Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions. Variants of HMC are available in popular software packages, enabling off-the-shelf implementations that have greatly benefited the statistics and machine learning communities. At the same time, the availability of such black-box implementations has made it challenging for users to understand the inner workings of HMC, especially when they are unfamiliar with the underlying physical principles. We provide a pedagogical overview of HMC that aims to bridge the gap between its theoretical foundations and practical applicability. This review article seeks to make HMC more accessible to applied researchers by highlighting its advantages, limitations, and role in enabling scalable and exact Bayesian inference for complex models.

翻译：近年来，基于采样的推理方法受到了广泛关注。哈密顿蒙特卡洛方法（HMC）作为一种强大的算法脱颖而出，它利用哈密顿动力学中的概念高效地探索复杂的目标分布。HMC的变体已在主流软件包中可用，这种即开即用的实现极大地惠及了统计学和机器学习社区。然而，这类黑箱实现的普及使得用户，尤其是不熟悉其底层物理原理的用户，难以理解HMC的内部工作机制。本文对HMC进行教学性概述，旨在弥合其理论基础与实际应用之间的差距。这篇综述文章通过强调HMC的优势、局限性及其在实现复杂模型的可扩展、精确贝叶斯推理中的作用，力求让应用研究人员更容易理解和掌握HMC。