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Dear Dirk Thanks for sharing the link - I look forward to reading it :-) By referring to your tutorial paper as 'relatively clear', I was making a massive understatement. It's the clearest explanation of VB I've come across, and the supplemental materials are a particularly useful resource, which I've been sharing widely :-) Many thanks for your time in putting it together. Best Peter -----Original Message----- From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of Ostwald, Dirk Sent: 18 November 2016 15:57 To: [log in to unmask] Subject: [SPM] AW: [SPM] EM algorithm for DCM in details Dear Sadjad, in addition to Peter's suggestions there is also http://www.sciencedirect.com/science/article/pii/S1053811916300593 which contains a somewhat lengthy, but explicit, derivation of the free energy objective function. For its maximization, it uses a different nonlinear optimization approach compared to the SPM implementation, however. For explicit relations to EM and (Re)ML in the linear model case see also http://biorxiv.org/content/early/2016/09/26/077461 Cheers, Dirk -----Ursprüngliche Nachricht----- Von: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] Im Auftrag von Zeidman, Peter Gesendet: Freitag, 18. November 2016 16:07 An: [log in to unmask] Betreff: Re: [SPM] EM algorithm for DCM in details Dear Sadjad, It's not really EM - it's Variational Bayes. For the equations used in DCM, see the appendix of this paper by Will Penny - http://www.sciencedirect.com/science/article/pii/S1053811911008160 . For the more general theory, which is where I would start, there's a very nice step by step tutorial for the simpler case of a 1-dimensional Gaussian on the Wikipedia - https://en.wikipedia.org/wiki/Variational_Bayesian_methods . Alternatively, there's this tutorial, which isn't about DCM per se but is relatively clear - http://www.sciencedirect.com/science/article/pii/S0022249614000352 . Best Peter. -----Original Message----- From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of Sadjad Sadeghi Sent: 17 November 2016 15:39 To: [log in to unmask] Subject: [SPM] EM algorithm for DCM in details Dear DCM experts, I am trying to understand the EM algorithm which is used in DCM for estimating the parameters, but I really have some problems in deriving the details of different steps especially in the M-step (specifically p. 480 Friston et.al 2002, classical and bayesian inference in neuroimaging: theory) Does anybody know a reference to explain this steps in more details? I more mean the exact equations which are used in DCM, not the general methods. Thank you so much in advance. Best regards, Sadjad Sadeghi