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The field of algorithmic randomness studies what it means for infinite binarysequences to be random for some given uncertainty model. Classically,martingale-theoretic notions of such randomness involve precise uncertaintymodels, and it is only recently that imprecision has been introduced into thiscontext. As a consequence, the investigation into how imprecision alters ourview on martingale-theoretic random sequences has only just begun. In thiscontribution, where we allow for non-computable uncertainty models, weestablish a close and surprising connection between precise and impreciseuncertainty models in this randomness context. In particular, we show thatthere are stationary imprecise models and non-computable non-stationary precisemodels that have the exact same set of random sequences. We also give apreliminary discussion of the possible implications of our result for astatistics based on imprecise probabilities, and shed some light on thepractical (ir)relevance of both imprecise and non-computable preciseuncertainty models in that context.

On the (dis)similarities between stationary imprecise and non-stationary precise uncertainty models in algorithmic randomness