The No-U-Turn Sampler as a Proposal Distribution in a Sequential Monte Carlo Sampler Without Accept/Reject

Markov Chain Monte Carlo (MCMC) is a method for drawing samples from non-standard probability distributions. Hamiltonian Monte Carlo (HMC) is a popular variant of MCMC that uses gradient information to explore the target distribution. The Sequential Monte Carlo (SMC) sampler is an alternative sampling method which, unlike MCMC, can readily utilise parallel computing architectures. It is typical within SMC literature to target a tempered distribution using a proposal with an accept/reject mechanism. In this letter, we show how the proposal used in the No-U-Turn Sampler (NUTS), an advanced variant of HMC, can be incorporated into an SMC sampler without an accept/reject mechanism. Empirical results show that this can remove the need for tempering and gives rise to accurate estimates being generated in fewer iterations which motivates this technique being deployed on parallel hardware.