Bayesian Analysis, Decision Theory, and Applications

讨论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，特别是在模型之间选择的自动贝叶斯方法的发展。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以预测为目标时模型的最优选择问题；贝叶斯模型选择中大样本近似的研究与比较；以及贝叶斯方法对单一模型的批评的发展。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。通过对前面提到的开发模型选择自动先验的方法的改进，还解决了混合建模问题。相当一般的混合模型，涉及不同的（和未知的）方向和测量误差的群体。第四个研究领域是为协方差矩阵和层次模型开发良好的先验分布，部分是通过决策理论可接受性的概念。最后一个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，例如由于温室效应变暖等原因引起的气候变化的检测。混合建模的发展已应用于天文学问题，特别是伽马射线暴源的建模问题。协方差矩阵的工作被用于研究气候领域的模式检测，如厄尔尼诺现象。对大型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。这项研究通过培养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，有利于教育和人类发展。

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.