# Depth prior **URL:** \ **Category:** Mailing List Archive (read-only)\ **Tags:** list-archive\ **Created:** [March 8, 2018, 5:18pm UTC](https://mne.discourse.group/t/depth-prior/1447 "2018-03-08T17:18:12Z")\ **Posts on this page:** 2\ **Page:** 1
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [March 8, 2018, 5:18pm UTC](https://mne.discourse.group/t/depth-prior/1447/1 "2018-03-08T17:18:12Z")
Hi All, I generally use fixed orientation forward models, and I've just started experimenting with using a depth prior for my MNE solutions. I noticed that make\_inverse\_operator requires the input forward model to be in free orientation mode in order to use depth weighting, because compute\_depth\_prior uses all three orientations to calculate the weights. Actually, compute\_depth\_prior can work with either free or fixed orientations, but it seems that make\_inverse\_operator enforces free orientations because the resulting depth prior is better in some sense. That is, the first singular value of dot(Gk.T,Gk) for each source location is a better normalizing factor than sum(G\*\*2, axis=0).    1. I don't think the original Fuchs et al 1999 or Lin et al 2006 papers    describing depth weighting use the singular value trick -- is there another    article that justifies its use?    2. I'm concerned that in my case where I ultimately use fixed    orientations, the singular-value based depth prior is introducing a    systematic bias against frontal sources. This may be related to a    systematic mismatch between the source direction chosen based on the    cortical patch statistics and the direction of the first singular vector    of dot(Gk.T,Gk). Is that possible?    3. How would you normally quantify bias as a function of source    location? I have been looking at a few things, including    1. the size of the rows of C^(-1/2)\*G\*R^(1/2), which I can reconstruct       from the eigenfields, eigenleads, and singular values in the inverse       operator       2. the magnitudes of the rows and columns of the resolution matrix Thanks, Emily -------------- next part -------------- An HTML attachment was scrubbed... URL: [http://mail.nmr.mgh.harvard.edu/pipermail/mne\_analysis/attachments/20180308/60df3b5f/attachment.html](http://mail.nmr.mgh.harvard.edu/pipermail/mne_analysis/attachments/20180308/60df3b5f/attachment.html) ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [March 29, 2018, 9:58am UTC](https://mne.discourse.group/t/depth-prior/1447/2 "2018-03-29T09:58:21Z")
hi Emily, sorry for the slow answer. > I generally use fixed orientation forward models, and I've just started > experimenting with using a depth prior for my MNE solutions. I noticed that > make\_inverse\_operator requires the input forward model to be in free > orientation mode in order to use depth weighting, because > compute\_depth\_prior uses all three orientations to calculate the weights. > > Actually, compute\_depth\_prior can work with either free or fixed > orientations, but it seems that make\_inverse\_operator enforces free > orientations because the resulting depth prior is better in some sense. That > is, the first singular value of dot(Gk.T,Gk) for each source location is a > better normalizing factor than sum(G\*\*2, axis=0). I convinced myself it the right approach by working on phantom data like here: [https://martinos.org/mne/dev/auto\_tutorials/plot\_brainstorm\_phantom\_elekta.html](https://martinos.org/mne/dev/auto_tutorials/plot_brainstorm_phantom_elekta.html) one intuition is that dot(Gk.T,Gk) is only sensitive to depth while sum(G\*\*2, axis=0). is sensitive also orientation. Basically with sparse solvers, using sum(G\*\*2, axis=0). you don't recover the correct orientation. > I don't think the original Fuchs et al 1999 or Lin et al 2006 papers > describing depth weighting use the singular value trick -- is there another > article that justifies its use? > I'm concerned that in my case where I ultimately use fixed orientations, the > singular-value based depth prior is introducing a systematic bias against > frontal sources. This may be related to a systematic mismatch between the > source direction chosen based on the cortical patch statistics and the > direction of the first singular vector of dot(Gk.T,Gk). Is that possible? can you show this with sensitivity maps? > How would you normally quantify bias as a function of source location? I > have been looking at a few things, including position a source at every location and see where the peak is found by solver. I am also looking at things like this these days. Alex