PRADAS: PRior-Assisted DAta Splitting for False Discovery Rate Control

TL;DR

This paper introduces PRADAS, a novel method for false discovery rate control that leverages prior information through a Bayes-optimal mirror statistic and an adaptive data-splitting strategy.

Contribution

It characterizes a broad class of mirror statistics for data splitting, derives a Bayes-optimal statistic, and develops PRADAS with an optimal stopping rule for improved FDR control.

Findings

PRADAS demonstrates superior power in simulations.

The method effectively controls FDR in real data applications.

Theoretical analysis confirms asymptotic FDR control under weak dependence.

Abstract

In the FDR-controlling literature, mirror statistics offer a flexible alternative to $p$-value based procedures. When prior information is available, however, it is unclear how to incorporate mirror statistics in a principled way, and the standard equal split used by data-splitting methods can be inefficient. In this paper, we characterize a broader class of mirror statistics for any fixed splitting scheme and establish asymptotic FDR control under mild weak-dependence conditions using a two-stage procedure inspired by \cite{li2021whiteout}. Within this class, we derive a Bayes-optimal mirror statistic. Theoretically, we demonstrate its power advantage through analyses in the Rare/Weak signal model. Building upon this Bayes-optimal mirror statistic, we propose \textsc{PRADAS} (PRior-Assisted DAta Splitting) that treats split ratio as a stopping time and recasts the data-splitting as an optional stopping over a natural filtration; the optimal stopping rule is characterized by the Snell envelope and computed efficiently via a Longstaff--Schwartz regression approximation. Both simulations and real data examples demonstrate the effectiveness of our proposed framework.