We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and concepts of the field, before discussing three well-known problems: phase transitions in the Ising model, the melting transition on a two-dimensional plane and simulation of an all-atom model for liquid water. We review the classical Metropolis, Glauber and molecular dynamics sampling algorithms before discussing several more recent approaches, including cluster algorithms, novel variations of hybrid Monte Carlo and Langevin dynamics and piece-wise deterministic processes such as event chain Monte Carlo. We highlight cross-over with statistics and machine learning throughout and present some results on event chain Monte Carlo and sampling from the Ising model using tools from the statistics literature. We provide a simulation study on the Ising and XY models, with reproducible code freely available online, and following this we discuss several open areas for interaction between the disciplines that have not yet been explored and suggest avenues for doing so.

翻译：我们讨论了几种用于从统计物理学中非归一化概率分布采样的算法，但采用了统计学与机器学习的语言。首先，我们对该领域的一些关键思想与概念进行了自成体系的介绍，随后探讨了三个著名问题：伊辛模型中的相变、二维平面上的熔融转变以及液态水全原子模型的模拟。我们回顾了经典的Metropolis算法、Glauber算法以及分子动力学采样算法，接着讨论了几种较新的方法，包括聚类算法、混合蒙特卡洛和朗之万动力学的新变体，以及事件链蒙特卡洛等分段确定性过程。我们强调了这些方法在统计学与机器学习中的交叉应用，并呈现了基于统计文献工具对事件链蒙特卡洛及伊辛模型采样的一些结果。我们针对伊辛模型和XY模型开展了模拟研究，相关的可复现代码已在线免费提供，随后讨论了这两个学科之间尚未探索的若干开放交互领域，并提出了开展研究的方向。