Computing Bayes: from then ‘til now

Gael M. Martin; David T. Frazier; Christian P. Robert

doi:10.1214/22-STS876

Computing Bayes: from then ‘til now

Gael M. Martin, David T. Frazier, Christian P. Robert

Econometrics & Business Statistics

Research output: Contribution to journal › Review Article › Research › peer-review

3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	3-19
Number of pages	17
Journal	Statistical Science
Volume	39
Issue number	1
DOIs	https://doi.org/10.1214/22-STS876
Publication status	Published - 2024

Keywords

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

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10.1214/22-STS876

Cite this

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title = "Computing Bayes: from then {\textquoteleft}til now",

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.",

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

author = "Martin, {Gael M.} and Frazier, {David T.} and Robert, {Christian P.}",

note = "Funding Information: 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{\textquoteright}Institut Universitaire de France and by a Prairie chair from the Agence Nationale de la Recherche (ANR-19-P3IA-0001). Funding Information: 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. Funding Information: Frazier has also been supported by Australian Research Council Discovery Early Career Researcher Award DE200101070. Funding Information: Robert has been partly supported by a senior chair (2016–2021) from l{\textquoteright}Institut Universitaire de France and by a Prairie chair from the Agence Nationale de la Recherche (ANR-19-P3IA-0001). Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2024",

year = "2024",

doi = "10.1214/22-STS876",

language = "English",

volume = "39",

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N1 - Funding Information: 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). Funding Information: 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. Funding Information: Frazier has also been supported by Australian Research Council Discovery Early Career Researcher Award DE200101070. Funding Information: 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). Publisher Copyright: © Institute of Mathematical Statistics, 2024

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N2 - 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.

AB - 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.

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Computing Bayes: from then ‘til now

Abstract

Keywords

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Other files and links

Loss-based Bayesian Prediction

Consequences of Model Misspecification in Approximate Bayesian Computation

The Validation of Approximate Bayesian Computation: Theory and Practice

Cite this

Computing Bayes: from then ‘til now

Abstract

Keywords

Access to Document

Other files and links

Projects

Loss-based Bayesian Prediction

Consequences of Model Misspecification in Approximate Bayesian Computation

The Validation of Approximate Bayesian Computation: Theory and Practice

Cite this