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Conditionals in a Markov category

Conditionals in a Markov category

May 09, 20251 min read

  • markov-category
  • monoidal-category

conditionals

  • conditionals are almost surely total
  • quasitotal conditional
  • structural conditional
  • conditionals of a composition
  • markov category - conditionals using do-notation
  • markov category - conditionals on multigraph signatures
  • conditionals of a family
  • conditionals are unique up to ranges
  • conditional composition in a Kleisli category
  • First action of produoidal Markov split
  • Second action of produoidal Markov split
  • Borel-Kolmogorov paradox

Definition, in copy-discard categories.

conditionals-in-string-diagrams

Related: Markov category, discrete partial Markov category, Synthetic Bayes theorem, disintegration.

References

  • A Synthetic Approach to Markov Kernels (Fritz, 2020)
  • Disintegration and Bayesian Inversion via String Diagrams (Cho, Jacobs, 2017)

Graph View

Backlinks

  • Markov category
  • Reading Bayesian inversion diagrams
  • conditional causal functions
  • conditional composition
  • conditionals are almost surely total
  • conditionals are unique up to ranges
  • conditionals of a composition
  • conditionals of a family
  • Copy-discard category
  • conditionals using do-notation

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