The Bayesian Synthetic Likelihood (BSL) method is a widely-used tool for likelihood-free Bayesian inference. This method assumes that some summary statistics are normally distributed, which can be incorrect in many applications. We propose a transformation, called the Wasserstein Gaussianization transformation, that uses a Wasserstein gradient flow to approximately transform the distribution of the summary statistics into a Gaussian distribution. BSL also implicitly requires compatibility between simulated summary statistics under the working model and the observed summary statistics. A robust BSL variant which achieves this has been developed in the recent literature. We combine the Wasserstein Gaussianization transformation with robust BSL, and an efficient Variational Bayes procedure for posterior approximation, to develop a highly efficient and reliable approximate Bayesian inference method for likelihood-free problems.

翻译：贝叶斯合成似然（BSL）方法是无似然贝叶斯推断中广泛使用的工具。该方法假设某些汇总统计量服从正态分布，但在许多应用中这一假设可能不成立。我们提出一种称为Wasserstein高斯化变换的变换方法，利用Wasserstein梯度流将汇总统计量的分布近似变换为高斯分布。BSL还隐式要求工作模型下模拟的汇总统计量与观测的汇总统计量之间具有兼容性。近期文献中已发展出一种实现该兼容性的稳健BSL变体。我们将Wasserstein高斯化变换与稳健BSL以及一种用于后验近似的高效变分贝叶斯方法相结合，开发出一种针对无似然问题的高效且可靠的近似贝叶斯推断方法。