# The Convergence of Markov chain Monte Carlo Methods: From the Metropolis method to Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/1706.01520 · HTML: https://mlsanity.com/paper/1706.01520/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2017.

## Built on by (most cited first, 2 of 2)

- [Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2111.08030/) (2021)
- [Enhanced BPINN Training Convergence in Solving General and Multi-scale Elliptic PDEs with Noise](https://mlsanity.com/paper/2408.09340/) (2024)

## Abstract (arXiv)

From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical computing. In that time its development has been fueled by increasingly difficult problems and novel techniques from physics. In this article I will review the history of Markov chain Monte Carlo from its inception with the Metropolis method to today's state-of-the-art in Hamiltonian Monte Carlo. Along the way I will focus on the evolving interplay between the statistical and physical perspectives of the method.