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.

9801401Joseph Kadanethe研究人员致力于贝叶斯统计和决策理论基础的三个方面：（i）他们制定了不一致的衡量标准，使他们能够量化非基督徒程序违反主观预期效用的原则。 （ii）根据同意概率/公用事业对的集合，他们根据其表示算法来评估部分有序的偏好。 这些与建模一组连贯的（贝叶斯）专家决策者的帕累托共识。 （iii）他们在所谓的“边缘化”悖论的背景下，探索仅有限加性概率和有效的计算之间的联系。Bayesian统计数据旨在通过建模统计决策制造商来销售或宣布的概率，该统计数据是在概率上销售的，该统计数据是在概率上销售的，该统计依据是概率或宣布的概率，该统计数据是在概率上销售的。一个重要的总体结果是，簿记要么表现为贝叶斯人，要么接受一系列赌注，这会使书本成为肯定的失败者。 研究人员探索了该理论的扩展，以说明非拜伊斯的行为，赌徒群和对概率的更一般的解释。