论文标题
关于算法随机性中固定不精确和非平稳精确不确定性模型之间的（dis）相似性
On the (dis)similarities between stationary imprecise and non-stationary precise uncertainty models in algorithmic randomness
论文作者
论文摘要
算法随机性领域研究了某些给定的不确定性模型，无限二进制序列是随机的。从经典上讲，这种随机性的Martingale理论概念涉及精确的不确定性模型，直到最近才将不精确引入到这种情况下。结果，对不精确的调查如何改变我们对Martingale理论随机序列的看法才刚刚开始。在我们允许不可兼容的不确定性模型的贡献中，我们在这种随机性环境中建立了确切和不精确模型之间的紧密而令人惊讶的联系。特别是，我们表明存在具有完全相同的随机序列集完全相同的固定不精确模型和不可兼容的非平稳精确模型。我们还对基于不精确概率的统计数据的可能含义进行了初步讨论，并阐明了这种情况下不精确和不可兼容的精确不确定性模型的实际（IR）相关性。
The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, martingale-theoretic notions of such randomness involve precise uncertainty models, and it is only recently that imprecision has been introduced into this context. As a consequence, the investigation into how imprecision alters our view on martingale-theoretic random sequences has only just begun. In this contribution, where we allow for non-computable uncertainty models, 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-computable non-stationary precise models that have the exact same set of random sequences. We also give a preliminary discussion of the possible implications of our result for a statistics based on imprecise probabilities, and shed some light on the practical (ir)relevance of both imprecise and non-computable precise uncertainty models in that context.
