Open Access
June 2020 A New Bayesian Approach to Robustness Against Outliers in Linear Regression
Philippe Gagnon, Alain Desgagné, Mylène Bédard
Bayesian Anal. 15(2): 389-414 (June 2020). DOI: 10.1214/19-BA1157


Linear regression is ubiquitous in statistical analysis. It is well understood that conflicting sources of information may contaminate the inference when the classical normality of errors is assumed. The contamination caused by the light normal tails follows from an undesirable effect: the posterior concentrates in an area in between the different sources with a large enough scaling to incorporate them all. The theory of conflict resolution in Bayesian statistics (O’Hagan and Pericchi (2012)) recommends to address this problem by limiting the impact of outliers to obtain conclusions consistent with the bulk of the data. In this paper, we propose a model with super heavy-tailed errors to achieve this. We prove that it is wholly robust, meaning that the impact of outliers gradually vanishes as they move further and further away from the general trend. The super heavy-tailed density is similar to the normal outside of the tails, which gives rise to an efficient estimation procedure. In addition, estimates are easily computed. This is highlighted via a detailed user guide, where all steps are explained through a simulated case study. The performance is shown using simulation. All required code is given.


Download Citation

Philippe Gagnon. Alain Desgagné. Mylène Bédard. "A New Bayesian Approach to Robustness Against Outliers in Linear Regression." Bayesian Anal. 15 (2) 389 - 414, June 2020.


Published: June 2020
First available in Project Euclid: 23 May 2019

MathSciNet: MR4078719
Digital Object Identifier: 10.1214/19-BA1157

Primary: 62F35
Secondary: 62J05

Keywords: ANCOVA , ANOVA , Built-in robustness , maximum likelihood estimation , super heavy-tailed distributions , Variable selection , whole robustness

Vol.15 • No. 2 • June 2020
Back to Top