A synthetic approach to Markov kernels, conditional independence and
theorems on sufficient statistics
release_rb2gh7dosjbglmwyua52b23jga
by
Tobias Fritz
2019
Abstract
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; as well as 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, Markov
processes of either of these kinds, and many others.
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1908.07021v2
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