Differentially private methods for managing model uncertainty in linear regression

In this article, we propose differentially private methods for hypothesis testing, model averaging, and model selection for normal linear models. We propose Bayesian methods based on mixtures of $g$-priors and non-Bayesian methods based on likelihood-ratio statistics and information criteria. The procedures are asymptotically consistent and straightforward to implement with existing software. We focus on practical issues such as adjusting critical values so that hypothesis tests have adequate type I error rates and quantifying the uncertainty introduced by the privacy-ensuring mechanisms.

article bayesian consistent hypothesis information likelihood linear linear regression model selection normal regression statistics testing uncertainty