A Bayesian Nonparametric Approach to the Analysis of fMRI Data

• Activity Number: 20
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Linlin Zhang*+ and Michele Guindani and Francesco Versace and Marina Vannucci
• Companies: Rice University and and MD Anderson Cancer Center and Rice University
• Keywords: Bayesian nonparametric ; Dirichlet process prior ; Discrete wavelet transform ; fMRI ; Long memory errors ; Markov random field prior

Abstract

In this paper we present a novel wavelet-based Bayesian nonparametric regression model for the analysis of functional magnetic resonance imaging (fMRI) data. Our goal is to provide a joint analytical framework that allows to detect regions of the brain which exhibit neuronal activity in response to a stimulus and, simultaneously, infer the association, or clustering, of spatially remote voxels that exhibit fMRI time series with similar characteristics. We start by modeling the data with an hemodynamic response function with a voxel-dependent shape parameter. We detect regions of the brain activated in response to a given stimulus by using mixture priors with a spike at zero on the coefficients of the regression model. We account for the complex spatial correlation structure of the brain by using a Markov Random Field prior on the parameters guiding the selection of the activated voxels. In order to infer association of the voxel time courses, we assume long memory errors, and exploit the whitening properties of discrete wavelet transforms. Furthermore, we achieve clustering of the voxels by imposing a Dirichlet Process prior on the parameters of the long memory process.