# Performance of Test Supermartingale Confidence Intervals for the Success Probability of Bernoulli Trials

@article{Wills2017PerformanceOT, title={Performance of Test Supermartingale Confidence Intervals for the Success Probability of Bernoulli Trials}, author={Peter Wills and Emanuel Knill and Kevin J. Coakley and Yanbao Zhang}, journal={arXiv: Statistics Theory}, year={2017} }

Given a composite null hypothesis H, test supermartingales are non-negative supermartingales with respect to H with initial value 1. Large values of test supermartingales provide evidence against H. As a result, test supermartingales are an effective tool for rejecting H, particularly when the p-values obtained are very small and serve as certificates against the null hypothesis. Examples include the rejection of local realism as an explanation of Bell test experiments in the foundations of…

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