Rethinking Robust Statistics with Modern Bayesian Methods

Abstract

Developing robust statistical methods is an important goal for psychological science. Whereas classical methods (i.e., sampling distributions, p-values, etc.) have been thoroughly characterized, Bayesian robust methods remain relatively uncommon in practice and methodological literatures. Here we propose a robust Bayesian model (BHS t ) that accommodates heterogeneous (H) variances by predicting the scale parameter on the log scale and tail-heaviness with a Student-t likelihood (S t). Through simulations with normative and contaminated (i.e., heavy-tailed) data, we demonstrate that BHS t has consistent frequentist properties in terms of type I error, power, and mean squared error compared to three classical robust methods. With a motivating example, we illustrate Bayesian inferential methods such as approximate leave-one-out cross-validation and posterior predictive checks. We end by suggesting areas of improvement for BHS t and discussing Bayesian robust methods in practice.

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