Detectability of Granger causality for subsampled continuous-time neurophysiological processes

TL;DR

This paper analyzes how subsampling affects the detection of true Granger causal relationships in continuous-time neurophysiological processes, revealing complex interactions between sampling rate, signal delays, and causality detectability.

Contribution

It provides an analytical framework linking sampling frequency and neural delay times to the detectability of Granger causality, highlighting optimal sampling strategies.

Findings

Detectability of causality decays exponentially with increased sampling interval.

Subsampling can sometimes improve causality detection.

Identifies 'black spots' and 'sweet spots' in sampling rates for causality detection.

Abstract

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, here we address the equally important issue of the effects of subsampling on the ability to reliably detect causal connections which do exist. 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. Our analysis reveals complex interactions between the time scale(s) of neural signal propagation and sampling frequency: we demonstrate that Granger causality decays exponentially as the sample time interval increases beyond causal delay times, identify detectability "black spots" and "sweet spots", and show that subsampling may sometimes improve detectability. We also demonstrate that the invariance of Granger causality under causal, invertible filtering fails at finite prediction horizons. We discuss the implications of our results for inference of Granger causality at the neural level from various neurophysiological recording modes, and emphasise that sampling rates for causal analysis of neurophysiological time series should be informed by domain-specific time scales.