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In this work, we propose differentially private methods for hypothesistesting, model averaging, and model selection for normal linear models. Weconsider Bayesian methods based on mixtures of $g$-priors and non-Bayesianmethods based on likelihood-ratio statistics and information criteria. Theprocedures are asymptotically consistent and straightforward to implement withexisting software. We focus on practical issues such as adjusting criticalvalues so that hypothesis tests have adequate type I error rates andquantifying the uncertainty introduced by the privacy-ensuring mechanisms.

Differentially private methods for managing model uncertainty in linear regression models