Notes on Hamiltonian Monte Carlo from a purely probabilistic perspective [P]

Overview

I’ve been studying Hamiltonian Monte Carlo and wrote a set of notes explaining HMC without relying on the usual physics-based motivation. The notes develop HMC from a probabilistic/MCMC perspective, starting from introducing an auxiliary variable and constructing the corresponding Markov chain, and then covering:

• Hamiltonian dynamics
• leapfrog integration
• reversibility and volume preservation

Motivation

The goal was to understand why HMC works rather than treating the physics analogy as a prerequisite.

Sharing and feedback

I’m sharing them here in case they’re useful to others learning HMC. I’d also appreciate any feedback, particularly if you notice errors or places where the exposition could be improved.

https://doi.org/10.5281/zenodo.21841087