Bayesian Analysis and Frequentist Interfaces

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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.