Variational Bayes with Synthetic Likelihood

Ong, Victor M-H., Nott, David J., Tran, Minh-Ngoc, Sisson, Scott A., & Drovandi, Christopher C. (2016) Variational Bayes with Synthetic Likelihood. [Working Paper] (Unpublished)


Synthetic likelihood is an attractive approach to likelihood-free inference when an approximately Gaussian summary statistic for the data, informative for inference about the parameters, is available. The synthetic likelihood method derives an approximate likelihood function from a plug-in normal density estimate for the summary statistic, with plug-in mean and covariance matrix obtained by Monte Carlo simulation from the model. In this article, we develop alternatives to Markov chain Monte Carlo implementations of Bayesian synthetic likelihoods with reduced computational overheads. Our approach uses stochastic gradient variational inference methods for posterior approximation in the synthetic likelihood context, employing unbiased estimates of the log likelihood. We compare the new method with a related likelihood free variational inference technique in the literature, while at the same time improving the implementation of that approach in a number of ways. These new algorithms are feasible to implement in situations which are challenging for conventional approximate Bayesian computation (ABC) methods, in terms of the dimensionality of the parameter and summary statistic.

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ID Code: 98023
Item Type: Working Paper
Refereed: No
Keywords: Approximate Bayesian computation, Stochastic gradient ascent, Synthetic likelihoods, Variational Bayes
Subjects: 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 > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2016 [please consult the authors]
Deposited On: 11 Aug 2016 23:07
Last Modified: 12 Aug 2016 16:25

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