In this work, we propose differentially private methods for hypothesis testing, model averaging, and model selection for normal linear models. We consider 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.

翻译：本文针对正态线性模型，提出了用于假设检验、模型平均和模型选择的差分隐私方法。我们考虑基于$g$-先验混合的贝叶斯方法，以及基于似然比统计量和信息准则的非贝叶斯方法。这些方法具有渐近一致性，且易于在现有软件中实现。我们聚焦于实际应用问题，例如调整临界值以确保假设检验具有适当的I类错误率，以及量化隐私保护机制所引入的不确定性。