In this dissertation, we develop two novel statistical models to analyze functional magnetic resonance imaging (fMRI) data. FMRI data is complex and pose considerable challenges when being analyzed. One issue, central to the models proposed, is the direct inclusion of where is activation expected and the physiological constraints that dictate where neural activity is plausible. In particular, information on areas of expected activation and biological plausibility of occurrence is incorporated within the statistical model. Inclusion of such information enables a cognitive scientist's expertise and belief to be an explicit component of the analysis. Smith et al. (2003) showed through a spatial Bayesian variable selection (SBVS) framework that such information may be readily dealt with. Although their model is restrictive in several dimensions, they have outlined a viable framework with great potential. The models proposed are built upon this framework and extend its applicability and flexibility.;The first model proposed in Chapter 3 modifies SBVS to include, what can be viewed as, a thresholding mechanism within. This allows activation to be favored if the regression parameter exceeds a prespecified threshold. The second model proposed, outlined in Chapter 4, defines a general SBVS framework to analyze data from a hierarchical structure. This model greatly enhances the applicability of SBVS since it permits inferences to be generalized to the larger population as opposed to a single subject. Furthermore, it allow us to account for anatomical heterogeneity across subjects. Both models are applied to two separate fMRI experiments and results suggest wide applicability of these methods.
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