In this short note, we consider posterior simulation for a linear regression model when the error distribution is given by a scale mixture of multivariate normals. We first show that the sampler of Backlund and Hobert (2020) for the case of the conditionally conjugate normal-inverse Wishart prior continues to be geometrically ergodic even when the error density is heavier-tailed. Moreover, we prove that the ergodicity is uniform by verifying the minorization condition. In the second half of this note, we treat an improper case and show that the sampler of Section 4 of Roy and Hobert (2010) is geometrically ergodic under significantly milder conditions.

翻译：在这篇简短说明中，我们考虑当误差分布由多元正态分布的尺度混合给出时，线性回归模型的后验模拟。我们首先证明，即使在误差密度具有更重尾部的情况下，Backlund 和 Hobert（2020）针对条件共轭正态-逆Wishart先验情形设计的采样器仍保持几何遍历性。此外，通过验证次优化条件，我们证明了该遍历性具有一致性。在本文的后半部分，我们处理了一个非恰当先验情形，并证明在显著更宽松的条件下，Roy 和 Hobert（2010）第4节中的采样器具有几何遍历性。