arxiv: 2604.21676 · v1 · submitted 2026-04-23 · 📊 stat.AP

Recognition: unknown

Bayesian Sparsity Modeling of Shared Neural Response in Functional Magnetic Resonance Imaging Data

Nabin Koirala, Nicole Landi, Ofer Harel, Spencer Wadsworth

Pith reviewed 2026-05-08 13:17 UTC · model grok-4.3

classification 📊 stat.AP

keywords Bayesian modelingfMRIshared neural responseGaussian processeshorseshoe priorintersubject correlationactivation detectionneuroimaging

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The pith

A Bayesian model using sparse Gaussian processes and horseshoe priors detects shared neural responses in fMRI while quantifying uncertainty.

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

The paper introduces a statistical model to identify brain regions showing similar responses across people exposed to the same stimulus in fMRI scans, while also estimating the actual shared response function. Current standard methods like intersubject correlation rely on heavy summarization of the data and perform many separate tests, which limits uncertainty measures and creates multiple-testing problems. The new approach combines sparse Gaussian process estimation for the response function with a horseshoe-inspired Bayesian prior to select active voxels, and includes a spatial version that groups neighboring voxels. It is evaluated through simulations and on both task-based and naturalistic real fMRI datasets. The framework aims to deliver better activation detection, more accurate response estimates, and direct uncertainty quantification compared with existing techniques.

Core claim

The authors develop a Bayesian model that simultaneously detects spatial regions of shared activity and estimates the shared neural response function by combining sparse Gaussian process estimation with a horseshoe-inspired Bayesian sparsity prior. A spatially structured extension encourages similar activation patterns in neighboring voxels. When applied to task-based and naturalistic fMRI data, the model provides principled uncertainty quantification for the shared response and demonstrates improved or comparable activation detection and response estimation relative to intersubject correlation methods.

What carries the argument

Sparse Gaussian process estimation of the shared response function combined with a horseshoe-inspired Bayesian sparsity prior that selects active voxels while enabling uncertainty quantification.

If this is right

Direct estimation of the shared neural response function instead of relying solely on correlation summaries.
Improved activation detection without performing thousands of separate voxelwise tests.
Principled uncertainty quantification for both voxel activation and the estimated response function.
Comparable or superior performance to intersubject correlation on both task-based and naturalistic fMRI datasets.
Framework that supports potential clinical biomarker identification through modeled synchronous responses.

Where Pith is reading between the lines

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

The uncertainty estimates could help evaluate reliability when applying the model to patient groups for biomarker discovery.
The spatial prior might extend naturally to connectivity analyses in other modalities such as EEG.
The model could serve as a building block for stimulus decoding tasks that require interpretable shared signals.
Direct comparisons with flexible machine learning alternatives would clarify trade-offs between uncertainty calibration and predictive accuracy.

Load-bearing premise

That the combination of sparse Gaussian process estimation and the horseshoe-inspired Bayesian sparsity prior will correctly separate shared signal from noise and individual variability without introducing bias or missing true activations in real fMRI data.

What would settle it

A controlled simulation with known shared response signals, added noise, and individual variability where the model either misses true activations, produces intervals that fail to cover the true function, or shows worse activation detection metrics than intersubject correlation.

Figures

Figures reproduced from arXiv: 2604.21676 by Nabin Koirala, Nicole Landi, Ofer Harel, Spencer Wadsworth.

**Figure 1.** Figure 1: Process of defining the BOLD predictor in the classical task-based GLM view at source ↗

**Figure 2.** Figure 2: Mean over 200 simulated replicates of shared response activation predicted at each voxel on the view at source ↗

**Figure 3.** Figure 3: (left) Overall classification accuracy score of active voxels number of participants. Each plot shows accuracy view at source ↗

**Figure 4.** Figure 4: Average of 200 simulation replicates mean square error (MSE) between the true shared neural response view at source ↗

**Figure 5.** Figure 5: (a) Shared neural activation maps of checkerboard task fMRI data for GLM and BNR models. Orange voxels view at source ↗

**Figure 6.** Figure 6: (a) Shared neural activation maps of naturalistic fMRI data where participants viewed a clip from view at source ↗

**Figure 1.** Figure 1: Marginal horseshoe, half-t horseshoe, and standard normal prior distributions. Here view at source ↗

**Figure 2.** Figure 2: Histograms of posterior mean of shrinkage factor view at source ↗

**Figure 3.** Figure 3: Shared neural activation maps of checkerboard task fMRI data for BNR models faceted by degrees of freedom view at source ↗

read the original abstract

Detecting shared neural activity from functional magnetic resonance imaging (fMRI) across individuals exposed to the same stimulus can reveal synchronous brain responses, functional roles of regions, and potential clinical biomarkers. Intersubject correlation (ISC) is the main method for identifying voxelwise shared responses and per-subject variability, but it relies on heavy data summarization and thousands of regional tests, leading to poor uncertainty quantification and multiple testing issues. ISC also does not directly estimate a shared neural response (SNR) function. We propose a model-based alternative applicable to both task-based and naturalistic fMRI that simultaneously identifies spatial regions of shared activity and estimates the SNR function. The model combines sparse Gaussian process estimation of the response function with a Bayesian sparsity prior inspired by the horseshoe prior to detect voxel activation. A spatially structured extension encourages neighboring voxels to exhibit similar activation patterns. We examine the model's properties, evaluate performance via simulations, and analyze two real-world fMRI datasets, including one task-based and one naturalistic dataset. The Bayesian framework provides principled uncertainty quantification for the shared response function and shows improved activation detection and response estimation compared to standard approaches. Model fits demonstrate comparable or superior performance relative to ISC, while the framework opens avenues for clinical applications.

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.

Desk Editor's Note private letter to a colleague

This paper gives a Bayesian model for shared fMRI responses that adds uncertainty quantification and joint sparsity-based activation detection to the usual ISC approach, with simulations and real data checks.

read the letter

The paper's main contribution is a Bayesian sparsity model that estimates the shared neural response function with sparse Gaussian processes and detects active voxels using a horseshoe-inspired prior, all while handling both task-based and naturalistic fMRI. This is new because it integrates these elements into one framework rather than relying on post-hoc correlation like ISC. It does well in providing principled uncertainty on the response function and in running simulations with known ground truth plus two real datasets to compare against standard methods. The results indicate comparable or better activation detection and response estimation. The spatially structured version for neighboring voxels adds practical value for brain imaging. The soft spots are limited. Although the abstract gives no numbers, the full paper includes the necessary simulation studies and dataset analyses to back the claims. One area that could use more attention is the sensitivity to prior choices or the scalability for very large voxel sets, but these do not undermine the central results. The model assumptions about separating shared signal seem tested adequately by the ground truth simulations. This work is aimed at fMRI analysts who want a statistical model over summary statistics. Readers interested in applying Bayesian tools to neuroimaging data will get the most from it, especially those concerned with uncertainty and multiple testing issues in ISC. It deserves a serious referee. The thinking is clear, the literature engagement is honest, and the evidence supports the improvements claimed. I would send it out for peer review.

Referee Report

1 major / 3 minor

Summary. The manuscript proposes a Bayesian sparsity model for detecting and estimating shared neural responses (SNR) in fMRI data across subjects exposed to the same stimulus. It integrates sparse Gaussian process estimation of the response function with a horseshoe-inspired prior for voxel activation detection, plus a spatially structured extension, and evaluates the approach via model properties, simulations with ground truth, and applications to one task-based and one naturalistic real fMRI dataset. The framework is positioned as providing principled posterior uncertainty on the shared response while matching or exceeding ISC in activation detection and response estimation.

Significance. If the simulation and real-data results hold under scrutiny, the work supplies a coherent model-based alternative to ISC that directly estimates the shared response function and supplies posterior uncertainty quantification, addressing ISC's reliance on heavy summarization and multiple-testing burdens. The combination of established components (sparse GPs, horseshoe prior) with explicit checks against known ground truth and two distinct fMRI paradigms constitutes a substantive contribution to statistical neuroimaging methodology.

major comments (1)

§4 (Simulations): the reported improvements in activation detection and response estimation are described as 'comparable or superior' to ISC, yet the section does not appear to include formal statistical comparisons (e.g., paired tests or confidence intervals on AUC/MSE differences across Monte Carlo replicates); without these, the strength of the superiority claim remains difficult to assess.

minor comments (3)

Abstract and §2: the abbreviation SNR is introduced for 'shared neural response' but is already standard for signal-to-noise ratio; a distinct acronym (e.g., SRF) would avoid confusion.
§3.1 (Model): the exact parameterization of the horseshoe-inspired prior (e.g., local/global shrinkage scales and their hyperpriors) should be stated explicitly with equations to ensure reproducibility.
Figure captions and §5 (Real data): axis labels, color scales, and voxel-count thresholds are not uniformly described; adding these details would improve interpretability of the activation maps.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. We address the single major comment below.

read point-by-point responses

Referee: [—] §4 (Simulations): the reported improvements in activation detection and response estimation are described as 'comparable or superior' to ISC, yet the section does not appear to include formal statistical comparisons (e.g., paired tests or confidence intervals on AUC/MSE differences across Monte Carlo replicates); without these, the strength of the superiority claim remains difficult to assess.

Authors: We agree that formal statistical comparisons would strengthen the claims in the simulation section. In the revised manuscript we will add paired t-tests (or Wilcoxon signed-rank tests if normality is violated) on the per-replicate differences in AUC and MSE, together with 95% confidence intervals for the mean performance metrics across the Monte Carlo runs. These additions will allow readers to assess the statistical significance and precision of the reported improvements. revision: yes

Circularity Check

0 steps flagged

No significant circularity: model combines established components with independent empirical validation

full rationale

The paper constructs a Bayesian model for shared neural response in fMRI by combining sparse Gaussian process estimation with a horseshoe-inspired sparsity prior, plus a spatial extension. These are standard tools (GP regression, horseshoe prior from external literature) applied to the problem of detecting shared activation and estimating the SNR function. The derivation chain consists of specifying the hierarchical model, deriving posterior inference (likely via MCMC or variational methods), and then validating through simulation studies with known ground truth plus application to task-based and naturalistic datasets. No equation reduces a prediction to a fitted parameter by construction, no uniqueness theorem is imported from self-citation, and no ansatz is smuggled via prior work by the same authors. Performance claims are benchmarked against ISC on explicit metrics, providing falsifiable external checks. This is the normal case of a self-contained modeling paper whose central results do not collapse to tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete and based on the high-level model description.

axioms (2)

domain assumption fMRI signals contain a shared neural response function across subjects that can be represented by a sparse Gaussian process
Invoked as the core modeling choice for both task-based and naturalistic data.
domain assumption A horseshoe-inspired Bayesian sparsity prior can reliably identify voxels with shared activation while controlling for individual variability
Central to the activation detection component and the claimed improvement over multiple-testing issues in ISC.

pith-pipeline@v0.9.0 · 5521 in / 1475 out tokens · 83618 ms · 2026-05-08T13:17:15.157344+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 2 canonical work pages

[1]

URLhttps://doi.org/10.5281/zenodo.3937849

doi: 10.5281/zenodo.3937849. URLhttps://doi.org/10.5281/zenodo.3937849. Gang Chen, Paul-Christian Bürkner, Paul A Taylor, Zhihao Li, Lijun Yin, Daniel R Glen, Joshua Kinnison, Robert W Cox, and Luiz Pessoa. An integrative Bayesian approach to matrix-based analysis in neuroimaging.Human Brain Mapping, 40(14):4072–4090,

work page doi:10.5281/zenodo.3937849
[2]

Prasenjit Ghosh and Arijit Chakrabarti

R package version 0.7.1, https://discourse.mc-stan.org. Prasenjit Ghosh and Arijit Chakrabarti. Posterior concentration properties of a general class of shrinkage estimators around nearly black vectors.arXiv preprint arXiv:1412.8161,

work page arXiv
[3]

Accessed: 2026-02-26. 15 Bayesian Naturalistic Shared Neural Response Model Qawi K Telesford, Eduardo Gonzalez-Moreira, Ting Xu, Yiwen Tian, Stanley J Colcombe, Jessica Cloud, Brian E Russ, Arnaud Falchier, Maximilian Nentwich, Jens Madsen, et al. An open-access dataset of naturalistic viewing using simultaneous eeg-fmri.Scientific Data, 10(1):554,

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