BayesFMM: Functional Regression Models for Complex Biomedical Imaging Data
 Jeffrey S. Morris (joint work with Hongxiao Zhu, Veera Baladandayuthapani, Hojin Yang, Michelle Miranda, Philip Rausch, Emma Zohner)
 
As new technologies taking automated measurements and producing complex, high-dimensional functional data are increasingly prominent, methods for functional data analysis, and in particular functional regression, are growing in importance.  I will overview BayesFMM, a framework developed from a series of Bayesian methods to regress functional responses on predictors.  This approach utilizes basis representations to capture structure within the functional objects, and can also capture inter-functional correlation between objects induced by the experimental design from spatial, temporal, or hierarchical sampling of functional units.  This approach is designed primarily for complex, high dimensional functional data, with local features and potentially non-Euclidean domains, with various examples highlighted including mass spectrometry, copy number genomic data, event-related potentials, functional MRI, corticol surface thickness, sonic signal data, MRI measurements on the scleral surface of the eye, and distributional data.  Several advanced modeling approaches will be featured, including semiparametric modeling of continuous predictors, spatial functional models to model spatial inter-functional correlation, and quantile functional regression models that treat distributional data as functions.