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Hypothesis testing with e-values
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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.
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Cited by 20 Pith papers
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A mathematical study of the excess growth rate
The excess growth rate is the unique functional, up to a constant, satisfying each of three axiom systems; its deterministic maximizer invests only in the best- and worst-performing assets.
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The e-Partitioning Principle of False Discovery Rate Control
The e-Partitioning Principle states that a procedure controls FDR if and only if it is a subset of a general e-value based partitioning procedure, yielding uniform improvements of eBH, BY and Su.
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Mean Estimation in Banach Spaces Under Infinite Variance and Martingale Dependence
A truncation-based estimator achieves the optimal heavy-tailed mean estimation rate in smooth Banach spaces under martingale dependence with time-uniform guarantees.
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Assessing Extrapolation of Peaks Over Thresholds with Martingale Testing
A gambling-style test over the largest observed rainfalls selects the extreme-value threshold that won the EVA2025 challenge — except on one target, where the authors overrode the game and paid for it.
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E-valuator: Reliable Agent Verifiers with Sequential Hypothesis Testing
A density-ratio e-process wrapper converts black-box verifier scores into sequential decisions that control the false-alarm rate for agent trajectories, with empirical gains in early stopping.
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Hypothesis Testing in Imaging Inverse Problems
Semantic hypotheses about reconstructed images are tested using CLIP embeddings and e-values, with calibrated Type I error control and higher power than zero-shot CLIP classification.
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On Stopping Times of Power-one Sequential Tests: Tight Lower and Upper Bounds
For arbitrary composite nulls and alternatives, any power-one sequential test needs at least log(1/alpha)/KL_inf samples when alpha is small, and at least a law-of-iterated-logarithm scale when the alternative is clos...
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Uniform mean estimation for monotonic processes
Coin-betting plus a monotonicity-based continuous union bound yields uniform, anytime-valid, variance-adaptive confidence bands for monotonic mean functions such as CDFs.
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Carefree multiple testing with e-processes
Running-maximum e-BH can exceed the nominal FDR under arbitrary dependence, while adjusted running maxima restore FDR-sup control.
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Calibrating Wireless AI via Meta-Learned Context-Dependent Conformal Prediction
ML-WCP meta-learns a context-dependent likelihood ratio and uses it inside weighted conformal prediction to calibrate wireless AI with zero runtime data.
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Optimal e-value testing for properly constrained hypotheses
For a hypothesis given by finitely many continuous moment constraints with the origin in the relative interior of the feasible convex hull, the optimal e-variable set is the dual class {1 - λ·Φ : λ ∈ Λ_Φ}.
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Hypothesis testing for community structure in temporal networks using e-values
A temporal-network community test averages e-values obtained from per-snapshot p-values, retaining valid type I error control under arbitrary dependence.
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Optimistic Interior Point Methods for Sequential Hypothesis Testing by Betting
A new 'test by betting' algorithm using interior-point barrier updates over the full decision domain rejects false null hypotheses faster than Online Newton Step while preserving anytime validity.
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On Continuous Monitoring of Risk Violations under Unknown Shift
A betting-based wealth process monitors whether a deployed predictor's bounded risk has crossed a safety level, raising a controlled-false-alarm signal under unknown distribution shift and a set of thresholds still co...
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Randomness, exchangeability, and conformal prediction
In classification, every confidence predictor that is valid under IID data can be transformed into a conformal predictor with an explicit, constant-free bound on the loss of efficiency.
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My Statistics is Better than Yours
A position paper advocating a context-dependent choice of statistical paradigm instead of a universal one.
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Multiple Testing in Generalized Universal Inference
Generalized universal inference e-values can be plugged into e-BH to control FDR for multiple tests on risk minimizers, with a quantile regression application.
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Ensuring Reliability via Hyperparameter Selection: Review and Advances
The paper reviews methods that cast hyperparameter selection as multiple hypothesis testing to deliver formal risk guarantees.
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Measuring Statistical Evidence: A Short Report
A report summarizing and motivating the Relative Belief Ratio framework for statistical evidence, adding one unproven modification to strength-of-evidence measurement.
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False Discovery Control in Multiple Testing: A Brief Overview of Theories and Methodologies
This is a survey of false discovery rate control methods, organized into ranking, FDP estimation, and thresholding steps.
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