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

加强对美国选举的正直和信任是很重要的。这个项目开发了一些方法和软件，以简化和降低提供有力证据证明获胜者确实获胜的成本，或者在没有获胜的情况下纠正结果。关键的统计工具是使用可信的纸质投票记录的风险限制审计(RLA)。该项目提高了RLA的效率(减少了在结果正确时确认结果所需的跑腿工作)、灵活性(以适应当地法律、法规和技术施加的限制)和适用性(以适应更多的投票规则，并使审计每次选举的每一场竞选都变得负担得起)。该项目构建并发布了实施改进的开源软件，并正在与州和地方选举官员合作试验这些方法。RLA是指任何程序，如果报告的竞选结果是错误的，则该程序具有已知的最大机会(风险限度)而不更正该结果。RLA通过手动列出有效投票的可信记录来纠正结果。RLA可以归结为一个核心统计问题的多个实例：检验有界非负数列表的平均值是否小于或等于1/2。这个项目开发了使用简单随机样本、集群样本、分层样本和伯努利样本对这些假设进行序贯和批量序贯检验的改进方法。这些方法涉及检验统计量，这些统计量是空值下的非负上鞅。通过“学习”样本中的真实平均值来适应的测试可以显著提高效率，就像优先从零似乎是假的地层中抽取的自适应分层抽样设计一样-导致多臂土匪问题的泛化。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优点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.