Bayesian Robustness: A Nonasymptotic Viewpoint

The goal is to capture the sensitivity of inferential proc edures to the presence of outliers in the data and misspecifications in the modelling a ssumptions, and to mitigate overly large sensitivity. The Bayesian approach has been fo cused on capturing possible anomalies in the observed data via the model and in choosing p riors that have minimal effect on inferences. The frequentist approach, on the other hand, has focused on the development of estimators that identify and guard against o utliers in the data. We refer the reader to [ Hub11, Chap 15] for a comprehensive discussion.