Disintegration and Bayesian inversion via string diagrams

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, bu...

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Bibliographic Details
Published inMathematical structures in computer science Vol. 29; no. 7; pp. 938 - 971
Main Authors Cho, Kenta, Jacobs, Bart
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.08.2019
Subjects
Bayesian analysis
Conditional probability
Disintegration
Formulations
Probability
Probability theory
Conditional probability
Bayesian inversion
disintegration
string diagram
monoidal category
Online AccessGet full text
ISSN0960-1295
1469-8072
1469-8072
DOI10.1017/S0960129518000488

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Summary: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.
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ISSN:0960-1295
1469-8072
1469-8072
DOI:10.1017/S0960129518000488