There is a significant interest in understanding how structural/functional changes in the brain explains symptoms caused by neurodegenerative diseases such as Alzheimer’s Disease (AD). Despite clear variations in the brain reported in the literature at the dementia stage of the AD, changes in the preclinical stage of AD still remain poorly characterized. Such preclinical datasets are typically small and the group differences are subtle, and thus makes their analyses challenging. This talk will describe some of my recent work to overcome these difficulties in an effort to elucidate how the human brain varies as a function of risk factors even in asymptomatic individuals. The theory driving these analyses is motivated by the multi-resolution scheme for performing statistical analysis on graph-structured data in neuroimaging. The framework derives a novel representation at each data point which captures its context at multiple resolutions using a spectral approach. Extensive empirical results using statistical group analysis (i.e., diseased vs. healthy) describing how this framework offers improved statistical power in the analyses of cortical thickness on brain meshes and tractography derived brain connectivity using Diffusion Tensor Images (DTI) to identify potentially subtle variation in the brain due to Ad or AD risk factors.