A short history of Markov chain Monte Carlo: Subjective recollections from incomplete data. (English) Zbl 1222.65006

Robert, Christian; Casella, George

Stat. Sci. 26, No. 1, 102-115 (2011).

Summary: We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research have led to the algorithms currently in use. More importantly, we see how the development of this methodology has not only changed our solutions to problems, but has changed the way we think about problems.

MSC:

65C05	Monte Carlo methods
65C40	Numerical analysis or methods applied to Markov chains
60J22	Computational methods in Markov chains
65-03	History of numerical analysis
01A60	History of mathematics in the 20th century

Keywords:

Gibbs sampling; Metropolis-Hasting algorithm; hierarchical models; Bayesian methods; Markov chain Monte Carlo

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