Here, we consider two different FMRI datasets, both of which are simple motor tasks:
For each subject, echo planar images (EPI) were acquired using a 3 Tesla system with TR=3 seconds, time to echo (TE) = 30ms, in-plane resolution 4mm and slice thickness 7mm. The first 4 scans were removed and the data was motion corrected using MCFLIRT (16) and high-pass filtered as described in (25).
The overall model for this group experiment consists of two levels. The first-level is a standard FMRI GLM with a design matrix for subject , , containing regressors modelling the response to the task within each subject's dataset. The second-level is a GLM which models the group mean of the individual subject's responses to the tasks, via a design matrix .
To infer on this two-level model we utilise the summary statistic approach we have laid out in this paper. To do this we firstly produce the multivariate non-central t-distribution summary statistics of equation 16 using a first-level analyses of standard generalised least squares (GLS). This GLS analysis was performed using FEAT (FSL). FEAT performs voxel-wise time-series statistical analysis using local autocorrelation estimation to prewhiten the data (25).
To infer the group mean, we now need to infer on the marginal posterior, , using the multivariate non-central t-distribution summary statistics obtained from these first-level analyses (equation 14).
To do this, we use two different approaches. Firstly, the [OLS] approach as described in section 6. Secondly, a hybrid approach which provides a compromise between the fast posterior approximation approach (section 3.5) and the slower but more accurate approach of using Markov Chain Monte Carlo (MCMC) sampling and the fitting of a non-central multivariate t-distribution (BIDET, section 3.7). The [HYBRID] approach is now described in detail. It is this which is implemented as the FLAME (FMRIB's Local Analysis of Mixed Effects) C++ program used for higher-level analyses in FEAT (part of FSL v3.1).