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Linear regression is ubiquitous in statistical analysis. It is wellunderstood that conflicting sources of information may contaminate theinference when the classical normality of errors is assumed. The contaminationcaused by the light normal tails follows from an undesirable effect: theposterior concentrates in an area in between the different sources with a largeenough scaling to incorporate them all. The theory of conflict resolution inBayesian statistics (O'Hagan and Pericchi (2012)) recommends to address thisproblem by limiting the impact of outliers to obtain conclusions consistentwith the bulk of the data. In this paper, we propose a model with superheavy-tailed errors to achieve this. We prove that it is wholly robust, meaningthat the impact of outliers gradually vanishes as they move further and furtheraway form the general trend. The super heavy-tailed density is similar to thenormal outside of the tails, which gives rise to an efficient estimationprocedure. In addition, estimates are easily computed. This is highlighted viaa detailed user guide, where all steps are explained through a simulated casestudy. The performance is shown using simulation. All required code is given.

A New Bayesian Approach to Robustness Against Outliers in Linear Regression