  Let $\pi$ denote the intractable posterior density that results when the
likelihood from a multivariate linear regression model with errors from a scale
mixture of normals is combined with the standard non-informative prior. There
is a simple data augmentation algorithm (based on latent data from the mixing
density) that can be used to explore $\pi$. Hobert et al. (2015)
[arXiv:1506.03113v1] recently performed a convergence rate analysis of the
Markov chain underlying this MCMC algorithm in the special case where the
regression model is univariate. These authors provide simple sufficient
conditions (on the mixing density) for geometric ergodicity of the Markov
chain. In this note, we extend Hobert et al.'s (2015) result to the
multivariate case.
