Detectability of Granger causality for subsampled continuous-time neurophysiological processes

Abstract

Background: Granger causality is well established within the neurosciences for inference of directed functional connectivity from neurophysiological data. These data usually consist of time series which subsample a continuous-time biophysiological process. While it is well known that subsampling can lead to imputation of spurious causal connections where none exist, less is known about the effects of subsampling on the ability to reliably detect causal connections which do exist.

New method: We present a theoretical analysis of the effects of subsampling on Granger-causal inference. Neurophysiological processes typically feature signal propagation delays on multiple time scales; accordingly, we base our analysis on a distributed-lag, continuous-time stochastic model, and consider Granger causality in continuous time at finite prediction horizons. Via exact analytical solutions, we identify relationships among sampling frequency, underlying causal time scales and detectability of causalities.

Results: We reveal complex interactions between the time scale(s) of neural signal propagation and sampling frequency. We demonstrate that detectability decays exponentially as the sample time interval increases beyond causal delay times, identify detectability "black spots" and "sweet spots", and show that downsampling may potentially improve detectability. We also demonstrate that the invariance of Granger causality under causal, invertible filtering fails at finite prediction horizons, with particular implications for inference of Granger causality from fMRI data.

Comparison with existing methods: Our analysis emphasises that sampling rates for causal analysis of neurophysiological time series should be informed by domain-specific time scales, and that state-space modelling should be preferred to purely autoregressive modelling.

Conclusions: On the basis of a very general model that captures the structure of neurophysiological processes, we are able to help identify confounds, and offer practical insights, for successful detection of causal connectivity from neurophysiological recordings.

Keywords: Continuous-time process; Distributed lags; Granger causality; Subsampling.