Robustness Against Conflicting Prior Information in Regression*

Including prior information about model parameters is a fundamental step of any Bayesian statistical analysis. It is viewed positively by some as it allows, among others, to quantitatively incorporate expert opinion about model param-eters. It is viewed negatively by others because it sets the stage for subjectivity in statistical analysis. Certainly, it creates problems when the inference is skewed due to a conflict with the data collected. According to the theory of conflict res-olution (O'Hagan and Pericchi, 2012), a solution to such problems is to diminish the impact of conflicting prior information, yielding inference consistent with the data. This is typically achieved by using heavy-tailed priors. We study both theo-retically and numerically the efficacy of such a solution in a regression framework where the prior information about the coefficients takes the form of a product of density functions with known location and scale parameters. We study functions with regularly-varying tails (Student distributions), log-regularly-varying tails (as introduced in Desgagne & PRIME; (2015)), and propose functions with slower tail decays that allow to resolve any conflict that can happen under that regression frame-work, contrarily to the two previous types of functions. The code to reproduce all numerical experiments is available online.& DDAG;

Automated summary

Including prior information about model parameters in Bayesian statistical analysis has both positive and negative views. It allows for incorporating expert opinion, but it also introduces subjectivity. Problems arise when there is a conflict with the collected data, and the impact of conflicting prior information can be diminished by using heavy-tailed priors. In this study, the efficacy of this solution is examined in a regression framework using different types of tail decay functions.