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

## TL;DR

This paper reviews the historical development of Markov chain Monte Carlo methods, highlighting the evolution from the Metropolis algorithm to Hamiltonian Monte Carlo, and discusses the interplay between statistical and physical perspectives.

## Contribution

It provides a comprehensive overview of MCMC methods' evolution, emphasizing the integration of physics-inspired techniques into statistical computing.

## Key findings

- Historical progression from Metropolis to Hamiltonian Monte Carlo
- Enhanced understanding of physics-statistics interplay in MCMC
- Identification of key innovations driving MCMC advancements

## Abstract

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.