The investigator will combine theoretical analysis and applied tools to develop innovative models, methodology, algorithms and data analysis for functional data. A major goal of this proposal is to extend the reach of functional data analysis methods to sparse, noisy and irregularly sampled longitudinal data. Functional data and longitudinal data are assumed to be generated by random trajectories that correspond to realizations of an underlying stochastic process. These trajectories may be either observable or hidden. Relevant theory for estimation and inference will be developed. Current functional data analysis approaches and tools require densely measured functions or completely observed functions on a common domain, and abandoning these assumptions requires new tools. Similarly, extensions of functional data analysis to situations where one has both longitudinal and survival time components will lead to new practical statistical methods as well as challenging research problems. The development and application of new tools for curve warping in cases where a large fraction of the variability of random curves lies in variation of time scale is another challenging problem that will be addressed.
The statistical methods that will be developed by the investigator are motivated by the need to analyze data that include large samples of gene expression profiles, longitudinal studies in medicine and biology with multivariate or generalized measurements, and time courses of behavioral measurements, coupled with age-at-death information. It is expected that the results of the proposed research will contribute in a significant way to the analysis and interpretation of such data and will lead to new insights into underlying mechanisms of gene regulation, complex dynamic interactions in biological systems, and aging and longevity.
