Bayesian linear regression models with flexible error distributions

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 behaviour. Moreover, the latter is specified in a way that no estimation of the degrees of freedom parameters is required. This way, the known statistical difficulties when dealing with those parameters are mitigated and yet model flexibility is not compromised. The inference is performed via a carefully designed Markov chain Monte Carlo algorithm and simulation studies are conducted to evaluate the performance of the proposed methodology. The analysis of two real data sets is also presented.

Keywords:

• Finite mixtures
• heavy tail distributions
• hierarchical modelling
• MCMC

2010 Mathematics Subject Classifications:

• 62F15
• 62J05
• 62J12

Acknowledgements

Marcos Prates acknowledges partial funding support from CNPq grants 436948/2018-4 and 307547/2018-4, and FAPEMIG grant PPM-00532-16. Flávio Gonçalves acknowledges partial funding support from CNPq grants 307928/2017-9 and FAPEMIG grant PPM-00745-18.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Marcos Prates acknowledges partial funding support from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) grants 436948/2018-4 and 307547/2018-4, and FAPEMIG grant PPM-00532-16. Flávio Gonçalves acknowledges partial funding support from CNPq grant 307928/2017-9 and FAPEMIG grant PPM-00745-18.