Game-theoretic statistics and safe anytime-valid inference

博弈论统计和安全且随时有效的推理

• 批准号: 2310718
• 负责人: Aaditya Ramdas
• 金额: $ 16万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2310718&HistoricalAwards=false
• 关键词: Game; theoretic; statistics; safe; anytime

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.

大多数统计推断--一个总括性的短语，指的是假设检验、置信区间、预测集和其他形式的不确定性量化--相当强烈地依赖于概率建模。然而，现实并不总是与统计学家的模型雅阁，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，它可能有不被检测到的动机）。使用传统的概率建模可能会导致非稳健的方法，容易被非随机数据愚弄。该项目将为最近被称为“博弈论统计推断”的统计推断的根本不同方法奠定广泛的基础。该项目还为研究生提供研究培训机会。博弈论的假设检验是基于一个广泛适用的原则，即“通过打赌来检验一个假设”（或简称为“通过打赌来检验”）。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。博弈论的置信序列将上述在测试中的进展扩展到估计的设置。由于数据通常不是随机的，估计的目标必须仔细指定，并可能随时间而变化。该项目将制定基本定义和方法来构建这样的信心集，并阐述非参数的例子。博弈论变点检测将直接建立在上述两个方向的进展。许多经典的变化检测方法假设参数（并且通常是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中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）它本质上是固有的顺序的，（2）它通常是非参数的和/或无模型的，（3）它自由地实现连续的监测和更新，以及（4）该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准。