Computing Bayes: From Then 'Til Now'

08/01/2022

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by   Gael M. Martin, et al.

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This paper takes the reader on a journey through the history of Bayesian computation, from the 18th century to the present day. Beginning with the one-dimensional integral first confronted by Bayes in 1763, we highlight the key contributions of: Laplace, Metropolis (and, importantly, his co-authors!), Hammersley and Handscomb, and Hastings, all of which set the foundations for the computational revolution in the late 20th century – led, primarily, by Markov chain Monte Carlo (MCMC) algorithms. A very short outline of 21st century computational methods – including pseudo-marginal MCMC, Hamiltonian Monte Carlo, sequential Monte Carlo, and the various `approximate' methods – completes the paper.