# A unified treatment of multiple testing with prior knowledge using the p-filter

arXiv: https://arxiv.org/abs/1703.06222 · HTML: https://mlsanity.com/paper/1703.06222/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2017.

## Built on by (most cited first, 10 of 10)

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- [The Lifecycle of a Statistical Model: Model Failure Detection, Identification, and Refitting](https://mlsanity.com/paper/2202.04166/) (2022)
- [A Locally Adaptive Algorithm for Multiple Testing with Network Structure](https://mlsanity.com/paper/2203.11461/) (2022)
- [Sample-and-Forward: Communication-Efficient Control of the False Discovery Rate in Networks](https://mlsanity.com/paper/2210.02555/) (2022)
- [QuTE: decentralized multiple testing on sensor networks with false discovery rate control](https://mlsanity.com/paper/2210.04334/) (2022)
- [Adaptive False Discovery Rate Control with Privacy Guarantee](https://mlsanity.com/paper/2305.19482/) (2023)
- [On Large-Scale Multiple Testing Over Networks: An Asymptotic Approach](https://mlsanity.com/paper/2211.16059/) (2022)
- [Multi-Objective Hyperparameter Selection via Hypothesis Testing on Reliability Graphs](https://mlsanity.com/paper/2501.13018/) (2025)
- [Controlling False Discovery Rates under Cross-Sectional Correlations](https://mlsanity.com/paper/2102.07826/) (2021)
- [Safe Urban Traffic Control via Uncertainty-Aware Conformal Prediction and World-Model Reinforcement Learning](https://mlsanity.com/paper/2602.04821/) (2026)

## Abstract (arXiv)

There is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision. Some common forms of prior knowledge include (a) beliefs about which hypotheses are null, modeled by non-uniform prior weights; (b) differing importances of hypotheses, modeled by differing penalties for false discoveries; (c) multiple arbitrary partitions of the hypotheses into (possibly overlapping) groups; and (d) knowledge of independence, positive or arbitrary dependence between hypotheses or groups, suggesting the use of more aggressive or conservative procedures. We present a unified algorithmic framework called p-filter for global null testing and false discovery rate (FDR) control that allows the scientist to incorporate all four types of prior knowledge (a)-(d) simultaneously, recovering a variety of known algorithms as special cases.