We present an application of Independent Component Analysis (ICA) to the discrimination of mental tasks for EEG-based Brain Computer Interface systems. ICA is most commonly used with EEG for artifact identification with little work on the use of ICA for direct discrimination of different types of EEG signals. By viewing ICA as a generative model, we can use Bayes' rule to form a classifier. We fit spatial filters and source distribution parameters simultaneously and investigate whether these are sufficiently informative to produce good results when compared to more traditional methods based on using temporal features as inputs to off-the-shelf classifiers. Experiments suggest that state-of-the-art results may indeed be found without explicitly using temporal features. We extend the method to using a mixture of ICA models, consistent with the assumption that subjects may have more than one approach to thinking about a specific mental task.