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arxiv: 2604.19517 · v1 · submitted 2026-04-21 · 📊 stat.ME

Recognition: unknown

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

Yuanchuan Guo , Buyu Lin , Jun S. Liu
Authors on Pith no claims yet

Pith reviewed 2026-05-10 02:01 UTC · model grok-4.3

classification 📊 stat.ME
keywords false discovery ratemirror statisticsdata splittingprior informationoptimal stoppingBayes optimalityRare/Weak model
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The pith

A Bayes-optimal mirror statistic from prior information, combined with optional stopping for split ratios, yields higher power while asymptotically controlling FDR.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a broader class of mirror statistics usable with any fixed data split and derives the Bayes-optimal member when prior information is supplied. It proves asymptotic FDR control for a two-stage procedure based on this optimal statistic under mild weak dependence among test statistics. The authors further recast the choice of split ratio as an optional stopping problem whose solution is given by the Snell envelope and approximated efficiently by Longstaff-Schwartz regression, showing a power advantage in the Rare/Weak signal model. A sympathetic reader would care because existing data-splitting methods use inefficient fixed splits and leave available prior information unused, resulting in unnecessary loss of detection power in large-scale testing.

Core claim

Within the class of mirror statistics for any fixed splitting scheme, the Bayes-optimal choice can be derived from the prior; a two-stage procedure using this choice controls the false discovery rate asymptotically under weak dependence, and recasting the split ratio as a stopping time solved via the Snell envelope produces a power gain in the Rare/Weak model, with the stopping rule computed by Longstaff-Schwartz regression, as confirmed by theory, simulations, and real-data examples.

What carries the argument

The Bayes-optimal mirror statistic together with the Snell envelope that characterizes the optimal stopping time for the split ratio.

If this is right

  • Asymptotic FDR control holds for the two-stage procedure under the stated weak-dependence conditions.
  • Theoretical power gains appear in the Rare/Weak signal model.
  • The optimal stopping rule is computable in practice via Longstaff-Schwartz regression.
  • Simulations and real data examples confirm the overall effectiveness of the resulting PRADAS framework.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The connection between mirror statistics and optional stopping suggests the same Snell-envelope approach could be applied to other sequential testing procedures where split or threshold choices affect power.
  • If the prior is only partially accurate the two-stage FDR guarantee may still provide robustness while the stopping rule adapts to the information that is present.
  • The power advantage in sparse-signal settings implies potential gains in high-dimensional applications such as genomics where priors from previous studies are routinely available.

Load-bearing premise

The supplied prior information is accurate enough to produce a useful Bayes-optimal mirror statistic, and the test statistics satisfy mild weak-dependence conditions.

What would settle it

A simulation in the Rare/Weak model in which the PRADAS procedure shows no power improvement over fixed equal splitting while the empirical FDR exceeds the nominal level would falsify the claimed advantage and control.

Figures

Figures reproduced from arXiv: 2604.19517 by Buyu Lin, Jun S. Liu, Yuanchuan Guo.

Figure 1
Figure 1. Figure 1: Left: The optimal rejection rule for M and Mf. Orange and purple areas mark the rejection regions for M while blue and purple areas mark the rejection region for Mf. Middle: Phase diagram for M and M⋆ with ρ = 0.7. Right: Phase diagram for M and M⋆ with ρ = 0.95. In both the middle and right figures, dashed lines separate ER and AFR regions, while solid lines separate AFR and NR region. Red lines correspon… view at source ↗
Figure 2
Figure 2. Figure 2: Power and FDP control (q = 0.1) for different methods in four different settings. Lfdr, we select features with the smallest Lfdr values such that the average Lfdr for the selected features does not exceed the nominal FDR level q (Sun and Cai, 2007). As shown in [PITH_FULL_IMAGE:figures/full_fig_p027_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Linear regression model with n = 1200, p = 2000 and an expected number of relevant features p1 = 100. Each row of the design matrix is generated from N(0, Σ(ρ)). The true coefficients β ⋆ j are drawn from N (0, 3 2 ) in the weak prior case (Left2 and Right1) and N (3, 0 2 ) in the strong prior case (Left1 and Right2). In all panels, we fix the signal and vary the correlation ρ. The nominal FDR control leve… view at source ↗
Figure 4
Figure 4. Figure 4: Logistic regression model with n = p = 400 (Left1 and Right2) and n = p = 800 (Left2 and Right1). The expected number of relevant features is p1 = 30. Each row of the design matrix is generated from N(0, Σ(ρ)). The true coefficient β ⋆ j are drawn from N (0, 1.5 2 ). In all panels, we fix the signal and vary the correlation ρ. The nominal FDR level q = 0.1. For each multiple run, we replete the base algori… view at source ↗
Figure 5
Figure 5. Figure 5: Numbers of the discovered mutations for the seven PI drugs. The grey and orange bars [PITH_FULL_IMAGE:figures/full_fig_p032_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Numbers of the discovered mutations for the six NRTI drugs. The grey and orange bars [PITH_FULL_IMAGE:figures/full_fig_p033_6.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript claims to characterize a broader class of mirror statistics applicable to any fixed splitting scheme, derive the Bayes-optimal member of this class, establish asymptotic FDR control under mild weak-dependence conditions via a two-stage procedure, demonstrate power gains for the Bayes-optimal statistic in the Rare/Weak model, and introduce PRADAS, which recasts the split ratio as a stopping time whose optimal rule is given by the Snell envelope and approximated via Longstaff-Schwartz regression, with supporting simulations and real-data examples.

Significance. If the FDR control and power results hold, particularly for the adaptive splitting procedure, the work would offer a principled method for incorporating prior information into mirror-statistic-based FDR control and a data-driven approach to choosing split ratios. The application of optimal stopping theory via the Snell envelope provides a novel technical contribution beyond fixed-split methods. The Rare/Weak model analysis and empirical validation are positive elements.

major comments (3)
  1. [§3 (asymptotic FDR control for fixed splits) and §4 (PRADAS stopping-time extension)] The asymptotic FDR control (via the two-stage procedure) is established for fixed splitting schemes. However, PRADAS treats the split ratio as a data-dependent stopping time adapted to the filtration generated by the data. No argument is supplied showing that the control carries over when the stopping decision can correlate with the mirror statistics, which could alter the null distribution or invalidate the threshold.
  2. [Rare/Weak model analysis (likely §3.3 or §4.3)] The power advantage in the Rare/Weak model is derived for the Bayes-optimal mirror statistic under a fixed split ratio. The analysis does not extend to the case where the split ratio is itself random and chosen via the Snell envelope approximation, leaving open whether the adaptive procedure preserves the claimed power gain.
  3. [Assumptions preceding the FDR theorem] The mild weak-dependence conditions invoked to justify the asymptotic FDR result are stated for the class of mirror statistics, but it is not shown that these conditions continue to hold uniformly when the mirror statistic is the data-dependent Bayes-optimal choice and the split is adaptive.
minor comments (2)
  1. [§4.1 (optional stopping setup)] The natural filtration with respect to which the stopping time is defined should be stated explicitly when the optional-stopping framework is introduced.
  2. [Simulation section] Simulation figures would benefit from reporting the exact Rare/Weak parameters (signal strength, sparsity level, dimension) used in each panel to facilitate direct comparison with the theoretical analysis.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of the work's significance, and constructive major comments. We address each point below and will make revisions to strengthen the theoretical treatment of the adaptive PRADAS procedure.

read point-by-point responses

  1. Referee: [§3 (asymptotic FDR control for fixed splits) and §4 (PRADAS stopping-time extension)] The asymptotic FDR control (via the two-stage procedure) is established for fixed splitting schemes. However, PRADAS treats the split ratio as a data-dependent stopping time adapted to the filtration generated by the data. No argument is supplied showing that the control carries over when the stopping decision can correlate with the mirror statistics, which could alter the null distribution or invalidate the threshold.

    Authors: We appreciate this observation, which correctly identifies that the FDR control in Section 3 is derived for fixed splits. For the adaptive case in Section 4, where the split ratio is a bounded stopping time, we acknowledge the manuscript does not supply an explicit extension accounting for possible correlation with the mirror statistics. In the revised version we will add a new subsection (or appendix) establishing that the two-stage procedure continues to control FDR asymptotically. The argument will use the boundedness of the stopping time together with the weak-dependence conditions to show that the null distribution of the mirror statistics and the threshold selection remain asymptotically unaffected. revision: yes

  2. Referee: [Rare/Weak model analysis (likely §3.3 or §4.3)] The power advantage in the Rare/Weak model is derived for the Bayes-optimal mirror statistic under a fixed split ratio. The analysis does not extend to the case where the split ratio is itself random and chosen via the Snell envelope approximation, leaving open whether the adaptive procedure preserves the claimed power gain.

    Authors: The referee is right that the Rare/Weak power comparison is stated for a fixed split ratio. While the manuscript already reports simulation evidence that the adaptive PRADAS procedure improves power, we agree a theoretical link is missing. In the revision we will add a remark or short extension in Section 4.3 showing that the Snell-envelope stopping rule achieves power at least as high as the best fixed-ratio Bayes-optimal statistic in the large-sample limit of the Rare/Weak model, or we will derive a bound on any finite-sample power loss due to adaptivity. revision: yes

  3. Referee: [Assumptions preceding the FDR theorem] The mild weak-dependence conditions invoked to justify the asymptotic FDR result are stated for the class of mirror statistics, but it is not shown that these conditions continue to hold uniformly when the mirror statistic is the data-dependent Bayes-optimal choice and the split is adaptive.

    Authors: We thank the referee for highlighting this uniformity issue. The weak-dependence conditions are written for the general class, yet the data-dependent Bayes-optimal statistic and adaptive split require verification that the conditions hold uniformly. In the revised manuscript we will add a short lemma (placed before the FDR theorem) proving uniformity: the Bayes-optimal mirror statistic is continuous in the split ratio, the stopping time is bounded, and therefore the dependence coefficients remain controlled uniformly over admissible splits. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses external inspiration and standard techniques

full rationale

The paper first characterizes a class of mirror statistics for any fixed splitting scheme and derives the Bayes-optimal member within that class. It then invokes an external two-stage procedure (inspired by li2021whiteout) to establish asymptotic FDR control under weak dependence. The PRADAS proposal recasts the split ratio as a stopping time and applies the Snell envelope plus Longstaff-Schwartz regression, both standard tools from optimal stopping theory. None of these steps reduces the claimed FDR control, power advantage, or Bayes-optimality result to a fitted parameter, self-defined quantity, or unverified self-citation chain. The central mathematical content remains independent of the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard weak-dependence assumptions from the multiple-testing literature and on the Rare/Weak model used only for power comparison; no new free parameters or invented entities are introduced beyond the stopping-time formulation.

axioms (2)
  • domain assumption Mild weak-dependence conditions on the test statistics
    Invoked to obtain asymptotic FDR control for the two-stage procedure.
  • domain assumption Rare/Weak signal model
    Used to demonstrate theoretical power advantage of the Bayes-optimal statistic.

pith-pipeline@v0.9.0 · 5494 in / 1385 out tokens · 43316 ms · 2026-05-10T02:01:39.032185+00:00 · methodology

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Reference graph

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