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Concept
Metropolis–Hastings algorithm
Summary
In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult. This sequence can be used to approximate the distribution (e.g. to generate a histogram) or to compute an integral (e.g. an expected value). Metropolis–Hastings and other MCMC algorithms are generally used for sampling from multi-dimensional distributions, especially when the number of dimensions is high. For single-dimensional distributions, there are usually other methods (e.g. adaptive rejection sampling) that can directly return independent samples from the distribution, and these are free from the problem of autocorrelated samples that is inherent in MCMC methods.
The algorithm is named in part for Nicholas Metropolis, the first coauthor of a 1953 paper, entitled Equation of State Calculations by Fast Computing Machines, with Arianna W. Rosenbluth, Marshall Rosenbluth, Augusta H. Teller and Edward Teller. For many years the algorithm was known simply as the Metropolis algorithm. The paper proposed the algorithm for the case of symmetrical proposal distributions, but in 1970, W.K. Hastings extended it to the more general case. The generalized method was eventually identified by both names, although the first use of the term "Metropolis-Hastings algorithm" is unclear.
Some controversy exists with regard to credit for development of the Metropolis algorithm. Metropolis, who was familiar with the computational aspects of the method, had coined the term "Monte Carlo" in an earlier article with Stanisław Ulam, and led the group in the Theoretical Division that designed and built the MANIAC I computer used in the experiments in 1952. However, prior to 2003 there was no detailed account of the algorithm's development. Shortly before his death, Marshall Rosenbluth attended a 2003 conference at LANL marking the 50th anniversary of the 1953 publication.
Official source
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