Efficient coherence inference on complex time-frequency coefficients using a general linear model

Statistical significance testing of neural coherence is essential for distinguishing genuine cross-signal coupling from spurious correlations. Surrogate-based inference-typically using time shifts or phase randomization-is widely used but computationally expensive and produces discrete and sometimes unstable p-values, limiting scalability for large EEG/iEEG datasets.

We introduce a parametric framework based on a general linear model (GLM) applied to complex-valued time-frequency coefficients (e.g., from the demodulated band transform or short-time Fourier transform). A likelihood ratio test provides continuous coherence significance estimates without surrogate resampling.

Using real respiration traces as a driver and simulated neural signals with Gaussian broadband noise, we performed dense sweeps of ground-truth coherence. The GLM achieved sensitivity comparable to or better than surrogate testing and produced stable continuous p-values. At 80% detection power, the GLM detected coherence at C≈0.16, whereas surrogate testing required C≈0.31, corresponding to an ∼8 dB improvement in signal-to-noise ratio. Runtime benchmarking showed an ∼190× speed increase over surrogate-based methods.

Compared with time-shift and phase-randomization surrogates, the GLM provided matched or superior sensitivity while eliminating the permutation floor and dramatically reducing computation, particularly for dense frequency grids and multichannel datasets.

GLM-based inference offers a robust, statistically principled, and computationally scalable alternative to surrogate-based coherence testing, enabling efficient analysis across channels, frequencies, and participants in large EEG/iEEG studies.