Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

D. Andrew Brown

Committee Member

Xinyi Li

Committee Member

Daniel B. Rowe

Committee Member

Xiaoqian Sun


Functional magnetic resonance imaging (fMRI) plays a crucial role in neuroimaging, enabling the exploration of brain activity through complex-valued signals. Traditional fMRI analyses have largely focused on magnitude information, often overlooking the potential insights offered by phase data, and therefore, lead to underutilization of available data and flawed statistical assumptions. This dissertation proposes two efficient, fully Bayesian approaches for the analysis of complex-valued functional magnetic resonance imaging (cv-fMRI) time series.

Chapter 2 introduces the model, referred to as CV-sSGLMM, using the real and imaginary components of cv-fMRI data and sparse spatial generalized linear mixed model prior. This model extends the Cartesian model proposed by Lee et al. (2007) through the incorporation of Gaussian Markov random fields (GMRFs) and autoregressive models, enabling the capture of both spatial and temporal correlations in cv-fMRI data. Notably, CV-sSGLMM utilizes brain parcellation and parallel computation techniques to achieve reduction in computational time comparing with the current state-of-the-art, without sacrificing predictive accuracy.

Chapter 3 presents the model characterizing magnitude and phase of the cv-fMRI data, referred to as CV-M&P, which builds upon the polar model proposed by Rowe (2005a) This model provides a nuanced mapping of brain activity by mapping magnitude and phase activations individually in response to a stimulus. In doing so, it addresses a significant gap in the current literature—specifically, the lack of models that efficiently incorporate phase information through Bayesian methods.

Collectively, both models outperform existing approaches in some key predictive metrics and deepen our understanding of the inherent complexities of cv-fMRI signals. These advancements are promising for enhancing our understanding of healthy brain functions and may offer valuable insights for early diagnosis of neurological disorders.



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