# A Conceptual Introduction to Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/1701.02434 · HTML: https://mlsanity.com/paper/1701.02434/

## Key facts

- Cited by 209 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2017.

## Built on by (most cited first, 30 of 209)

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## Abstract (arXiv)

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.