Efficient Coherence Inference Using the Demodulated Band Transform and a Generalized Linear Model

Abstract: Statistical significance testing of neural coherence is essential for distinguishing genuine cross-signal coupling from spurious correlations. A widely accepted approach uses surrogate-based inference, where null distributions are generated via time-shift or phase-randomization procedures. While effective, these methods are computationally expensive and yield discrete p-values that can be unstable near decision thresholds, limiting scalability to large EEG/iEEG datasets. We introduce and validate a parametric alternative based on a generalized linear model (GLM) applied to complex-valued time--frequency coefficients (e.g., from DBT or STFT), using a likelihood-ratio test. Using real respiration belt traces as a driver and simulated neural signals contaminated with broadband Gaussian noise, we perform dense sweeps of ground-truth coherence and compare GLM-based inference against time-shift/phase-randomized surrogate testing under matched conditions. GLM achieved comparable or superior sensitivity while producing continuous, stable p-values and a substantial computational advantage. At 80% detection power, GLM detects at C=0.25, whereas surrogate testing requires C=0.49, corresponding to an approximately 6--7 dB SNR improvement. Runtime benchmarking showed GLM to be nearly 200x faster than surrogate approaches. These results establish GLM-based inference on complex time--frequency coefficients as a robust, scalable alternative to surrogate testing, enabling efficient analysis of large EEG/iEEG datasets across channels, frequencies, and participants.