Bayesian Hierarchical Multisubject Multiscale Analysis of Functional MRI Data

• Activity Number: 503
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Nilotpal Sanyal*+ and Marco A. R. Ferreira
• Companies: University of Missouri at Columbia and University of Missouri
• Keywords: Bayesian ; Wavelet ; fMRI ; Spatiotemporal analysis ; Smoothing

Abstract

We develop methodology for Bayesian hierarchical multi-subject multiscale analysis of functional Magnetic Resonance Imaging (fMRI) data. After modeling the brain images temporally with a standard general linear model, we transform the resulting estimated standardized regression coefficient maps by a discrete wavelet transformation to obtain a sparse representation in the wavelet space. Next, we assign to the wavelet coefficients a prior that is a mixture of a point mass at zero and a Gaussian noise. Further, we assign for the mixture probabilities a prior that depends on few hyperparameters. We develop empirical Bayes methodology to estimate the hyperparameters and use these estimates to perform inference in the wavelet space. Finally, we obtain smoothed images of the regression coefficients by inverse wavelet transformation of the posterior means of the wavelet coefficients. An application to synthetic data shows that, when compared to single subject analysis, our multi-subject methodology performs better in terms of mean squared error overall and also individually. Finally, we illustrate the utility and flexibility of our methodology with an application to a real fMRI dataset.