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Computing Bayes: From Then 'Til Now
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DOI：10.1214/22-STS876.png)
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Abstract
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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 coauthors), 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.
Keywords:
History of Bayesian computation
Laplace ap- proximation
Metropolis-Hastings algorithm
importance sampling
Markov chain Monte Carlo
pseudo-marginal methods
Hamiltonian Monte Carlo
se- quential Monte Carlo
approximate Bayesian methods
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