Bayesian estimation and uncertainty quantification for high dimensional data

North Carolina State University, Raleigh NC

Investigators

Abstract

Statistical data in modern context appear in increasing size, form and complexity such as images, videos, functions, trees from diverse sources including barcodes, internet searches, social networks, mobile devices, satellites, genomics, medical scans etc. Such data are typically huge in size and dimension. Nevertheless, some lower dimensional structures is commonly hidden within such data. The Bayesian approach to decision making is particularly useful in the context since structural property in the data can be easily incorporated in its framework and can automatically quantify the uncertainty in the decision making process. Computation however remains a challenge in the big data regime since common computing methods do not scale well, especially when a large number of models are involved in the analysis. Some of the newest cutting-edge techniques for computing and evaluating methods will be used in the proposed research. It will have significant impact on studying relations between variables in human brain development, gene-pathway analysis and other applications. Computational packages will be developed and users will be given free access. Results will be disseminated through articles, seminars and talks given at various places. The proposed research will connect various concepts together and synthesize into a powerful approach for analyzing high dimensional data appropriate for subject specific and interdisciplinary research in STEM disciplines. The educational component of the proposal will impact human resource development in the form of graduate student advising and offering of special topics courses. The PI is committed to involving female students and students from under-represented groups to promote diversity. The proposed research will have all round involvement in theory, computation and application concerning Bayesian analysis of high dimensional data of various types. Both parametric and nonparametric models will be considered and important issues of estimation, prediction, clustering and assessing model uncertainty will be addressed for a variety of data types including graphs, networks, pathways and trees. Techniques of prior construction, scalable computation and uncertainty quantification will be developed and study of frequentist convergence properties of the resulting procedures will be initiated. Some of the most recent ideas on continuous shrinkage priors which have computational advantage in the high dimensional setting will be employed in the proposed research. Study of posterior convergence properties is extremely delicate in nonparametric and high dimensional models. Using the theoretical tools developed by the PI and other researchers will be employed to study convergence properties of the posterior distributions, and thus will help identify the most efficient methods. The methods developed from the proposed research will be applied in studying brain images, cancer studies and various other contexts.