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Large covariance estimation for spatial functional data with an application to twin studies

Banff International Research Station for Mathematical Innovation and Discovery

Twin studies can be used to disentangle the environmental and genetic contributions to brain structure and function. A trait's heritability can be estimated using Fisher's Additive, Common, and unique Environmental (ACE) model, which can be formulated as a structural equation model (SEM). The Human Connectome Project has generated large amounts of preprocessed imaging data from twin pairs. A massive univariate analysis would estimate an SEM at each location in the brain. An important question is whether the genetic contribution is significant over a region-of-interest. Extending the ACE model to spatial domains requires an estimation of the covariance functions. Here we propose a spatial functional SEM. We develop a method for large covariance estimation using functional PCA. Our framework allows for inference over arbitrary domains of the cortex. Additionally, the approach improves predictions. Joint work with Dr. Hongtu Zhu

Mathematics; Statistics; Game theory, economics, social and behavioral sciences

video/mp4

Author affiliation: Statistical and Applied Mathematical Sciences Institute and University of North Carolina

2016-08-03

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58655

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/