  A challenging problem in probabilistic programming is to develop inference
algorithms that work for arbitrary programs in a universal probabilistic
programming language (PPL). We present the nonparametric involutive Markov
chain Monte Carlo (NP-iMCMC) algorithm as a method for constructing MCMC
inference algorithms for nonparametric models expressible in universal PPLs.
Building on the unifying involutive MCMC framework, and by providing a general
procedure for driving state movement between dimensions, we show that NP-iMCMC
can generalise numerous existing iMCMC algorithms to work on nonparametric
models. We prove the correctness of the NP-iMCMC sampler. Our empirical study
shows that the existing strengths of several iMCMC algorithms carry over to
their nonparametric extensions. Applying our method to the recently proposed
Nonparametric HMC, an instance of (Multiple Step) NP-iMCMC, we have constructed
several nonparametric extensions (all of which new) that exhibit significant
performance improvements.
