The Logical Essentials of Bayesian Reasoning

This chapter offers an accessible introduction to the channel-based approach to Bayesian probability theory. This framework rests on algebraic and logical foundations, inspired by the methodologies of programming language semantics. It offers a uniform, structured and expressive language for describing Bayesian phenomena in terms of familiar programming concepts, like channel, predicate transformation and state transformation. The introduction also covers inference in Bayesian networks, which will be modelled by a suitable calculus of string diagrams.