Bayesian Tensor Modeling of High-Dimensional Neuroimaging Data

Neuroimaging has played a pivotal role in advancing the understanding of neurological and psychiatric conditions by providing comprehensive insights into structural and functional brain changes. Techniques such as magnetic resonance imaging (MRI), positron emission tomography (PET), and diffusion tensor imaging (DTI) generate high-dimensional data that can be used to identify biomarkers indicative of disease progression. While these data offer valuable opportunities for early diagnosis and personalized treatment, their sheer dimensionality and spatial complexity present significant challenges, including the risk of overfitting, increased computational demands, and the curse of dimensionality. In this thesis, we contribute to research in high-dimensional neuroimaging data by developing several novel statistical approaches to (1) classify disease phenotype, (2) predict median or the tails of the distribution of cognitive scores, and (3) investigate brain voxels that are associated with different parts of the distribution of cognitive performance scores, bringing insights into the longitudinal trajectory of the disease progression. First, we introduce a data augmentation-based Bayesian classification model incorporating tensor-valued covariates that achieves dimension reduction and the preservation of spatial information. We propose two data augmentations: a support vector machine (SVM) type of classifier, and a logistic regression classifier. Implementation follows an efficient Markov chain Monte Carlo (MCMC). After assessing the classification accuracy and parameter estimation through simulation studies, we further illustrate our method in a neuroimaging application using cortical thickness MRI data from the Alzheimer’s Disease Neuroimaging Initiative. Second, we introduce a novel Bayesian tensor quantile regression for high-dimensional longitudinal imaging data with the aim of investigating how brain-behavior associations change over time. The model estimates both effects that are consistent across visits and patterns unique to each visit that contribute to the overall longitudinal trajectory. A tensor decomposition is employed on the tensor coefficients to reduce dimensionality and preserve spatial configuration. We incorporate multiway shrinkage priors to model the visit-invariant tensor coefficients and variable selection priors on the tensor margins of the visit-specific effects. A Markov chain Monte Carlo sampling algorithm is developed. We examine the model performance in parameter estimation, feature selection, and prediction through simulation studies. In the end, we bring new insights into the analysis of Alzheimer's disease data by providing a fuller picture of the relationship between the imaging voxels and different parts of the distributions of the cognitive scores. Finally, we conclude the thesis by summarizing the research performed and discussing future work.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2025

Author dc:creator

• Lyu, Rongke

Advisors dc:contributor.advisor

• Vannucci, Marina
• Kundu, Suprateek

• Bayesian Statistics
• High-dimensional neuroimaging

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/118515

OAI identifier oai:identifier

oai:repository.rice.edu:1911/118515