Studies on Foundations of Statistics

约瑟夫·卡达内研究人员致力于贝叶斯统计学和决策理论基础的三个方面的工作：(I)他们开发了不连贯的测量方法，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)根据偏序偏好以一致概率/效用对集合的形式表示，实现用于评估偏序偏好的算法。这些对于建立一组连贯的(贝叶斯)专家决策者的帕累托共识模型是相关的。(Iii)在所谓的“边际化”悖论的背景下，他们探索了仅仅是有限相加的概率和具有“不适当”先验的有效计算之间的联系。贝叶斯统计学旨在通过将理性的统计决策者建模为他或她就像是博彩公司一样，宣布作为风险赌注可以买卖的价格的概率，从而使统计学建立在坚实的理论基础上。一个重要的普遍结果是，博彩公司要么表现得像贝叶斯人，要么会接受一系列会让博彩公司成为必然输家的赌注。研究人员探索了这一理论的扩展，以解释非贝叶斯行为、博彩集团以及对概率的更一般解释。

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.