Multiscale Adaptive Spatial-Temporal Models for Functional Image Data

• Activity Number: 285
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Hongtu Zhu*+ and Jianqing Fan and Weili Lin and Japing Wang
• Companies: The University of North Carolina and Princeton University and ENAR/IMS/ASA and ENAR/IMS/ASA
• Keywords: multiscale adaptive ; spatial-temporal ; functional imaging ; wavelet thresholding

Abstract

We develop a multiscale adaptive spatial-temporal model (MASTM) for functional imaging data with complex spatial patterns on a two-dimensional (2D) slice or in a 3D volume. Most statistical methods, including wavelet thresholding, focus on independently estimating functional activity at each spatial location (voxel). MASTM, however, is to specifically count for the complex spatial patterns in functional images and build a comprehensive statistical model in order to simultaneously estimate all unknown functions across all voxels. MASTM has four features: being spatial, being connected, being hierarchical, and being adaptive. MASTM analyzes all observations in the ellipsoid of each voxel and its homogeneous groups. These consecutively connected ellipsoids across all voxels can capture spatial dependence among imaging observations, while these homogeneous groups allow for the combination of spatially disconnected clusters. Our simulation studies and real data analysis confirm that MASTM significantly outperforms the existing methods. This is joint work with Japing Wang, Weili Lin, and Jianqing Fan.