Bayesian linear regression models with flexible error distributions

TL;DR

This paper proposes a flexible Bayesian linear regression approach using finite mixtures of Student-t distributions to better model error distributions, capturing multimodality, skewness, and tail behavior without estimating degrees of freedom.

Contribution

Introduces a hierarchical mixture model for errors in linear regression that handles multimodality and skewness without estimating degrees of freedom, simplifying inference.

Findings

Model effectively captures complex error distributions.

Simulation studies show improved fit over traditional models.

Real data analysis demonstrates practical applicability.

Abstract

This work introduces a novel methodology based on finite mixtures of Student-t distributions to model the errors' distribution in linear regression models. The novelty lies on a particular hierarchical structure for the mixture distribution in which the first level models the number of modes, responsible to accommodate multimodality and skewness features, and the second level models tail behavior. Moreover, the latter is specified in a way that no degrees of freedom parameters are estimated and, therefore, the known statistical difficulties when dealing with those parameters is mitigated, and yet model flexibility is not compromised. Inference is performed via Markov chain Monte Carlo and simulation studies are conducted to evaluate the performance of the proposed methodology. The analysis of two real data sets are also presented.