Spatial-extent inference and prediction in brain imaging data

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The proposed research program focuses on developing statistical methods that address a crucial issue in magnetic resonance imaging (MRI) technology for the human brain. Brain imaging data are rich with information but are high-dimensional and complex, exhibiting spatial autocorrelations that require statistical modelling and inference to disentangle and improve power. In particular, because the number of subjects used in brain imaging studies is relatively small, it is necessary to develop a powerful statistical model to capture most variations of the brain imaging data. Despite high-resolution images obtained by recent MRI technology, current statistical methods do not fully take advantage of the rich information. A key challenge is the massive computational cost of applying the spatial Gaussian process to high dimensional data and permutation to control false positives. Furthermore, even when the computational cost is relaxed, it is unclear how it can be used for clusterwise inference, which is commonly used to improve sensitivity. As a result, current statistical practices include downsampling and smoothing (blurring) the images, which are insufficient and underpowered. This program will develop a novel and unified methodology that addresses statistical and computational challenges for spatial-extent inference. The proposed research program has three specific objectives. First, the PI will consider a sparsity-informed Gaussian process, apply it to compute multivariate test statistics, and then develop a clusterwise inference method that extends scan statistics and a computationally efficient permutation method. Second, the PI will extend it to research in brain imaging by modelling spatial autocorrelation to estimate intermodal correspondence and heritability. Lastly, the proposed approach will be linked to the high-dimensional mediation analysis, which is essential for understanding the brain functions and anatomies related to genotypes and phenotypes. The PI will validate the proposed methodology through applications to large-scale brain imaging databases, including the Adolescent Brain Cognitive Development (ABCD) study, Human Connectome Project (HCP), and UK BioBank. The proposed program addresses a timely statistical methodology that will attract significant attention from both statisticians and practitioners. The proposed methodology will be widely implementable through an R package for reproducibility. It will provide invaluable opportunities for student trainees, and they will be encouraged to participate in the whole process of research, from implementation to publication.