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Volume 25, Number 12—December 2019
Etymologia

Etymologia: Markov Chain Monte Carlo

Ronnie HenryComments to Author 

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Markov Chain Monte Carlo

A Markov chain Monte Carlo (MCMC) simulation is a method of estimating an unknown probability distribution for the outcome of a complex process (a posterior distribution). Prior (capturing the concept prior to seeing any data) distributions are used to simulate sampling from variables that have known or closely approximated distributions in the complex process. Thus, the prior distributions are known probability distributions that represent uncertainty about a particular attribute of a population prior to data sampling, and the posterior distribution represents estimated uncertainty about a population attribute after data sampling and is conditional on the observed data.

Monte Carlo (named for the casino in Monaco) methods estimate a distribution by random sampling. Many samples of the prior distributions must be obtained (e.g., many rolls of the dice) to obtain a stable and accurate posterior distribution. The modern version of the Monte Carlo was invented by Stanislaw Ulam and developed early on by John von Neumann and Nicholas Metropolis, the latter of whom suggested the name, as part of follow on work to the Manhattan Project. Ulam was trying to calculate the probability of laying out a winning game of solitaire from a shuffled deck of 52 cards. Because of the complexity of the calculations, he decided it would be easier to play 100 games of solitaire and count the percentage that won.

Figure

Thumbnail of Andrey Markov (1856–1922), photographer unknown, public domain, https://commons.wikimedia.org/w/index.php?curid=1332494

Figure. Andrey Markov (1856–1922), photographer unknown, public domain, https://commons.wikimedia.org/w/index.php?curid=1332494

In a Markov chain (named for Russian mathematician Andrey Markov [Figure]), the probability of the next computed estimated outcome depends only on the current estimate and not on prior estimates. For example, if you shuffle a deck of cards 3 times, the outcome of the third shuffle depends only on the state of the cards at the second shuffle, not at the first shuffle. Markov chain Monte Carlo simulations allow researchers to approximate posterior distributions that cannot be directly calculated.

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References

  1. Eckhardt  R. Stan Ulam, John von Neumann, and the Monte Carlo method. Los Alamos Sci. 1987;15:1317.
  2. Hamra  G, MacLehose  R, Richardson  D. Markov chain Monte Carlo: an introduction for epidemiologists. Int J Epidemiol. 2013;42:62734. DOIPubMed
  3. van Ravenzwaaij  D, Cassey  P, Brown  SD. A simple introduction to Markov Chain Monte-Carlo sampling. Psychon Bull Rev. 2018;25:14354. DOIPubMed

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Figure

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Suggested citation for this article: Etymologia: Markov chain Monte Carlo. Emerg Infect Dis. 2019 Dec [date cited]. https://doi.org/10.3201/eid2512.ET2512

DOI: 10.3201/eid2512.et2512

Original Publication Date: 11/6/2019

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Table of Contents – Volume 25, Number 12—December 2019

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Ronnie Henry, Centers for Disease Control and Prevention, 1600 Clifton Rd NE, Mailstop E28, Atlanta, GA 30329-4027, USA

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Page created: November 06, 2019
Page updated: November 06, 2019
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The conclusions, findings, and opinions expressed by authors contributing to this journal do not necessarily reflect the official position of the U.S. Department of Health and Human Services, the Public Health Service, the Centers for Disease Control and Prevention, or the authors' affiliated institutions. Use of trade names is for identification only and does not imply endorsement by any of the groups named above.
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