E-Values, Bayes Risk, Dual Role of Markov's Inequality
Statistics Theory
2026-04-02 v1 Statistics Theory
Abstract
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).
Keywords
Cite
@article{arxiv.2604.00337,
title = {E-Values, Bayes Risk, Dual Role of Markov's Inequality},
author = {Nicholas G. Polson and Daniel Zantedeschi},
journal= {arXiv preprint arXiv:2604.00337},
year = {2026}
}