Hamiltonian Monte Carlo for (Physics) Dummies

TL;DR

This paper provides an accessible overview of Hamiltonian Monte Carlo, explaining its physical principles, advantages, and limitations to help researchers apply it effectively in Bayesian inference.

Contribution

It offers a pedagogical review that bridges the gap between HMC's theoretical foundations and practical use, making it more accessible.

Findings

HMC efficiently explores complex distributions using Hamiltonian dynamics.

Black-box implementations have increased HMC's adoption in statistics and machine learning.

The review clarifies HMC's advantages and limitations for applied researchers.

Abstract

Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions. Variants of HMC are available in popular software packages, enabling off-the-shelf implementations that have greatly benefited the statistics and machine learning communities. At the same time, the availability of such black-box implementations has made it challenging for users to understand the inner workings of HMC, especially when they are unfamiliar with the underlying physical principles. We provide a pedagogical overview of HMC that aims to bridge the gap between its theoretical foundations and practical applicability. This review article seeks to make HMC more accessible to applied researchers by highlighting its advantages, limitations, and role in enabling scalable and exact Bayesian inference for complex models.