Figure 8.

The percentage of multivariate timeseries from each indicated simulation regime (and the real rs-fMRI study on which the simulated data was modeled) that present significant evidence (p < 0.05) of having been generated by some process that is not a stationary multivariate Gaussian. The explicitly implemented spectral and statistical non-stationarities of the two SS Non-stationary regimes (columns 5 and 6) are effectively never found to exhibit significant evidence against being generated by stationary multivariate Gaussians. In the two explicitly covariance-non-stationary regimes (columns 4 and 6), one of which is also spectrally and statistically non-stationary variations (column 6), at most 5% of the 1,000 simulated subjects—each of which exhibits the explicit non-stationarity—are identified as unlikely to have arisen from a stationary multivariate Gaussian process. Like the SCC Gaussian simulations (column 2), the SS Non-stationary simulations (columns 5 and 6) and the covariance-non-stationary simulations (columns 4 and 6), empirical observations from real subjects (column 1) in whom the phenomenon of interest (FRBD) is ubiquitous are not statistically distinguishable from realizations of a stationary multivariate Gaussian process. The only regime that multivariate kurtosis reliably distinguishes from realizations of a stationary multivariate Gaussian process is the case of SCC Gaussians in which a single high-amplitude, high-frequency spike is inserted into between 3 and 15 of the 47 univariate timeseries from the multivariate observation (column 3). This regime is basically just a lightly contaminated version of the SCC Gaussian regime (column 2) and of all of the simulation regimes exhibits the least evidence of functionally relevant brain dynamics. The behavior underlying upper-tail observations of multivariate kurtosis looks more like scan contamination than anything task-paradigm fMRI studies suggest would be strongly associated with FRBD.