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arxiv: 2605.02587 · v1 · submitted 2026-05-04 · 📊 stat.ME

Prior elicitation for Bayesian estimation of single-subject connectivity networks

Yiye Jiang , Alice Chevaux , Wendy Meiring , Alex Petersen , Guillaume Kon Kam King , Julyan Arbel , Sophie Achard This is my paper

Pith reviewed 2026-05-08 18:47 UTC · model grok-4.3

classification 📊 stat.ME
keywords Bayesian inferencefunctional connectivityfMRIprior elicitationcorrelation matricessingle-subject analysisuncertainty quantificationneuroimaging
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The pith

Expert-informed Bayesian priors on correlation matrices enable robust single-subject functional connectivity inference from fMRI data with built-in uncertainty quantification.

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

This paper develops Bayesian methods for inferring functional connectivity graphs from single-subject resting-state fMRI time series. It introduces novel priors on correlation matrices and a dedicated elicitation framework that converts expert beliefs about expected correlation levels and variability into interpretable hyperparameters. Paired with a Gaussian likelihood, the priors deliver computational advantages while producing full posterior distributions over connectivity weights instead of fixed point estimates. These posteriors regularize the estimates for robustness, quantify uncertainty, and support follow-on tasks such as identifying significant connections through credible sets. The approach fills a gap where few Bayesian options exist for single-subject data and shows better performance than existing methods in the reported experiments.

Core claim

The paper claims that novel priors on correlation matrices, constructed via a prior elicitation procedure translating beliefs on correlation magnitude and spread into hyperparameters, when combined with a Gaussian likelihood yield posterior distributions for the connectivity graph. These distributional weights produce more robust point estimates through regularization, permit evaluation of uncertainty, and enable procedures for identifying significant connectivities based on posterior probabilities and credible sets. The framework also confers computational advantages and outperforms most existing constant-weight methods on single-subject resting-state fMRI data.

What carries the argument

The central mechanism is the prior elicitation framework that maps expert beliefs about the expected level and variability of correlations into hyperparameters for constructing priors on correlation matrices.

Load-bearing premise

Expert beliefs about the expected level and variability of correlations can be reliably translated into hyperparameter values that improve inference on real single-subject fMRI data without introducing bias or over-regularization.

What would settle it

A controlled simulation study with known ground-truth connectivity graphs where the method either recovers the graph with higher error than competing approaches or produces credible sets that systematically exclude true edges would falsify the claims of robustness and reliable significance identification.

Figures

Figures reproduced from arXiv: 2605.02587 by Alex Petersen, Alice Chevaux, Guillaume Kon Kam King, Julyan Arbel, Sophie Achard, Wendy Meiring, Yiye Jiang.

Figure 1
Figure 1. Figure 1: First-order approximation of ERkk′ by Pkk′. Motivated by the asymptotic relation in Theorem 5, the black line shows the simple linear approximation ERkk′ ≈ 0.066Pkk′, for K = 20. Therefore, we propose to use a IW/SIW1 mixture as a feasible computational alternative of SIW, b ∈ (0, 1), via which we explore an enhanced solution of IW. Next, view at source ↗
Figure 2
Figure 2. Figure 2: Approximation of V(Rkk′) by ν. The fitted approximation is 0.09 + exp(−0.23ν − 1.55). We summarize the proposed approximation formulas for E(Rkk′) and V(Rkk′) in Prop￾erty 7, as a counterpart of Proposition 1 for IW. Property 7. Let Σ ∼ SIW1(P, ⃗σ, ν) with K = 20, ν > 3, and denote R = R(Σ). For 14 view at source ↗
Figure 3
Figure 3. Figure 3: Values of EΣ∼SIW1(P,⃗σ,ν)(Σkk) projected onto σ 2 k . The red dots corresponds to ν = 4. In practice, we fix first ν according to the desired VΣ∼SIW1(P,⃗σ,ν)(Rll′). Given the value fixed, we approximate EΣ∼SIW1(P,⃗σ,ν)(Σkk) using a linear function of σk. Then σk is fixed such that EΣ∼SIW1(P,⃗σ,ν)(Σkk) equals sample variance. a similar model interpretation, that νr, r = 0, 1 controls the weight of prior cor… view at source ↗
Figure 4
Figure 4. Figure 4: Posterior mean correlation matrices from the two rats. The hyperparameter settings view at source ↗
Figure 5
Figure 5. Figure 5: Sample correlations between the 20 selected regions of the live rat. view at source ↗
Figure 6
Figure 6. Figure 6: Posterior mean correlation matrices for dead and live rats. view at source ↗
Figure 7
Figure 7. Figure 7: Posterior distributions of two Rkk′ are shown. By taking into account the uncer￾tainty that is variance, Bayesian inference gives a more robust result than thresholding point estimates. Correlation −1.0 −0.5 0.0 0.5 1.0 Correlation −1.0 −0.5 0.0 0.5 1.0 (a) (b) (c) (d) view at source ↗
Figure 8
Figure 8. Figure 8: Posterior mode correlation matrices masked by insignificant pairs, of the dead rat view at source ↗
Figure 9
Figure 9. Figure 9: Edge detection results for dead and live rats (top/bottom). view at source ↗
read the original abstract

Inference of brain functional connectivity networks from resting-state fMRI data is a key focus in neuroimaging. This paper introduces new Bayesian approaches for inferring a functional connectivity graph from multivariate resting-state fMRI time series of a single subject. Our methods rely on novel Bayesian priors on correlation matrices and a dedicated prior elicitation framework, which translates prior beliefs about the expected level and variability of correlations into interpretable hyperparameter choices, enabling the construction of expert-informed priors. When combined with a Gaussian likelihood, these priors also exhibit computational advantages. Compared to most existing methods for this problem that estimate constant weights, our model provides distributional weights defined by the posterior distributions for the connectivity graph, yielding more robust point estimates through the regularizing effect of expert-informed priors, evaluating uncertainty, and enabling a range of post-inference analyses. In particular, we derive a procedure for identifying significant connectivities based on posterior distributions of weights and credible sets. To the best of our knowledge, only one existing Bayesian functional connectivity model is applicable to single-subject resting-state fMRI data, making our approach a valuable addition to the field and demonstrating superior performance in our experiments.

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 introduces a Bayesian framework for single-subject functional connectivity inference from resting-state fMRI time series. It proposes novel priors on correlation matrices together with an elicitation procedure that converts expert beliefs about expected correlation level and variability into hyperparameter values. Combined with a Gaussian likelihood, the model is claimed to deliver computational advantages, posterior distributional weights on edges, regularized point estimates, uncertainty quantification, and a credible-set procedure for declaring significant connections. The authors position the work as a valuable addition to the field, noting that only one prior Bayesian single-subject method exists and asserting superior performance in their experiments.

Significance. If the elicitation procedure can be shown to improve inference without systematic bias, the framework would supply a practical route for incorporating domain knowledge into single-subject connectivity estimation. This would add uncertainty-aware, regularized estimates and post-hoc significance testing that are absent from most existing single-subject approaches.

major comments (2)
  1. [Abstract] Abstract: the claim of 'superior performance in our experiments' and 'computational advantages' is stated without any quantitative metrics, baseline comparisons, data-exclusion criteria, or model-checking results. This absence makes it impossible to evaluate whether the elicitation step actually delivers the asserted robustness or efficiency gains.
  2. [Prior elicitation framework (methods)] The central modeling assumption that expert beliefs about correlation level and variability can be translated into hyperparameter values that improve real-data inference without introducing bias or over-regularization is load-bearing for all performance claims, yet no sensitivity analyses, simulation recovery studies, or cross-validation against held-out expert judgments are described.
minor comments (2)
  1. [Abstract] The abstract states that 'only one existing Bayesian functional connectivity model is applicable to single-subject resting-state fMRI data' but does not cite that reference; the claim should be supported by a specific citation.
  2. [Methods] Notation for the correlation-matrix prior and its hyperparameters should be introduced with an explicit equation early in the methods section to allow readers to trace how elicited beliefs map to the prior.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of 'superior performance in our experiments' and 'computational advantages' is stated without any quantitative metrics, baseline comparisons, data-exclusion criteria, or model-checking results. This absence makes it impossible to evaluate whether the elicitation step actually delivers the asserted robustness or efficiency gains.

    Authors: We agree that the abstract would be strengthened by including specific quantitative support for the performance and computational claims. The experiments section provides comparisons against existing single-subject methods with metrics on edge recovery, regularization effects, and runtime, along with details on data processing. We will revise the abstract to concisely report key metrics (e.g., improvements in accuracy and computational efficiency) and reference the relevant experimental setup, while retaining the high-level summary tone. revision: yes

  2. Referee: [Prior elicitation framework (methods)] The central modeling assumption that expert beliefs about correlation level and variability can be translated into hyperparameter values that improve real-data inference without introducing bias or over-regularization is load-bearing for all performance claims, yet no sensitivity analyses, simulation recovery studies, or cross-validation against held-out expert judgments are described.

    Authors: The elicitation procedure is indeed central, and the manuscript details how expert beliefs are mapped to hyperparameters with application to real data. We acknowledge that explicit validation against bias is needed to support the claims. We will add sensitivity analyses (varying hyperparameter settings and assessing impact on posterior estimates), simulation recovery experiments (recovering known correlation matrices under elicited priors), and, where feasible, checks against held-out expert assessments in the revised methods and results sections. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper's core contribution is a prior elicitation procedure that maps external expert beliefs about correlation levels and variability into hyperparameters for correlation-matrix priors, then combines these with a standard Gaussian likelihood for single-subject fMRI time series. No equations, derivations, or claimed predictions reduce by construction to fitted parameters, self-defined quantities, or load-bearing self-citations. The posterior weights, credible sets, and significance procedure follow directly from standard Bayesian updating without tautological reduction to the inputs. The single existing Bayesian comparator is cited externally rather than via author-overlapping uniqueness theorems. This structure yields an independent modeling framework whose performance claims rest on external validation rather than internal redefinition.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on a standard Gaussian likelihood for fMRI time series and on the assumption that expert beliefs can be faithfully encoded as hyperparameters; no new physical entities are postulated.

free parameters (1)
  • hyperparameters of the correlation-matrix prior
    Chosen via the elicitation procedure to reflect expected level and variability of correlations; these are not fitted to the observed data but set from prior beliefs.
axioms (1)
  • domain assumption fMRI time series follow a multivariate Gaussian distribution
    Invoked when combining the new priors with the likelihood; standard in many connectivity models but not derived here.

pith-pipeline@v0.9.0 · 5512 in / 1370 out tokens · 100471 ms · 2026-05-08T18:47:58.630571+00:00 · methodology

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    Relation between the paper passage and the cited Recognition theorem.

    Our methods rely on novel Bayesian priors on correlation matrices and a dedicated prior elicitation framework, which translates prior beliefs about the expected level and variability of correlations into interpretable hyperparameter choices

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Reference graph

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