Functional Models for Complex and High-Dimensional Data

University Of California-Davis, Davis CA

Investigators

Abstract

Innovative methodology for Functional Data Analysis facilitates improved data analysis for longitudinal studies, e-commerce online bidding, genomic studies, (bio)demography and many other areas of the social, biological and physical sciences problems. The proposed functional approaches provide highly flexible ways to characterize such data, and especially to study their time-dynamic aspects. The investigator extends the applicability of Functional Data Analysis to data structures that have not been widely considered within this framework. This includes point processes, high-dimensional (large p, small n) data and sparsely observed stochastic processes as they occur in longitudinal and repeated measurements data. Especially for high-dimensional non-functional and point process data, Functional Data Analysis approaches have the potential to lead to transformative rather than merely incremental improvements. The investigator develops flexible functional and varying-coefficient models for functional regression and correlation. Current modeling approaches are too restrictive to be of broad applicability and more general models are needed. Similarly, the subarea of curve warping has seen much development lately but there remain many important open questions to be investigated. The investigator combines theoretical analysis, simulations, and data applications to conduct this research and applies the methods to data from e-commerce, biodemography, longitudinal studies and gene expression. The investigator develops statistical methodology that is immediately useful for the analysis of large and complex data in genomics, demography and biodemography. These new analysis tools, which fall into the field of Functional Data Analysis, are geared towards gaining a better understanding of time-dependent processes. These include a variety of commonly observed phenomena such as growth, aging, bidding during an online auction, or repeated observations of a recurring incident such as an asthma attack. The methods developed by the investigator elucidate the underlying dynamics of such phenomena. Application of these methods in particular enables insights into the mechanisms of aging and longevity, the dynamics of on-line auctions, and other instances of e-commerce. The investigator extends the scope of these methods further such that for example improved prediction of specific risks becomes feasible, based on a recording of a subject's gene expression profile.