Geometric statistical reasoning is useful for addressing variability and covariability in quantitative analyses of functional neuroimaging experiments. General image smoothness, i.e., intrinsic temporal and spatial autocorrelation, must be accommodated adequately in order to obtain reliable statistical inferences and meaningful practical conclusions. Several exploratory displays and models for such images in the temporal, spatial and spectral domains are summarized. These tools are applicable in functional magnetic resonance imaging, positron emission tomography and other modalities that produce spatial time series. Construction of an objective binary mask that excludes irrevelant voxels from the search volume increases statistical power. Further improvements in sensitivity and consistency are possible when intrasubject replications are available. A recent experiment that uses functional magnetic resonance imaging to detect focal activations significantly cross-correlated with a designed mental arithmetic task demonstrates the utility of these techniques.
"Variability and covariability in magnetic resonance functional neuroimaging", Proc. SPIE 2299, Mathematical Methods in Medical Imaging III, (8 July 1994); doi: 10.1117/12.179246; https://doi.org/10.1117/12.179246