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Title of Journal: Appl Categor Struct

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Abbravation: Applied Categorical Structures

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Springer Netherlands

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1572-9095

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A Categorical Foundation for Bayesian Probability

Authors: Jared Culbertson Kirk Sturtz
Publish Date: 2013/08/21
Volume: 22, Issue: 4, Pages: 647-662
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Abstract

Building on the work of Lawvere and others we develop a categorical framework for Bayesian probability This foundation will then allow for Bayesian representations of uncertainty to be integrated into other categorical modeling applications The main result uses an existence theorem for regular conditional probabilities by Faden which holds in more generality than the standard setting of Polish spaces This more general setting is advantageous as it allows for nontrivial decision rules Eilenberg–Moore algebras on finite as well as non finite spaces In this way we obtain a common framework for decision theory and Bayesian probability

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Other Papers In This Journal:
  1. On the Notion of a Semi-Abelian Category in the Sense of Palamodov
  2. Complexity Analysis via Approach Spaces
  3. Axioms for Sequential Convergence
  4. Quasi Left Factorization Structures as Presheaves
  5. Absolute Lax 2-categories
  6. Auslander–Buchweitz Context and Co- t -structures
  7. Homotopy Gerstenhaber Structures and Vertex Algebras
  8. Perfect MV -algebras and their Logic
  9. Insertion of Continuous Real Functions on Spaces, Bispaces, Ordered Spaces and Pointfree Spaces—A Common Root
  10. A Generalization of De Vries Duality Theorem
  11. Bounded Equivalence of Hull Classes in Archimedean Lattice-Ordered Groups with Unit
  12. Normal Subgroups of B u Aut(Ω)
  13. Lawvere Completeness in Topology
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