Dear Brian,
Thank you for your interesting e-mail. The (probable) explanation for this drift is that the drift terms are included in the Bayesian model inversion as confounds - with uninformative shrinkage priors. When you specify very tight hyper-priors, you effectively override the shrinkage priors on the effective connectivity parameters. I suspect that what is happening is that the drift terms are being constrained because their prior covariance is no longer negligible with a very high expected precision (exp(10)).
I would recommend using an expected log precision (hE) for between -3 and -6. This corresponds to an expected signal to noise of 100*(1 - exp(-3)) = 95% to about 99.5% (assuming the variance of the signal is one).
I hope this helps.
With very best wishes,
Karl
-----Original Message-----
From: Brian Numelin Haagensen [mailto:[log in to unmask]]
Sent: 11 April 2014 14:28
To: Friston, Karl
Subject: question concerning DCM hyper-priors
Dear Karl Friston,
may I kindly disturb with a question concerning DCM (version 10) for fMRI?
I'm a PhD-student in Hartwig Siebner's lab in Copenhagen and we would appreciate very much if you could help us with some advice on a problem we have encountered that also in general might be of relevance to others using DCM.
We apply bilinear DCM on fMRI data acquired during an event-related decison-making paradigm. We use one of the main conditions as direct input and its 1st parametric modulation as modulatory input. The eigenvariates used are from two regions showing a strong main effect of the parametric modulation at the 2nd level. We extract from voxels thresholded at 0.05 uncorrected.
Initially we had flat-line fits in most of our subjects- I guess a problem is that this event-related design with parametric input is not optimal for DCM. We then changed the hyper-priors on the mean and covariance on the observed responses and the models began to fit.
Typically, the % explained variance would be around 10%. We used the default EM algorithm for deterministic DCMs.
In the proces we tried some different combinations, and when using quite extreme hyper-priors (M.hE = 10 and M.hC=exp(-10) we observed in two subjects that in one of the models, the observed response began to drift from around 0 to around 3 as model inversion proceeded. The model "followed" this, obtaining very high % variance explained around 90 %.
I've attached a slide with a screen-shot from time-step 6 and time-step
124 where the drift is apparent. This drift was not present at less extreme values such as M.hE = 6 and M.hC = exp(-4).
I've looked into the spm_nlsi_GN script and the observed data is calculated iteratively, as I understand it, from the model-prediction + the prediction error. So I wonder if this drift appears because of this?
Our concern now is, when we use non-default hyper-priors, if there might be a drift also in other subjects that just went unnoticed and whether it's advisable not to change the hyper-priors at all?
Thanks a lot for your help and time!
Best regards, Brian Haagensen
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