Identifiability, Improper Priors, and Gibbs Sampling for Generalized Linear Models
本文研究了广义线性模型拟合中参数可识别性和后验分布是否合理的问题，指出非可识别性在常见GLM中普遍存在，并讨论了其对模拟拟合的影响；同时给出了后验合理的简便检验条件，并说明即使后验不当，吉布斯抽样输出仍可用于某些未知参数的有意义推断。
Abstract Markov chain Monte Carlo algorithms are widely used in the fitting of generalized linear models (GLMs). Such model fitting is somewhat of an art form, requiring suitable trickery and tuning to obtain results in which one can have confidence. A wide range of practical issues arise. The focus here is on parameter identifiability and posterior propriety. In particular, we clarify that nonidentifiability arises for usual GLMs and discuss its implications for simulation-based model fitting. Because often some part of the prior specification is vague, we consider whether the resulting posterior is proper, providing rather general and easily checked results for GLMs. We also show that if a Gibbs sampler is run with an improper posterior, then it may be possible to use the output to obtain meaningful inference for certain model unknowns.