伯努利试验成功概率检验上鞅置信区间的性能
Performance of Test Supermartingale Confidence Intervals for the Success Probability of Bernoulli Trials
摘要：
给定一个复合原假设H，检验上鞅是初始值为1的关于H的非负上鞅。大的测试上鞅的值提供了证据反对H。因此，检验上鞅是拒绝H的有效工具，特别是当得到的p值非常小，并作为对原假设的证明。例子包括拒绝局域实在论作为解释贝尔测试实验在物理学的基础和量子信息科学的纠缠的认证。测试上鞅的优点是在实验过程中适应性强，并允许任意的停止规则。通过接受区域的反演，它们也可以用于确定置信集。我们用一个例子来比较测试上鞅的性能计算p值和置信区间的Boff-Hoeffding界和“精确”的p值。这个例子是在一系列伯努利试验中推断成功概率的问题。对于一个特殊的检验上鞅，使用一个对停止规则没有限制的技术是有代价的，我们的研究量化了这个代价。
英文摘要：
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 physics and the certification of entanglement in quantum information science. Test supermartingales have the advantage of being adaptable during an experiment and allowing for arbitrary stopping rules. By inversion of acceptance regions, they can also be used to determine confidence sets. We use an example to compare the performance of test supermartingales for computing p-values and confidence intervals to Chernoff-Hoeffding bounds and the "exact" p-value. The example is the problem of inferring the probability of success in a sequence of Bernoulli trials. There is a cost in using a technique that has no restriction on stopping rules, and for a particular test supermartingale, our study quantifies this cost.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
