License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2017.1
URN: urn:nbn:de:0030-drops-80517
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8051/
Simpson, Alex
Probability Sheaves and the Giry Monad
Abstract
I introduce the notion of probability sheaf, which is a mathematical structure capturing the relationship between probabilistic concepts (such as random variable) and sample spaces. Various probability-theoretic notions can be (re)formulated in terms of category-theoretic structure on the category of probability sheaves.
As a main example, I consider the Giry monad, which, in its original formulation, constructs spaces of probability measures. I show that the Giry monad generalises to the category of probability sheaves, where it turns out to have a simple, purely category-theoretic definition.
BibTeX - Entry
@InProceedings{simpson:LIPIcs:2017:8051,
author = {Alex Simpson},
title = {{Probability Sheaves and the Giry Monad}},
booktitle = {7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
pages = {1:1--1:6},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-033-0},
ISSN = {1868-8969},
year = {2017},
volume = {72},
editor = {Filippo Bonchi and Barbara K{\"o}nig},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8051},
URN = {urn:nbn:de:0030-drops-80517},
doi = {10.4230/LIPIcs.CALCO.2017.1},
annote = {Keywords: Random variable, conditional independence, category theory, sheaves, Giry monad}
}
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Keywords: |
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Random variable, conditional independence, category theory, sheaves, Giry monad |
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Collection: |
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7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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17.11.2017 |
