论文标题
贝叶斯的更新是光学构成的
Bayesian Updates Compose Optically
论文作者
论文摘要
贝叶斯的规则告诉我们如何扭转因果过程，以根据新的证据来更新我们的信念。如果该过程被认为具有复杂的组成结构，我们可能会询问组成组件过程的反转是否给出与整体反转相同的信念更新。我们肯定地回答了这个问题，表明相关的组成结构恰恰是镜头模式的，并且我们可以将贝叶斯倒置视为相应纤维类别中国家依赖性形态的特定实例。我们定义了（混合）贝叶斯镜头的一般概念，并讨论这些镜头的（未）合法性，而当它们的违反组件是确切的贝叶斯倒置时。对于离散状态和连续状态，我们都在抽象和具体地证明了我们的主要结果，并注意说明共同的结构。
Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component processes gives the same belief update as the inversion of the whole. We answer this question affirmatively, showing that the relevant compositional structure is precisely that of the lens pattern, and that we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a corresponding fibred category. We define a general notion of (mixed) Bayesian lens, and discuss the (un)lawfulness of these lenses when their contravariant components are exact Bayesian inversions. We prove our main result both abstractly and concretely, for both discrete and continuous states, taking care to illustrate the common structures.
