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Abstract:
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The application of functional data analysis to functional brain imaging has seen the development of a robust set of techniques for statistical estimation and inference in multivariate and highly structured settings. Beyond regression on the mean structure, we inquire how differential heterogeneity affects patterns of co-variation through a general regression framework involving both the mean function and the covariance operator. Inference is based on a shrinkage framework exploiting rank regularization in infinite factor models, which avoids ad hock truncations typical of functional principal components representations. Our methodological contribution is illustrated on several case studies including functional brain imaging of implicit learning and brain function during sleep. Time permitting, beyond variability attributable to observed covariates, we discuss the notion of latent functional features, and their role in functional brain imaging
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