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

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.