Bayesian Inference Under Differential Privacy: Prior Selection Considerations with Application to Univariate Gaussian Data and Regression

• URL: http://arxiv.org/abs/2405.13801v1
• Date: Wed, 22 May 2024 16:27:20 GMT
• Title: Bayesian Inference Under Differential Privacy: Prior Selection Considerations with Application to Univariate Gaussian Data and Regression
• Authors: Zeki Kazan, Jerome P. Reiter,
• Abstract summary: We show that analysts can take constraints imposed by the bounds into account when specifying prior distributions. We provide theoretical and empirical results regarding what classes of default priors produce valid inference for a differentially private release.
• Score: 0.3683202928838613
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We describe Bayesian inference for the mean and variance of bounded data protected by differential privacy and modeled as Gaussian. Using this setting, we demonstrate that analysts can and should take the constraints imposed by the bounds into account when specifying prior distributions. Additionally, we provide theoretical and empirical results regarding what classes of default priors produce valid inference for a differentially private release in settings where substantial prior information is not available. We discuss how these results can be applied to Bayesian inference for regression with differentially private data.

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