In statistical inference, retrodiction is the act of inferring potential causes in the past based on knowledge of the effects in the present and the dynamics leading to the present. Retrodiction is applicable even when the dynamics is not reversible, and it agrees with the reverse dynamics when it exists, so that retrodiction may be viewed as an extension of inversion, i.e., time-reversal. Recently, an axiomatic definition of retrodiction has been made in a way that is applicable to both classical and quantum probability using ideas from category theory. Almost simultaneously, a framework for information flow in in terms of semicartesian categories has been proposed in the setting of categorical probability theory. Here, we formulate a general definition of retrodiction to add to the information flow axioms in semicartesian categories, thus providing an abstract framework for retrodiction beyond classical and quantum probability theory. More precisely, we extend Bayesian inference, and more generally Jeffrey's probability kinematics, to arbitrary semicartesian categories.

翻译：在统计推断中，回溯推断是指基于当前效应的知识以及导致当前状态的动力学过程，推断过去潜在原因的行为。即使动力学过程不可逆，回溯推断依然适用；当存在逆动力学过程时，它与之保持一致，因此回溯推断可被视为逆过程（即时间反转）的一种扩展。近期，基于范畴论的思想，研究者提出了一种既适用于经典概率也适用于量子概率的回溯推断公理化定义。几乎同时，在范畴概率论框架下，基于半笛卡尔范畴的信息流框架也被提出。本文中，我们为半笛卡尔范畴的信息流公理补充了回溯推断的一般性定义，从而建立了超越经典与量子概率理论的回溯推断抽象框架。更精确地说，我们将贝叶斯推断以及更为一般的杰弗里概率动力学，推广至任意半笛卡尔范畴。