Bayesian Analysis and Frequentist Interfaces

贝叶斯分析的四个方面及其与频率统计推理的接口将被探讨。首先是模型选择，特别是在模型之间进行选择的自动贝叶斯方法急需发展。模型选择中的其他问题还包括以预测为目标时模型的最优选择问题，以及贝叶斯模型选择中大样本近似的研究和比较。第二个研究领域是客观贝叶斯分析，这将在准备关于该主题的研究专著（与实际实施相关的软件）中达到高潮。为了实现这一目标，必须进行的研究包括协方差矩阵的客观先验分布的发展和实际上非常重要的一类层次模型。第三个领域是非参数贝叶斯分析，特别是涉及到小波的使用。最后要讨论的研究领域是条件频率测试，以及它与贝叶斯测试的统一。在模型选择和非参数贝叶斯方法方面的进展将用于造父变星振荡的研究，这是确定天文距离的关键。客观贝叶斯推理的研究将影响物理学中置信度限的设置。条件频率测试的发展将在各种生物统计环境中进行，特别是涉及临床试验。除了这些跨学科的影响外，这项研究还将通过对研究生的密集培训和将开发的方法纳入杜克大学和其他地方的统计课程，从而有利于教育和人类发展。

James O BergerFour areas in Bayesian analysis and its interfaces with frequentist statistical reasoning will be pursued. The first is model selection, in particular the greatly needed development of automatic Bayesian methodology for choosing between models. Other problems in model selection that will be considered include the question of optimal choice of a model when prediction is the goal, and study and comparison of large sample approximations in Bayesian model selection. The second area of research is objective Bayesian analysis, which will culminate in the preparation of a research monograph on the subject (with associated software for practical implementation). Included in the research that must be performed to reach this goal is the development of objective prior distributions for covariance matrices and the practically very important class of hierarchical models. The third area is nonparametric Bayesian analysis, especially involving use of wavelets. The final area of research that will be addressed is conditional frequentist testing, and its unification with Bayesian testing.The advances in model selection and nonparametric Bayesian methodology will be utilized in the study of Cepheid variable star oscillations, which are key to establishing astronomical distances. The work on objective Bayesian inference will impact the setting of confidence limits in physics. The development of conditional frequentist tests will be undertaken in a variety of biostatistical settings, especially involving clinical trials. In addition to these interdisciplinary impacts, the research will benefit education and human development through intensive training of graduate students and the incorporation of the developed methodology in statistics courses at Duke University and elsewhere.