2019/08/31 by Tobias Fritz · 2 citations
Computer Science · Mathematics · #cs.LO #math.CT #math.PR #math.ST #msc:18D10 #msc:60A05 #msc:62A01 #msc:62B05 #msc:68Q55 #stat.TH
paper · pdf · doi:10.1016/j.aim.2020.107239
published as Adv. Math. 370, 107239 (2020) · 98 pages. v6: fixed error in Section 7. v7: incorporates referee's comments. v8: minor correction
arxiv created 2020/05/31 · arxiv updated 2020/06/02
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.