# False Discovery Rate Control via Bayesian Mirror Statistic

arXiv: https://arxiv.org/abs/2510.00875 · HTML: https://mlsanity.com/paper/2510.00875/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Sparsity information and regularization in the horseshoe and other shrinkage priors](https://mlsanity.com/paper/1707.01694/) (2017)
- [False Discovery Rate Control via Data Splitting](https://mlsanity.com/paper/2002.08542/) (2020)
- [Controlling False Discovery Rate Using Gaussian Mirrors](https://mlsanity.com/paper/1911.09761/) (2019)
- [A Scale-free Approach for False Discovery Rate Control in Generalized Linear Models](https://mlsanity.com/paper/2007.01237/) (2020)

## Abstract (arXiv)

Simultaneously performing variable selection and inference in high-dimensional models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of specific statistical procedures to accurately select the most important predictors in a high-dimensional space, while being able to control some form of selection error. In this work we adapt the Mirror Statistic approach to False Discovery Rate (FDR) control into a Bayesian modelling framework. The Mirror Statistic, developed in the classic frequentist statistical framework, is a flexible method to control FDR, which only requires mild model assumptions, but requires two sets of independent regression coefficient estimates, usually obtained after splitting the original dataset. Here we propose to rely on a Bayesian formulation of the model and use the posterior distributions of the coefficients of interest to build the Mirror Statistic and effectively control the FDR without the need to split the data. Moreover, the method is very flexible since it can be used with continuous and discrete outcomes and more complex predictors, such as with mixed models. We keep the approach scalable to high-dimensions by relying on Automatic Differentiation Variational Inference and fully continuous prior choices.