The topic of this paper is testing exchangeability using e-values in the batch mode, with the Markov model as alternative. The null hypothesis of exchangeability is formalized as a Kolmogorov-type compression model, and the Bayes mixture of the Markov model w.r. to the uniform prior is taken as simple alternative hypothesis. Using e-values instead of p-values leads to a computationally efficient testing procedure. In the appendixes I explain connections with the algorithmic theory of randomness and with the traditional theory of testing statistical hypotheses. In the standard statistical terminology, this paper proposes a new permutation test. This test can also be interpreted as a poor man's version of Kolmogorov's deficiency of randomness.

翻译：本文研究在批量模式下，以马尔可夫模型作为备择假设，利用e值检验可交换性的问题。可交换性的零假设被形式化为柯尔莫哥洛夫型压缩模型，而马尔可夫模型相对于均匀先验的贝叶斯混合则被作为简单备择假设。使用e值代替p值得到了计算高效的检验程序。在附录中，本文阐释了该方法与算法随机性理论及传统统计假设检验理论的联系。按照标准统计术语，本文提出了一种新的置换检验。该检验也可视为柯尔莫哥洛夫随机性缺陷的简易版本。