Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the construction of the resulting likelihood function. However, sometimes the model is so complicated that evaluation of the likelihood is infeasible, which renders exact Bayesian inference impossible. Bayesian synthetic likelihood (BSL) is a posterior approximation procedure that can be used to conduct inference in situations where the likelihood is intractable, but where simulation from the model is straightforward. In this entry, we give a high-level presentation of BSL, and its extensions aimed at delivering scalable and robust posterior inferences.

翻译：贝叶斯统计关注于在给定统计模型中对未知量进行后验推断。传统的贝叶斯推断需要为观测数据指定概率模型并构造相应的似然函数。然而，当模型过于复杂导致似然函数难以计算时，精确的贝叶斯推断便无法实现。贝叶斯合成似然（BSL）是一种后验近似方法，适用于似然不可处理但可方便地从模型进行仿真的场景。本文简要介绍了BSL及其旨在提供可扩展且稳健的后验推断的扩展方法。