Groupe d’études et de recherche en analyse des décisions

Multilevel Functional Principal Component Analysis

Ciprian Crainiceanu

Modern research data have become increasingly complex, raising non-traditional modeling and inferential challenges. In particular, advancements in technology and computation have made recording and processing of functional data possible. Examples of functional data are time series of electroencephalographic (EEG) activity, anatomical shape, and functional MRI. The purpose of this talk is to describe statistical models for feature extraction from single-level (one or multiple functions per subject at one visit) and clustered or longitudinal (one or multiple functions per subject at multiple visits) functional data having a large number of subjects and large within- and between-subject heterogeneity. We introduce the framework and inferential tools for multilevel functional data (MFD) obtained by recording of functional characteristics at multiple visits. Though motivated by a novel experimental setting, the proposed methodology is general, with potential broad applicability to many high-throughput scientific studies. A prototypical example of MFD is the Sleep Heart Health Study (SHHS), which contains electroencephalographic (EEG) signals for each subject at two visits.