Posterior distribution of hierarchical models using CAR(1) distributions
Posterior distribution of hierarchical models using CAR(1) distributions
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DOI：
10.1093/biomet/86.2.341
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发表时间：
1999-06-01
期刊：
影响因子：
2.7
通讯作者：
Speckman, PL
中科院分区：
文献类型：
--
作者：
Sun, DC;Tsutakawa, RK;Speckman, PL
我们研究了条件自回归模型（CAR（1）模型）的性质，该模型通常用于表示贝叶斯死亡率分析中的区域效应。我们考虑了一个贝叶斯分层线性混合模型，其中固定效应具有模糊先验（如常数先验），随机效应遵循一类CAR（1）模型，包括那些区域效应的联合先验分布不正确的模型。我们给出了固定效应和随机效应以及方差分量的后验分布存在的充分条件。然后，我们证明了条件的必要性，并给出了一个单向方差分析的例子，后验可能存在或可能不存在。最后，我们将结果扩展到广义线性混合模型，其中包括作为一个特例的泊松对数线性模型中常用的疾病映射。
We examine properties of the conditional autoregressive model, or CAR(1) model, which is commonly used to represent regional effects in Bayesian analyses of mortality rates. We consider a Bayesian hierarchical linear mixed model where the fixed effects have a vague prior such as a constant prior and the random effect follows a class of CAR(1) models including those whose joint prior distribution of the regional effects is improper. We give sufficient conditions for the existence of the posterior distribution of the fixed and random effects and variance components. We then prove the necessity of the conditions and give a one-way analysis of variance example where the posterior may or may not exist. Finally, we 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.