A Conceptual Introduction to Hamiltonian Monte Carlo
2017/01/10 by Michael Betancourt, Betancourt, Michael · 7 voices · 554 citations
Engineering · Mathematics · #Calculus (dental) #Computer science #Engineering #Epistemology #GRASP #Hamiltonian (control theory) #Hybrid Monte Carlo #Implementation #Intuition #Management science #Markov Chains and Monte Carlo Methods #Markov chain Monte Carlo #Mathematical Approximation and Integration #Mathematical economics #Mathematical optimization #Mathematics #Monte Carlo method #Philosophy #Physics #Statistical physics #Statistician #Stochastic processes and statistical mechanics #stat.ME
paper · pdf · doi:10.48550/arxiv.1701.02434
published in arXiv (Cornell University) (Cornell University) · 60 pages, 42 figures
openalex publication_date 2017/01/10 · arxiv created 2018/07/16 · arxiv updated 2018/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.
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- Hamiltonian Monte Carlo [wikipedia]
Discussions
- A Conceptual Introduction to Hamiltonian Monte Carlo [hn, 155 points, 33 comments]
- Overview of differential geometry for Hamiltonian Monte Carlo [hn, 8 points, 0 comments]
- A Conceptual Introduction to Hamiltonian Monte Carlo [lobsters, 5 points, 1 comments]
- A Conceptual Introduction to Hamiltonian Monte Carlo [pdf] [hn, 1 points, 0 comments]
- Hamiltonian Monte Carlo for practitioners (light on differential geometry rigor, heavy on nice cartoons) https://arxiv.org/abs/1701.02434 [bsky, 0 points, 0 comments]
- Experiential learning of Hamiltonian Monte Carlo while skiing. I SHALL EMBODY THE FRICTIONLESS PARTICLE! (reference: arxiv.org/abs/1701.02434 [bsky, 0 points, 1 comments]
- Much of @betanalpha's great #stancon2017 talk comes from his recent paper on arXiv: arxiv.org/abs/1701.02434 [bsky, 0 points, 0 comments]
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