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From its inception in the 1950s to the modern frontiers of appliedstatistics, Markov chain Monte Carlo has been one of the most ubiquitous andsuccessful methods in statistical computing. In that time its development hasbeen fueled by increasingly difficult problems and novel techniques fromphysics. In this article I will review the history of Markov chain Monte Carlofrom its inception with the Metropolis method to today's state-of-the-art inHamiltonian Monte Carlo. Along the way I will focus on the evolving interplaybetween the statistical and physical perspectives of the method.

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