Robust Bayesian model selection for heavy-tailed linear regression using finite mixtures

TL;DR

This paper introduces a Bayesian model selection method for heavy-tailed linear regression using finite mixtures, enabling simultaneous analysis of multiple models with improved inference over traditional criteria.

Contribution

It proposes a novel finite mixture Bayesian approach for model selection in heavy-tailed linear regression, including an extension to censored data.

Findings

Better model selection accuracy demonstrated in simulations

Effective handling of heavy-tailed distributions in regression

Extension to censored linear regression models

Abstract

In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture corresponds to one possible model within the symmetrical class of normal independent distributions. Naturally, the Gaussian model is one of the possibilities. This allows for a simultaneous analysis based on the posterior probability of each model. Inference is performed via Markov chain Monte Carlo - a Gibbs sampler with Metropolis-Hastings steps for a class of parameters. Simulated examples highlight the advantages of this approach compared to a segregated analysis based on arbitrarily chosen model selection criteria. Examples with real data are presented and an extension to censored linear regression is introduced and discussed.