Game-theoretic statistics and safe anytime-valid inference

大多数统计推断--指假设检验、可信区间、预测集和其他形式的不确定性量化的总括短语--相当强烈地依赖于概率建模。然而，现实并不总是符合统计学家的模型，特别是当它涉及非随机但不确定的事件(如体育比赛的结果)时，或者当数据源不是被动的但可能具有主动作用时(例如，它可能有不被发现的动机)。使用传统的概率建模可能导致不稳健的方法，容易被非随机数据愚弄。这个项目将发展一种完全不同的统计推断方法的广泛基础，这种方法最近被称为“博弈论统计推断”。该项目还为研究生提供了研究培训机会。博弈论假设检验基于一个广泛适用的原则，即“通过打赌来检验假设”(或简称“打赌检验”)。这是一个为非参数问题开发基本理论和方法的项目，其中关于数据来源的假设被最小化。博弈论置信度序列将上述测试方面的进步扩展到估计设置。由于数据通常不被假定为随机的，估计的目标必须仔细地指定，并且可能随时间而改变。该项目将制定构建这种置信集的基本定义和方法，并阐述非参数实例。博弈论变点检测将直接建立在上述两个方向的进展之上。许多经典的变化检测方法假定参数(通常是I.I.D.)结构。该项目将开发在非参数假设下的非平稳和非随机环境下工作的变化检测方法。这项工作与经典的统计推断有几个不同之处：(1)本质上是连续的，(2)它通常是非参数的和/或无模型的，(3)它自由地实现了持续的监测和更新，(4)它融合了频率主义和贝叶斯思想。这个奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The majority of statistical inference — a catchall phrase that refers to hypothesis testing, confidence intervals, prediction sets, and other forms of uncertainty quantification — relies rather strongly on probabilistic modeling. However, reality does not always accord with the statistician’s models, especially when it involves non-random but yet uncertain events (like outcomes of sports games) or when the data source is not passive but may have an active role (for example, it may have an incentive not to be detected). The use of traditional probabilistic modeling may result in non-robust methodology, susceptible to being fooled by non-stochastic data. This project will develop broad foundations of a fundamentally different approach to statistical inference that was recently termed “game-theoretic statistical inference.” The project also provides research training opportunities to graduate students. Game-theoretic hypothesis testing is based on a broadly applicable principle of “testing a hypothesis by betting against it” (or testing by betting for short). This is a project to develop a basic theory and methodology for nonparametric problems, where the assumption about the source of the data is minimized. Game-theoretic confidence sequences extend the aforementioned advances in testing to the setting of estimation. Since the data is not typically assumed as stochastic, the target of estimation must be carefully specified and could change with time. The project will develop the basic definitions and methodology for constructing such confidence sets and expound on nonparametric examples. Game-theoretic changepoint detection will directly build on the advances in the aforementioned two directions. Many classical change detection methods assume a parametric (and often i.i.d.) structure. The project will develop change detection methods that work in nonstationary and non-stochastic settings under nonparametric assumptions. This work has a few distinguishing points from classical statistical inference: (1) it is inherently sequential in nature, (2) it is often nonparametric and/or model-free, (3) it freely enables continuous monitoring and updating, and (4) it merges frequentist and Bayesian ideas.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.