The conventional testing process quickly fails when applied to ML-based systems such as obstacle detection in vehicles: if an obstacle is not detected in a test, classical bug fixing is impossible and an AI system will always retain shortcomings. Test results can therefore only be interpreted statistically, which in turn requires test sets that are not only complete with respect to the operational design domain (ODD) of the system, but also representative of it. To this end, we introduce probabilistically extended ontologies (PEONs): ontologies describing the ODD, augmented with a probability distribution over the partitioning they induce. Instead of unmaintainable conditional probability tables, only marginal distributions and functionally described dependencies need to be specified; algorithms based on couplings and optimal transport complete this specification to a Bayesian network. From a PEON we derive the sampling of representative test cases, rigorous end-of-test criteria for given quality targets and significance levels, and methods for re-evaluating existing test results and for assessing the balance of training data. We demonstrate the practical modelling of a complex ODD using the example of automatic train operation.

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