Differentially private methods for managing model uncertainty in linear regression models

Statistical methods for confidential data are in high demand due to an increase in computational power and changes in privacy law. This article introduces differentially private methods for handling model uncertainty in linear regression models. More precisely, we provide differentially private Bayes factors, posterior probabilities, likelihood ratio statistics, information criteria, and model-averaged estimates. Our methods are asymptotically consistent and easy to run with existing implementations of non-private methods.