A brain-computer interface (BCI) is a system that enables control of devices or communication with other persons, only through cerebral activity, without using muscles. The main application for BCIs is assistive technology for disabled persons. Examples for devices that can be controlled by BCIs are artificial limbs, spelling devices, or environment control systems. BCI research has seen renewed interest in recent years, and it has been convincingly shown that communication via a BCI is in principle feasible. However, present day systems still have shortcomings that prevent their widespread application. In part, these shortcomings are caused by limitations in the functionality of the pattern recognition algorithms used for discriminating brain signals in BCIs. Moreover, BCIs are often tested exclusively with able-bodied persons instead of conducting tests with the target user group, namely disabled persons. The goal of this thesis is to extend the functionality of pattern recognition algorithms for BCI systems and to move towards systems that are helpful for disabled users. We discuss extensions of linear discriminant analysis (LDA), which is a simple but efficient method for pattern recognition. In particular, a framework from Bayesian machine learning, the so-called evidence framework, is applied to LDA. An algorithm is obtained that learns classifiers quickly, robustly, and fully automatically. An extension of this algorithm allows to automatically reduce the number of sensors needed for acquisition of brain signals. More specifically, the algorithm allows to perform electrode selection. The algorithm for electrode selection is based on a concept known as automatic relevance determination (ARD) in Bayesian machine learning. The last part of the algorithmic development in this thesis concerns methods for computing accurate estimates of class probabilities in LDA-like classifiers. These probabilities are used to build a BCI that dynamically adapts the amount of acquired data, so that a preset, approximate bound on the probability of misclassifications is not exceeded. To test the algorithms described in this thesis, a BCI specifically tailored for disabled persons is introduced. The system uses electroencephalogram (EEG) signals and is based on the P300 evoked potential. Datasets recorded from five disabled and four able-bodied subjects are used to show that the Bayesian version of LDA outperforms plain LDA in terms of classification accuracy. Also, the impact of different static electrode configurations on classification accuracy is tested. In addition, experiments with the same datasets demonstrate that the algorithm for electrode selection is computationally efficient, yields physiologically plausible results, and improves classification accuracy over static electrode configurations. The classification accuracy is further improved by dynamically adapting the amount of acquired data. Besides the datasets recorded from disabled and able-bodied subjects, benchmark datasets from BCI competitions are used to show that the algorithms discussed in this thesis are competitive with state-of-the-art electroencephalogram (EEG) classification algorithms. While the experiments in this thesis are uniquely performed with P300 datasets, the presented algorithms might also be useful for other types of BCI systems based on the EEG. This is the case because functionalities such as robust and automatic computation of classifiers, electrode selection, and estimation of class probabilities are useful in many BCI systems. Seen from a more general point of view, many applications that rely on the classification of cerebral activity could possibly benefit from the methods developed in this thesis. Among the potential applications are interrogative polygraphy ("lie detection") and clinical applications, for example coma outcome prognosis and depth of anesthesia monitoring.