Geometric ergodicity of Gibbs samplers for Bayesian error-in-variable regression

TL;DR

This paper proves geometric ergodicity for Gibbs samplers in multivariate Bayesian error-in-variable regression models, ensuring reliable statistical inference and demonstrating practical effectiveness through simulations and astrophysics data.

Contribution

It introduces a Gibbs sampler for multivariate EIV regression with proven geometric ergodicity, a key property for statistical validity.

Findings

Gibbs samplers are always geometrically ergodic for these models.

The method performs well with large datasets and is robust to misspecification.

Application to astrophysics data demonstrates practical utility.

Abstract

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 samplers 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.