Theoretical properties of Bayesian Student-$t$ linear regression

TL;DR

This paper analyzes the theoretical properties of Bayesian Student-$t$ linear regression, focusing on its robustness and efficiency trade-offs in different asymptotic scenarios, to better understand its behavior as a robust alternative.

Contribution

It provides the first detailed theoretical analysis of Bayesian Student-$t$ linear regression's properties in asymptotic regimes, clarifying robustness-efficiency trade-offs.

Findings

Characterizes robustness and efficiency trade-offs asymptotically.

Provides insights into the influence of degrees of freedom on model performance.

Enhances understanding of Bayesian Student-$t$ regression's theoretical foundations.

Abstract

Bayesian Student-$t$ linear regression is a common robust alternative to the normal model, but its theoretical properties are not well understood. We aim to fill some gaps by providing analyses in two different asymptotic scenarios. The results allow to precisely characterize the trade-off between robustness and efficiency controlled through the degrees of freedom (at least asymptotically).