Probabilistic programming with densities in SlicStan: efficient, flexible, and deterministic

  • Maria I. Gorinova ,
  • Andy Gordon ,
  • Charles Sutton

Proceedings of the ACM on Programming Languages | , Vol 3(POPL)

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Stan is a probabilistic programming language that has been increasingly used for real-world scalable projects. However, to make practical inference possible, the language sacrifices some of its usability by adopting a block syntax, which lacks compositionality and flexible user-defined functions. Moreover, the semantics of the language has been mainly given in terms of intuition about implementation, and has not been formalised.

This paper provides a formal treatment of the Stan language, and introduces the probabilistic programming language SlicStan — a compositional, self-optimising version of Stan. Our main contributions are (1) the formalisation of a core subset of Stan through an operational density-based semantics; (2) the design and semantics of the Stan-like language SlicStan, which facilities better code reuse and abstraction through its compositional syntax, more flexible functions, and information-flow type system; and (3) a formal, semantic-preserving procedure for translating SlicStan to Stan.