基于串图的分解与贝叶斯反演
Disintegration and Bayesian Inversion via String Diagrams
摘要：
分解和贝叶斯反演的概念是条件概率论的基础。它们从一个联合状态或从一个已经给定的通道（在相反的方向上）产生通道，作为条件概率。这些概念存在于文献中，在具体的情况下，但在这里提出了抽象的图形公式。由此产生的抽象描述用于证明条件概率论中的基本结果。分解和贝叶斯反演的存在性进行了讨论离散概率，也为测度论概率-通过标准波莱尔空间和通过似然。最后，分解和贝叶斯反演的有用性说明了几个例子。
英文摘要：
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability --- via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
