Bayesian synthetic likelihood (BSL) is now a well-established method for performing approximate Bayesian parameter estimation for simulation-based models that do not possess a tractable likelihood function. BSL approximates an intractable likelihood function of a carefully chosen summary statistic at a parameter value with a multivariate normal distribution. The mean and covariance matrix of this normal distribution are estimated from independent simulations of the model. Due to the parametric assumption implicit in BSL, it can be preferred to its nonparametric competitor, approximate Bayesian computation, in certain applications where a high-dimensional summary statistic is of interest. However, despite several successful applications of BSL, its widespread use in scientific fields may be hindered by the strong normality assumption. In this paper, we develop a semi-parametric approach to relax this assumption to an extent and maintain the computational advantages of BSL without any additional tuning. We test our new method, semiBSL, on several challenging examples involving simulated and real data and demonstrate that semiBSL can be significantly more robust than BSL and another approach in the literature.

中文翻译：

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通过半参数方法进行稳健的贝叶斯综合似然

贝叶斯综合似然（BSL）现在是一种行之有效的方法，用于对不具有可处理似然函数的基于仿真的模型执行近似贝叶斯参数估计。BSL在参数值具有多元正态分布的情况下，对经过精心选择的摘要统计量的难解似然函数进行近似。此正态分布的均值和协方差矩阵是通过模型的独立仿真估算的。由于BSL中隐含的参数假设，因此在某些需要关注高维摘要统计信息的应用中，它可能比其非参数竞争对手（近似贝叶斯计算）更受欢迎。但是，尽管BSL取得了一些成功的应用，但强大的正态性假设可能会阻碍其在科学领域的广泛使用。在本文中，我们开发了一种半参数方法，可以在某种程度上放松这一假设并保持BSL的计算优势，而无需任何其他调整。我们在涉及模拟和真实数据的几个具有挑战性的示例上测试了我们的新方法semiBSL，并证明了SemiBSL比BSL和文献中的另一种方法要强大得多。