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

Yasuyuki Hamura

doi:10.1016/j.jmva.2025.105506

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arXiv · 2410.17070

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

Yasuyuki Hamura

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Abstract

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.

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Yasuyuki Hamura. 2024-10-22. A Short Note on the Efficiency of Markov Chains for Bayesian Linear Regression Models with Heavy-Tailed Errors. https://doi.org/10.1016/j.jmva.2025.105506

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