Bayesian strategies: probabilistic programs as generalised graphical models

We introduce Bayesian strategies, a new interpretation of probabilistic programs in game semantics. This interpretation can be seen as a refinement of Bayesian networks. Bayesian strategies are based on a new form of event structure, with two causal dependency relations respectively modelling control flow and data flow. This gives a graphical representation for probabilistic programs which resembles the concrete representations used in modern implementations of probabilistic programming. From a theoretical viewpoint, Bayesian strategies provide a rich setting for denotational semantics. To demonstrate this we give a model for a general higher-order programming language with recursion, conditional statements, and primitives for sampling from continuous distributions and trace re-weighting. This is significant because Bayesian networks do not easily support higher-order functions or conditionals.