Hamiltonian Monte Carlo (HMC) is one of the most popular MCMC inference methods. The No-U-Turn Sampler (NUTS), an adaptive extension of HMC, eliminates the need to tune trajectory lengths, to which HMC is sensitive. Generalizing HMC, the Nonparametric HMC (NP-HMC) algorithm can be applied to models with a parameter space of varying dimension.

We introduce NP-NUTS, a hybrid of NUTS and NP-HMC. This new algorithm automatically adjusts trajectory lengths and gives a dynamically tuned version of NP-HMC. We address the main challenges in devising NP-NUTS: ensuring correct and efficient sampling from the constructed tree, and adjusting the stopping conditions to preserve detailed balance.