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.

翻译：充分统计量是一种确定性函数，它捕捉了概率函数（通道、核）的关键性质。正如Tobias Fritz最近指出的那样，充分统计量可以用弦图以伴随形式优雅地表示。这一重新表述凸显了分裂幂等元在Fisher-Neyman分解定理中的作用。文献中已有充分统计量的相关例子，但主要出现在连续概率领域。本文证明，离散概率中也存在若干基础的充分统计量实例。这些实例在完成揭示相关dagger分裂幂等元的组合基础工作后显现，并表明充分统计量是一个确定性dagger满态射。