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

Hill教授建议继续发展B. de Finetti和L. J. Savage关于贝叶斯概率论的基础问题，这些问题对贝叶斯推理和决策理论的应用有重要的影响，并继续发展由他发起的应用。这些中心是关于Hill （1968, 1988b, 1993a）的贝叶斯非参数过程A(n)和H(n)，以及Hill（1975）的尾指数估计。对于任何epsilon 0，除了一组概率不超过epsilon的观测值外，提出在有限模型中构造精确满足a (n)和H(n)假设的显式交换过程。还提出利用Hill， Lane, Sudderth（1980, 1987）的广义urn过程理论和Hill （1993a）的分裂过程模型来扩展Hill （1993c, 1993d）的贝叶斯预测方法。Hill教授建议继续发展B. de Finetti和L. J. Savage关于贝叶斯概率论的基础问题，这些问题对贝叶斯推理和决策理论的应用有重要的影响，并继续发展由他发起的应用。这些中心是关于贝叶斯非参数过程，Hill （1968, 1988b, 1993a）的A(n)和H(n)以及Hill（1975）的尾指数估计量。还提出利用Hill， Lane, Sudderth（1980, 1987）的广义urn过程理论和Hill （1993a）的分裂过程模型来扩展Hill （1993c, 1993d）的预测方法。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。

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.