Probabilistic ICA for FMRI

Independent component analysis is becoming a popular exploratory method for analysing data from FMRI experiments. Its application, however, has been somewhat restricted by the lack of ability to quantify statistical significance. We present an integrated approach to probabilistic ICA for FMRI data that allows for nonsquare mixing in the presence of Gaussian noise. In order to avoid overfitting, we estimate the number of source processes from the eigen-spectrum of the sample covariance matrix of the observations. Voxel-wise noise variance is estimated from the residuals and spatial IC maps are transformed into Z-statistic maps. We use an alternative-hypothesis testing approach for inference on these maps based on a Gaussian/Gamma mixture model. The technique is illustrated on artificial and real FMRI data and is compared to the spatio-temporal accuracy of standard ICA and standard GLM analysis.