Bayesian statistics based on shrinkage prior

本文研究了一般球对称误差分布线性模型中的贝叶斯变量选择问题。我们构造后验概率的基础上，一个可分离的先验函数，这是作为一类混合高斯。非零模型之间的比较后验几率被证明是独立的潜在的误差分布，只要分布是球对称的。由于这种不变性球对称误差分布，我们把我们的方法作为一个强大的贝叶斯变量选择方法。我们证明了我们的后验概率具有模型选择的一致性。此外，我们证明了我们的类先验函数是唯一的一类混合高斯在文献中研究的是强大的，在我们的意义上。

We study Bayesian variable selection in linear models with general spherically symmetric error distributions. We construct the posterior odds based on a separable prior function, which arises as a class of mixtures of Gaussians. The posterior odds for comparing among non-null models are shown to be independent of the underlying error distribution, provided that the distribution is spherically symmetric. Because of this invariance to spherically symmetric error distributions, we refer to our method as a robust Bayesian variable selection method. We demonstrate that our posterior odds have model selection consistency. Additionally we demonstrate that our class of prior function are the only ones within a large class of mixtures of Gaussians studied in the literature which are robust in our sense.