The Compositional Structure of Bayesian Inference — Dylan Braithwaite, Jules Hedges & Toby St Clere Smithe (2023). arXiv:2305.06112 (v2, PDF).
Builds Bayesian lenses as the Grothendieck construction of the fibrewise opposite of the state-indexed category and shows that Bayesian inversion is a functor into them up to almost-sure equality. Introduces dependent Bayesian lenses, and makes inversion strictly functorial by restricting to supports, proving uniqueness of Bayesian inverses with support.
Sources: the paper, arXiv:2305.06112v2, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definition 1: Bayesian inversion in a Markov category
- Definitions 8–9: the Stat construction and BLens as a Grothendieck construction
- Proposition 11: Bayesian inversion is almost functorial
- Definition 15: dependent Bayesian lenses
- Theorem 20: unique Bayesian inversion with support
Concept notes
Bayesian Lens, Bayesian Inversion, Grothendieck Construction, Almost-Sure Equality