The goal of this article is to introduce the Hamiltonian Monte Carlo (HMC) method -- a Hamiltonian dynamics-inspired algorithm for sampling from a Gibbs density $\pi(x) \propto e^{-f(x)}$. We focus on the "idealized" case, where one can compute continuous trajectories exactly. We show that idealized HMC preserves $\pi$ and we establish its convergence when $f$ is strongly convex and smooth.

翻译：本篇文章的目的是介绍汉密尔顿蒙特卡洛(HMC)方法,即汉密尔顿动态激励算法,用于从Gibbs密度$\pi(x)\ propto e ⁇ -f(x)}$进行取样。我们关注“理想化”案例,在这个案例中,人们可以精确地计算连续的轨迹。我们展示了理想化的HMC保存$\pi$,当美元强烈和顺畅时,我们就建立其趋同。