A Categorical Basis for Conditional Probability
نویسنده
چکیده
This paper identifies several key properties of a monad that allow us to formulate the basics of conditional probability theory, using states for distributions/measures and predicates for events/probability density functions (pdf’s). The distribution monad for discrete probability and the Giry monad for continuous probability are leading examples. Our categorical description handles discrete and continuous probability uniformly, and includes: an abstract Fubini theorem with a very simple proof, conditional states satisfying Bayes’ rule, and (conditional) non-entwinedness for joint states.
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