# Optimal Multiple Testing Under a Gaussian Prior on the Effect Sizes

arXiv: https://arxiv.org/abs/1504.02935 · HTML: https://mlsanity.com/paper/1504.02935/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2015.

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## Abstract (arXiv)

We develop a new method for frequentist multiple testing with Bayesian prior information. Our procedure finds a new set of optimal p-value weights called the Bayes weights. Prior information is relevant to many multiple testing problems. Existing methods assume fixed, known effect sizes available from previous studies. However, the case of uncertain information is usually the norm. For a Gaussian prior on effect sizes, we show that finding the optimal weights is a non-convex problem. Despite the non-convexity, we give an efficient algorithm that solves this problem nearly exactly. We show that our method can discover new loci in genome-wide association studies. On several data sets it compares favorably to other methods. Open source code is available.