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Abstract
Subtle alterations in brain network topology often evade detection by traditional statistical methods. To address this limitation, we introduce a Bayesian inference framework for topological comparison of brain networks that probabilistically models within- and between-group dissimilarities. The framework employs Markov chain Monte Carlo sampling to estimate posterior distributions of test statistics and Bayes factors, enabling graded evidence assessment beyond binary significance testing. Simulations confirmed statistical consistency to permutation testing. Applied to fMRI data from the Duke-UNC Alzheimer’s Disease Research Center, the framework detected topology-based network differences that conventional permutation tests failed to reveal, highlighting its enhanced sensitivity to early or subtle brain network alterations in clinical neuroimaging.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/5303_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/XukunZhu-6/Bayesian-Topological-Brain-Networks
Link to the Dataset(s)
Duke/UNC Alzheimer’s Disease Research Center (ADRC) resting-state fMRI dataset: https://dukeuncadrc.org/
BibTex
@InProceedings{ZhuXuk_Bayesian_MICCAI2026,
author = { Zhu, Xukun AND Lutz, Michael W. AND Songdechakraiwut, Tananun},
title = { { Bayesian Topological Analysis of Brain Networks } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16894},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
This paper introduces a Bayesian framework that uses probability to compare brain network structures. It provides richer evidence through Bayes factors, allowing researchers to measure the exact strength of differences between clinical groups. Real-world tests on Alzheimer’s data show this method is much more sensitive to early, subtle brain changes that traditional methods often miss. Additionally, the approach is more computationally efficient, making it better suited for analyzing large medical datasets.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
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Enhanced Sensitivity to Subtle Alterations: A key strength is the method’s superior sensitivity in detecting early pathological changes. The framework successfully identified topological network differences related to amyloid accumulation, which traditional permutation tests failed to reveal.
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Superior Computational Efficiency: The Bayesian approach demonstrates better scalability for large datasets compared to standard permutation testing. While permutation test execution time grows linearly with the number of resamples, the MCMC-based Bayesian framework requires significantly less total execution time, making it highly feasible for large-cohort clinical studies.
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Rigorous Multi-Stage Evaluation: The work is supported by a strong evaluation strategy that includes both simulated experiments (confirming consistency with classical tests) and real-world application to fMRI data from an Alzheimer’s Disease Research Center.
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- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
The authors acknowledge that confirming very subtle network shifts in preclinical stages requires much larger datasets than the one used in this study. The current sample size may not be enough to definitively prove these early changes across different populations.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The major factor for accept is that the paper introduces a novel Bayesian framework that shows superior sensitivity in detecting subtle preclinical Alzheimer’s biomarkers where traditional tests fail.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #2
- Please describe the contribution of the paper
The main contribution of this paper is the use and validation of a Bayesian framework for analyzing topological features of functional brain network derived from fMRI data.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
The major strength of this work is the introduction of a Bayesian framework to better capture network topology compared to traditional frequentist statistics. This makes the results more interpretable and transparent while eliminating arbitrary statistical cutoffs.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
There are several major weaknesses in this paper. First and foremost, I am not confident this is a novel application. The authors even mention that use of Bayesian hierarchical/multilevel models in the future directions. But this approach has been established for several years now (Chen et al., 2019, Neuroinformatics). So, I am not sure what this paper is adding to the literature and I did not see anything currently in the work that explicitly states how this is different than other Bayesian fMRI network approaches. Second, there needs to be more details about fMRI processing, especially the connectivity metric used to generate the connectivity matrices. This can have a massive effect on results. Third, there is no justification given for the use of Wasserstein distance within this approach. The first paragraph is all about this metric but the clinical or neurobiological meaning for differences in this metric are never given. Last, an image of a brain with subnetworks that have dissimilar Wasserstein distance or even a schematic explaining the metric and intended analyses.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not provide sufficient information for reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(2) Reject — should be rejected, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
While I do prefer Bayesian statistics, it is difficult to see how this adds anything to the literature since their future directions section named analyses that have been around since at least 2019, but likely earlier. It also isn’t clear how the framework is specific to MIC or CAI since it is a general Bayesian framework instead of one that is imaging specific.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #3
- Please describe the contribution of the paper
The paper proposes a Bayesian framework for comparing brain network topology by modeling pairwise topological distances between subjects derived from persistent homology. Instead of relying on permutation tests, the method estimates posterior distributions of within- and between-group differences, providing credible intervals, probabilities, and Bayes factors to quantify uncertainty and evidence. Applied to fMRI data, the approach aims to offer a more informative and potentially more sensitive alternative for detecting group-level differences in functional brain networks.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.The paper combines persistent homology–based representations of brain networks with Bayesian statistical inference. This integration is interesting because it replaces traditional permutation testing with a probabilistic framework that provides richer outputs (e.g., posterior distributions and Bayes factors), enabling more nuanced interpretation of group differences. 2.The authors model Wasserstein-based distances using a Gamma distribution with suitable priors, acknowledging their non-negative and skewed nature. This is a principled choice that improves over naive Gaussian assumptions and shows good alignment between data properties and modeling. 3.The method is applied to fMRI data stratified by amyloid and tau status, which is an important and timely problem. The observed stronger effects for tau compared to amyloid are consistent with known disease progression, supporting the biological plausibility of the approach.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1.The main components are already well established: persistent homology for brain networks, Wasserstein distances for persistence diagrams, and Bayesian hypothesis testing. The method mainly combines these by replacing permutation tests with a Bayesian model, representing an incremental extension. 2.The model assumes independence of pairwise distances, which is incorrect since distances share subjects. This likely inflates confidence and Bayes factors. The key amyloid result is not robust and disappears in the sensitivity analysis, weakening the main claim. 3.Experiments are not sufficiently comprehensive. Simulations are simplistic, and real-data evaluation uses a private dataset with limited protocol details. The method should be validated on public datasets with clearly described preprocessing and evaluation protocols, and compared with stronger baselines (such as other graph-based methods or machine learning methods) to demonstrate practical advantage.
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper tackles an important problem, group-level discrimination of brain networks in Alzheimer’s disease, by combining topological analysis with Bayesian inference. While the individual components (persistent homology, Wasserstein distances, and Bayesian testing) are well known, bringing them together into a single probabilistic framework is still interesting and offers a more informative alternative to standard permutation testing. The work would benefit from stronger validation. In particular, simulation experiments on more complex and realistic scenarios (for example, varying noise levels or effect sizes), as well as evaluation on public datasets with clearly described protocols, would significantly strengthen the paper and make the conclusions more convincing.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Author Feedback
We thank the reviewers and AC for their careful reading. We address the major concerns below, grouped by theme.
1.Novelty vs. existing Bayesian fMRI methods (R3, R4). R3 notes that our future-work mention of Bayesian hierarchical models overlaps with Chen et al. (2019) and asks how this work differs from existing Bayesian fMRI approaches. The distinction lies in the modeling target. Chen et al. and related methods place priors on regional scalar effects (activation values, connectivity-matrix entries) to address multiple testing in mass-univariate analyses. Our framework instead performs Bayesian inference on a fundamentally different object: pairwise Wasserstein distances between persistence diagrams(Sec. 2.1), global, multiscale topological summaries of the functional connectome. To our knowledge, no prior work performs Bayesian inference on the distribution of topological network distances. The specific contribution (Sec. 2.2) is a gamma likelihood on within/between Wasserstein distances with log-normal priors on the mean, yielding posterior inference and Bayes factors. Our future-work mention of “Bayesian hierarchical” denotes extending this topological-distance likelihood with subject-level priors, a different pipeline level from Chen-style region-level modeling.
2.Independence assumption and amyloid robustness (R4). R4 raises that within/between distances share subjects, violating independence, and notes that the amyloid effect attenuates under the subject-level analysis. This is addressed in Sec. 3 Sensitivity Analysis (Table 3): a patient-level summary aggregates distances per subject, removing shared-subject dependence. Two findings are central. (i) Tau-related topological differences remain decisive under both the primary and patient-level models(BF10 = 1.12×10^36 and 6.53×10^3), demonstrating robustness to the independence assumption. (ii) The amyloid effect attenuates under the stricter model, which is biologically consistent with amyloid representing an earlier, subtler preclinical stage than tau (Sec. 3; Discussion). The framework correctly separates strong from subtle signals rather than uniformly inflating evidence — a methodological strength.
3.fMRI pipeline, connectivity, and Wasserstein interpretation (R3). Sec. 3 reports fMRIPrep preprocessing on the ADRC cohort with AAL-116 parcellation, following the pipeline of [19]; connectivity matrices were computed via Pearson correlation between regional BOLD time series, with a filtration over correlation thresholds yielding the persistence diagrams used in Sec. 2.1.Wasserstein distances quantify differences in the birth/death structure of connected components (H0) and cycles (H1) — capturing how functional modules form, merge, and dissolve across scales. Such multiscale reorganization is a recognized correlate of large-scale network disruption in neurodegeneration (Sec. 1; ref. [19]; see also Songdechakraiwut, Shen & Chung, MICCAI21; Chung et al., ISBI19; Lee et al., TMI12).
4.Validation, baselines, simulations (R2, R4). R2 raises sample-size concerns; R4 asks about public datasets and method baselines. Permutation testing — the standard non-parametric baseline — is reported alongside our Bayesian results in all experiments (Tables 1–3). Simulations on stochastic block models provide controlled validation with known ground truth. The ADRC cohort further provides biological ground truth via amyloid and tau PET, a stronger anchor than label-only validation. Replication in larger preclinical cohorts is the principal limitation, stated in Sec. 4. 5.MIC/CAI relevance (R3). The framework targets and is validated on fMRI-based discrimination of clinical groups in Alzheimer’s disease — a core medical-imaging-and-computing problem. Topological brain-network analysis is an active MICCAI direction this Bayesian framework extends.
We hope these clarifications address the major concerns and respectfully ask the reviewers to reconsider their assessments.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
The paper received mixed scores (WA, WA, and R) in the initial review. While the methodological contribution is appreciated by all reviewers, weaknesses including limited data size and description, validity of assumption, and rational on the experiments. Please address the concerns from the reviewers especially the ones from Rev#3.
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
There is a debate that this work is a simple Bayesian analysis approach. While the method may be straight forward, it captures subtle changes in graph topology from brain fMRI with statistical evidence. Moreover, majority of the reviewers suggest acceptance of the paper.
Meta-review #2
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
The authors have done a good job addressing the main critiques. This work would be of interest to MICCAI.
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
This paper introduces a Bayesian framework that operates on Wasserstein distances between persistence diagrams to compare brain network topologies, offering a probabilistic alternative to traditional permutation tests. The authors clarified that prior works focus on region-level scalar effects, whereas their framework uniquely models global, multiscale topological summaries. Furthermore, the authors addressed Reviewer 4’s concern regarding the independence assumption of pairwise distances by pointing to their patient-level sensitivity analysis. Overall, the methodological integration of persistent homology with Bayesian inference is sound and represents a valuable contribution to the community.