Computing Bayes: from then ‘til now

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

Research output: Contribution to journalReview ArticleResearchpeer-review


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 languageEnglish
Number of pages17
JournalStatistical Science
Publication statusAccepted/In press - 2023


  • 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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