Objective. Most BCIs have to undergo a calibration session in which data is recorded to train decoders with machine learning. Only recently zero-training methods have become a subject of study. This work proposes a probabilistic framework for BCI applications which exploit event-related potentials (ERPs). For the example of a visual P300 speller we show how the framework harvests the structure suitable to solve the decoding task by (a) transfer learning, (b) unsupervised adaptation, (c)

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... model and (d) dynamic stopping. Approach. A simulation study compares the proposed probabilistic zero framework (using transfer learning and task structure) to a state-of-the-art supervised model on n = 22 subjects. The individual influence of the involved components (a)-(d) are investigated. Main results. Without any need for a calibration session, the probabilistic zero-training framework with inter-subject transfer learning shows excellent performance-competitive to a state-of-the-art supervised method using calibration. Its decoding quality is carried mainly by the effect of transfer learning in combination with continuous unsupervised adaptation. Significance. A high-performing zero-training BCI is within reach for one of the most popular BCI paradigms: ERP spelling. Recording calibration data for a supervised BCI would require valuable time which is lost for spelling. The time spent on calibration would allow a novel user to spell 29 symbols with our unsupervised approach. It could be of use for various clinical and non-clinical ERP-applications of BCI.