This project concerns developing innovative advanced statistical tools for the analysis of ultra-high dimensional functional data with spatial-temporal correlation. The primary motivating application is neuroimaging analysis, relevant to the BRAIN Initiative. (However, the developed methods and theory are applicable to a much broader range of fields involving spatial-temporal modeling.) The research program has a strong multidisciplinary collaborative component, with key team members drawn from biostatistics/statistics, computer science, psychiatry, radiology, and psychology. The tools and software under development can have immediate impacts in clinical research, and have wider applications in medical studies of HIV/AIDS, major neuropsychiatric and neurodegenerative disorders, normal brain development, and cancer, among many others. The problems addressed are also of broad interest to general society, since they relate to pressing issues such as health care policies and social security planning.
With modern imaging techniques, many large-scale studies have been or are being widely conducted to collect a wealthy set of functional data and clinical data. Functional data share four common and important features: (i) extremely high dimensional, (ii) piecewise smooth, (iii) temporally, and (iv) spatially dependent. The analysis of such data and integration of them with clinical data have been hindered by lack of effective statistical tools and theory, underscoring the great need for methodological and theoretical development from a statistical perspective. The project addresses challenges from three broader perspectives in both time and frequency domains. The first perspective develops spatial-temporal models for adaptive function estimation. The models can effectively extract informative markers from noisy functional data. The second perspective concerns reduced rank models for groups of functional data with spatial-temporal correlation. In addition, the third perspective develops advanced functional mixed effects models for modeling varying association function between repeated functional responses and a set of covariates of interest, while accounting for complex spatial-temporal correlation.
