PROBABILITY & STATISTICS

Towards a Categorical Account of Conditional Probability

Resource type
Authors/contributors
Title
Towards a Categorical Account of Conditional Probability
Abstract
This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and joint probabilities, in the Kleisli category of the distribution monad. The conditional probabilities are induced by a map together with a predicate (the condition). The latter is a predicate in the logic of effect modules on this Kleisli category. This same approach can be transferred to the category of C*-algebras (with positive unital maps), whose predicate logic is also expressed in terms of effect modules. Conditional probabilities can again be expressed via a triangle-fill-in property. In the literature, there are several proposals for what quantum conditional probability should be, and also there are extra difficulties not present in the classical case. At this stage, we only describe quantum systems with classical parametrization.
Publication
Electronic Proceedings in Theoretical Computer Science
Volume
195
Pages
179-195
Date
2015-11-4
Journal Abbr
Electron. Proc. Theor. Comput. Sci.
DOI
10/ggdf9w
ISSN
2075-2180
Accessed
2019-11-21T20:40:59Z
Library Catalog
Extra
ZSCC: NoCitationData[s0] arXiv: 1306.0831
Notes

Comment: In Proceedings QPL 2015, arXiv:1511.01181

Citation
Jacobs, B., & Furber, R. (2015). Towards a Categorical Account of Conditional Probability. Electronic Proceedings in Theoretical Computer Science, 195, 179–195. https://doi.org/10/ggdf9w
CATEGORICAL LOGIC
PROBABILITY & STATISTICS
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