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This is sampled from using MetropolisHastings. We loop through
all voxels sampling from the continuous weights vector a voxel at
a time. Recall that
is the
deterministic logistic transform in
equation 12 at voxel . The logistic
transform can only take us from a vector
to a
vector . Hence, in practice we propose jumps on
and then calculate the vector this
gives us. Then, for model 1 we need to recalculate:



(32) 
or for models 2 and 3:



(33) 
Plus for models 2 and 3 we also need to update the parts of the
MRF prior that change when we change . These are:



(34) 
where
is the set of voxels in the spatial
neighbourhood of voxel .
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