The investigators propose new advancements for the problem of variable and model selection, one of the most fundamental and widespread problems in statistics. Bayesian methods are appealing for this problem, due to the natural probabilistic framework which addresses both model and parameter uncertainty. The implementation of Bayesian methods, however, becomes challenging as the number of models or variables grows, an all too common problem where massive data sets provide many potential predictors. The PI and co-PI investigate two major challenges in the implementation of Bayesian model selection and model averaging: prior specification and posterior calculation. They investigate new families of automatic objective priors that have desirable risk properties, adapt to unknown degree of sparsity and also permit tractable computation for large scale model search. To implement the new methodology, they develop efficient software for stochastic search and model averaging for high dimensional model spaces. Applications in industrial and biological problems will be developed using the new methodology.
Finding and using models to describe relationships between variables in massive datasets is a fundamental problem in both statistics and the sciences. Bayesian methods have been shown to be very successful for this problem, however, the implementation of Bayesian methods becomes challenging in applications where the number of possible models is astronomical. The PI and co-PI develop innovative new methods and software in statistical computing and modeling for selecting and combining models. These methodological developments are driven by applications in industrial and biological problems. The automatic procedures proposed by the investigators for selecting and combining models have applicability to many other important application areas where variable selection is utilized.
