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（指的是假设测试，置信区间，预测集和其他形式的不确定性定量）的概述。但是，现实并不总是按照统计学家的模型，尤其是当它涉及非随机但事件（例如体育游戏的结果）或数据源不是被动的，但可能具有积极作用时（例如，可能没有检测到动机）。传统概率建模的使用可能会导致非稳定方法，从而容易被非传统数据足球。该项目将为统计推断的根本不同的方法开发广泛的基础，该方法最近被称为“游戏理论统计推断”。该项目还为研究生提供了研究培训机会。游戏理论假设检验基于“通过对其进行投注来检验假设”的广泛适用原则（或通过投注进行测试）。这是一个针对非参数问题开发基本理论和方法的项目，其中将有关数据源的假设最小化。游戏理论置信序列将测试中的Priore关系扩展到估算的设置。由于通常不认为数据为随机性，因此必须仔细指定估计的目标，并且可能随时间变化。该项目将开发基本的定义和方法，用于在非参数示例中构建此类置信度集和极端。游戏理论更改点检测将直接基于Priore两个方向的进步。许多经典的变更检测方法都假定一个参数（通常是I.I.D.）结构。该项目将开发在非参数假设下在非组织和非策略设置中起作用的变更检测方法。这项工作与经典统计推断有一些区别：（1）它本质上是顺序的，（2）它通常是非参数和/或无模型的，（3）它可以自由地实现持续的监视和更新，并且（4）它合并了频率和贝叶斯的思想。这些奖项通过nsf的智力和良好的支持，是由NSF的众多奖励进行的，其始终是由智力的梅尔特（Intfortional Indection）所产生的，并且始终如一地支持了始终的支持。 标准。