Dear Sam,
Sam Gershman wrote:
> Just to clarify why I bring this up: In the SPM5 GUI, when you select
> variational Bayes estimation, it gives you options for spatial priors on the AR
> coefficients and states that the GMRF priors were favored by Bayesian model
> comparison, which I don't think is a correct statement
It is a correct statement, as far as I understand.
In the paper referred to in the previous email three different
parametric forms of the prior were proposed.
1. Non-spatial. AR coeffs were drawn from a Gaussian (its mean and dev
were estimated using empirical bayes)
2. Discrete spatial. AR coeffs drawn from a separate Gaussian for each
tissue type (grey,white,csf; the three means and devs were again estimated)
3. Continuous spatial. AR coeffs drawn from a GMRF (spatial precision
param estimated)
The formal model comparisons in the paper provided the first inferential
evidence (ie. in the form of a statistical test) that AR coeffs vary as
a function of tissue type. This was implemented by computing the
Bayes factor (ratio of model evidences) for model 2 versus model 1.
Overall, out of the 3 models, the GMRF model had the highest model
evidence. This shows that the AR coeffs vary significantly over space
and that the variation is continuous rather than discrete.
This sort of Bayesian model comparison is used routinely in various
parts of SPM eg. in DCM for ERPs to select the optimal prior (ie. how
many ECD sources).
(even if GMRF priors are
> in fact an accurate representation of one's prior beliefs). That said, in practice
> these priors are probably reasonable most of the time, and something similar is
> being done by spm_reml in the classical inference scheme anyways.
>
The use of spm_reml in fMRI processing currently assumes that AR coeffs
do not vary over space.
Best wishes,
Will.
> Sam Gershman
> Department of Psychology
> Princeton University
>
>
--
William D. Penny
Wellcome Trust Centre for Neuroimaging
University College London
12 Queen Square
London WC1N 3BG
Tel: 020 7833 7475
FAX: 020 7813 1420
Email: [log in to unmask]
URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
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