Metropolis–Hastings algorithm: Difference between revisions

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The algorithm was named after [[Nicholas Metropolis]] and [[W.K. Hastings]]. Metropolis was the first author to appear on the list of authors of the 1953 article ''[[Equation of State Calculations by Fast Computing Machines]]'' together with [[Arianna W. Rosenbluth]], [[Marshall Rosenbluth]], [[Augusta H. Teller]] and [[Edward Teller]]. This article proposed the algorithm for the case of symmetrical proposal distributions, and for many years was known 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> In 1970, Hastings extended it to the more general case.<ref name=Hastings/> The generalized method eventually was given 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, priorPrior 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 then-wife Arianna did the work, and that Metropolis played no role in the development other than providing computer time.

This contradicts an account by Edward Teller, who states in his memoirs that the five authors of the 1953 article worked together for "days (and nights)".<ref name=Teller/> In contrast, the detailed account by Marshall Rosenbluth credits Teller with a crucial but early suggestion to "take advantage of statistical mechanics and take ensemble averages instead of following detailed kinematics". This, says Rosenbluth, started him thinking about the generalized Monte Carlo approach – a topic which he says he had discussed often with [[John von Neumann|John Von Neumann]]. Arianna Rosenbluth recounted (to Gubernatis in 2003) that Augusta Teller started the computer work, but that Arianna herself took it over and wrote the code from scratch. In an oral history recorded shortly before his death,<ref name=Barth/> Marshall Rosenbluth again credits Teller with posing the original problem, himself with solving it, and Arianna with programming the computer.

==Intuition==