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，基于采样的推断方法受到了广泛关注。哈密顿蒙特卡洛（HMC）作为一种强大的算法，利用哈密顿动力学中的概念，能够高效探索复杂的目标分布。HMC的多种变体已在主流软件包中实现，提供了开箱即用的解决方案，极大地推动了统计学和机器学习领域的发展。与此同时，此类黑箱式实现的普及也使得用户难以理解HMC的内部机制，尤其当他们不熟悉其底层物理原理时。本文提供了一份教学性综述，旨在弥合HMC理论基础与实际应用之间的鸿沟。通过重点阐述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断中的作用，本综述致力于让应用领域的研究人员更易掌握该方法。