An Introduction to Hamiltonian Monte Carlo Method for Sampling

08/27/2021

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by   Nisheeth K. Vishnoi, et al.

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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.