Approximating Bayes in the 21st century

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

Research output: Contribution to journalReview ArticleResearchpeer-review


The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain “intractable” statistical problems that challenge exact methods like Markov chain Monte Carlo: for instance, models with unavailable likelihoods, high-dimensional models and models featuring large data sets. These approximate methods are the subject of this review. The aim is to help new researchers in particular—and more generally those interested in adopting a Bayesian approach to empirical work—distinguish between different approximate techniques, understand the sense in which they are approximate, appreciate when and why particular methods are useful and see the ways in which they can can be combined.
Original languageEnglish
Number of pages26
JournalStatistical Science
Publication statusAccepted/In press - 2023


  • Approximate Bayesian inference
  • intractable Bayesian problems
  • approximate Bayesian computation
  • Bayesian synthetic likelihood
  • variational Bayes
  • integrated nested Laplace approximation

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