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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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    Cited by:

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    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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