Bayesian Analysis and Frequentist Interfaces

贝叶斯分析和频率接口

• 批准号: 0103265
• 负责人: James Berger
• 金额: $ 63.21万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-06-01 至 2007-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103265&HistoricalAwards=false
• 关键词: Bayesian; Analysis; Frequentist; Interfaces

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.

詹姆斯O伯格在贝叶斯分析和它的接口与频率统计推理的四个领域将继续下去。 第一个是模型选择，特别是迫切需要发展自动贝叶斯方法来选择模型。 模型选择中的其他问题将被考虑包括预测为目标时模型的最佳选择问题，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，最终将编写一本关于这一主题的研究专著（并附有用于实际执行的相关软件）。 为了达到这一目标，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分层模型。 第三个领域是非参数贝叶斯分析，特别是涉及小波的使用。 最后一个研究领域是条件频率论检验及其与贝叶斯检验的统一，在模型选择和非参数贝叶斯方法学方面的进展将用于造父变星星星振荡的研究，这是确定天文距离的关键。 客观贝叶斯推理的工作将影响物理学中置信限的设定。 条件频率论检验的发展将在各种生物统计学环境中进行，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强化培训以及将所制定的方法纳入杜克大学和其他地方的统计课程，使教育和人类发展受益。