Five research areas in Bayesian analysis, involving theory, methodology and application, will be pursued: objective Bayesian analysis, multiplicity adjustment, search and approximations in model selection, analysis of complex computer models, and differences between Bayes and empirical Bayes analysis. Research in objective Bayesian analysis will focus on the development of objective priors, together with their computational implementation, in semi-invariant contexts, which include spatial problems and problems arising in psychiatry. The Bayesian approach to multiplicity correction has the attraction that it does not depend on the error structure of the data; multiplicity correction is done only through the prior probabilities assigned to models or other multiplicity features. Understanding which probability assignments do, and do not, adjust for multiplicity will be an important feature of this research. A focus of the research on model selection will be the development of a generalization of BIC which is much more widely applicable than the standard version, especially overcoming the major hurdle of defining effective sample size for a parameter. Advances in these areas will have application to research involving the analysis and use of complex computer models of processes. Also, surprising differences between Bayes and empirical Bayes analysis arise in several of the above settings, and better understanding of these differences will also be a focus of the research.
Objective Bayesian analysis has existed for over 250 years, but interest in the field has increased markedly in recent years. A major reason is that many of the significant scientific problems today (such as much of climate change research) involve some type of assimilation of data and physical modeling, typically done by Bayesian methods. Many of today?s most challenging problems ? including microarray and other bioinformatic analyses, syndromic surveillance, high-throughput screening, and many others ? involve consideration of multiple-testing with a huge number of possible tests, and require major multiplicity adjustments. For instance, the work on multiplicity will be done in the context of subgroup analysis in clinical trials, providing major new insights into HIV vaccine trials, and in refining detection methodology in high-energy physics.
