Multinomial and Hypergeometric Distributions in Markov Categories

Bart Jacobs
(Institute for Computing and Information Sciences (iCIS), Radboud University Nijmegen, The Netherlands)

Markov categories, having tensors with copying and discarding, provide a setting for categorical probability. This paper uses finite colimits and what we call uniform states in such Markov categories to define a (fixed size) multiset functor, with basic operations for sums and zips of multisets, and a graded monad structure. Multisets can be used to represent both urns filled with coloured balls and also draws of multiple balls from such urns. The main contribution of this paper is the abstract definition of multinomial and hypergeometric distributions on multisets, as draws. It is shown that these operations interact appropriately with various operations on multisets.

In Ana Sokolova: Proceedings 37th Conference on Mathematical Foundations of Programming Semantics (MFPS 2021), Hybrid: Salzburg, Austria and Online, 30th August - 2nd September, 2021, Electronic Proceedings in Theoretical Computer Science 351, pp. 98–115.
Published: 29th December 2021.

ArXived at: bibtex PDF

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