论文标题
离散概率理论中的足够统计和分裂的基础
Sufficient Statistics and Split Idempotents in Discrete Probability Theory
论文作者
论文摘要
足够的统计量是捕获概率函数（通道，内核）的基本属性的确定性函数。正如托比亚斯·弗里茨（Tobias Fritz）最近以伴随形式显示的那样，可以用弦图来很好地表达足够的统计量。这种重新构造凸显了分裂的基础在Fisher-neyman分解定理中的作用。文献中出现了足够的统计量的例子，但主要是连续的概率。本文表明，在离散概率上还有几个基本示例。它们是在一些组合基础工作之后出现的，该基础揭示了相关的匕首分裂的基础，并表明足够的统计量是确定性的匕首。
A sufficient statistic is a deterministic function that captures an essential property of a probabilistic function (channel, kernel). Being a sufficient statistic can be expressed nicely in terms of string diagrams, as Tobias Fritz showed recently, in adjoint form. This reformulation highlights the role of split idempotents, in the Fisher-Neyman factorisation theorem. Examples of a sufficient statistic occur in the literature, but mostly in continuous probability. This paper demonstrates that there are also several fundamental examples of a sufficient statistic in discrete probability. They emerge after some combinatorial groundwork that reveals the relevant dagger split idempotents and shows that a sufficient statistic is a deterministic dagger epi.
