Resampling-based empirical Bayes multiple testing procedures for controlling generalized tail probability and...

Area of Science:

• Statistical Inference
• Multiple Hypothesis Testing
• Computational Statistics

Background:

• Existing multiple testing procedures often struggle with complex data dependencies and controlling generalized error rates.
• The false discovery rate (FDR) is a crucial metric for managing Type I errors in high-dimensional data analysis.
• There is a need for robust methods that offer Type I error control across diverse data-generating distributions.

Purpose of the Study:

• To propose novel resampling-based empirical Bayes multiple testing procedures.
• To control generalized tail probability (gTP) and generalized expected value (gEV) error rates.
• To enhance statistical power in multiple testing scenarios, particularly for FDR control.

Main Methods:

• Development of resampling-based empirical Bayes procedures for Type I error control.
• Definition of generalized tail probability (gTP) and generalized expected value (gEV) error rates.
• Incorporation of guessed sets of true null hypotheses and sampled null statistics to account for data dependence.

Main Results:

• The proposed procedures offer Type I error control for general distributions and arbitrary dependence structures.
• Empirical Bayes methods demonstrate competitive or superior power compared to established FDR procedures (Storey & Tibshirani, Benjamini & Hochberg).
• Simulation studies confirm the Type I error and power trade-off advantages of the empirical Bayes approach.

Conclusions:

• Resampling-based empirical Bayes methods provide a flexible and powerful alternative for multiple testing.
• These procedures effectively control generalized error rates and improve power across various testing scenarios.
• The approach offers a valuable enhancement to existing statistical methodologies for analyzing complex datasets.