The challenge of non-ergodicity in network neuroscience

Abstract

Ergodicity can be assumed when the structure of data is consistent across individuals and time. Neural network approaches do not frequently test for ergodicity in data which holds important consequences for data integration and intepretation. To demonstrate this problem, we present several network models in healthy and clinical samples where there exists considerable heterogeneity across individuals. We offer suggestions for the analysis, interpretation, and reporting of neural network data. The goal is to arrive at an understanding of the sources of non-ergodicity and approaches for valid network modeling in neuroscience.

• functional neuroimaging
• traumatic brain injury
• network modeling
• neuroscience

Notes

Note: η indicates the ROI time series, u a one-vector input series (which may be expanded to include more inputs) convolved with a hemodynamic response function, A the contemporaneous relations among ROIs, Φ the lagged associations, γ input effects, τ the bilinear associations, and ζ error assumed to be a white noise process (see Gates et al. 2011).