Dear Brian,
In fact, you should use positive numbers (of hE) between 3 and 6 – that was my mistake. The log precision is positive (and the log variance is negative – or the variance is less than one). I would stick with a tighter hyperprior than hC = 1. I would use the default settings or use values around hC = 1/128.
You can see this intuitively: if you want the log precision to be bounded around the hyperprior expectation within +1/2 or -1/2 (roughly a scaling of two). Then the standard deviation of the hyperprior should be about 1/8 to 1/16 giving a variance of 1/64 to 1/256. I hope this makes sense :)
With very best wishes – Karl
-----Original Message-----
From: briannh [mailto:[log in to unmask]]
Sent: 15 April 2014 11:39
To: Friston, Karl
Subject: RE: question concerning DCM hyper-priors
Dear Karl Friston,
thank you very much for your help on this!
Just to make sure I get it right: for the hE variable we use numbers beteen -3 and -6 (we actually used positive numbers, but it makes sense to me seeing your SNR calculation that it should be negative numbers) and we keep the prior covariance hC at 1?
Best regards, Brian Haagensen
On 2014-04-11 15:48, Friston, Karl wrote:
> 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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