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At 12:13 18/05/2005, you wrote:
>Hi guys
>
>I'm trying to understand how PPm works and the question is how and from
>where do you get prior values???
>
>Thank you
>
>
>Bernie


Dear Bernie,

PPMs are based on a hierarchical model of the following form (y = data,
beta = parameters, e = error, index in brackets = level):

First level: y = X(1)*beta(1) + e(1)
Second level: beta(1) = 0*beta(2) + e(2)

The first level is just a normal GLM characterising effects at a single
voxel.  At the second level,  beta(2) is the average effect over voxels and
e(2) is its voxel-to-voxel variation.  As the parameters of interest,  i.e.
the parameters at the first level, beta(1), reflect regionally specific
effects, one can assume that they sum to zero over all voxels.  This
corresponds to using a shrinkage prior (i.e. zero mean) at the second
level; the variance of this prior is implicitly estimated by estimating the
variance of  e(2).  This empirical prior can then be used to estimate the
posterior probability of  beta(1) being greater than some threshold at each
voxel.

Or, in more simple terms: The first level of the hierarchy corresponds to
the experimental effects at any particular voxel and the second level
comprises the effects over voxels.  The variation in a parameter (or
contrast), over voxels, can be used as the prior variance of that parameter
(or contrast) at any particular voxel.

Don't confuse this hierarchy with the usual "first level" and "second
level" models which one uses to refer to single subjects and group
analyses.  Here the hierarchy is over voxels, not over single subjects and
groups.  PPMs can operate both on single-subject data as well as on a set
of contrast images.

Best wishes,
Klaas

_____________________________________
Dr Klaas Enno Stephan
Wellcome Dept. of Imaging Neuroscience
12 Queen Square, WC1N 3BG, London, UK
phone: +44-207-8337485
fax: +44-207-8131420
web: http://www.fil.ion.ucl.ac.uk/~kstephan/