Studies on Foundations of Statistics

统计学基础研究

• 批准号: 9801401
• 负责人: Joseph Kadane
• 金额: $ 28.86万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-15 至 2002-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801401&HistoricalAwards=false
• 关键词: Studies; Foundations; Statistics

9801401Joseph KadaneThe investigators work on three aspects of the foundations of Bayesianstatistics and decision theory: (i) They develop measures of incoherence which permit them to quantify the extent to which non-Bayesian procedures violate principles of subjective expected utility. (ii) They implement algorithms for assessing partially ordered preferences, according to their representation in terms of sets of agreeing probability/utility pairs. These are relevant for modeling Pareto consensus of a group of coherent (Bayesian) expert decision makers. (iii) They explore connections between merely finitely additive probability and valid computations with "improper" priors, in the context of so-called "Marginalization" paradoxes.Bayesian statistics aims to put statistics on a sound theoretical footing by modeling a rational statistical decision maker as if he or she were a bookie, announcing probabilities which act as prices at which risky bets can be bought or sold. An important general result is that a bookie either behaves as a Bayesian, or would accept a series of bets that would make the bookie a sure loser. The investigators explore extensions of this theory to account for non-Bayesian behavior, groups of bookies, and more general interpretations of probability.

[808014 . 01]约瑟夫·卡达纳调查者研究贝叶斯统计学和决策理论基础的三个方面：(i)他们发展了不一致性的度量方法，使他们能够量化非贝叶斯程序违反主观预期效用原则的程度。（ii）他们实现了评估部分有序偏好的算法，根据它们在一致概率/效用对集合方面的表示。这些都与一组连贯的（贝叶斯）专家决策者的帕累托共识建模有关。他们在所谓的“边缘化”悖论的背景下，探讨仅仅有限相加概率与具有“不适当”先验的有效计算之间的联系。贝叶斯统计学的目的是把一个理性的统计决策者当作一个赌徒来建模，把他或她当作一个可以买卖风险赌注的价格来宣布概率，从而把统计学建立在一个健全的理论基础上。一个重要的一般结果是，赌徒要么表现得像贝叶斯主义者，要么接受一系列使赌徒肯定输掉的赌注。研究人员探索了这一理论的扩展，以解释非贝叶斯行为，赌徒群体和更一般的概率解释。