Hamiltonian Monte Carlo

Brian Keng — Fri, 24 Dec 2021 00:07:05 GMT

Here's a topic I thought that I would never get around to learning because it was "too hard". When I first started learning about Bayesian methods, I knew enough that I should learn a thing or two about MCMC since that's the backbone of most Bayesian analysis; so I learned something about it (see my previous post). But I didn't dare attempt to learn about the infamous Hamiltonian Monte Carlo (HMC). Even though it is among the standard algorithms used in Bayesian inference, it always seemed too daunting because it required "advanced physics" to understand. As usual, things only seem hard because you don't know them yet. After having some time to digest MCMC methods, getting comfortable learning more maths (see here, here, and here), all of a sudden learning "advanced physics" didn't seem so tough (but there sure was a lot of background needed)!

This post is the culmination of many different rabbit holes (many much deeper than I needed to go) where I'm going to attempt to explain HMC in simple and intuitive terms to a satisfactory degree (that's the tag line of this blog after all). I'm going to begin by briefly motivating the topic by reviewing MCMC and the Metropolis-Hastings algorithm then move on to explaining Hamiltonian dynamics (i.e., the "advanced physics"), and finally discuss the HMC algorithm along with some toy experiments I put together. Most of the material is based on [1] and [2], which I've found to be great sources for their respective areas.

Bounded Rationality (Posts about Hamiltonian)

Hamiltonian Monte Carlo