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arXiv:1701.02434stat.ME

A Conceptual Introduction to Hamiltonian Monte Carlo

Michael Betancourt

Abstract

Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately, that understanding is confined within the mathematics of differential geometry which has limited its dissemination, especially to the applied communities for which it is particularly important. In this review I provide a comprehensive conceptual account of these theoretical foundations, focusing on developing a principled intuition behind the method and its optimal implementations rather of any exhaustive rigor. Whether a practitioner or a statistician, the dedicated reader will acquire a solid grasp of how Hamiltonian Monte Carlo works, when it succeeds, and, perhaps most importantly, when it fails.

arXiv comments
60 pages, 42 figures
Journal reference
DOI
Subjects
stat.MEMethodology (Statistics)

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Linked by 8 identifiable commenters in 8 comments across 8 threads, from May 2017 to Dec 2025. Found in 3 HN submissions from Feb 2017 to Sep 2025. Open submission discussions.

Comments linking this paper, per year.

Discussed in comments8 threads

  1. What I don’t like about chains of thoughts (2023) 1 comment

    • I think you're confusing the sampling process and the convergence of those samples with the warmup process (also called 'burn-in') in HMC. When doing HMC MCMC we typically don't start sampling right away (or, more precisely we throw out those samples) because we may be…

      crystal_revengeView on HNParent context

  2. Claude 3 Opus reinvented this quantum algorithm from scratch in just 2 prompts 1 comment

    • Also did a bit of QC research. Since I'm tipsy, I skimmed the Twitter post. Here's a pdf on arxiv about HMC (2017) which I found in 20 seconds: https://arxiv.org/abs/1701.02434 Seems like Claude3 is decently logical in paraphrasing key parts of text in a good order, but with…

      winwangView on HNParent context

  3. Ask HN: What's the best paper you've read in 2020? 1 comment
  4. Ask HN: Best place to start learning about Markov Chains? 1 comment
  5. Hamiltonian Monte Carlo explained 1 comment

    • Also check out Michael Betancourt’s (one of the developers of Stan) introduction: https://arxiv.org/abs/1701.02434

      aportnoyView on HNParent context

  6. Bayes’ Theorem in the 21st Century (2013) [pdf] 1 comment
  7. Gaussian Distributions Are Soap Bubbles 1 comment

    • I won't dispute the main point of the article but a couple minor errors bug me. First, he kept referring to a Gaussian distribution as being the unit sphere, when of course the radius depends upon the parameters of the Gaussian (the standard deviation). If not, then it wouldn't…

      tgbView on HNParent context

  8. How Bayesian Inference Works (2016) 1 comment

    • In case anyone is wondering how Bayesian inference works on non-trivial problems: https://arxiv.org/pdf/1701.02434.pdf

      jamiiView on HNParent context

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