# On Benjamini-Hochberg procedure applied to mid p-values

arXiv: https://arxiv.org/abs/1906.01701 · HTML: https://mlsanity.com/paper/1906.01701/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2019.

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

- [Technically Love: The Evolution of Human-AI Romance Discourse on Reddit](https://mlsanity.com/paper/2604.15333/) (2026)

## Abstract (arXiv)

Multiple testing with discrete p-values routinely arises in various scientific endeavors. However, procedures, including the false discovery rate (FDR) controlling Benjamini-Hochberg (BH) procedure, often used in such settings, being developed originally for p-values with continuous distributions, are too conservative, and so may not be as powerful as one would hope for. Therefore, improving the BH procedure by suitably adapting it to discrete p-values without losing its FDR control is currently an important path of research. This paper studies the FDR control of the BH procedure when it is applied to mid p-values and derive conditions under which it is conservative. Our simulation study reveals that the BH procedure applied to mid p-values may be conservative under much more general settings than characterized in this work, and that an adaptive version of the BH procedure applied to mid p-values is as powerful as an existing adaptive procedure based on randomized p-values.