Disintegration and Bayesian Inversion via String Diagrams — Kenta Cho & Bart Jacobs (2017). arXiv:1709.00322 (v3, PDF); Math. Struct. Comp. Sci. 29 (2019) 938-971.
Develops conditional probability graphically in affine copy-discard (CD) categories: disintegration (splitting a joint state into a marginal and a channel) and Bayesian inversion (reversing a channel given a prior) as string-diagram equations, with existence results for discrete and measure-theoretic probability, almost-equality, equality strengthening, conditional independence, and conditioning via likelihoods.
Sources: the paper, arXiv:1709.00322v3, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definitions 2.2–2.3: CD-categories, causal morphisms, affine CD-categories
- Definition 3.5: disintegration; §3: Bayesian inversion
- Theorem 3.11: disintegrations exist for standard Borel codomains
- Definition 5.1, Propositions 5.2–5.4: almost-equality
- Definition 6.6, Proposition 6.10: conditional independence and its properties
Concept notes
Copy-Discard Category, Conditionals and Disintegration, Bayesian Inversion, Almost-Sure Equality, Conditional Independence