An Introduction to Hamiltonian Monte Carlo Method for Sampling
It provides a foundational introduction to HMC for researchers in computational statistics and machine learning, focusing on theoretical properties in an idealized setting.
The article introduces the Hamiltonian Monte Carlo (HMC) method for sampling from Gibbs densities, showing that it preserves the target distribution and converges under strong convexity and smoothness conditions.
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 $π(x) \propto e^{-f(x)}$. We focus on the "idealized" case, where one can compute continuous trajectories exactly. We show that idealized HMC preserves $π$ and we establish its convergence when $f$ is strongly convex and smooth.