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arXiv · 2108.12107

An Introduction to Hamiltonian Monte Carlo Method for Sampling

Nisheeth K. Vishnoi
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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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Nisheeth K. Vishnoi. 2021-08-27. An Introduction to Hamiltonian Monte Carlo Method for Sampling. https://arxiv.org/abs/2108.12107

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