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arxiv: 2510.05559 · v1 · submitted 2025-10-07 · 📡 eess.SP

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

Md Rakibul Mowla , Sukhbinder Kumar , Ariane E. Rhone , Brian J. Dlouhy , Christopher K. Kovach This is my paper

Pith reviewed 2026-05-18 09:42 UTC · model grok-4.3

classification 📡 eess.SP
keywords neural coherencegeneralized linear modeltime-frequency analysissurrogate data testingEEGiEEGstatistical significancedemodulated band transform
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The pith

A generalized linear model on complex time-frequency coefficients tests neural coherence more sensitively and two hundred times faster than surrogate methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that fitting a generalized linear model directly to the complex-valued coefficients produced by time-frequency transforms such as the demodulated band transform offers a practical replacement for surrogate-based significance testing in neural coherence analysis. Surrogate methods require generating many shuffled versions of the data and therefore scale poorly to the large numbers of tests needed in multichannel EEG and iEEG recordings. The GLM method yields continuous p-values that remain stable near the decision threshold and detects genuine coherence at lower strengths than the surrogate approach. In the reported experiments the GLM reached 80 percent detection power at a coherence value of 0.25 while surrogates needed 0.49, an improvement equivalent to roughly six to seven decibels in signal-to-noise ratio. Runtime comparisons showed the new method running nearly two hundred times faster.

Core claim

By applying a generalized linear model to complex time-frequency coefficients obtained from the demodulated band transform or short-time Fourier transform and using a likelihood-ratio test, the authors obtain statistical inference for coherence that is comparable or superior in sensitivity to time-shift and phase-randomized surrogate testing while providing continuous p-values and a substantial computational speedup.

What carries the argument

Generalized linear model fitted to complex-valued time-frequency coefficients, tested via likelihood-ratio test for the presence of coherence.

If this is right

  • Large multichannel EEG and iEEG datasets can be analyzed for coherence across many frequencies and participants without excessive computation.
  • Decision thresholds for significance become more reliable because p-values are continuous rather than discrete.
  • Weaker true coherence relationships become detectable under the same noise conditions.
  • The method scales to real-time or near-real-time processing of neural signals.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Researchers studying functional connectivity could apply the same GLM framework to other coupling measures beyond coherence.
  • Integration with existing time-frequency toolboxes would allow immediate adoption for routine analysis pipelines.
  • Validation on additional types of neural signals, such as those with non-Gaussian noise, would further establish the method's robustness.
  • The continuous p-values enable more flexible multiple-comparison corrections across the many tests performed in a typical study.

Load-bearing premise

The complex-valued time-frequency coefficients must follow the probability distribution required by the generalized linear model family and link function for the likelihood-ratio test to produce correctly calibrated p-values.

What would settle it

Generate many independent trials under the null hypothesis of zero coherence, compute GLM p-values for each, and verify that those p-values are uniformly distributed between zero and one; any systematic deviation would indicate that the distributional assumption does not hold.

Figures

Figures reproduced from arXiv: 2510.05559 by Ariane E. Rhone, Brian J. Dlouhy, Christopher K. Kovach, Md Rakibul Mowla, Sukhbinder Kumar.

Figure 1
Figure 1. Figure 1: Representative driver and observation. Top: 20 s snippet of the respiration driver x(t) (blue, z-scored) and simulated observation y(t) = x(t) + n(t) (gray). Middle: Power spectral densities of x and y (0–1.2 Hz, dB scale; Welch); the dashed line marks the breathing frequency fbr. Bottom: Coherence amplitude C(f) computed from DBT coefficients via (1). Example shown at Ctrue = 0.60; the DBT-measured observ… view at source ↗
Figure 3
Figure 3. Figure 3: Detection power (raw p < 0.05) as a function of observed coherence amplitude at the breathing bin. GLM (orange) and phase ran￾domization (green) achieve higher power at lower observed coherence than circular-shift surrogates (blue). Thresholds for 50%, 80%, and 90% detection (C50/C80/C90) are summarized in Table I. TABLE I POWER THRESHOLDS AND SNR AT 80% POWER USING RAW p<0.05 (LOWER IS BETTER FOR C; MORE … view at source ↗
Figure 5
Figure 5. Figure 5: P-value agreement between GLM and the phase-randomization [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Runtime comparison. (Left) Runtime scaling versus number of surrogates (nperm; log scale) on the subsampled dataset (Ncoh = 100). Surrogate methods (circular shift, phase randomization) scale nearly linearly with nperm, whereas GLM is flat. (Right) Runtimes at nperm = 2000 over 10 runs (median ± std): circular shift 8.022 ± 0.411 s, phase randomization 7.558 ± 0.331 s, GLM 0.041 ± 0.002 s (∼ 198× and ∼ 186… view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a parametric GLM-based method for statistical inference on neural coherence using complex-valued time-frequency coefficients from the Demodulated Band Transform (DBT) or STFT. It validates the approach against surrogate-based testing (time-shift and phase randomization) on simulated neural signals driven by real respiration traces, claiming comparable or superior sensitivity, continuous stable p-values, and a roughly 200x computational speedup, with GLM detecting at coherence C=0.25 versus C=0.49 for surrogates at 80% power.

Significance. If the distributional assumptions of the GLM hold for real neural time-frequency coefficients, the method would provide a scalable, efficient alternative to surrogate testing for large EEG/iEEG datasets, enabling denser analyses across channels, frequencies, and subjects while avoiding discrete and unstable p-values.

major comments (2)
  1. [Validation and Results] Validation and Results sections: The simulations use broadband Gaussian noise added to signals, which satisfies Gaussian GLM assumptions by construction, but the manuscript provides no residual diagnostics, QQ plots, or goodness-of-fit tests on real EEG/iEEG DBT/STFT coefficients to verify that real/imaginary parts match the assumed family and link under both null (zero coherence) and alternative hypotheses. This assumption is load-bearing for the validity of the likelihood-ratio p-values and the reported sensitivity gains.
  2. [Results] Comparison of detection thresholds: The claim that GLM achieves detection at C=0.25 versus C=0.49 for surrogates (corresponding to 6-7 dB SNR improvement) at 80% power is presented without error bars, confidence intervals, or details on the number of Monte Carlo repetitions, making it difficult to evaluate the robustness of the sensitivity advantage.
minor comments (2)
  1. [Abstract] The abstract states that GLM produces 'continuous, stable p-values' but does not specify the exact GLM family, link function, or how complex coefficients are handled (e.g., real/imaginary parts or circular complex model).
  2. [Results] Runtime benchmarking claims a nearly 200x speedup; including the specific hardware, implementation details (e.g., number of surrogates used), and scaling with dataset size would strengthen the computational advantage claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the scope and limitations of our validation. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Validation and Results] Validation and Results sections: The simulations use broadband Gaussian noise added to signals, which satisfies Gaussian GLM assumptions by construction, but the manuscript provides no residual diagnostics, QQ plots, or goodness-of-fit tests on real EEG/iEEG DBT/STFT coefficients to verify that real/imaginary parts match the assumed family and link under both null (zero coherence) and alternative hypotheses. This assumption is load-bearing for the validity of the likelihood-ratio p-values and the reported sensitivity gains.

    Authors: We agree that direct verification of the distributional assumptions on real neural time-frequency data is important for establishing the method's broader applicability. The simulations were designed with broadband Gaussian noise specifically to create a controlled setting in which the GLM assumptions hold by construction, enabling an apples-to-apples comparison of inference procedures without confounding factors from unknown signal statistics. In the revised manuscript we will add residual diagnostics, QQ plots, and goodness-of-fit tests performed on real EEG and iEEG DBT/STFT coefficients drawn from publicly available datasets, evaluated separately under null (zero-coherence) and alternative conditions. revision: yes

  2. Referee: [Results] Comparison of detection thresholds: The claim that GLM achieves detection at C=0.25 versus C=0.49 for surrogates (corresponding to 6-7 dB SNR improvement) at 80% power is presented without error bars, confidence intervals, or details on the number of Monte Carlo repetitions, making it difficult to evaluate the robustness of the sensitivity advantage.

    Authors: We acknowledge that the detection-threshold comparison would be more robust if accompanied by quantitative uncertainty measures and explicit experimental details. The revised manuscript will report the exact number of Monte Carlo repetitions used to generate the power curves, include error bars or bootstrap confidence intervals on the estimated detection thresholds, and describe the precise procedure employed to identify the coherence values that yield 80% power for each method. revision: yes

Circularity Check

0 steps flagged

No circularity: standard GLM likelihood-ratio test on precomputed TF coefficients

full rationale

The paper proposes applying a GLM with likelihood-ratio test directly to complex-valued DBT or STFT coefficients for coherence significance testing. This is a standard parametric procedure whose validity rests on distributional assumptions rather than any equation that defines the target coherence in terms of the fitted GLM parameters or vice versa. Validation uses simulated Gaussian-noise signals and real respiration traces, but the reported sensitivity gains and speedups are empirical comparisons against surrogate methods, not reductions by construction. No self-citation chains, uniqueness theorems, or ansatzes are invoked to force the central result. The derivation chain is self-contained and does not collapse to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard statistical assumptions for GLM applicability to complex coefficients and on the validity of the simulation protocol; no new entities are postulated.

axioms (1)
  • domain assumption Complex time-frequency coefficients from DBT or STFT follow a distribution compatible with the chosen GLM family and link function for likelihood-ratio testing.
    Invoked when the GLM is applied directly to the coefficients to generate p-values.

pith-pipeline@v0.9.0 · 5796 in / 1253 out tokens · 35380 ms · 2026-05-18T09:42:11.763840+00:00 · methodology

discussion (0)

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Reference graph

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