Computational issues in using Bayesian hierarchical methods for the spatial modeling of fMRI data.

University of Minnesota Ph.D. dissertation. August 2010. Major: Statistics. Advisor: Jones, Galin. 1 computer file (PDF); xii, 152 pages, appendices A. Ill. (some col.)One of the major objectives of fMRI (functional magnetic resonance imaging) studies is to determine which areas of the brain are activated in response to a stimulus or task. To make inferences about task-specific changes in underlying neuronal activity, various statistical models are used such as general linear models (GLMs). Frequentist methods assessing human brain activity using data from fMRI experiments rely on results from the theory of Gaussian random fields. Such methods have several limitations. The Bayesian paradigm provides an attractive framework for making inference using complex models and bypassing the multiple comparison problems. We propose a Bayesian model which not only takes into account the complex spatio-temporal relationships in the data while still being computationally feasible, but gives a framework for addressing other interesting questions related to how the human brain works. We study the properties of this approach and demonstrate its performance on simulated and real examples