Publisher Summary It is noted that classical and recent approaches do not explicitly estimate the covariance structure of the noise in the data. With the help of modern approaches the experimenter expects to model types of covariation in the data. This estimation can be noisy and, therefore, is best conducted over pooled collections of voxels. The use of this technique allows the experimenter to perform types of analysis that were previously “forbidden” under the less sophisticated schemes. These techniques are of real interest to many researchers and generally includes better estimation of the autocorrelation structure for functional magnetic resonance imaging (fMRI) data and demonstrates the ability to take more than one scan per subject to the second level, thus conduct F tests in order to draw conclusions about populations. In event-related studies where the exact form of the haemodynamic response can be critical, more than one aspect of this response can be analyzed in a random-effects context. The chapter also addresses the issue of estimation of relative values of the voxel-independent hyperparameters and their precision.