Abstract The article of Cho and Rubinstein-Salzedo seeks to cast doubt on our previous paper, which described a rigorous statistical test which can be applied to reversible Markov chains. In particular, Cho and Rubinstein-Salzedo seem to suggest that the test we describe might not be a reliable indicator of gerrymandering, when the test is applied to certain redistricting Markov chains. However, the examples constructed by Cho and Rubinstein-Salzedo in fact demonstrate a different point: that our test is not the same as another class of gerrymandering tests, which Cho and Rubinstein-Salzedo prefer. But we agree and emphasized this very distinction in our original paper. In this reply, we reply to the criticisms of Cho and Rubinstein-Salzedo, and discuss, more generally, the advantages of the various tests available in the context of detecting gerrymandering of political districtings.

中文翻译：

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了解我们的马尔可夫链重要性检验：对Cho和Rubinstein-Salzedo的答复

摘要Cho和Rubinstein-Salzedo的文章试图对我们先前的论文提出疑问，该论文描述了可以应用于可逆马尔可夫链的严格统计检验。特别是，Cho和Rubinstein-Salzedo似乎暗示，当该测试应用于某些重新划分的马尔可夫链时，该测试可能不是可靠的指标。但是，Cho和Rubinstein-Salzedo构造的示例实际上表明了不同的观点：我们的测试与Cho和Rubinstein-Salzedo偏爱的另一类gerrymandering测试不同。但是我们同意并在原始论文中强调了这一区别。在此回复中，我们回复了对Cho和Rubinstein-Salzedo的批评，并更广泛地讨论了