# Private Sequential Hypothesis Testing for Statisticians: Privacy, Error Rates, and Sample Size

arXiv: https://arxiv.org/abs/2204.04597 · HTML: https://mlsanity.com/paper/2204.04597/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 10 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [The Structure of Optimal Private Tests for Simple Hypotheses](https://mlsanity.com/paper/1811.11148/) (2018)
- [Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing](https://mlsanity.com/paper/1602.03090/) (2016)
- [Differentially Private Nonparametric Hypothesis Testing](https://mlsanity.com/paper/1903.09364/) (2019)
- [Locally Private Hypothesis Testing](https://mlsanity.com/paper/1802.03441/) (2018)
- [Local Private Hypothesis Testing: Chi-Square Tests](https://mlsanity.com/paper/1709.07155/) (2017)
- [Differentially Private Change-Point Detection](https://mlsanity.com/paper/1808.10056/) (2018)
- [Privately detecting changes in unknown distributions](https://mlsanity.com/paper/1910.01327/) (2019)
- [Distributed Sequential Detection for Gaussian Shift-in-Mean Hypothesis Testing](https://mlsanity.com/paper/1411.7716/) (2014)

## Built on by (most cited first, 2 of 2)

- [DP-SPRT: Differentially Private Sequential Probability Ratio Tests](https://mlsanity.com/paper/2508.06377/) (2025)
- [Optimal Rates for Differentially Private Hypothesis Testing with E-values](https://mlsanity.com/paper/2605.28952/) (2026)

## Abstract (arXiv)

The sequential hypothesis testing problem is a class of statistical analyses where the sample size is not fixed in advance. Instead, the decision-process takes in new observations sequentially to make real-time decisions for testing an alternative hypothesis against a null hypothesis until some stopping criterion is satisfied. In many common applications of sequential hypothesis testing, the data can be highly sensitive and may require privacy protection; for example, sequential hypothesis testing is used in clinical trials, where doctors sequentially collect data from patients and must determine when to stop recruiting patients and whether the treatment is effective. The field of differential privacy has been developed to offer data analysis tools with strong privacy guarantees, and has been commonly applied to machine learning and statistical tasks. In this work, we study the sequential hypothesis testing problem under a slight variant of differential privacy, known as Renyi differential privacy. We present a new private algorithm based on Wald's Sequential Probability Ratio Test (SPRT) that also gives strong theoretical privacy guarantees. We provide theoretical analysis on statistical performance measured by Type I and Type II error as well as the expected sample size. We also empirically validate our theoretical results on several synthetic databases, showing that our algorithms also perform well in practice. Unlike previous work in private hypothesis testing that focused only on the classical fixed sample setting, our results in the sequential setting allow a conclusion to be reached much earlier, and thus saving the cost of collecting additional samples.