Markov categories are copy-discard categories of total morphisms that have conditionals. From conditionals, we can prove the existence of Bayesian inversions. The main example is the category of distributions (Stoch, the Kleisli category of the finitary distribution monad); continuous examples are given by standard Borel spaces (see Giry monad) and normal Gaussian noise (see Gaussian probability theory).
- conditional
- partial Markov category
- discrete partial Markov category
- First action of produoidal Markov split
- Second action of produoidal Markov split
- distributions that are marginally independent of the parameter
- divergence on a Markov category
Tags: probability, monoidal category.
References.
- Disintegration and Bayesian Inversion via String Diagrams (Cho, Jacobs, 2017)
- A Synthetic Approach to Markov Kernels (Fritz, 2020)
- Free GS-Monoidal Categories and Free Markov Categories (Fritz, Liang, 2023)
- Markov Categories and Entropy (Perrone, 2023)
- Representable Markov Categories and Comparison of Statistical Experiments in CAtegorical Probability (Fritz, Gonda, Perrone, Rischel, 2023)
- Dilations and information flow axioms in categorical probability (Fritz, Gonda, Houghton-Larsen, Perrone, Stein, 2022)
- Evidential Decision Theory via Partial Markov Categories (Di Lavore, Roman, 2023)
- Causal Inference by String Diagram Surgery (Jacobs, Kissinger, Zanasi)
- A Simple Formal Language for Probabilistic Decision Problems (Di Lavore, Jacobs, Román, 2024)