We establish a bijection between marginal independence models on $n$ random variables and split closed order ideals in the poset of partial set partitions. We also establish that every discrete marginal independence model is toric in cdf coordinates. This generalizes results of Boege, Petrovic, and Sturmfels and Drton and Richardson, and provides a unified framework for discussing marginal independence models.

翻译：我们在$n$个随机变量上的边际独立性模型与部分集合划分偏序集中的分裂闭序理想之间建立了双射。同时，我们证明每个离散边际独立性模型在累积分布函数坐标下都是环面的。这一结果推广了Boege、Petrovic与Sturmfels以及Drton与Richardson的结论，并为讨论边际独立性模型提供了统一框架。