The purpose of brain mapping is to advance the

understanding of the relationship between structure and function in the human brain. Several techniques---with different advantages and

disadvantages---exist for recording neural activity. Functional magnetic resonance imaging (fMRI) has a high spatial resolution, but low temporal resolution. It also suffers from a low-signal-to-noise ratio in event-related experimental designs, which are commonly used to investigate neuronal brain activity. On the other hand, the high temporal resolution of electroencephalography (EEG) recordings allows to capture provoked event-related potentials. Though, 3D maps derived by EEG source reconstruction methods have a low spatial resolution, they provide complementary information about the location of neuronal activity. There is a strong interest in combining data from both modalities to gain a deeper knowledge of brain functioning through advanced statistical modeling.

In this thesis, a new Bayesian method is proposed for enhancing fMRI activation detection by the use of EEG-based spatial prior information in stimulus based experimental paradigms. This method builds upon a newly developed mere fMRI activation detection method. In general, activation detection corresponds to stimulus predictor components having an effect on the fMRI signal trajectory in a voxelwise linear model. We model and analyze stimulus influence by a spatial Bayesian variable selection scheme, and extend existing high-dimensional regression methods by incorporating prior information on binary selection indicators via a latent probit regression. For mere fMRI activation detection, the predictor consists of a spatially-varying intercept only. For EEG-enhanced schemes, an EEG effect is added, which is either chosen to be spatially-varying or constant. Spatially-varying effects are regularized by different Markov random field priors.

Statistical inference in resulting high-dimensional hierarchical models becomes rather challenging from a modeling perspective as well as with regard to numerical issues. In this thesis, inference is based on a Markov Chain Monte Carlo (MCMC) approach relying on global updates of effect maps. Additionally, a faster algorithm is developed based on single-site updates to circumvent the computationally intensive, high-dimensional, sparse Cholesky decompositions.

The proposed algorithms are examined in both simulation studies and real-world applications. Performance is evaluated in terms of convergency properties, the ability to produce interpretable results, and the sensitivity and specificity of corresponding activation classification rules. The main question is whether the use of EEG information can increase the power of fMRI models to detect activated voxels.

In summary, the new algorithms show a substantial increase in sensitivity compared to existing fMRI activation detection methods like classical SPM. Carefully selected EEG-prior information additionally increases sensitivity in activation regions that have been distorted by a low signal-to-noise ratio.