On Mon, Nov 14, 2016 at 11:13 AM, Penny, William <[log in to unmask]> wrote:
>
> The spatial regularisation that's mentioned on the list is not just
> smoothing the data. It uses a regularisation term 'lambda' that
> encourages beta estimates to be similar at nearby voxels (actually
> one for each regressor, allowing the smoothness to be different for
> each of the effects in your data). Thes lambda's are estimated from
> data by maximising the model evidence (not cross validation).
>
> If you want to know more about it you can read the 'Bayesian analysis' section

Dear Will,

Many thanks indeed for the info. It's interesting that the Bayesian
version of the GLM fitting involved spatial regularisation of that
sort. I confess that I didn't know that.

For my particular purposes, however (and I'm guessing other people
probably have a similar goal), the aim is to use the beta estimates as
the input to a subsequent pattern-based analysis. For that, I wouldn't
want to enforce any local smoothness, as nearby voxels might encode
usefully different information from each other.

E.g. for a Mitchell/Gallant-style voxelwise encoding model, one could
construct the model simply by building an SPM GLM with a
larger-than-usual number of parametrically modulated regressor
columns. This larger number of regressors would make regularisation
useful at the GLM-fitting stage, but that regularisation would
preferably be carried out for each voxel independently, as opposed to
a spatial regularisation that encourages neighbouring voxels to have
similar beta estimates.

Having said that, I just now ran across the following interesting
paper by Wehbe et al., which suggests that spatial smoothing has a
surprisingly similar effect to voxelwise regularisation, in terms of
neural decoding performance:

Regularized brain reading with shrinkage and smoothing
Leila Wehbe, Aaditya Ramdas, Rebecca C. Steorts, and Cosma Rohilla Shalizi
Ann. Appl. Stat. Volume 9, Number 4 (2015), 1997-2022.
http://projecteuclid.org/euclid.aoas/1453994188

So, maybe SPM's Bayesian spatially smoothing regularisation would meet
the requirements after all.

If I may, I'd like to ask a perhaps slightly statistically naive
question: given that a main aim of the regularisation is to reduce the
impact of noisy voxels, might one in effect achieve the same result
by, instead of using beta-coefficients as the input to an encoding
model, instead using the voxelwise t-statistic values? By
down-weighting each voxel's beta-value by the standard-error for that
voxel, would the t-statistic in effect be just the sort of
noise-regularised output for each voxel that is desired?

Many thanks,

Raj