3.3 Group-level inference

In equation 9, the estimated spatial maps are given by the projection of the original data $\mbox{\protect\boldmath$X$}$ transformed into its 2-D representation $\mbox{\protect\boldmath$X$}_{IK\times J}$ and projected onto the estimated 'unmixing' matrix $\left(\mbox{\protect\boldmath$C$}\vert\!\!\otimes\!\!\vert\mbox{\protect\boldmath$A$}\right)^\dagger$. To generate statistic values we transform spatial maps $\mbox{\protect\boldmath$B$}$ into voxel-wise $Z$-scores by dividing the estimated spatial maps by the residual mixed-effects variance and model the histogram of $Z$-statistics values using the Gaussian/Gamma mixture model approach [Beckmann et al., 2003b,Woolrich et al., 2004]. The fitted mixture model can then be used to threshold spatial maps using the voxel-wise posterior probability of 'activation' or the expected false positive rate over the brain or over the voxels classified as 'non-background noise' (FDR).