Open Access
2024 Geometric ergodicity of Gibbs samplers for Bayesian error-in-variable regression
Austin Brown
Author Affiliations +
Electron. J. Statist. 18(1): 1495-1516 (2024). DOI: 10.1214/24-EJS2235


Multivariate Bayesian error-in-variable (EIV) linear regression is considered to account for additional additive Gaussian error in the features and response. A 3-variable deterministic scan Gibbs sampler is constructed for multivariate EIV regression models using classical and Berkson errors with independent normal and inverse-Wishart priors. These Gibbs samplers are proven to always be geometrically ergodic which ensures a central limit theorem for many time averages from the Markov chains. We demonstrate the strengths and limitations of the Gibbs sampler with simulated data for large data problems, robustness to misspecification and also analyze a real-data example in astrophysics.


Thanks to Galin L. Jones for helpful guidance and insightful comments for developing this article. Thanks to the anonymous referees for recommendations to improve and extend some results from a previous version of this manuscript.


Download Citation

Austin Brown. "Geometric ergodicity of Gibbs samplers for Bayesian error-in-variable regression." Electron. J. Statist. 18 (1) 1495 - 1516, 2024.


Received: 1 April 2023; Published: 2024
First available in Project Euclid: 27 March 2024

arXiv: 2209.08301
Digital Object Identifier: 10.1214/24-EJS2235

Primary: 60J22
Secondary: 62F15

Keywords: Bayesian statistics , Convergence analysis , error-in-variable models , Gibbs sampling , Markov chain Monte Carlo , measurement error models

Vol.18 • No. 1 • 2024
Back to Top