On Disintegration in Probabilistic Semantics
We give a version of disintegration based on weaker assumptions than previously known. The result is derived using an enhanced version of the Radon-Nikodym theorem that makes explicit the approximating functions, thereby allowing the coordinated construction of multiple simultaneous derivatives. Using this, a category of joint distributions can be independently defined in which a category of Markov kernels on countably generated spaces is fully and faithfully embedded.
probabilistic programming; disintegration; Bayesian inference; conditioning