Mathematical Sciences: "Foundations and Applications of Bayesian Probability Theory"

数学科学：“贝叶斯概率论的基础与应用”

• 批准号: 9504488
• 负责人: Bruce Hill
• 金额: $ 5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504488&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Foundations; Applications; Bayesian

Professor Hill proposes to continue to develop the Bayesian theory of probability of B. de Finetti and L. J. Savage with respect to foundational issues that have important implications for applications of Bayesian inference and decision theory, and to continue the development of such applications as have been initiated by him. These center about the Bayesian nonparametric procedures A(n) and H(n) of Hill (1968, 1988b, 1993a), and the tail-index estimator of Hill (1975). For any epsilon 0, it is proposed to constuct explicit exchangeable processes in a finite model, that satisfy the A(n) and H(n) assumptions exactly, apart from a set of observational values with probability at most epsilon. It is also proposed to extend the Bayesian methods of forecasting of Hill (1993c, 1993d) using the theory of generalized urn processes of Hill, Lane, Sudderth (1980, 1987) and the splitting process models of Hill (1993a). Professor Hill proposes to continue to develop the Bayesian theory of probability of B. de Finetti and L. J. Savage with respect to foundational issues that have important implications for applications of Bayesian inference and decision theory, and to continue the development of such applications as have been initiated by him. These center about the Bayesian nonparametric procedures, A(n) and H(n) of Hill (1968, 1988b, 1993a) and the tail-index estimator of Hill (1975). It is also proposed to extend the methods of forecasting of Hill (1993c, 1993d) using the theory of generalized urn processes of Hill, Lane, Sudderth (1980, 1987) and the splitting process models of Hill (1993a). These methods make use of the Bayesian theory of optimal decision-making for the purpose of predicting time series that arise in business, economics, and engineering.

希尔教授建议继续发展B的概率贝叶斯理论。de Finetti和L.萨维奇关于基础问题，有重要意义的贝叶斯推理和决策理论的应用，并继续发展这些应用程序，因为已经启动了他。 这些集中于Hill（1968，1988 b，1993 a）的贝叶斯非参数过程A（n）和H（n），以及Hill（1975）的尾指数估计。 对于任意的λ 0，本文提出在有限模型中构造显式的可交换过程，使其精确地满足A（n）和H（n）的假设，除了一组概率至多为λ 0的观测值。 本文还提出用Hill，Lane，Sudderth（1980，1987）的广义URN过程理论和Hill（1993a）的分裂过程模型来推广Hill（1993c，1993d）的贝叶斯预测方法。 希尔教授建议继续发展B的概率贝叶斯理论。de Finetti和L.萨维奇关于基础问题，有重要意义的贝叶斯推理和决策理论的应用，并继续发展这些应用程序，因为已经启动了他。 这些集中于贝叶斯非参数方法，Hill（1968，1988 b，1993 a）的A（n）和H（n）以及Hill（1975）的尾指数估计。 本文还提出用Hill，Lane，Sudderth（1980，1987）的广义URN过程理论和Hill（1993a）的分裂过程模型来推广Hill（1993c，1993d）的预报方法。 这些方法利用贝叶斯最优决策理论来预测商业、经济和工程中出现的时间序列。