A Central Limit Theorem for High-Dimensional Spatially Correlated Processes

• Activity Number: 288
• Type: Contributed
• Date/Time: Tuesday, August 8, 2006 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Danielle Harvey*+ and Qian Weng and Evan Fletcher and Charles DeCarli and Laurel Beckett
• Companies: University of California, Davis and University of California, Davis and University of California, Davis and University of California, Davis and University of California, Davis
• Keywords: central limit theorem ; spatial data ; MRI ; orthogonal decomposition

Abstract

Alzheimer's disease and other forms of dementia affect the underlying structure of the brain. Magnetic Resonance Imaging (MRI) enables researchers to observe tissue atrophy, strokes, and white matter damage in the brain. These images may be broken up into tiny volumes, or voxels, of information, of which there are hundreds of thousands in a single image. Most analyses have reduced these data to a one-number summary, such as a volume. However, such a summary may be too limited to capture adequately, the ways in which images vary. Alternative summaries may include decompositions of the voxel data. We present a general central limit theorem for decompositions of correlated spatial data, followed by simulations of a spatial decomposition of the data. We then apply the decomposition to actual MRI data from two groups of subjects to illustrate differences in location and extent of disease.