterior distribution of the xed and random e ects and
more » ... d random e ects and variance components. We then prove the necessity of the conditions and give a one-way analysis of variance example where the posterior may o r m a y not exist. Finally, w e extend the result to the generalised linear mixed model, which includes as a special case the Poisson log-linear model commonly used in disease mapping.
doi:10.1093/biomet/86.2.341 fatcat:x2fga2upuzcothuresusilooui