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Markov Chain Monte Carlo (MCMC) is a powerful method for drawing samples fromnon-standard probability distributions and is utilized across many fields anddisciplines. Methods such as Metropolis-Adjusted Langevin (MALA) andHamiltonian Monte Carlo (HMC), which use gradient information to explore thetarget distribution, are popular variants of MCMC. The Sequential Monte Carlo(SMC) sampler is an alternative sampling method which, unlike MCMC, can readilyutilise parallel computing architectures and also has tuning parameters notavailable to MCMC. One such parameter is the L-kernel which can be used tominimise the variance of the estimates from an SMC sampler. In this letter, weshow how the proposal used in the No-U-Turn Sampler (NUTS), an advanced variantof HMC, can be incorporated into an SMC sampler to improve the efficiency ofthe exploration of the target space. We also show how the SMC sampler can beoptimized using both a near-optimal L-kernel and a Hamiltonian proposal

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