# Pearl's and Jeffrey's Update as Modes of Learning in Probabilistic Programming

arXiv: https://arxiv.org/abs/2309.07053 · HTML: https://mlsanity.com/paper/2309.07053/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 13 Sep 2023.

## Builds on (most cited first, 4 of 4)

- [Disintegration and Bayesian Inversion via String Diagrams](https://mlsanity.com/paper/1709.00322/) (2017)
- [Learning from What's Right and Learning from What's Wrong](https://mlsanity.com/paper/2112.14045/) (2021)
- [From Multisets over Distributions to Distributions over Multisets](https://mlsanity.com/paper/2105.06908/) (2021)
- [A Monad for Probabilistic Point Processes](https://mlsanity.com/paper/2101.10479/) (2021)

## Abstract (arXiv)

The concept of updating a probability distribution in the light of new evidence lies at the heart of statistics and machine learning. Pearl's and Jeffrey's rule are two natural update mechanisms which lead to different outcomes, yet the similarities and differences remain mysterious. This paper clarifies their relationship in several ways: via separate descriptions of the two update mechanisms in terms of probabilistic programs and sampling semantics, and via different notions of likelihood (for Pearl and for Jeffrey). Moreover, it is shown that Jeffrey's update rule arises via variational inference. In terms of categorical probability theory, this amounts to an analysis of the situation in terms of the behaviour of the multiset functor, extended to the Kleisli category of the distribution monad.