# A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics

arXiv: https://arxiv.org/abs/1908.07021 · HTML: https://mlsanity.com/paper/1908.07021/

## Key facts

- Cited by 55 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 19 Aug 2019.

## Built on by (most cited first, 30 of 55)

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- [A Markov Categorical Framework for Language Modeling](https://mlsanity.com/paper/2507.19247/) (2025)
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- [Odds Law: The Decomposition Algebra On How Intelligence Organizes Itself to Solve Difficult Problems Reliably](https://mlsanity.com/paper/2606.15712/) (2026)
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## Abstract (arXiv)

We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions of theorems on sufficient statistics due to Fisher--Neyman, Basu, and Bahadur. Besides the conceptual clarity offered by our categorical setup, its main advantage is that it provides a uniform treatment of various types of probability theory, including discrete probability theory, measure-theoretic probability with general measurable spaces, Gaussian probability, stochastic processes of either of these kinds, and many others.