Reversible Jump Probabilistic Programming

In this paper we present a method for automatically deriving a Reversible Jump Markov chain Monte Carlo sampler from probabilistic programs that specify the target and proposal distributions. The main challenge in automatically deriving such an inference procedure, in comparison to deriving a generic Metropolis-Hastings sampler, is in calculating the Jacobian adjustment to the proposal acceptance ratio. To achieve this, our approach relies on the interaction of several different components, including automatic differentiation, transformation inversion, and optimised code generation. We also present Stochaskell, a new probabilistic programming language embedded in Haskell, which provides an implementation of our method.