My understanding of Craddock et al. (2012), page 1917, is that they consider two different similarity measures: r_t, which is the correlation between the time-series; r_s which is the correlation between the spatial maps (maps of voxel-wise time-series correlations like r_t, if I've understood correctly). Isn't the former just your D_mn, rather than transforming D to W to S?

On a somewhat r...

In the first line, I think "n" in the term "(pi)^(-n/2)" should be "L".

In the last segment of the second line, I think "\mu_{mn}" should be "A_{mn}" (though this doesn't really matter, since the term doesn't feature in the marginal likelihood anyway).