Studies on Foundations of Statistics

9801401 Joseph Kadane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） 他们开发的措施，使他们能够量化的程度，非贝叶斯程序违反主观预期效用的原则不一致。 (ii)他们实现算法评估偏序偏好，根据他们的代表性的同意概率/效用对的集合。 这些是相关的建模帕累托共识的一组连贯的（贝叶斯）专家决策者。 (iii)他们在所谓的“边缘化”悖论的背景下，探索了仅仅是可加性概率和具有“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建模一个理性的统计决策者，将他或她视为赌注经纪人，宣布作为风险赌注可以买卖的价格的概率，从而将统计学置于合理的理论基础之上。一个重要的一般结果是，一个赌注经纪人要么表现得像贝叶斯，要么会接受一系列的赌注，这将使赌注经纪人成为一个肯定的输家。 研究人员探索了这一理论的扩展，以解释非贝叶斯行为，赌博集团和更一般的概率解释。

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.