Bayesian synthetic likelihood
Price, Leah F., Drovandi, Christopher C., Lee, Anthony, & Nott, David J. (2016) Bayesian synthetic likelihood. [Working Paper] (Unpublished)

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Abstract
Having the ability to work with complex models can be highly beneficial, but the computational cost of doing so is often large. Complex models often have intractable likelihoods, so methods that directly use the likelihood function are infeasible. In these situations, the benefits of working with likelihoodfree methods become apparent. Likelihoodfree 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 good alternative when the model of interest is complex. One of these methods is called the synthetic likelihood (SL), which assumes a multivariate normal approximation to the likelihood of a summary statistic of interest. This paper 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 pseudomarginal methods and propose to use an alternative SL that uses an unbiased estimator of the exact working normal likelihood when the summary statistic has a multivariate normal distribution. Several applications of varying complexity are considered to illustrate the findings of this paper.
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ID Code:  92795 

Item Type:  Working Paper 
Refereed:  No 
Keywords:  indirect inference, Bayesian indirect likelihood, approximate Bayesian computation, synthetic likelihood, pseudomarginal methods 
Subjects:  Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Applied Statistics (010401) Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Statistical Theory (010405) Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Stochastic Analysis and Modelling (010406) 
Divisions:  Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS) Current > Schools > School of Mathematical Sciences Current > QUT Faculties and Divisions > Science & Engineering Faculty 
Facilities:  Science and Engineering Centre 
Copyright Owner:  Copyright 2016 The Author(s) 
Deposited On:  10 Feb 2016 23:18 
Last Modified:  21 Oct 2016 09:38 
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