论文标题
Borel数据结构中的可交换法律
Exchangeable Laws in Borel Data Structures
论文作者
论文摘要
通过统计实践的激励，类别理论术语用于在抽象框架中引入Borel数据结构和研究交换性。显示了De Finetti定理的概括，并使用自然变换来呈现功能表示定理（FRTS）。后者的证明是基于D.N. Hoover提供的经典结果，为整数有限元组提供了可交换阵列的功能表示，以及Borel数据结构的普遍性结果。一类特殊的Borel数据结构是阵列型数据结构，它们是使用索引系统的新概念引入的。研究映射到阵列的自然变换提供了明确的FRT版本，在示例中与众所周知的Aldous-Hoover-hoover-kallenberg-type frts相吻合（共同）可交换阵列。摘要“索引算术”提出了统一并概括了有关交换性理论文献中常见的技术论证。最后，类别理论方法用于概述如何从统计实践中激发分开交换性的抽象概念。
Motivated by statistical practice, category theory terminology is used to introduce Borel data structures and study exchangeability in an abstract framework. A generalization of de Finetti's theorem is shown and natural transformations are used to present functional representation theorems (FRTs). Proofs of the latter are based on a classical result by D.N.Hoover providing a functional representation for exchangeable arrays indexed by finite tuples of integers, together with an universality result for Borel data structures. A special class of Borel data structures are array-type data structures, which are introduced using the novel concept of an indexing system. Studying natural transformations mapping into arrays gives explicit versions of FRTs, which in examples coincide with well-known Aldous-Hoover-Kallenberg-type FRTs for (jointly) exchangeable arrays. The abstract "index arithmetic" presented unifies and generalizes technical arguments commonly encountered in the literature on exchangeability theory. Finally, the category theory approach is used to outline how an abstract notion of seperate exchangeability can be derived, again motivated from statistical practice.
