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 show that the sampler of Backlund and Hobert (2020) for the case of the conditionally conjugate normal-inverse Wishart prior is geometrically ergodic even when the error density is heavier-tailed. Moreover, we prove that their sampler is uniformly ergodic if, in addition, the columns of the design matrix are linearly independent.

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具有几何遍历性。此外，我们证明若设计矩阵的列向量线性无关，则他们的采样器具有一致遍历性。