Efficiency of Markov chains for Bayesian linear regression models with heavy-tailed errors

Abstract

In this paper, 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 a sampler given in the literature 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, using a simple energy function, show that a data augmentation algorithm in the literature is geometrically ergodic under a significantly different condition.