Abstract

Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian computation. In comparison with the traditional Metropolis–Hastings algorithm, HMC offers greater computational efficiency, especially in higher dimensional or more complex modeling situations. To most statisticians, however, the idea of HMC comes from a less familiar origin, one that is based on the theory of classical mechanics. Its implementation, either through Stan or one of its derivative programs, can appear opaque to beginners. A lack of understanding of the inner working of HMC, in our opinion, has hindered its application to a broader range of statistical problems. In this article, we review the basic concepts of HMC in a language that is more familiar to statisticians, and we describe an HMC implementation in R, one of the most frequently used statistical software environments. We also present hmclearn, an R package for learning HMC. This package contains a general-purpose HMC function for data analysis. We illustrate the use of this package in common statistical models. In doing so, we hope to promote this powerful computational tool for wider use. Example code for common statistical models is presented as supplementary material for online publication.

摘要

哈密​​顿蒙特卡罗 (HMC) 是贝叶斯计算的强大工具。与传统的 Metropolis-Hastings 算法相比，HMC 提供了更高的计算效率，特别是在更高维度或更复杂的建模情况下。然而，对于大多数统计学家来说，HMC 的概念来自一个不太熟悉的起源，它基于经典力学理论。它的实现，无论是通过 Stan 还是其衍生程序之一，对于初学者来说可能显得不透明。我们认为，对 HMC 内部工作原理缺乏了解，阻碍了其在更广泛的统计问题中的应用。在本文中，我们用统计学家更熟悉的语言回顾了 HMC 的基本概念，并描述了 R（最常用的统计软件环境之一）中的 HMC 实现。我们还推出了 hmclearn，一个用于学习 HMC 的 R 包。该软件包包含用于数据分析的通用 HMC 函数。我们说明了该包在常见统计模型中的使用。在此过程中，我们希望推广这一强大的计算工具以得到更广泛的使用。常见统计模型的示例代码作为在线出版的补充材料提供。