We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper extend their theoretical results to the case of unknown error variance . Under proper sparsity assumption, we achieve model selection consistency, posterior contraction rates as well as Bernstein von-Mises theorem by analyzing multivariate t-distribution.

翻译：我们研究了全巴伊西亚高维线性回归程序。我们采用了[1] 中引入的基于数据的经验前科。在他们的论文中,这些前科具有良好的后部收缩特性,并且容易计算。我们的论文将其理论结果扩大到未知错误差异的情况。在适当的宽度假设下,我们通过分析多变量 t分布,实现了选择模式的一致性、后端收缩率以及Bernstein von-Mises定理。