We study Doob's Consistency Theorem and Freedman's Inconsistency Theorem from the vantage point of computable probability and algorithmic randomness. We show that the Schnorr random elements of the parameter space are computably consistent, when there is a map from the sample space to the parameter space satisfying many of the same properties as limiting relative frequencies. We show that the generic inconsistency in Freedman's Theorem is effectively generic, which implies the existence of computable parameters which are not computably consistent. Taken together, this work provides a computability-theoretic solution to Diaconis and Freedman's problem of ``know[ing] for which [parameters] the rule [Bayes' rule] is consistent'', and it strengthens recent similar results of Takahashi on Martin-L\"of randomness in Cantor space.

翻译：我们从可计算概率与算法随机性的视角研究杜布一致性定理与弗里德曼非一致性定理。我们证明，当存在从样本空间到参数空间的映射满足与极限相对频率相似的诸多性质时，参数空间的施诺尔随机元素是可计算一致的。我们证明弗里德曼定理中的泛型非一致性是有效泛型的，这意味着存在不可计算一致的可计算参数。综合而言，本工作为戴康尼斯与弗里德曼提出的“确定[贝叶斯法则]对哪些[参数]具有一致性”问题提供了可计算性理论解，并强化了高桥近期在康托空间关于马丁-洛夫随机性的类似结果。