Bayesian Probit Model with Spatially Varying Coefficients and Its Application to Functional Magnetic Resonance Imaging

• Activity Number: 362
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Fengqing (Zoe) Zhang*+ and Wenxin Jiang and Patrick C.M. Wong and Ji-Ping Wang
• Companies: Northwestern University and Northwestern University and Northwestern University and Northwestern University
• Keywords: variable selection ; classification ; high dimensional learning ; fMRI ; Bayesian modeling ; spatial correlation

Abstract

We consider the problem of variable selection in classification for high dimensional spatially correlated data. Identification of reliable classification patterns is challenging due to the large number of variables, the small sample size, and spatial correlation among variables. In the motivating example of Functional Magnetic Resonance Imaging (fMRI) data, each variable represents the brain signal from one voxel in response to the stimuli, which tends to be spatially correlated with nearby voxels. Ignoring the spatial correlation may prevent inclusion of correlated variables in the model. Thus we propose a Bayesian probit model with spatially varying coefficients. We further develop a region selection strategy and demonstrate with simulation and real data that the proposed approach is effective in selection of the clustered true variables even with high correlation while achieving sparsity. One undergoing debate in brain decoding concerns whether brain representation of sound categories is localized or distributed. We show that localized or clustered pattern can be artificially identified as distributed if without proper usage of the spatial correlation information in fMRI data.