# Differentially Private Bayesian Inference for Exponential Families

arXiv: https://arxiv.org/abs/1809.02188 · HTML: https://mlsanity.com/paper/1809.02188/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2018.

## Built on by (most cited first, 18 of 18)

- [Incentives in Private Collaborative Machine Learning](https://mlsanity.com/paper/2404.01676/) (2024)
- [Noise-Aware Statistical Inference with Differentially Private Synthetic Data](https://mlsanity.com/paper/2205.14485/) (2022)
- [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021)
- [Statistic Selection and MCMC for Differentially Private Bayesian Estimation](https://mlsanity.com/paper/2203.13377/) (2022)
- [Dirichlet Mechanism for Differentially Private KL Divergence Minimization](https://mlsanity.com/paper/2110.01984/) (2021)
- [Differentially private partitioned variational inference](https://mlsanity.com/paper/2209.11595/) (2022)
- [DPVIm: Differentially Private Variational Inference Improved](https://mlsanity.com/paper/2210.15961/) (2022)
- [Locally Differentially Private Bayesian Inference](https://mlsanity.com/paper/2110.14426/) (2021)
- [Decentralized Collaborative Learning with Probabilistic Data Protection](https://mlsanity.com/paper/2208.10674/) (2022)
- [Differentially Private Online Bayesian Estimation With Adaptive Truncation](https://mlsanity.com/paper/2301.08202/) (2023)
- [Differentially Private Statistical Inference through β-Divergence One Posterior Sampling](https://mlsanity.com/paper/2307.05194/) (2023)
- [Simulation-based Bayesian Inference from Privacy Protected Data](https://mlsanity.com/paper/2310.12781/) (2023)
- [Private Statistical Estimation via Truncation](https://mlsanity.com/paper/2505.12541/) (2025)
- [Fiducial Matching: Differentially Private Inference for Categorical Data](https://mlsanity.com/paper/2507.11762/) (2025)
- [Computation-Utility-Privacy Tradeoffs in Bayesian Estimation](https://mlsanity.com/paper/2603.18254/) (2026)
- [Noise-Aware Differentially Private Variational Inference](https://mlsanity.com/paper/2410.19371/) (2024)
- [Optimal Survey Design for Private Mean Estimation](https://mlsanity.com/paper/2501.18121/) (2025)
- [Noise-Calibrated Inference from Differentially Private Sufficient Statistics in Exponential Families](https://mlsanity.com/paper/2603.02010/) (2026)

## Abstract (arXiv)

The study of private inference has been sparked by growing concern regarding the analysis of data when it stems from sensitive sources. We present the first method for private Bayesian inference in exponential families that properly accounts for noise introduced by the privacy mechanism. It is efficient because it works only with sufficient statistics and not individual data. Unlike other methods, it gives properly calibrated posterior beliefs in the non-asymptotic data regime.