In many applications in the biomedical and environmental sciences, the complexity of available data makes the selection of statistical models challenging. The goal of this project is to advance basic scientific methodology that will help improve the selection of models using state-of-the-art Bayesian methods. For complex data with a large number of features, it is now routine to entertain an enormous number of competing models. The Bayesian approach to model uncertainty provides a natural solution to many problems in the sciences. In particular, new algorithms for model selection and prediction in a Bayesian framework will be developed. The research is motivated by applications ranging from genetics to climate models. Software will be developed and made publicly available so that the new methods are readily accessible.
When the number of features/predictors is large, Markov Chain Monte Carlo (MCMC) algorithms are often used to identify promising models. For high-dimensional problems, these algorithms exhibit slow convergence and have extremely long running times. This project addresses the development of flexible models and algorithms for Bayesian variable selection and prediction that scale well to high dimensions. The assumption of normal errors for the linear regression model may not always be appropriate. However, the validity of this assumption is often overlooked for high-dimensional data, when the number of predictors exceeds the sample size. In this project, Bayesian variable selection methods for robust error distributions will be developed that adapt to unknown degrees of tail heaviness and sparsity. Flexible hierarchical models will be considered for probabilistic prediction of North Atlantic tropical cyclone activity.
