Flexible Spatial Priors in Bayesian Neuroimaging: GMRF, NNGP, and Deep GMRF

Author

Boyoung Hur, Clemson UniversityFollow

Date of Award

12-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Committee Chair/Advisor

D. Andrew Brown

Committee Member

Christopher McMahan

Committee Member

Qiong Zhang

Committee Member

Xinyi Li

Abstract

Structural neuroimaging is essential for understanding neurological disorders such as Alzheimer’s disease, enabling accurate delineation of brain regions through image segmentation. Among various segmentation methods, multi-atlas-based approaches like label fusion have become leading techniques. In statistics, Bayesian hierarchical models for label fusion are increasingly favored for their ability to incorporate uncertainty and prior knowledge. Also, a key challenge in modeling neuroimaging data is spatial dependence among image voxels, making the choice of spatial prior critical—particularly in high-resolution settings where segmentation accuracy and computational efficiency are both essential.

This dissertation proposes fully Bayesian spatial hierarchical models that explore two flex- ible spatial priors. Chapter 2 introduces a model with the Nearest Neighbor Gaussian Process (NNGP) prior, which replaces the traditional Gaussian Markov Random Field (GMRF). By con- ditioning only on a small set of nearest neighbors to approximate the full Gaussian Process (GP), the NNGP achieves a balance between flexibility and scalability. Chromatic Gibbs sampling and spatial parcellation are employed to reduce Markov Chain Monte Carlo (MCMC) runtime without sacrificing segmentation accuracy.

Chapter 3 presents a Deep GMRF (DGMRF) prior learned from multiple atlas images using Convolutional Neural Networks (CNNs). This approach constructs a data-driven precision matrix Q, allowing more adaptive spatial structure than predefined models like GMRF or NNGP. The resulting hybrid framework combines deep learning with Bayesian inference, offering both flexibility and interpretability.

Simulation studies and hippocampal segmentation on ADNI MRI data show that NNGP and DGMRF priors outperform traditional GMRFs. These results highlight the value of combining modern spatial priors with Bayesian methods to improve neuroimaging segmentation.

Recommended Citation

Hur, Boyoung, "Flexible Spatial Priors in Bayesian Neuroimaging: GMRF, NNGP, and Deep GMRF" (2025). All Dissertations. 4147.
https://open.clemson.edu/all_dissertations/4147