# Dependent Bayesian Lenses: Categories of Bidirectional Markov Kernels with Canonical Bayesian Inversion

arXiv: https://arxiv.org/abs/2209.14728 · HTML: https://mlsanity.com/paper/2209.14728/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2022.

## Built on by (most cited first, 1 of 1)

- [The Compositional Structure of Bayesian Inference](https://mlsanity.com/paper/2305.06112/) (2023)

## Abstract (arXiv)

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.