Bart Jacobs - Sufficient Statistics and Split Idempotents in Discrete Probability Theory

entics:10520 - Electronic Notes in Theoretical Informatics and Computer Science, February 22, 2023, Volume 1 - Proceedings of MFPS XXXVIII - https://doi.org/10.46298/entics.10520
Sufficient Statistics and Split Idempotents in Discrete Probability TheoryArticle

Authors: Bart Jacobs

    A sufficient statistic is a deterministic function that captures an essential property of a probabilistic function (channel, kernel). Being a sufficient statistic can be expressed nicely in terms of string diagrams, as Tobias Fritz showed recently, in adjoint form. This reformulation highlights the role of split idempotents, in the Fisher-Neyman factorisation theorem. Examples of a sufficient statistic occur in the literature, but mostly in continuous probability. This paper demonstrates that there are also several fundamental examples of a sufficient statistic in discrete probability. They emerge after some combinatorial groundwork that reveals the relevant dagger split idempotents and shows that a sufficient statistic is a deterministic dagger epi.


    Volume: Volume 1 - Proceedings of MFPS XXXVIII
    Published on: February 22, 2023
    Accepted on: December 22, 2022
    Submitted on: December 21, 2022
    Keywords: Computer Science - Logic in Computer Science,03B70, 68Q87, 18C50,F.3.2,G.3

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