A sparse linear model for the analysis of fMRI data with non stationary noise

In this work we present a Bayesian approach for the estimation of the regression parameters in the analysis of fMRI data when the noise is non - stationary. The proposed approach is based on the variational Bayesian (VB) methodology and the generalized linear model (GLM). The VB methodology permits the use of prior distributions over the parameters of the noise. This results to a very elegant approach to estimate the time varying variance of the noise and to overcome the problem of over-parameterization which is present in the estimation procedure. The proposed approach is compared to the weighted least square (WLS) and is evaluated using simulated and real fMRI time series. The proposed approach shows better performance than WLS.