February 2024 Computing Bayes: From Then ‘Til Now
Gael M. Martin, David T. Frazier, Christian P. Robert
Author Affiliations +
Statist. Sci. 39(1): 3-19 (February 2024). DOI: 10.1214/22-STS876


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).


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.


Download 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


Published: February 2024
First available in Project Euclid: 18 February 2024

MathSciNet: MR4718524
Digital Object Identifier: 10.1214/22-STS876

Keywords: approximate Bayesian methods , Hamiltonian Monte Carlo , History of Bayesian computation , importance sampling , Laplace approximation , Markov chain Monte Carlo , Metropolis–Hastings algorithm , pseudo-marginal methods , sequential Monte Carlo

Rights: Copyright © 2024 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.39 • No. 1 • February 2024
Back to Top