Bayesian Synthetic Likelihood

L. F. Price*, C. C. Drovandi, Anthony Lee, D. J. Nott

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

39 Citations (Scopus)


Having the ability to work with complex models can be highly beneficial. However, complex models often have intractable likelihoods, so methods that involve evaluation of the likelihood function are infeasible. In these situations, the benefits of working with likelihood-free methods become apparent. Likelihood-free methods, such as parametric Bayesian indirect likelihood that uses the likelihood of an alternative parametric auxiliary model, have been explored throughout the literature as a viable alternative when the model of interest is complex. One of these methods is called the synthetic likelihood (SL), which uses a multivariate normal approximation of the distribution of a set of summary statistics. This article explores the accuracy and computational efficiency of the Bayesian version of the synthetic likelihood (BSL) approach in comparison to a competitor known as approximate Bayesian computation (ABC) and its sensitivity to its tuning parameters and assumptions. We relate BSL to pseudo-marginal methods and propose to use an alternative SL that uses an unbiased estimator of the SL, when the summary statistics have a multivariate normal distribution. Several applications of varying complexity are considered to illustrate the findings of this article. Supplemental materials are available online. Computer code for implementing the methods on all examples is available at

Original languageEnglish
Number of pages11
JournalJournal of Computational and Graphical Statistics
Early online date7 Mar 2017
Publication statusE-pub ahead of print - 7 Mar 2017


  • Approximate Bayesian computation
  • Bayesian indirect likelihood
  • Indirect inference
  • Pseudo-marginal methods
  • Synthetic likelihood

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