Bayesian Uncertainty Quantification for fMRI Functional Connectivity via Simulation-Based Inference

Simon Carter; Zeming Kuang; Lilianne R. Mujica-Parodi; Helmut H. Strey

stat.MLSep 24, 2026

Bayesian Uncertainty Quantification for fMRI Functional Connectivity via Simulation-Based Inference

Authors: Simon Carter, Zeming Kuang, Lilianne R. Mujica-Parodi, Helmut H. Strey

Organizations: Applied Mathematics and Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook NY 11794-5281, USA · Biomedical Engineering Department and Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook NY 11794-5281, USA · Santa Fe Institute, Santa Fe, NM, USA

Abstract

Optimizing fMRI scan duration and spatial resolution is critical for experimental design, yet traditional correlation-based approaches cannot quantify uncertainty or disentangle scanner measurement noise from true neural variability across subjects. Without principled uncertainty bounds, researchers cannot know whether a protocol is long enough to reliably estimate connectivity, or whether between-subject differences reflect biological variation or noise. We present a Bayesian framework modeling BOLD dynamics as coupled Ornstein-Uhlenbeck processes, using Sequential Neural Posterior Estimation to obtain connectivity posteriors while accounting for frequency-independent measurement noise across the BOLD spectrum. Applied to N = 28 healthy controls (55 scans) at 7T using a functional network atlas (65 DMN regions), the framework quantifies uncertainty across its sources: scanner noise, subject variability, and acquisition length. Spatial analysis identifies a mean of 46 voxels per ROI, roughly half of typical region sizes, as sufficient to achieve 90% of asymptotic precision. At the single-subject level, 7T reaches its within-session precision plateau in approximately 7 minutes versus 10 minutes for 3T, a 40% reduction in required scan time, providing the first direct, model-based quantification of the scan-time advantage conferred by higher field strength. At the population level, 3T requires roughly 37 times more per-subject scan time than 7T for the pooled curves to converge, confirming a consistent advantage of higher field strength at every timescale. Together these findings provide concrete, scanner-specific guidance for protocol optimization, with direct implications for reducing acquisition costs and improving the reliability of connectivity-based clinical biomarkers. We provide code enabling researchers to derive these bounds from their own data.

Figures & tables

Figure 1: A. Example posterior distribution from the toy model for a case with high true correlation ( $\rho>0.5$ ). The posterior distribution (blue) is centered close to the true correlation value (red dashed line), with the noisy Pearson correlation coefficient (orange dashed line) and posterior mean (green solid line) also indicated. B. The equivalent case for low true correlation ( $|\rho|<0.1$ ), showing the posterior distribution (blue) again centered near the true value (red dashed line). C. A calibration plot showing empirical coverage versus credibility level. The curve lying above the diagonal reference line ( $y=x$ ) indicates conservative posterior distributions, with actual coverage exceeding nominal credibility levels.

Figure 2: A. Each point represents a pair of regions within the Default Mode Network. Of 2,080 total candidate region pairs, 1,302 were removed for failing a voxel homogeneity test ( $R^{2}<0.5$ ), which assesses whether the correlation estimate behaves asymptotically as voxels are added. The remaining 411 pairs are those where the ratio of the posterior standard deviation to the posterior mean was less than 1, indicating sufficient confidence in the correlation estimate. The x-axis shows the number of voxels required to reach 90% of the final correlation estimate (obtained by averaging all voxels), and the y-axis shows this ratio, where lower values indicate greater confidence that a true correlation exists. Notably, many region pairs achieve reliable estimates with half or fewer of the total voxels. B. Density distribution of the number of voxels at which each region pair reached 90% of its asymptotic correlation estimate, across the 411 pairs shown in A . The approximately uniform distribution, with a mean of 46 voxels, indicates that the minimum number of voxels required for stable estimates is highly region-specific rather than governed by a single global threshold.

Figure 3: A. Average number of inconclusive region pairs as a function of relative scan length $\lambda$ for the Bipolar (7T) and HCP-YA (3T) datasets, extended to the extrapolated global regime. Here $\lambda=1$ corresponds to the full 730-timepoint Bipolar acquisition ( $\approx$ 10 minutes). Bipolar (7T) matches the conclusiveness that HCP-YA (3T) attains at $\lambda_{\mathrm{eq}}^{\mathrm{glob}}=200$ with only $\lambda\approx 162.38$ , confirming that higher field strength requires less scan time to achieve equivalent precision. Both global thresholds fall far outside any practical session, shown here to establish the theoretical precision ceiling of each field strength. Regions are defined by the Seitzman atlas (2,080 pairs). B. Local within-session view, restricted to $\lambda\in[0.1,1]$ . Bipolar (7T) matches the conclusiveness of the full 10-minute HCP-YA (3T) acquisition at $\lambda_{\mathrm{eq}}^{\mathrm{loc}}=0.715$ (approximately 7 minutes). A 7T scan of only 7 minutes therefore achieves the same within-session precision as a full 10-minute 3T scan.

Figure 4: A. Proportion of inconclusive region pairs as a function of number of subjects $N$ for the Bipolar (7T) and HCP-YA (3T) resting-state datasets. Individual posteriors are rescaled under the $1/\sqrt{n}$ approximation before concatenation to form the population-level distribution. The Bipolar (7T) cohort consistently yields fewer inconclusive region pairs than HCP-YA (3T) at equivalent $N$ , confirming that the scan-time advantage of 7T extends to and is amplified at the population level. B. Per-subject scan-length view showing relative acquisition length $\lambda\in[0.1,1]$ for the pooled distributions. Bipolar (7T) matches the conclusiveness of the full HCP-YA (3T) acquisition at $\lambda_{\mathrm{eq}}^{\mathrm{loc}}\approx 0.492$ , meaning 7T requires only about half the per-subject scan time of 3T to achieve equivalent population-level precision within session. In the extrapolated global regime, the advantage widens further: Bipolar (7T) matches the conclusiveness that HCP-YA (3T) attains at $\lambda_{\mathrm{eq}}^{\mathrm{glob}}=200$ with only $\lambda\approx 5.46$ , meaning pooled 3T requires roughly 37 times more per-subject scan time than pooled 7T to reach the same precision.

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Time Series Forecasting Spatiotemporal Forecasting Neuroimaging Multivariate Time Series Forecasting

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Functional magnetic resonance imaging (fMRI) enables noninvasive investigation of brain function, while short clinical scan durations, arising from human and non-human factors, usually lead to reduced data quality and limited statistical power for neuroimaging research. In this paper, we propose BrainCast, a novel spatio-temporal forecasting framework specifically tailored for whole-brain fMRI time series forecasting, to extend informative fMRI time series without additional data acquisition. It formulates fMRI time series forecasting as a multivariate time series prediction task and jointly models temporal dynamics within regions of interest (ROIs) and spatial interactions across ROIs. Specifically, BrainCast integrates a Spatial Interaction Awareness module to characterize inter-ROI dependencies via embedding every ROI time series as a token, a Temporal Feature Refinement module to capture intrinsic neural dynamics within each ROI by enhancing both low- and high-energy temporal components of fMRI time series at the ROI level, and a Spatio-temporal Pattern Alignment module to combine spatial and temporal representations for producing informative whole-brain features. Experimental results on resting-state and task fMRI datasets from the Human Connectome Project demonstrate the superiority of BrainCast over state-of-the-art time series forecasting baselines. Moreover, fMRI time series extended by BrainCast improve downstream cognitive ability prediction, highlighting the clinical and neuroscientific impact brought by whole-brain fMRI time series forecasting in scenarios with restricted scan durations.

Abstract

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