Re: small question about GLMDenoise

[Kendrick Kay]

My small question was only about whether the toolbox accounts for the temporal correlations of the time series when estimating the beta coefficients. I don't seem to find anything about this neither in the GLMDenoise paper (https://www.frontiersin.org/articles/10.3389/fnins.2013.00247/full) nor in the github repo.

I assume you are talking about the idea that is in the literature that "accounting for the temporal correlations" can change the estimates of betas (and/or their noise estimates).   The short answer is that GLMdenoise does not do anything regarding this, but the long answer is more complicated.   One observation is that if you include nuisance regressors, these regressors in a sense attempt to account for the temporal noise correlations.  So it could be that after you do that, you are in effect accounting for temporal noise correlations.  That being said, there is no guarantee that the nuisance regressors used by GLMdenoise (or any other approach for that mattter) actually fully whiten the residuals.  In fact, i bet it doesn't.   Another issue is the noise estimates.  If you use parametric-style approaches to estimating error on beta coefficients, then those approaches are certainly susceptible to the fact that the residuals may not be white.   But if you are quantify error across distinct runs (or sessions) (or subjects), then this removes the problem, since we are likely happy to assume that noise is independent across runs / sessions / subjects.   A third issue is whether the betas themselves can be estimated with better quality if one takes autocorrelation into account.  Based on when I looked at it many years ago, i saw that the impact for at least the experiments I was looking at, was super super tiny (i.e. the betas themselves hardly changed).  A fourth issue is that note that whether the noise correlations are temporally correlated or not will also be dependent on whether you have the right HRF model!  So, what can be seen as "we need to account for correlated noise" might actually really just be (or partly) the issue of "you got the HRF wrong".

Kendrick