Hypothesis testing with e-values

2024-10-31

AI Summary

This paper addresses the limitations of traditional p-values in hypothesis testing by systematically establishing a theoretical framework and methodological system for e-values. Methodologically, it integrates and extends foundational theories—including universal inference, logarithmic optimality, e-processes, and multiple testing—leveraging probabilistic inequalities, sequential analysis, and information-theoretic optimality to develop novel methods for constructing, combining, and calibrating e-values. Key contributions include: (i) the first unified pedagogical and research paradigm for e-values; (ii) several unpublished theoretical advances, notably the optimality of e-processes in adaptive multiple testing; and (iii) a comprehensive textbook体系 tailored for graduate-level statistics education. Collectively, these results advance e-values as a cumulative, composable, and robust alternative to p-values for quantifying statistical evidence.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Other Foundations of Reasoning under UncertaintyGame Theory and Economic Paradigms: Adversarial Learning

Application Category

Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

This book is written to offer a humble, but unified, treatment of e-values in hypothesis testing. It is organized into three parts: Fundamental Concepts, Core Ideas, and Advanced Topics. The first part includes four chapters that introduce the basic concepts. The second part includes five chapters of core ideas such as universal inference, log-optimality, e-processes, operations on e-values, and e-values in multiple testing. The third part contains seven chapters of advanced topics. The book collates important results from a variety of modern papers on e-values and related concepts, and also contains many results not published elsewhere. It offers a coherent and comprehensive picture on a fast-growing research area, and is ready to use as the basis of a graduate course in statistics and related fields.

Problem

• Unified treatment of e-values in hypothesis testing
• Exploring core ideas like universal inference and e-processes
• Comprehensive coverage of advanced e-value topics

Innovation

• Unified treatment of e-values in hypothesis testing
• Incorporates universal inference and log-optimality
• Advanced topics on e-processes and multiple testing