Bayesian Nonparametric Models for Structured Functional and Object Data with Application to Genomic Studies

• Activity Number: 372
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Jeffrey S Morris and Veera Baladandayuthapani*+
• Companies: MD Anderson Cancer Center and
• Keywords: genomics ; functional data analysis ; bayesian ; spatial ; nonparametric ; high-dimensional

Abstract

We consider Bayesian nonparameteric models for high-dimensional functional (single-domain) and object (multi-domain) data. Estimation and inference in such models presents a major challenge not only due high-dimensionality but also structured dependencies (e.g. serial and spatial correlations) induced by the nature of the data collection. We propose a general nonparametric framework to model such data using adaptive basis functions that not only serves as a dimension reduction device but also, more importantly, accommodates a wide variety of behaviors of the underlying process in the presence of multiple sources of variation. Our methods allow for simultaneously characterization of these high-dimensional functions, borrowing strength between replicated functions and detection of local features in the data -- to answer several important biological questions. We motivate our methodology using high-throughout and multi-platform genomic datasets in cancer.