The assumption that the human brain employs information processing in terms of probability distributions and uses Bayesian inference to update beliefs about the world has been summed up in the Bayesian brain hypothesis (BBH). Because of its unifying quality of how to understand brain functioning, the BBH has gained increasing attention in computational neuroscience. Particularly in information processing of sequences spread out in time, the BBH provides an apt framework for computational models of ways in which the human brain updates beliefs about its environment according to new input. Since there is no direct measure of the belief distributions that are assumed under the BBH, empirical research relies on studying neural surprise responses such as the preattentive mismatch negativity (MMN), that can be measured using electroencephalography (EEG). Usually, the MMN is found as a more negative EEG potential in response to a rare deviant auditory event embedded in a stream of frequent standard stimuli. Because the magnitude of any surprise-related activity should depend on the current belief held by the observer, surprise can be quantified in relation to this belief. However, there are multiple ways to realize a computational Bayesian model of sequential belief updates as well as of surprise quantification. The scope of this thesis comprises the analysis of several computational Bayesian models for surprise responses as well as their application to the somatosensory MMN as a proxy for surprise. After an introduction into computational models of brain functioning in Chapter 1, Chapter 2 examines various Bayesian models for belief updates of two-item sequences, categorizes their respective features and derives specific surprise functions for each model category. Further, as an illustration of the models’ properties on a test case, I determine surprise regressors from an extensive model space and contrast them against each other. Chapter 3 complements this theoretical approach by empirically investigating neural surprise in the MMN. Moreover, it addresses the question of perceptual modality-independence of mismatch- related surprise by concentrating on the little-studied somatosensory system. Here, participants received consecutive median nerve stimulation of two clearly perceivable but differentiable intensi- ties according to a Markov-chain roving-like paradigm. To investigate surprise in the somatosensory system as measured from EEG, I use not only established averaging-techniques for event-related potentials, but also a much more fine-grained single-trial analysis approach that employs the com- putational models and surprise functions from Chapter 2. As a result, the analysis of surprise regressors from Bayesian models shows that seemingly small differences in model specifications can lead to vastly disparaging, and sometimes counter-intuitive surprise-estimates. While the EEG-study revealed a small MMN-effect after stimulus-alternations, no definite evidence was found regarding an underlying computational model and surprise function. However, on a descriptive level, confidence corrected surprise for stimulus as well as transition probability had the best explanatory value of all computational models tested. In conclusion, my theoretical approach emphasizes the importance of scrutiny in constructing Bayesian models for surprise. The mere definition of a computational model for surprise responses as “Bayesian” is insufficient, since multiple Bayesian models can make contradicting predictions about data patterns. Hence, Bayesian models have to be carefully built and their assumptions made specific. Furthermore, in light of the study from Chapter 3, the nature of the somatosensory MMN does not warrant the assumption of a modality-independent process in the brain to be the basis of the component. Further research should vary factors of attention and predictability in somatosensory MMN paradigms as well as scrutinize computational models of surprise for the MMN in all perceptual modalities in order to discern a modality-independent part inherent in the MMN relating to surprise.