Reference Bayesian Methods for Generalized Linear Mixed Models
研究了广义线性混合模型中两种参考先验（近似均匀收缩先验和近似杰弗里斯先验），证明标准不变先验会导致后验分布不当，并通过模拟和癫痫数据实例展示了近似均匀收缩先验的优势。
Abstract Bayesian methods furnish an attractive approach to inference in generalized linear mixed models. In the absence of subjective prior information for the random-effect variance components, these analyses are typically conducted using either the standard invariant prior for normal responses or diffuse conjugate priors. Previous work has pointed out serious difficulties with both strategies, and we show here that as in normal mixed models, the standard invariant prior leads to an improper posterior distribution for generalized linear mixed models. This article proposes and investigates two alternative reference (i.e., “objective” or “noninformative”) priors: an approximate uniform shrinkage prior and an approximate Jeffreys's prior. We give conditions for the existence of the posterior distribution under any prior for the variance components in conjunction with a uniform prior for the fixed effects. The approximate uniform shrinkage prior is shown to satisfy these conditions for several families of distributions, in some cases under mild constraints on the data. Simulation studies conducted using a logit-normal model reveal that the approximate uniform shrinkage prior improves substantially on a plug-in empirical Bayes rule and fully Bayesian methods using diffuse conjugate specifications. The methodology is illustrated on a seizure dataset.