An Introduction to Hamiltonian Monte Carlo Method for Sampling

• URL: http://arxiv.org/abs/2108.12107v1
• Date: Fri, 27 Aug 2021 03:28:20 GMT
• Title: An Introduction to Hamiltonian Monte Carlo Method for Sampling
• Authors: Nisheeth K. Vishnoi
• Abstract summary: Hamiltonian Monte Carlo (HMC) is a Hamiltonian dynamics-inspired algorithm for sampling from a Gibbs density $pi(x) propto e-f(x)$. We show that idealized HMC preserves $pi$ and we establish its convergence when $f$ is strongly convex and smooth.
• Score: 26.555110725656963
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\pi(x) \propto e^{-f(x)}$. 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.

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