An Introduction to Hamiltonian Monte Carlo Method for Sampling

2021/08/27 by Nisheeth K. Vishnoi, Vishnoi, Nisheeth K.
Mathematics · Physics and Astronomy · #Computation (stat.CO) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2108.12107

openalex publication_date 2021/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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) ∝ 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.

Citations

• Constrained reaction coordinate dynamics for the simulation of rare events
• Stochastic Gradient Hamiltonian Monte Carlo
• On the convergence of Hamiltonian Monte Carlo
• Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

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