For bounded e-variables the GROW value equals the relative entropy of the weak-* joint information projection pair between arbitrary P and Q.
Safe testing
7 Pith papers cite this work. Polarity classification is still indexing.
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Finite-horizon optimal e-value designs for adaptive single-arm binary trials are constructed via dynamic programming and shown to have competitive operating characteristics with automatic futility indication.
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.
Power-one sequential tests exist for testing any weakly compact null set of distributions against its complement.
A game-theoretic reformulation of sequential detection shows the LIL as the minimax boundary, with the optimal mixing prior being the Jeffreys prior on the scale-of-scales selected by the Erdős-Kolmogorov test, yielding a 3/2 coefficient for the first iterated-log correction.
A distribution-free sequential test for return-to-baseline detection that aggregates a universal-inference discrepancy into a super-martingale and empirically calibrates it into an e-process with finite-sample bounds.
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Adaptive clinical trials based on design-optimal e-values with automatic curtailment: An application to single-arm trials with binary data
Finite-horizon optimal e-value designs for adaptive single-arm binary trials are constructed via dynamic programming and shown to have competitive operating characteristics with automatic futility indication.
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Return-to-Baseline Testing via Empirically Calibrated e-processes
A distribution-free sequential test for return-to-baseline detection that aggregates a universal-inference discrepancy into a super-martingale and empirically calibrates it into an e-process with finite-sample bounds.