SaTC: CORE: Small: LESS DOUBT: Learning Efficiently form Statistical Samples-Demonstrating Outcomes Using Better Tests

加强美国选举的公正性和信任是很重要的。该项目开发了一些方法和软件，以简化并降低提供有力证据的成本，证明报道的获胜者真的赢了，或者纠正结果，如果没有。关键的统计工具是风险限制审计（RLA），使用可信赖的投票纸质记录。该项目提高了效率（减少了在结果正确时确认结果所需的跑腿工作）、灵活性（适应当地法律、法规和技术施加的约束）和rla的适用性（适应更多的投票规则，并使审计每次选举中的每一场竞赛的费用负担得起）。该项目建立并发布了实施这些改进的开源软件，并正在与州和地方选举官员合作，对这些方法进行试点。RLA是任何已知最大概率（风险限制）的程序，如果报告的比赛结果是错误的，则不纠正该结果。rla通过手动制表有效投票的可靠记录来纠正结果。rla可以简化为一个核心统计问题的多个实例：测试非负数的有界列表的平均值是否小于或等于1/2。本项目开发了使用简单随机样本、聚类样本、分层样本和伯努利样本对这些假设进行顺序和批量顺序检验的改进方法。这些方法涉及null下非负上鞅的检验统计量。通过从样本中“学习”真实均值来适应的测试可以大大提高效率，自适应分层抽样设计也可以优先从零值似乎为假的层中抽取样本，从而导致多臂强盗问题的普遍化。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

It is important to bolster the integrity of and trust in U.S. elections. This project develops methods and software to simplify and reduce the cost of providing strong evidence that reported winners really won--or correcting the results if not. The key statistical tool is a risk-limiting audit (RLA) using a trustworthy paper record of the votes. This project increases the efficiency (reducing the legwork needed to confirm outcomes when outcomes are correct), flexibility (to accommodate constraints imposed by local laws, regulations, and technology), and applicability of RLAs (to accommodate more voting rules and to make it affordable to audit every contest in every election). The project builds and publishes open-source software implementing the improvements and is working with state and local election officials to pilot the methods.An RLA is any procedure with a known maximum chance (the risk limit) of not correcting a reported contest outcome if that outcome is wrong. RLAs correct outcomes by manually tabulating a trustworthy record of the validly cast votes. RLAs can be reduced to multiple instances of a core statistical problem: testing whether the mean of a bounded list of nonnegative numbers is less than or equal to 1/2. This project develops improved methods for sequential and batch-sequential tests of such hypotheses using simple random samples, cluster samples, stratified samples, and Bernoulli samples. The methods involve test statistics that are nonnegative supermartingales under the null. Tests that adapt by "learning" the true mean from the sample can improve efficiency substantially, as can adaptive stratified sampling designs that preferentially draw from strata where the null appears to be false--leading to a generalization of the multi-armed bandit problem.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.