相依贝叶斯透镜：具有典型贝叶斯反演的双向马尔可夫核范畴
Dependent Bayesian Lenses: Categories of Bidirectional Markov Kernels with Canonical Bayesian Inversion
摘要：
我们概括了现有的贝叶斯透镜的结构，以允许在向后的对象依赖于向前的对象的状态（解释为概率分布）的对象对之间的透镜。这给了一个自然的设置，研究随机地图与贝叶斯逆限制在一个给定的先验支持的点。为了正式说明这一点，我们提出了一个定义弗里茨的支持对象在马尔可夫范畴，并表明，这些产生了一个部分到类别的依赖贝叶斯镜头编码一个更规范的概念贝叶斯反演。
英文摘要：
We generalise an existing construction of Bayesian Lenses to admit lenses between pairs of objects where the backwards object is dependent on states on the forwards object (interpreted as probability distributions). This gives a natural setting for studying stochastic maps with Bayesian inverses restricted to the points supported by a given prior. In order to state this formally we develop a proposed definition by Fritz of a support object in a Markov category and show that these give rise to a section into the category of dependent Bayesian lenses encoding a more canonical notion of Bayesian inversion.
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