Development of Composite Likelihood Method in High-Dimensional Correlated Data Analysis: Estimation, Inference and Model Selection

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111‐5).Recent advances in computing and measurement technologies have given subject-matter scientists opportunities to develop large scale experiments and ambitious information collection schemes that have led to various types of high-dimensional correlated data. This proposal focuses on the development of statistical theory and methods of composite likelihood for analyzing such high-dimensional correlated data. In particular, the principle investigator plans to achieve three research goals: To develop a new algorithm analogous to the EM algorithm in the context of composite likelihood theory for the analysis of incomplete high-dimensional data; to develop a new model selection criterion analogous to the Bayesian Information Criterion for the scenario where the number of model parameters may increase in the sample size; and to develop a new procedure to evaluate and boost the efficiency loss due to dimension reduction in the composite likelihood methodology.All the developed methods will be applied to the analysis of data from practical studies to facilitate the understanding of subject-matter sciences and ultimately to improve human knowledge and quality of life. The principle investigator has close connections with researchers in other fields such as Biology, Computer Science, Epidemiology, Health and Medical Sciences at University of Michigan. He has been working closely with these scientists who will serve as local users of the methodologies and provide valuable feedback. The project is also devoted to substantial educational initiatives that will involve undergraduate and graduate students and expose them to state-of-the-art research in various interdisciplinary topics related to the proposed research. These include new courses, short courses at major conferences, summer workshops, mentoring, and software development. These and other dissemination activities will increase awareness of modern powerful methods for data analysis among scientists from other fields.