Probabilistic programs, computability, and de Finetti measures

The complexity of probabilistic models, especially those involving recursion, has far exceeded the representational capacity of graphical models. Functional programming languages with probabilistic choice operators have recently been proposed as universal representations for statistical modeling (e.g., IBAL [Pfe01], λ◦ [PPT08], Church [GMR08]). The conditional independence structure of a probabilistic program is not, in general, representable by a graphical model. Rather, it is dynamic and is given by the random control and data flow of the program. These functional probabilistic languages are allied with imperative probabilistic languages (e.g., Infer.NET) and a similar tradition of augmenting logical representations with probabilistic quantifiers (e.g., BLOG [MMR05], iBLOG [MMG08], PRISM [SK97], BLP [KR07], SLP [Mug96], Markov Logic [RD06], Independent Choice Logic [Poo08]).