Dai, Ning2019-06-122019-06-122019-04https://hdl.handle.net/11299/203581University of Minnesota Ph.D. dissertation. April 2019. Major: Statistics. Advisors: Galin Jones, Mark Fiecas. 1 computer file (PDF); x, 107 pages.Alzheimer’s disease (AD) is a degenerative brain disease and the most common form of dementia, yet no prevention methods or cures have been discovered. Neuroimaging studies of AD can help identify the causes and risk factors, improve diagnostic accuracy, and develop new treatments and preventions. Since the pathological processes that lead to AD begin years before the clinical syndrome, longitudinal studies are essential in characterizing regional changes in the structure and function of the brain that can be attributed to normal aging or disease progression. The statistical analysis of neuroimaging data is challenging due to the massive amount of data, a relatively weak signal of interest, and complicated temporal or spatial correlation structure in the data. Additionally, the longitudinal design exacerbates the modeling challenges in that one must account for correlation between the repeated measures. We analyze longitudinal clinical and imaging data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). In two case studies that address essentially different problems, we develop novel Bayesian models for analyzing longitudinal structural magnetic resonance imaging (MRI) and functional magnetic resonance imaging (fMRI) data to study potential markers for AD. Fitting the models requires Markov chain Monte Carlo (MCMC). To assess the reliability of estimating a vector of means associated with the target distribution using MCMC, we propose a multivariate method for assessing the Monte Carlo error, which is used for Bayesian inference in our case studies.enThesis or Dissertation