A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics release_rb2gh7dosjbglmwyua52b23jga

by Tobias Fritz

Released as a article .

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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Date   2019-09-01
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Language   en ?
arXiv  1908.07021v2
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