标题： 通过物理学基础和实例理解哈密顿蒙特卡洛方法 显示英文标题

标题： Understanding the Hamiltonian Monte Carlo through its Physics Fundamentals and Examples

摘要： 哈密顿蒙特卡洛（HMC）算法是一种强大的马尔可夫链蒙特卡洛（MCMC）方法，它利用哈密顿动力学从目标分布生成样本。为了充分发挥其潜力，我们必须理解哈密顿动力学的工作原理及其为何能在MCMC算法中使用。本研究阐明了蒙特卡洛哈密顿概念，提供了基础物理概念的全面解释。它面向那些具备扎实数学基础但可能对特定物理概念（如与哈密顿动力学相关的概念）不够熟悉的读者。此外，我们提供了HMC算法的Python代码示例，并与随机游走的Metropolis-Hastings（RWMH）算法和t-walk算法进行了比较，以突出HMC在应用于贝叶斯推断时的优势和劣势。 显示英文摘要

摘要： The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how Hamiltonian dynamics work and why they can be used in a MCMC algorithm. This work elucidates the Monte Carlo Hamiltonian, providing comprehensive explanations of the underlying physical concepts. It is intended for readers with a solid foundation in mathematics who may lack familiarity with specific physical concepts, such as those related to Hamiltonian dynamics. Additionally, we provide Python code for the HMC algorithm, examples and comparisons with the Random Walk Metropolis-Hastings (RWMH) and t-walk algorithms to highlight HMC's strengths and weaknesses when applied to Bayesian Inference.