E-values: Calibration, combination and applications
Vladimir Vovk,Ruodu Wang +1 more
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TLDR
It is demonstrated that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e- Values can be merged simply by averaging them, which allows to develop efficient procedures using e- values for testing multiple hypotheses.Abstract:
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper, we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors and likelihood ratios. We demonstrate that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e-values can be merged simply by averaging them. This allows us to develop efficient procedures using e-values for testing multiple hypotheses.read more
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Classical Descriptive Set Theory
TL;DR: The classical descriptive set theory is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.
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Testing exchangeability: fork-convexity, supermartingales and e-processes
TL;DR: A “safe e-process” is derived, which is a nonnegative process with expectation at most one under the null at any stopping time, and is upper bounded by a martingale, but is not itself an NSM.
Posted Content
False discovery rate control with e-values
Ruodu Wang,Aaditya Ramdas +1 more
TL;DR: In this article, a natural analog of the BH procedure for false discovery control (FDR) control that utilizes e-values (e-BH) and compare it with the standard procedure for p-values is presented.
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Testing Randomness Online
TL;DR: In this paper, the authors present a review of the existing online methods for testing the two hypotheses of randomness and exchangeability, focusing on the online mode of testing, when the observations arrive sequentially.
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Testing exchangeability: Fork-convexity, supermartingales and e-processes
TL;DR: In particular, this paper showed that the fork-convex hull of the exchangeable null consists of all possible laws over binary sequences, which implies that any NSM under exchangeability is necessarily nonincreasing, hence always yields a powerless test for any alternative.
References
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TL;DR: In this paper, a simple and widely accepted multiple test procedure of the sequentially rejective type is presented, i.e. hypotheses are rejected one at a time until no further rejections can be done.
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John D. Storey,Robert Tibshirani +1 more
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TL;DR: In this article, a modification of the Bonferroni procedure for testing multiple hypotheses is presented, based on the ordered p-values of the individual tests, which is less conservative than the classical BFP but is still simple to apply.