Abstract
It is of great interest to quantify the contributions of genetic variation to brain structure and function, which are usually measured by high-dimensional imaging data (e.g., magnetic resonance imaging). In addition to the variance, the covariance patterns in the genetic effects of a functional phenotype are of biological importance, and covariance patterns have been linked to psychiatric disorders. The aim of this article is to develop a scalable method to estimate heritability and the nonstationary covariance components in high-dimensional imaging data from twin studies. Our motivating example is from the Human Connectome Project (HCP). Several major big-data challenges arise from estimating the genetic and environmental covariance functions of functional phenotypes extracted from imaging data, such as cortical thickness with 60 000 vertices. Notably, truncating to positive eigenvalues and their eigenfunctions from unconstrained estimators can result in large bias. This motivated our development of a novel estimator ensuring positive semidefiniteness. Simulation studies demonstrate large improvements over existing approaches, both with respect to heritability estimates and covariance estimation. We applied the proposed method to cortical thickness data from the HCP. Our analysis suggests fine-scale differences in covariance patterns, identifying locations in which genetic control is correlated with large areas of the brain and locations where it is highly localized.