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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 anddoi:10.1093/biomet/86.2.341 fatcat:x2fga2upuzcothuresusilooui