Saved in:
Bibliographic Details
Main Author: Hamura, Yasuyuki
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.17070
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914047738249216
author Hamura, Yasuyuki
author_facet Hamura, Yasuyuki
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_17070
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Short Note on the Efficiency of Markov Chains for Bayesian Linear Regression Models with Heavy-Tailed Errors
Hamura, Yasuyuki
Statistics Theory
Computation
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.
title A Short Note on the Efficiency of Markov Chains for Bayesian Linear Regression Models with Heavy-Tailed Errors
topic Statistics Theory
Computation
url https://arxiv.org/abs/2410.17070