# Differentially private Bayesian tests

arXiv: https://arxiv.org/abs/2401.15502 · HTML: https://mlsanity.com/paper/2401.15502/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 27 Jan 2024.

## Builds on (most cited first, 14 of 14)

- [Differentially Private Bayesian Linear Regression](https://mlsanity.com/paper/1910.13153/) (2019)
- [Differentially Private Markov Chain Monte Carlo](https://mlsanity.com/paper/1901.10275/) (2019)
- [Differentially private significance tests for regression coefficients](https://mlsanity.com/paper/1705.09561/) (2017)
- [Differentially Private Nonparametric Hypothesis Testing](https://mlsanity.com/paper/1903.09364/) (2019)
- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [Differentially Private Permutation Tests](https://mlsanity.com/paper/2310.19043/) (2023)
- [Improved Differentially Private Analysis of Variance](https://mlsanity.com/paper/1903.00534/) (2019)
- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [Differentially Private Hypothesis Testing with the Subsampled and Aggregated Randomized Response Mechanism](https://mlsanity.com/paper/2208.06803/) (2022)
- [Mechanisms for Global Differential Privacy under Bayesian Data Synthesis](https://mlsanity.com/paper/2205.05003/) (2022)
- [A Survey on Differential Privacy with Machine Learning and Future Outlook](https://mlsanity.com/paper/2211.10708/) (2022)
- [A Short Note on Almost Sure Convergence of Bayes Factors in the General Set-Up](https://mlsanity.com/paper/1703.04956/) (2017)
- [Differentially private methods for managing model uncertainty in linear regression models](https://mlsanity.com/paper/2109.03949/) (2021)
- [Bayes Factors Based on Test Statistics and Non-Local Moment Prior Densities](https://mlsanity.com/paper/2310.16213/) (2023)

## Built on by (most cited first, 1 of 1)

- [A unified Bayesian framework for interval hypothesis testing in clinical trials](https://mlsanity.com/paper/2402.13890/) (2024)

## Abstract (arXiv)

Differential privacy has emerged as an significant cornerstone in the realm of scientific hypothesis testing utilizing confidential data. In reporting scientific discoveries, Bayesian tests are widely adopted since they effectively circumnavigate the key criticisms of P-values, namely, lack of interpretability and inability to quantify evidence in support of the competing hypotheses. We present a novel differentially private Bayesian hypotheses testing framework that arise naturally under a principled data generative mechanism, inherently maintaining the interpretability of the resulting inferences. Furthermore, by focusing on differentially private Bayes factors based on widely used test statistics, we circumvent the need to model the complete data generative mechanism and ensure substantial computational benefits. We also provide a set of sufficient conditions to establish results on Bayes factor consistency under the proposed framework. The utility of the devised technology is showcased via several numerical experiments.