E-Values, Bayes Risk, Dual Role of Markov's Inequality
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911558776389632 |
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| author | Polson, Nicholas G. Zantedeschi, Daniel |
| author_facet | Polson, Nicholas G. Zantedeschi, Daniel |
| contents | Two approaches to hypothesis testing, e-value testing and Bayes risk minimisation, both invoke Markov's inequality to control error probabilities. They differ in which distribution certifies the unit-moment condition: the null for Type I error, the alternative for Type II error. The likelihood ratio is not intrinsically an e-value; it acquires that status only relative to the experiment under which its expectation is certified. This note makes the resulting role-reversal symmetry explicit, traces its asymptotic sharpening through the information-theoretic arguments of Barron and Clarke (1994), and situates the duality within the typed evidence calculus of Polson, Sokolov, and Zantedeschi (2026). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00337 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | E-Values, Bayes Risk, Dual Role of Markov's Inequality Polson, Nicholas G. Zantedeschi, Daniel Statistics Theory 62F03, 62C10, 94A17 Two approaches to hypothesis testing, e-value testing and Bayes risk minimisation, both invoke Markov's inequality to control error probabilities. They differ in which distribution certifies the unit-moment condition: the null for Type I error, the alternative for Type II error. The likelihood ratio is not intrinsically an e-value; it acquires that status only relative to the experiment under which its expectation is certified. This note makes the resulting role-reversal symmetry explicit, traces its asymptotic sharpening through the information-theoretic arguments of Barron and Clarke (1994), and situates the duality within the typed evidence calculus of Polson, Sokolov, and Zantedeschi (2026). |
| title | E-Values, Bayes Risk, Dual Role of Markov's Inequality |
| topic | Statistics Theory 62F03, 62C10, 94A17 |
| url | https://arxiv.org/abs/2604.00337 |