Stan is a popular declarative probabilistic programming language with a
high-level syntax for expressing graphical models and beyond. Stan differs by
nature from generative probabilistic programming languages like Church,
Anglican, or Pyro. This paper presents a comprehensive compilation scheme to
compile any Stan model to a generative language and proves its correctness.
This sheds a clearer light on the relative expressiveness of different kinds of
probabilistic languages and opens the door to combining their mutual strengths.
Specifically, we use our compilation scheme to build a compiler from Stan to
Pyro and extend Stan with support for explicit variational inference guides and
deep probabilistic models. That way, users familiar with Stan get access to new
features without having to learn a fundamentally new language. Overall, our
paper clarifies the relationship between declarative and generative
probabilistic programming languages and is a step towards making deep
probabilistic programming easier