A categorical foundation for Bayesian probability

DOI10.1007/s10485-013-9324-9zbMath1302.60011arXiv1205.1488OpenAlexW3101547338MaRDI QIDQ742929

Jared Culbertson, Kirk Sturtz

Publication date: 19 September 2014

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.1488

zbMATH Keywords

decision rulesBayesian probabilityregular conditional probabilityGiry monad

Mathematics Subject Classification ID

Bayesian problems; characterization of Bayes procedures (62C10) Axioms; other general questions in probability (60A05)

Related Items (11)

A non-commutative Bayes' theorem ⋮ The factorization of the Giry monad ⋮ From probability monads to commutative effectuses ⋮ Categorical approach to modelling and to coupling of models ⋮ Pointless Learning ⋮ Quantum GestART: identifying and applying correlations between mathematics, art, and perceptual organization ⋮ Giry and the Machine ⋮ Weak and TV consistency in Bayesian uncertainty quantification using disintegration ⋮ A channel-based perspective on conjugate priors ⋮ Disintegration and Bayesian inversion via string diagrams ⋮ Unnamed Item

Cites Work

• Kleisli morphisms and randomized congruences for the Giry monad
• Statistical decision theory and Bayesian analysis. 2nd ed
• The existence of regular conditional probabilities: Necessary and sufficient conditions
• Perfect mixtures of perfect measures
• Nuclear and trace ideals in tensored \(^*\)-categories
• Commutative monads as a theory of distributions
• Disintegration and compact measures.
• Probability Theory
• Real Analysis and Probability
• Optimal transportation with capacity constraints
• Perfect Probability Measures and Regular Conditional Probabilities
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