A Short Note on the Efficiency of Markov Chains for Bayesian Linear Regression Models with Heavy-Tailed Errors

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.