We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced probabilistic divide-and-conquer (PDC) technique. Our first application is a recursive PDC: it samples the least significant bit of each entry in the table, motivated by the fact that the bits of a geometric random variable are independent. The second application is via PDC deterministic second half, where one divides the sample space into two pieces, one of which is deterministic conditional on the other; this approach is highlighted via an exact sampling algorithm in the \(2\times n\) case. Finally, we also present a generalization to the sampling algorithm where each entry of the table has a specified marginal distribution.

中文翻译：

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通过概率分治法随机抽样列联表

我们基于最近引入的概率分而治之（PDC）技术，提出了一种对任意大小和约束条件的权变表进行随机抽样的新方法。我们的第一个应用是递归PDC：由于几何随机变量的位是独立的，因此对表中每个条目的最低有效位进行采样。第二个应用程序是通过PDC确定性下半部分进行的，其中一个将样本空间分为两部分，其中一个是确定性的，而另一条件是确定性的。这种方法在\（2 \ times n \）情况下通过精确的采样算法得到强调。最后，我们还对采样算法进行了概括，其中表的每个条目都有指定的边际分布。