I thought it might be interesting to draw your attention to some work we’ve done to integrate NUTS inside a Sequential Monte Carlo (SMC) sampler. See here:
We are working to integrate this into a future version of Stan. Comments welcome!
PS We see this paper is a key component of our ongoing work to improve the ability to use SMC (as an alternative to MCMC) inside Stan. We hope and anticipate that this broader work will culminate in a version of Stan that, by using SMC, can fully exploit modern computing resources. We hope and anticipate that this will result in significant speed-ups and thereby increase the community’s ambition with respect to the complexity of models that Stan can consider.