Five 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.
