The Monte Carlo Method / Metropolis Algorithm

Editorial record

Plain-language summary

Working on nuclear physics problems at Los Alamos, Stanislaw Ulam, John von Neumann, Nicholas Metropolis, and colleagues realized that random sampling on a computer could approximate answers to equations too complex to solve directly. The 1953 Metropolis algorithm added a rule for sampling from a probability distribution by accepting or rejecting proposed moves, making it possible to simulate systems in equilibrium. These techniques became standard tools across physics, statistics, and later machine learning. Much of modern probabilistic modeling and Bayesian computation traces back to this sampling idea.