arXiv subjects

Wendy Meiring

Publications and source records attributed to Wendy Meiring.

7 recordsLinked to original sources

arXiv2026

Prior elicitation for Bayesian estimation of single-subject connectivity networks

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.

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arXiv2023

Clustering-Based Inter-Regional Correlation Estimation

A novel non-parametric estimator of the correlation between grouped measurements of a quantity is proposed in the presence of noise. This work is primarily motivated by functional brain network construction from fMRI data, where brain regions correspond to groups of spatial units, and correlation between region pairs defines the network. The challenge resides in the fact that both noise and intra-regional correlation lead to inconsistent inter-regional correlation estimation using classical approaches. While some existing methods handle either one of these issues, no non-parametric approaches tackle both simultaneously. To address this problem, we propose a trade-off between two procedures: correlating regional averages, which is not robust to intra-regional correlation; and averaging pairwise inter-regional correlations, which is not robust to noise. To that end, we project the data onto a space where Euclidean distance is used as a proxy for sample correlation. We then propose to leverage hierarchical clustering to gather together highly correlated variables within each region prior to inter-regional correlation estimation. We provide consistency results, and empirically show our approach surpasses several other popular methods in terms of quality. We also provide illustrations on real-world datasets that further demonstrate its effectiveness.

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arXiv2023

Predicting Distributions of Physical Activity Profiles in the NHANES Database Using a Partially Linear Fr\'echet Single Index Model

Object-oriented data analysis is a fascinating and evolving field in modern statistical science, with the potential to make significant contributions to biomedical applications. This statistical framework facilitates the development of new methods to analyze complex data objects that capture more information than traditional clinical biomarkers. This paper applies the object-oriented framework to analyze physical activity levels, measured by accelerometers, as response objects in a regression model. Unlike traditional summary metrics, we utilize a recently proposed representation of physical activity data as a distributional object, providing a more nuanced and complete profile of individual energy expenditure across all ranges of monitoring intensity. A novel hybrid Fr\'echet regression model is proposed and applied to US population accelerometer data from National Health and Nutrition Examination Survey (NHANES) 2011-2014. The semi-parametric nature of the model allows for the inclusion of nonlinear effects for critical variables, such as age, which are biologically known to have subtle impacts on physical activity. Simultaneously, the inclusion of linear effects preserves interpretability for other variables, particularly categorical covariates such as ethnicity and sex. The results obtained are valuable from a public health perspective and could lead to new strategies for optimizing physical activity interventions in specific American subpopulations.

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arXiv2022

A Mixed Model Approach for Estimating Regional Functional Connectivity from Voxel-level BOLD Signals

Resting-state brain functional connectivity quantifies the synchrony between activity patterns of different brain regions. In functional magnetic resonance imaging, each region comprises a set of spatially contiguous voxels at which blood-oxygen-level-dependent signals are acquired. The ubiquitous Correlation of Averages (CA) estimator, and other similar metrics, are computed from spatially aggregated signals within each region, and remain the quantifications of inter-regional connectivity most used by neuroscientists. Their popularity is primarily due to computational simplicity despite their demonstrable bias and lack of statistically principled justification. By leveraging linear mixed-effects models, both inter-regional and intra-regional correlation and measurement error can be explicitly modeled as signal variability sources. A novel computational pipeline, focused on subject-level inter-regional correlation parameters of interest, is developed to address the challenges of applying maximum likelihood estimation to such structured, high-dimensional spatiotemporal data. Simulation results confirm the superiority of the proposed estimator relative to CA in terms of both decreased bias and accurate confidence interval coverage across simulation settings. The proposed method is also applied to construct individual human brain networks for subjects from a Human Connectome Project test-retest database. Concordances between inter-regional correlation estimates demonstrate the potentially substantial scientific benefits of the proposed approach that reliably produces more consistent results than CA for test-retest scans of the same subject.

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arXiv2021

Fr\'echet single index models for object response regression

With the increasing availability of non-Euclidean data objects, statisticians are faced with the task of developing appropriate statistical methods for their analysis. For regression models in which the predictors lie in $\mathbb{R}^p$ and the response variables are situated in a metric space, conditional Fr\'echet means can be used to define the Fr\'echet regression function. Global and local Fr\'echet methods have recently been developed for modeling and estimating this regression function as extensions of multiple and local linear regression, respectively. This paper expands on these methodologies by proposing the Fr\'echet Single Index model, in which the Fr\'echet regression function is assumed to depend only on a scalar projection of the multivariate predictor. Estimation is performed by combining local Fr\'echet along with M-estimation to estimate both the coefficient vector and the underlying regression function, and these estimators are shown to be consistent. The method is illustrated by simulations for response objects on the surface of the unit sphere and through an analysis of human mortality data in which lifetable data are represented by distributions of age-of-death, viewed as elements of the Wasserstein space of distributions.

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arXiv2017

Analytic tractography: A closed-form solution for estimating local white matter connectivity with diffusion MRI

White matter structures composed of myelinated axons in the living human brain are primarily studied by diffusion-weighted MRI (dMRI). These long-range projections are typically characterized in a two-step process: dMRI is used to estimate the orientation of axons within each voxel, then these local orientations are linked together to estimate the spatial extent of putative white matter bundles. Tractography, the process of tracing bundles across voxels, either requires computationally expensive (probabilistic) simulations to model uncertainty in fiber orientation or ignores it completely (deterministic). Probabilistic simulation necessarily generates a finite number of trajectories, introducing "simulation error" to trajectory estimates. Here we introduce a method to analytically (via a closed-form solution) take an orientation distribution function (ODF) from each voxel and calculate the probabilities that a trajectory projects from a voxel into each directly adjacent voxel. We validate our method by demonstrating that probabilistic simulations converge to our analytically computed probabilities at the voxel level as the number of simulated seeds increases. We show that our method accurately calculates the ground-truth transition probabilities from a phantom dataset. As a demonstration, we incoroporate our analytic method for voxel transition probabilities into the Voxel Graph framework, creating a quantitative framework for assessing white matter structure that we call "analytic tractography". The long-range connectivity problem is reduced to finding paths in a graph whose adjacency structure reflects voxel-to-voxel analytic transition probabilities. We demonstrate this approach performs comparably to many current probabilistic and deterministic approaches at a fraction of the computational cost. Open source software software is provided.

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arXiv2014

Spatial prediction variance estimation based on covariance penalty

In practice rarely (if ever) is the spatial covariance known in spatial prediction problems. Often, prediction is performed after estimated spatial covariance parameters are plugged into the prediction equation. The estimated spatial association parameters arealso plugged into the prediction variance of the spatial predictor. However, simply plugging in spatial covariance parameter estimates into the prediction variance of the spatial predictor does not take into account the uncertainty in the true values of the spatial covariance parameters. Therefore the plug-in prediction variance estimate will underestimate the true prediction variance of the estimated spatial predictor, especially for small datasets. We propose a new way to estimate the prediction variance of the estimated spatial predictor based on a covariance penalty using parametric bootstrapping. Our new estimator is compared to three other prediction variance estimators proposed in literature. The new prediction variance estimator generally performs better than the plug in method for small datasets with weak spatial association, although sometimes it is second best among the four prediction variance estimators compared. Furthermore, the new prediction variance estimator could potentially be used in the case of non-normal prediction.

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