Feature selection is a machine learning technique that has many interesting applications in the area of brain-computer interfaces (BCIs). Here we show how automatic relevance determination (ARD), which is a Bayesian feature selection technique, can be applied in a BCI system. We present an computationally efficient algorithm that uses ARD to compute sparse linear discriminants. The algorithm is tested with data recorded in a P300 BCI and with P300 data from the BCI competition 2004. The achieved classification accuracy is competitive with the accuracy achievable with a support vector machine (SVM). At the same time the computational complexity of the presented algorithm is much lower than that of the SVM. Moreover, it is shown how visualization of the computed discriminant vectors allows to gain insights about the neurophysiological mechanisms underlying the P300 paradigm.