The No-U-Turn Sampler as a Proposal Distribution in a Sequential Monte Carlo Sampler with a Near-Optimal L-Kernel

Markov Chain Monte Carlo (MCMC) is a powerful method for drawing samples from non-standard probability distributions and is utilized across many fields and disciplines. Methods such as Metropolis-Adjusted Langevin (MALA) and Hamiltonian Monte Carlo (HMC), which use gradient information to explore the target distribution, are popular variants of MCMC. The Sequential Monte Carlo (SMC) sampler is an alternative sampling method which, unlike MCMC, can readily utilise parallel computing architectures and also has tuning parameters not available to MCMC. One such parameter is the L-kernel which can be used to minimise the variance of the estimates from an SMC sampler. 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 to improve the efficiency of the exploration of the target space. We also show how the SMC sampler can be optimized using both a near-optimal L-kernel and a Hamiltonian proposal