An Introduction to Hamiltonian Monte Carlo Method for Sampling

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.