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Dear Nurul,
Yes, the sign can sometimes be confusing here.
The negative free energy is an approximation to the log model evidence.
The optimisation algorithm that fits (deterministic) DCMs to data is called spm_nlsi_GN.m.
It returns a value F which is the negative free energy (see help for that function).
The model evidence is then exp(F) – this is likely to be a very small number – but the absolute value is not so
important.
Its the relative evidences for different models that is more important.
If you have eg. fitted models 1 and 2 to data from 12 subjects then you can make a table of log model evidences
with two columns and 12 rows (ie all the F’s for model 1 in column 1, F’s for model 2 in column 2). Then call the function spm_BMS.m which implements random effects model inference – you can read more about that here [1].
All the best,
Will.
[1] Stephan KE, Penny WD, Daunizeau J, Moran RJ, Friston KJ (2009)
Bayesian Model Selection for Group Studies. NeuroImage 46:1004-1017
From:
Md. Nurul Islam [mailto:[log in to unmask]]
Sent: 05 June 2013 17:00
To: [log in to unmask]
Subject: Help needed for some DCM issues
Dr. Penny,
I am working on a project where I use DCM to see the effective connectivity of ROIs. I am at the stage of model selection where I am to compare the models from different
perspective instead of just getting the relative to minimum log-evidence that is a default inplementation in spm_DCM_compare. I am having a problem in understanding what free energy stands for in relation to model evidence, as I got following two statements
in Scholarpedia and your paper titled 'Variational free energy and the Laplace approximation' .
1. in Scholarpedia (by Merreiros): free-energy approximates the negative log-evidence (where the sign before the KL divergence is positive)
2. in your paper: " free energy used in expectation maximisation and is equivalent to log evidence". (where in the equation of F, the divergence term takes a negative sign) and " In this note, all the energies are the negative of energies considered in statistical
physics."
In my cases, I found all the DCM.F value negative. So, what is my model evidence? -DCM.F(the absolute value) or DCM.F itself?
Again, is it possible to calculate exceedence probability/ Posterior Model Probability for my models? Is there any function for that?
In case of one-sapmle t-test for a group of subjects (to see if a particular model is significant for that group) what should I use as mean of normally distributed population? Or, should I always use two sets of evidence for 2 models (in case of choosing the
better one for a particular group) and make a 2-sample t-test among the competing models?
Regards,
Md Nurul Islam