Metropolis–Hastings algorithm: Difference between revisions

Revision as of 03:25, 20 March 2023

Revision as of 03:26, 20 March 2023

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==History==

The algorithm is named for [[Nicholas Metropolis]] and [[W.K. Hastings]], coauthors 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]],. but forFor many years the algorithm was known simply as the ''Metropolis algorithm''.<ref>{{Cite book |last=Kalos |first=Malvin H. |title=Monte Carlo Methods Volume I: Basics |last2=Whitlock |first2=Paula A. |publisher=Wiley |year=1986 |___location=New York |pages=78-88}}</ref><ref>{{Cite journal |last=Tierney |first=Luke |date=1994 |title=Markov chains for exploring posterior distributions |url=https://projecteuclid.org/journals/annals-of-statistics/volume-22/issue-4/Markov-Chains-for-Exploring-Posterior-Distributions/10.1214/aos/1176325750.full |journal=The Annals of Statistics |volume=22 |issue=4 |pages=1701-1762}}</ref> The paper proposed the algorithm for the case of symmetrical proposal distributions, but in 1970, Hastings extended it to the more general case.<ref name=Hastings/> The generalized method was eventually identified by both names, although the first use of the term "Metropolis-Hastings algorithm" is unclear; it may have first appeared in a 1995 review by Chib and Greenberg.<ref>{{Cite journal |last=Chib |first=Siddhartha |last2=Greenberg |first2=Edward |date=1995 |title=Understanding the Metropolis-Hastings Algorithm |url=https://www.jstor.org/stable/2684568 |journal=The American Statistician |volume=49 |issue=4 |pages=327-335 |via=JSTOR}}</ref>

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. At this conference, Rosenbluth described the algorithm and its development in a presentation titled "Genesis of the Monte Carlo Algorithm for Statistical Mechanics".<ref name=Rosenbluth/> Further historical clarification is made by Gubernatis in a 2005 journal article<ref name=Gubernatis/> recounting the 50th anniversary conference. Rosenbluth makes it clear that he and his wife Arianna did the work, and that Metropolis played no role in the development other than providing computer time.