A General Method for Robust Bayesian Modeling
This work provides a general solution for robust Bayesian modeling, addressing a common challenge in statistical inference for researchers and practitioners dealing with noisy data, though it appears incremental by building on existing approaches like empirical Bayes.
The authors tackled the problem of developing robust Bayesian models to handle outliers and model assumption violations, presenting a general method that transforms existing Bayesian models into robust variants and demonstrating its application across several models including linear, Poisson, and logistic regression, as well as topic models.
Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case basis; examples include robust linear regression, robust mixture models, and bursty topic models. In this paper we develop a general approach to robust Bayesian modeling. We show how to turn an existing Bayesian model into a robust model, and then develop a generic strategy for computing with it. We use our method to study robust variants of several models, including linear regression, Poisson regression, logistic regression, and probabilistic topic models. We discuss the connections between our methods and existing approaches, especially empirical Bayes and James-Stein estimation.