论文标题
随机换位表
Random Transpositions on Contingency Tables
论文作者
论文摘要
应变表是代表2条数据的统计信息中有用的对象。使用固定的行和列总和，总共$ n $条目，应急表对应于$ s_n $的抛物线双coset。 $ s_n $的统一分布引起了Fisher-Yates分配，该分布经典，用于用于独立的卡方测试。然后，$ s_n $上的Markov链可以通过双cosets通信在应急表的空间上诱导随机过程。 $ s_n $上的随机转置马尔可夫链在应急表的空间上诱导了自然的“交换”马尔可夫链。马尔可夫链的固定分布是Fisher-Yates分布。本文描述了马尔可夫链，并表明本征函数是Fisher-Yates分布的正交多项式。讨论了混合时间的结果，以及与应急表上均匀分布的采样的连接以及数据分析。
Contingency tables are useful objects in statistics for representing 2-way data. With fixed row and column sums, and a total of $n$ entries, contingency tables correspond to parabolic double cosets of $S_n$. The uniform distribution on $S_n$ induces the Fisher-Yates distribution, classical for its use in the chi-squared test for independence. A Markov chain on $S_n$ can then induce a random process on the space of contingency tables through the double cosets correspondence. The random transpositions Markov chain on $S_n$ induces a natural `swap' Markov chain on the space of contingency tables; the stationary distribution of the Markov chain is the Fisher-Yates distribution. This paper describes this Markov chain and shows that the eigenfunctions are orthogonal polynomials of the Fisher-Yates distribution. Results for the mixing time are discussed, as well as connections with sampling from the uniform distribution on contingency tables, and data analysis.
