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）方法是当前广泛使用的无似然贝叶斯推断工具。该方法假设某些摘要统计量服从正态分布，但在许多实际应用中这一假设可能不成立。本文提出一种称为Wasserstein高斯化变换的转换方法，该方法利用Wasserstein梯度流将摘要统计量的分布近似转换为高斯分布。BSL方法还隐含要求工作模型下模拟的摘要统计量与观测摘要统计量之间具有兼容性。近期文献已发展出一种实现该要求的鲁棒BSL变体。本文将Wasserstein高斯化变换与鲁棒BSL方法相结合，并采用高效的变分贝叶斯过程进行后验近似，从而为无似然问题构建了一种高效可靠的近似贝叶斯推断方法。