Firstly, we can determine bounds on the accuracy of the fast approximation's z-statistic bounds by using artificial data with ``worst case scenario'' variance components by comparing the [LOWER] and [UPPER] inference approaches with [BIDET] (as described in section 6). For the design matrices we are using here, the corresponding artificial dataset we need to use is Dataset 1 from section 6.
We can then run the fast approximation approach on our real FMRI
data first, and subsequently only run the computationally
expensive MCMC sampling (with 30,000 samples and a burnin of 1000
samples) and the fitting of a non-central multivariate
t-distribution (BIDET, section 3.7) on voxels at which
the desired 
threshold lies within the estimated bounds.
This hybrid approach takes approximately 1 hour (for the datasets considered here) on a 2GHz Intel PC on a full volume.