Bayesian linear regression models with flexible error distributions

摘要

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.