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The Bayesian Synthetic Likelihood (BSL) method is a widely-used tool forlikelihood-free Bayesian inference. This method assumes that some summarystatistics are normally distributed, which can be incorrect in manyapplications. We propose a transformation, called the WassersteinGaussianization transformation, that uses a Wasserstein gradient flow toapproximately transform the distribution of the summary statistics into aGaussian distribution. BSL also implicitly requires compatibility betweensimulated summary statistics under the working model and the observed summarystatistics. A robust BSL variant which achieves this has been developed in therecent literature. We combine the Wasserstein Gaussianization transformationwith robust BSL, and an efficient Variational Bayes procedure for posteriorapproximation, to develop a highly efficient and reliable approximate Bayesianinference method for likelihood-free problems.

Wasserstein Gaussianization and Efficient Variational Bayes for Robust Bayesian Synthetic Likelihood