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Computing Bayes: From Then `Til Now

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

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.

Suggested Citation

  • Gael M. Martin & David T. Frazier & Christian P. Robert, 2022. "Computing Bayes: From Then `Til Now," Monash Econometrics and Business Statistics Working Papers 14/22, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2022-14
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/wp14-2022.pdf
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    References listed on IDEAS

    as
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    Cited by:

    1. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    2. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    3. Tore Selland Kleppe, 2024. "Log‐density gradient covariance and automatic metric tensors for Riemann manifold Monte Carlo methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1206-1229, September.

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    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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