A remarkable equivalence between non-stationary precise and stationary imprecise uncertainty models in computable randomness

The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, such randomness involves precise uncertainty models, and it is only recently that imprecision has been introduced into this field. As a consequence, the investigation into how imprecision alters our view on random sequences has only just begun. In this contribution, we establish a close and surprising connection between precise and imprecise uncertainty models in this randomness context. In particular, we show that there are stationary imprecise models and non-stationary precise models that have the exact same set of computably random sequences. We also discuss the possible implications of this result for a statistics based on imprecise probabilities