The Ninth q-bio Summer School - Albuquerque: Lecture 15

In 1953, Nicholas Metropolis, Arianna Rosenbluth, Marshall Rosenbluth, Augusta Teller and Edward Teller published an article titled "Equation of state calculations by fast computing machines" [J. Chem. Phys. 21, 1087 (1953)]. This article contains the first implementation of what is today recognized as one of the top 10 algorithms of the 20th century: the Metropolis Monte Carlo algorithm. The Metropolis Algorithm is the very first Markov chain Monte Carlo (MCMC) algorithm appearing in the scientific literature. All MCMC algorithms and techniques currently in use directly derive from the ideas presented in Metropolis' seminal paper.

The publication of the Metropolis Monte Carlo algorithm opened the way to the use of computer simulations in the physical sciences, de facto initiating a new era in scientific research where computing power is an essential tool for establishing the real predicting power of the fundamental laws of nature.

In this lecture I will report first some historical facts about the origins of the Metropolis algorithm followed by a quick introduction to some essential concepts and ideas from statistical physics and Markov processes. I will continue with an introduction to the use of the Metropolis algorithm in different statistical ensembles and to the idea of parallel tempering (a generalized implementation of the Metropolis algorithm that is particularly suitable for the simulation of biomolecular systems). At the end of the first part I will shift gear and give an example of the use of general Markov chain Monte Carlo methods in bayesian inference.

The flow of my presentation will be randomly interrupted by some simple but, nevertheless relevant, coding problems that we will try to solve on the fly. All programming languages are welcome ... even FORTRAN.