Markov chain Monte Carlo (MCMC) methods have existed for a long time and the field is well-explored. The purpose of MCMC methods is to approximate a distribution through repeated sampling; most MCMC algorithms exhibit asymptotically optimal behavior in that they converge to the true distribution at the limit. However, what differentiates these algorithms are their practical convergence guarantees and efficiency. While a sampler may eventually approximate a distribution well, because it is used in the real world it is necessary that the point at which the sampler yields a good estimate of the distribution is reachable in a reasonable amount of time. Similarly, if it is computationally difficult or intractable to produce good samples from a distribution for use in estimation, then there is no real-world utility afforded by the sampler. Thus, most MCMC methods these days focus on improving efficiency and speeding up convergence. However, many MCMC algorithms suffer from random walk behavior and often only mitigate such behavior as outright erasing random walks is difficult. Hamiltonian Monte Carlo (HMC) is a class of MCMC methods that theoretically exhibit no random walk behavior because of properties related to Hamiltonian dynamics. This paper introduces modifications to a specific HMC algorithm known as the no-U-turn sampler (NUTS) that aims to explore the sample space faster than NUTS, yielding a sampler that has faster convergence to the true distribution than NUTS.

翻译：马尔可夫链蒙特卡洛（MCMC）方法已有悠久历史，该领域已得到充分探索。MCMC方法旨在通过重复采样来近似概率分布；大多数MCMC算法具有渐近最优行为，即在极限条件下收敛到真实分布。然而，这些算法的区别在于其实践中的收敛保证与效率。尽管采样器最终能较好近似分布，但鉴于其应用于现实世界，必须在合理时间内达到能给出良好分布估计的采样点。同样，若从分布中生成可用于估计的良好样本在计算上困难或不可行，则采样器不具备实际效用。因此，当前多数MCMC方法聚焦于提升效率与加速收敛。但许多MCMC算法仍存在随机游走行为，且通常仅能缓解该行为，因为彻底消除随机游走极为困难。哈密顿蒙特卡洛（HMC）是一类理论上因哈密顿动力学特性而不存在随机游走行为的MCMC方法。本文对特定HMC算法——无回转采样器（NUTS）进行改进，旨在比NUTS更快探索样本空间，从而获得比NUTS更快收敛至真实分布的采样器。