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The goal of any scientific discipline is to learn about nature, usually through the process of evaluating competing hypotheses for explaining observations. Brain research is no exception. Investigating brain function usually entails comparing models, expressed as mathematical equations, of how the brain works. The aim of this thesis is to provide and evaluate new model comparison techniques that facilitate this research. In addition, it applies existing comparison methods to disambiguate between hypotheses of how neuronal activity relates to blood ow, a topic known as neurovascular coupling. In neuroimaging, techniques such as functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) allow to routinely image the brain, whilst statistical frameworks, such as statistical parametric mapping (SPM), allow to identify regionally specific responses, or brain activations. In this thesis, SPM is first used to address the problem of neurovascular coupling, and compare different putative coupling functions, which relate fMRI signals to different features of the EEG power spectrum. These inferences are made using linear models and a model selection approach based on F-tests. Although valid, this approach is restricted to nested models. This thesis then focuses on the development of a Bayesian technique, to construct posterior model probability maps (PPMs) for group studies. PPMs are analogous to F-tests but not limited to nested hypotheses. The work presented here then focuses again on neurovascular coupling, this time from a mechanistic perspective, not afforded by linear models. For this purpose, a detailed biophysical framework is used to explore the contribution of synaptic and spiking activity in the generation of hemodynamic signals in visual cortex, using simultaneous EEG-fMRI. This approach is a special case of brain connectivity models. Finally, using fMRI data, this thesis validates a recently proposed Bayesian approach for quickly comparing large numbers of connectivity models based on inverting a single model.