PROBABILITY & STATISTICS

Disintegration and Bayesian Inversion via String Diagrams

Resource type
Authors/contributors
Title
Disintegration and Bayesian Inversion via String Diagrams
Abstract
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability --- via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.
Publication
Mathematical Structures in Computer Science
Volume
29
Issue
7
Pages
938-971
Date
08/2019
Journal Abbr
Math. Struct. Comp. Sci.
DOI
10/ggdf9v
ISSN
0960-1295, 1469-8072
Accessed
2019-11-21T20:35:15Z
Library Catalog
Extra
ZSCC: 0000007 arXiv: 1709.00322
Notes
Comment: Accepted for publication in Mathematical Structures in Computer Science
Citation
Jacobs, B., & Cho, K. (2019). Disintegration and Bayesian Inversion via String Diagrams. Mathematical Structures in Computer Science, 29(7), 938–971. https://doi.org/10/ggdf9v
Methodology
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