The paper develops Bernstein von Mises Theorem under hierarchical $g$ -priors for linear regression models. The results are obtained both when the error variance is known, and also when it is unknown. An inverse gamma prior is attached to the error variance in the later case. The paper also demonstrates some connection between the total variation and $\alpha$-divergence measures.

翻译：本文在线性回归模型的层次化$g$先验下发展了Bernstein von-Mises定理。研究结果分别在误差方差已知与未知两种情形下获得。在误差方差未知的情形中，我们为其附加了逆伽马先验。此外，本文还揭示了总变差度量与$\alpha$散度度量之间的若干关联。