A Bayesian Model for Brain Network Functional Connectivity using PyMC3
Our brain network, as a complex integrative system, consists of many different regions. Each region has its own task and function and simultaneously shares structural and functional information. With the developed imaging techniques such as functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI), researchers can investigate the underlying brain functions related to human behaviors and some diseases or disorders in the nervous system such as major depressive disorder (MDD). In this thesis, we developed a Bayesian hierarchical spatiotemporal model that combined fMRI and DTI data jointly to enhance the estimation of resting-state functional connectivity. Structural connectivity from DTI data was utilized to construct an informative prior for functional connectivity based on resting-state fMRI data through the Cholesky decomposition in a mixture model. The analysis took the advantages of probabilistic programming package as PyMC3 and next-generation Markov Chain Monte Carlo (MCMC) sampling algorithm as No-U-Turn Sampler (NUTS). The simulation study with this advanced algorithm, illustrated reduced mean squared errors (MSEs) of estimation. Furthermore, through a case study of MDD, we applied our model to examine how the estimated functional connectivity was associated with tasks of episodic memory, executive function, processing speed and working memory.