Bayesian Methods for fMRI Time-Series Analysis Using a Nonstationary Model for the Noise

In this paper, the Bayesian framework is used for the analysis of functional MRI (fMRI) data. Two algorithms are proposed to deal with the nonstationarity of the noise. The first algorithm is based on the temporal analysis of the data, while the second algorithm is based on the spatiotemporal analysis. Both algorithms estimate the variance of the noise across the images and the voxels. The first algorithm is based on the generalized linear model (GLM), while the second algorithm is based on a spatiotemporal version of it. In the GLM, an extended design matrix is used to deal with the presence of the drift in the fMRI time series. To estimate the regression parameters of the GLM as well as the variance components of the noise, the variational Bayesian (VB) methodology is employed. The use of the VB methodology results in an iterative algorithm, where the estimation of the regression coefficients and the estimation of variance components of the noise, across images and voxels, are interchanged in an elegant and fully automated way. The performance of the proposed algorithms (under the assumption of different noise models) is compared with the weighted least-squares (WLSs) method. Results using simulated and real data indicate the superiority of the proposed approach compared to the WLS method, thus taking into account the complex noise structure of the fMRI time series.