Confidence envelopes for the false discoveries with heterogeneous data

2026-04-10

AI Summary

This study addresses the loss of statistical power in existing methods for heterogeneous discrete data, which arises from the unrealistic assumption that p-values follow a uniform distribution under the null, leading to overestimation of false discoveries. To overcome this limitation, the authors propose a novel approach for constructing false discovery confidence envelopes tailored to such data. By extending the framework developed for homogeneous settings, the method integrates a family of local tests with a path interpolation strategy and leverages new theoretical tools based on the Bretagnolle inequality and a refined Simes inequality to properly accommodate the heterogeneity in p-value distributions. Simulation studies demonstrate that the proposed method achieves more accurate control of the number of false discoveries and substantially improves statistical power compared to conventional homogeneous approaches.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Ensemble Methods
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

In the context of selective inference, confidence envelopes for the false discoveries allow the user to select any subset of null hypotheses while having a statistical guarantee on the number of false discoveries in the selected set. Many constructions of such envelopes have been proposed recently, using local test families (Genovese and Wasserman, 2006; Goeman and Solari, 2011), paths (Katsevich and Ramdas, 2020) or interpolation (Blanchard et al., 2020a). All those methods have in common that they have been well-studied for the homogeneous case where all p-values under the null have a uniform distribution over [0, 1]. However, in many applications the data are heterogeneous and discrete, hence the p-values have heterogeneous, discrete distributions, and the previous constructions may incur a loss of power, in the sense that they over-estimate the number of false discoveries. In this paper, we bridge the previous constructions under the homogeneous case with new tools. We also apply these tools to propose several confidence envelopes based on tools tailored for heterogeneous data, like the Bretagnolle inequality, or a new variant of the Simes inequality. We compare these new envelopes to their homogeneous counterparts on simulated data.

Problem

• confidence envelopes
• false discoveries
• heterogeneous data
• selective inference
• discrete p-values

Innovation

• confidence envelopes
• heterogeneous data
• false discovery
• selective inference
• Simes inequality