It's not necessary for the distributions to be normal for this approach to be relevant. A lot of the (very powerful) Gaussian machinery for e.g. graphical mode

It's not necessary for the distributions to be normal for this approach to be relevant. A lot of the (very powerful) Gaussian machinery for e.g. graphical models, can still be rigorously applied to a many non-normal distributions by using the Nonparanormal transform: http://jmlr.csail.mit.edu/papers/volume10/liu09a/liu09a.pdf http://jmlr.csail.mit.edu/papers/volume10/liu09a/liu09a.pdf