title: A spatio-temporal nonparametric Bayesian variable selection model of fMRI data for clustering correlated time courses.
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 a hemodynamic response function (HRF) 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 (MRF) prior on the parameters guiding the selection of the activated voxels, therefore capturing correlation among nearby voxels. In order to infer association of the voxel time courses, we assume correlated errors, in particular long memory, and exploit the whitening properties of discrete wavelet transforms. Furthermore, we achieve clustering of the voxels by imposing a Dirichlet process (DP) prior on the parameters of the long memory process. For inference, we use Markov Chain Monte Carlo (MCMC) sampling techniques that combine Metropolis-Hastings schemes employed in Bayesian variable selection with sampling algorithms for nonparametric DP models. We explore the performance of the proposed model on simulated data, with both block- and event-related design, and on real fMRI data.
authors.affiliation: Department of Statistics, Rice University, Houston, USA. Electronic address: linlin.zhang@rice.edu.
authors.forename: Linlin
authors.initials: L
authors.lastname: Zhang
authors.affiliation: Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, USA. Electronic address: mguindani@mdanderson.org.
authors.forename: Michele
authors.initials: M
authors.lastname: Guindani
authors.affiliation: Department of Behavioral Science, The University of Texas MD Anderson Cancer Center, Houston, USA. Electronic address: fversace@mdanderson.org.
authors.forename: Francesco
authors.initials: F
authors.lastname: Versace
authors.affiliation: Department of Statistics, Rice University, Houston, USA. Electronic address: marina@rice.edu.
authors.forename: Marina
authors.initials: M
authors.lastname: Vannucci
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001931:Brain Mapping / Q000379:methods*; D016000:Cluster Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging; D008959:Models, Neurological
keywords: Bayesian nonparametric; Dirichlet process prior; Discrete wavelet transform; Long memory errors; Markov random field prior; fMRI