Confidence and Discoveries with E-values

Vovk, Vladimir; Wang, Ruodu

doi:10.1214/22-sts874

Cited by 7 publications

(2 citation statements)

References 45 publications

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“…Once we have the e-values (35), we have the e-confidence regions for the changepoint τ : at a significance level α, the e-confidence region is {τ | E τ ≤ 1/α} (see [37]). A natural direction of further research is to find a computationally efficient version of the e-confidence regions based on (35).…”

Section: Confidence Regionsmentioning

confidence: 99%

Testing Exchangeability

Vovk

Gammerman²,

Shafer³

2022

Algorithmic Learning in a Random World

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The topic of this paper is testing exchangeability using e-values in the batch mode, with the Markov model as alternative. The null hypothesis of exchangeability is formalized as a Kolmogorov-type compression model, and the Bayes mixture of the Markov model w.r. to the uniform prior is taken as simple alternative hypothesis. Using e-values instead of p-values leads to a computationally efficient testing procedure. In the appendixes I explain connections with the algorithmic theory of randomness and with the traditional theory of testing statistical hypotheses. In the standard statistical terminology, this paper proposes a new permutation test. This test can also be interpreted as a poor man's version of Kolmogorov's deficiency of randomness.The version of this paper at http://alrw.net (Working Paper 38) is updated most often.

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Section: Confidence Regionsmentioning

confidence: 99%

Testing Exchangeability

Vovk

Gammerman²,

Shafer³

2022

Algorithmic Learning in a Random World

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“…An alternative approach to using p-values is provided by e-values, see Shafer et al (2011), Vovk and Wang (2023) and Grunwald et al (2024). An evariable for a hypothesis…”

Section: P-values E-values and Confidence Regionmentioning

confidence: 99%

The Concept of Statistical Evidence

Evans¹

2021

Proceedings of the 3rd International Conference on Statistics: Theory and Applications

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The concept of statistical evidence has proven to be somewhat elusive in the development of the discipline of statistics. Still there is a conviction that appropriately collected data contains evidence concerning the answers to questions of scientific interest. We discuss some of the attempts at making the concept of evidence precise and, in particular, present an approach based upon measuring how beliefs change from a priori to a posteriori. Of necessity this is Bayesian in nature as a proper prior is required that reflects beliefs about where the truth lies before the data is observed.Bayesian inference is often criticized for its subjective nature. It is possible, however, to deal with this subjectivity in a scientifically sound manner. In part, this is done by assessing and controlling the bias the prior and model induce into inferences and this depends intrinsically on being clear about statistical evidence. In addition, the model and the prior are falsifiable through model checking and checking for prior-data conflict. Both the assessment of bias and the falsification steps are essentially frequentist in nature so this provides a degree of unity between sometimes conflicting philosophies. This approach to statistical reasoning can be seen as dealing with the inevitable subjectivity required in the choice of ingredients to an analysis so that a statistical analysis can approach the goal of objectivity that is central to scientific work..

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Comment on “A Scale-Free Approach for False Discovery Rate Control in Generalized Linear Models” by Chengguang Dai, Buyu Lin, Xin Xing, and Jun S. Liu

Zhang

2023

Journal of the American Statistical Association

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Confidence and Discoveries with E-values

Cited by 7 publications

References 45 publications

Testing Exchangeability

Testing Exchangeability

The Concept of Statistical Evidence

Comment on “A Scale-Free Approach for False Discovery Rate Control in Generalized Linear Models” by Chengguang Dai, Buyu Lin, Xin Xing, and Jun S. Liu

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