Dear DCM experts,
I’m currently working on DCM with resting state fMRI.
I'd like to ask about the effect of modeling with and without prior.
I constructed two models with spectral DCM with exactly same time series.
The first one is constructed with no prior(initial full prior which is filled with spm_dcm_fmri_priors.m), and another is constructed with specific priors(values for pE.A) based on functional connectivity matrix.
The effective connectivity results of both model were highly similar(R=0.95), but later model has much lower free energy than first one.
I think it may be very naive question but I'd like to get some comments or advice on why this is happening.
From the standpoint of statisticians, I know that the model with flat prior doesn’t have hyperparameters while model with specific prior has. This means that these two model have different parameter space, so these models cannot be compared with free energy.
As I know, free energy is linear combination of parameter set and each model has its own parameter set. If a model get another parameter set by given specific prior, the model will get another free energy value.
So If the two models have different parameter sets, we cannot identify this difference of free energy is caused by whether the effect of the parameter set or the distribution of the estimates in the parameter set.
However, these stories are theoretical arguments and may not be relevant the way DCM is handled in SPM.
In summary, I built two spectral DCM with same time series with different prior(initial full prior / priors from functional connectivity). And I would like to ask if it is fair to compare these two models with free energy value(DCM.F).
Any comments and advices are really appreciated.
Thank you very much for your time, and wish you have a great day! :)
Chris
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