Bayesian Analysis, Decision Theory, and Applications

James O.BergerDMS-9802261介绍了贝叶斯分析和统计决策理论的五个研究领域。最大的努力是在模型选择方面，特别是开发用于在模型之间选择的自动贝叶斯方法。这是基于自动先验分布的构造。模型选择中考虑的其他问题包括：当预测为目标时模型的最佳选择问题；贝叶斯模型选择中大样本近似的研究和比较；以及发展对单一拟议模型的贝叶斯批评措施。第二个研究领域是条件频率测试，以及它与贝叶斯测试的统一，特别是在临床试验中的应用。利用上面提到的建立模型选择的自动先验的方法的改进，也解决了混合建模问题。考虑了涉及具有不同(和未知的)取向和测量误差的总体的相当一般的混合模型。第四个研究领域是开发协方差矩阵和分层模型的良好先验分布，部分是通过决策理论可容许性的概念。最后的研究领域是涉及大数据集的贝叶斯分析。模型选择方法的进步被用于研究全球变化问题，如检测由温室气体变暖等原因引起的气候变化。混合模型的发展应用于天文问题，特别是对伽马射线爆发的源进行建模的问题。协方差矩阵的工作被用于研究气候领域中的模式检测，如厄尔尼诺现象。对大数据集的贝叶斯分析的研究跨越了这些问题，找到了分析这些数据集的通用工具。这项研究通过培训研究生和将开发的方法纳入杜克大学和其他地方的统计课程，使教育和人的发展受益。

James O. BergerDMS-9802261Five research areas in Bayesian analysis and statistical decision theory are addressed. The greatest effort is in model selection, in particular the development of automatic Bayesian methodology for choosing between models. This is based on construction of automatic prior distributions. Other problems in model selection that are considered include the question of optimal choice of a model when prediction is the goal; study and comparison of large sample approximations in Bayesian model selection; and development of Bayesian measures of criticism of a single proposed model. The second area of research is conditional frequentist testing, and its unification with Bayesian testing, especially as applied to clinical trials. Using a modification of the approach to developing automatic priors for model selection that was mentioned above, the mixture modelling problem is also addressed. Quite general mixture models, involving populations with differing (and unknown) orientation and measurement errors are considered. A fourth area of research is the development of good prior distributions for covariance matrices and hierarchical models, in part through the concept of decision-theoretic admissibility. The final area of research is Bayesian analysis involving large data sets.The advances in model selection methodology are used to study global change problems such as detection of climatic changes due to causes such as greenhouse warming. The developments in mixture modeling are applied to astronomical problems, in particular the problem of modeling the source of gamma ray bursts. The work on covariance matrices is used to study detection of patterns, such as El Nino, in climatological fields. The investigations in Bayesian analysis of large data sets span these problems, finding general tools for analyzing such data sets. The research benefits education and human development through the training of graduate studentsm and the incorporation of the developed methodology in statistics courses at Duke University and elsewhere.