New Directions in Envelope Models and Methods with Applications to Public Health and Medical Science

University Of Florida, Gainesville FL

Investigators

Abstract

Multivariate linear regression (MLR) is an approach to understand relationships between predictors and responses, and it is broadly applied for estimation or prediction in many disciplines. With the development of modern technology, it is possible to measure more and more characteristics and potential factors for a subject, resulting in very large data sets in many contemporary problems. In such situations, MLR is inefficient because it fails to distinguish between information that is useful to the scientific goal and a likely overabundance of irrelevant information that can obscure the useful information. The envelope model is a new area in statistics. By identifying the irrelevant information, the envelope analysis is based on the useful information only and is therefore more efficient. In this project, new directions will be explored to broaden the applicability of the envelope models, especially the applicability in public health and medical sciences. Students involved in the project will have opportunities to interact with faculty from other disciplines, and gain crucial experience on how to operate across traditional disciplinary boundaries. Software will be developed to make the new methodologies available to the statistical community. This project will develop new models that enrich the area of envelopes, making the envelope method more flexible and adaptive to more practical problems. For example, prior information is often available from medical history, past experience and other sources, the Bayesian envelope model will enable investigators to incorporate prior information in the analysis. As medical studies often involve missing data, envelope models that handle missing data will be studied. While most existing variable selection methods are applied to the predictors, sparse envelope model focuses on identifying inactive individual responses, leading to more efficient and interpretable results. The project connects the envelope model with several branches in statistics, including Bayesian analysis, Markov chain Monte Carlo, variable selection and covariance estimation, which will generate new theory, methods and algorithms in the area of envelope models.