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Bayesian synthetic likelihood

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Price, Leah F., Drovandi, Christopher C., Lee, Anthony and Nott, David J. (2018) Bayesian synthetic likelihood. Journal of Computational and Graphical Statistics, 27 (1). p. 1. doi:10.1080/10618600.2017.1302882

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Official URL: http://dx.doi.org/10.1080/10618600.2017.1302882

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Abstract

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 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 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 paper. Supplemental materials are available online.

Item Type: Journal Article
Divisions: Faculty of Science > Statistics
Journal or Publication Title: Journal of Computational and Graphical Statistics
Publisher: American Statistical Association
ISSN: 1061-8600
Official Date: 2018
Dates:
DateEvent
2018Published
7 March 2017Available
23 January 2017Accepted
Volume: 27
Number: 1
Page Range: p. 1
DOI: 10.1080/10618600.2017.1302882
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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