A framework for optimal posterior e-values with non-convex composite hypotheses, demonstrated via statistical tests for multiple voting systems including the first treatment of Schulze.
arXiv preprint arXiv:2601.11347 , year=
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The GROW value for bounded e-variables equals the minimal relative entropy between weak-* closed convex hulls of arbitrary composite null and alternative sets.
The optimal wealth growth rate equals lim n→∞ of n^{-1} times inf KL(Q^n, P) over the bipolar of the n-fold null set, which is achievable and cannot be exceeded.
We derive powerful e-processes for sequential stochastic-dominance testing, with power-one guarantees for first- and higher-order dominance.
Power-one sequential tests exist for testing any weakly compact null set of distributions against its complement.
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The GROW value for bounded e-variables equals the minimal relative entropy between weak-* closed convex hulls of arbitrary composite null and alternative sets.
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The optimal wealth growth rate equals lim n→∞ of n^{-1} times inf KL(Q^n, P) over the bipolar of the n-fold null set, which is achievable and cannot be exceeded.
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