Chen Ming-Hui, Ibrahim Joseph G, Kim Sungduk
Ming-Hui Chen is Professor, Department of Statistics, University of Connecticut, Storrs, CT 06269 (E-mail:
J Am Stat Assoc. 2008 Dec 1;103(484):1659-1664. doi: 10.1198/016214508000000779.
We study several theoretical properties of Jeffreys's prior for binomial regression models. We show that Jeffreys's prior is symmetric and unimodal for a class of binomial regression models. We characterize the tail behavior of Jeffreys's prior by comparing it with the multivariate t and normal distributions under the commonly used logistic, probit, and complementary log-log regression models. We also show that the prior and posterior normalizing constants under Jeffreys's prior are linear transformation-invariant in the covariates. We further establish an interesting theoretical connection between the Bayes information criterion and the induced dimension penalty term using Jeffreys's prior for binomial regression models with general links in variable selection problems. Moreover, we develop an importance sampling algorithm for carrying out prior and posterior computations under Jeffreys's prior. We analyze a real data set to illustrate the proposed methodology.
我们研究了二项回归模型中杰弗里斯先验的几个理论性质。我们表明，对于一类二项回归模型，杰弗里斯先验是对称且单峰的。通过在常用的逻辑斯蒂、概率单位和互补对数-对数回归模型下将其与多元t分布和正态分布进行比较，我们刻画了杰弗里斯先验的尾部行为。我们还表明，杰弗里斯先验下的先验和后验归一化常数在协变量中是线性变换不变的。在变量选择问题中，对于具有一般链接的二项回归模型，我们进一步利用杰弗里斯先验在贝叶斯信息准则和诱导维度惩罚项之间建立了有趣的理论联系。此外，我们开发了一种重要性抽样算法，用于在杰弗里斯先验下进行先验和后验计算。我们分析了一个真实数据集以说明所提出的方法。
