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A predicate/state transformer semantics for Bayesian learning

06 Oct 2016 [ proceedings (MFPS 2016) · preprint ]

Bayesian inference is describe in terms of state and predicate transformation.

This paper establishes a link between Bayesian inference (learning) and predicate and state transformer operations from programming semantics and logic. Specifically, a very general definition of backward inference is given via first applying a predicate transformer and then conditioning. Analogously, forward inference involves first conditioning and then applying a state transformer. These definitions are illustrated in many examples in discrete and continuous probability theory and also in quantum theory.