Abstract
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.
Funding Statement
Martin and Frazier have been supported by Australian Research Council Discovery Grants DP170100729 and DP200101414, and the Australian Centre of Excellence in Mathematics and Statistics.
Frazier has also been supported by Australian Research Council Discovery Early Career Researcher Award DE200101070.
Robert has been partly supported by a senior chair (2016–2021) from l’Institut Universitaire de France and by a Prairie chair from the Agence Nationale de la Recherche (ANR-19-P3IA-0001).
Acknowledgments
Material that appeared in an earlier paper, entitled: “Computing Bayes: Bayesian Computation from 1763 to the 21st Century” (Martin, Frazier and Robert, 2020), now appears (in amended form) in two separate papers: the current one, in which a historical overview of and timeline for all computational developments is presented; and a second one (Martin, Frazier and Robert, 2023), which provides a detailed review of 21st century approximate Bayesian methods. The authors would like to thank the Editor, an Associate Editor and two anonymous reviewers for very helpful and insightful comments on earlier drafts of the paper.
Citation
Gael M. Martin. David T. Frazier. Christian P. Robert. "Computing Bayes: From Then ‘Til Now." Statist. Sci. 39 (1) 3 - 19, February 2024. https://doi.org/10.1214/22-STS876
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