The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a random walk in state space, and random walks allow for sampling from complex distributions. However, paradoxically, it is necessary to carefully suppress the randomness of the random walk to improve computational efficiency. By breaking detailed balance, we can create a probability flow in the state space and perform more efficient sampling along this flow. Motivated by this idea, practical and efficient nonreversible MCMC methods have been developed over the past ten years. In particular, the lifting technique, which introduces probability flows in an extended state space, has been applied to various systems and has proven more efficient than conventional reversible updates. We review and discuss several practical approaches to implementing nonreversible MCMC methods, including the shift method in the cumulative distribution and the directed-worm algorithm.

翻译：马尔可夫链蒙特卡洛（MCMC）方法作为一种强大的数值积分技术，在多自由度系统中被广泛应用于各个领域。在MCMC方法中，概率状态转移可视为状态空间中的随机游走，而随机游走允许从复杂分布中进行采样。然而，矛盾的是，为了提高计算效率，必须仔细抑制随机游走的随机性。通过打破细致平衡，我们可以在状态空间中创建概率流，并沿着该流进行更高效的采样。受这一思想启发，过去十年间已发展出实用且高效的非可逆MCMC方法。特别是提升技术——通过在扩展状态空间中引入概率流——已应用于多种系统，并被证明比传统的可逆更新更高效。本文回顾并讨论了实现非可逆MCMC方法的几种实用途径，包括累积分布中的平移方法和有向蠕虫算法。