标题： 具有次调和先验的鲁棒贝叶斯变量选择 显示英文标题

标题： Robust Bayesian variable selection with sub-harmonic priors

摘要： 本文研究了具有广义球对称误差分布的线性模型中的贝叶斯变量选择。我们提出了次调和先验，这些先验作为Zellner的g先验的混合类，其贝叶斯因子在误差分布属于球对称类的情况下，与底层误差分布无关。由于对球对称误差分布的这种不变性，我们将我们的方法称为稳健贝叶斯变量选择方法。我们证明了我们的贝叶斯因子具有模型选择一致性和一致性。我们还为一些最近在文献中出现的g先验混合体（包括我们自己的）开发了贝叶斯因子的拉普拉斯近似，适用于高斯误差。这些近似，在每种情况下，由基于BIC的高斯贝叶斯因子乘以先验超参数和相应模型的R^2的简单有理函数给出。我们还将基于g先验的贝叶斯因子方法在高斯误差下的模型选择一致性扩展到整个球对称误差分布类。此外，我们证明了我们的次调和先验类是在文献中研究的大量g先验混合体中唯一在我们意义上稳健的先验类。模拟研究和两个真实数据集的分析表明，我们的稳健贝叶斯因子相对于BIC和其他基于g先验混合的方法表现良好。 显示英文摘要

摘要： This paper studies Bayesian variable selection in linear models with general spherically symmetric error distributions. We propose sub-harmonic priors which arise as a class of mixtures of Zellner's g-priors for which the Bayes factors are independent of the underlying error distribution, as long as it is in the spherically symmetric class. Because of this invariance to spherically symmetric error distribution, we refer to our method as a robust Bayesian variable selection method. We demonstrate that our Bayes factors have model selection consistency and are coherent. We also develop Laplace approximations to Bayes factors for a number of recently studied mixtures of g-priors that have recently appeared in the literature (including our own) for Gaussian errors. These approximations, in each case, are given by the Gaussian Bayes factor based on BIC times a simple rational function of the prior's hyper-parameters and the R^2's for the respective models. We also extend model selection consistency for several g-prior based Bayes factor methods for Gaussian errors to the entire class of spherically symmetric error distributions. Additionally we demonstrate that our class of sub-harmonic priors are the only ones within a large class of mixtures of g-priors studied in the literature which are robust in our sense. A simulation study and an analysis of two real data sets indicates good performance of our robust Bayes factors relative to BIC and to other mixture of g-prior based methods.