Bayesian Synthetic Likelihood
L. F. Price, Christopher Drovandi, Anthony Lee, David John Nott · Journal of Computational and Graphical Statistics · 2017
L. F. Pricea* http://orcid.org/0000-0002-5646-2963, C. C. Drovandia http://orcid.org/0000-0001-9222-8763, A. Leeb http://orcid.org/0000-0001-7765-0616 & D. J. Nottca School of Mathematical Sciences, Queensland University of Technology, Australia and Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)b Department of Statistics, University of Warwick, Coventry, UKc Department of Statistics and Applied Probability, National University of Singapore, SingaporeCONTACT L. F. Price [email protected] School of Mathematical Sciences, Queensland University of Technology, Brisbane City, QLD 4000, Australia; and Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JCGS.Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JCGS.ABSTRACTHaving 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 https://github.com/cdrovandi/Bayesian-Synthetic-Likelihood.