Various categories have been proposed as targets for the denotational semantics of higher-order probabilistic programming languages. One such proposal involves joint probability distributions (couplings) used in Bayesian statistical models with conditioning. In previous treatments, composition of joint measures was performed by disintegrating to obtain Markov kernels, composing the kernels, then reintegrating to obtain a joint measure. Disintegrations exist only under certain restrictions on the underlying spaces. In this paper we propose a category whose morphisms are joint finite measures in which composition is defined without reference to disintegration, allowing its application to a broader class of spaces. The category is symmetric monoidal with a pleasing symmetry in which the dagger structure is a simple transpose.

翻译：多种范畴已被提出作为高阶概率编程语言指称语义的目标。其中一种方案涉及贝叶斯统计模型中带有条件化的联合概率分布（耦合）。在以往的处理中，联合测度的组合通过以下步骤实现：先进行分解以获得马尔可夫核，再组合这些核，最后重新积分得到联合测度。然而，分解操作仅在特定空间约束下存在。本文提出了一种以有限联合测度为态射的范畴，其组合定义无需借助分解，从而可应用于更广泛的空间类别。该范畴具有对称幺半结构及令人愉悦的对称性，其dagger结构表现为简单的转置操作。