Dear DCMers,
in a recent publication by Friston and Penny (2011, 'Post-hoc Bayesian
Model Selection' NeuroImage), a new approach of post-hoc model selection
was suggested. This post-hoc BMS uses a "full model" of all possible
connections between previously defined regions in order to get an
optimised model which is expected to be sparser than the full one.
The reason for us to choose post-hoc BMS was the fact that an exhaustive
search is almost impossible since about 2^60 models would have to be
inverted for each subject (we had 4 regions and 5 different modulatory
inputs). Using post-hoc BMS we obtained an optimised (reduced) model
which was expectedly much less complex than the full model and had a
posterior close to 1.
However, we had previously tried to approach an optimal model by a
standard BMS for which we specified hundreds of different models. After
inversion of all these models and subsequent (standard) BMS, the
posteriors peaked on one model (posterior probability >0.99).
Having done this work, we were curious if a standard BMS would select
the optimised model using post-hoc BMS when we included this in the
model space. After standard BMS (including the optimised DCMs of all
subjects) the posteriors surprisingly still peaked on the same model
which had been selected in the previously described standard BMS - again
with a posterior of >0.99.
(We tried both: on the one hand, we included the "DCM_opt_*.mat" for
each subject which was automatically created during post-hoc BMS. On the
other hand we manually defined and inverted DCMs which had the same
structure compared to the optimised DCMs (ones for all non-zero
parameters) but this did not affect the results of the BMS.)
The logical question now is obvious (I guess): Which of these BMSs
should we trust and rely on?
On the one hand one might think that the standard BMS is more
"accurate" (whatever this means...), because conclusions are based on
inverted models within the model space. On the other hand one wouldn't
necessarily expect that a model space comprised of "only" several
hundreds of models (compared to about 2^60 possible ones) includes a DCM
which is superior to one based on post-hoc BMS (that quickly
searches the subspace of a full model).
Any comments are appreciated.
Kind regards,
Thilo
--
Thilo Kellermann
RWTH Aachen University
Department of Psychiatry, Psychotherapy and Psychosomatics
JARA Translational Brain Medicine
Pauwelsstr. 30
52074 Aachen
Germany
Tel.: +49 (0)241 / 8089977
Fax.: +49 (0)241 / 8082401
E-Mail: [log in to unmask]
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