Synthetic Likelihood in Misspecified Models
研究了当模型与实际数据生成过程不一致时，贝叶斯合成似然后验的异常行为（如多峰和非高斯性），并指出常用稳健方法失效，而新提出的稳健合成似然方法能改善推断。
Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behavior of the Bayesian synthetic likelihood posterior when the assumed model differs from the actual data generating process. We demonstrate that the Bayesian synthetic likelihood posterior can display a wide range of nonstandard behaviors depending on the level of model misspecification, including multimodality and asymptotic non-Gaussianity. Our results suggest that likelihood tempering, a common approach for robust Bayesian inference, fails for synthetic likelihood whilst recently proposed robust synthetic likelihood approaches can ameliorate this behavior and deliver reliable posterior inference under model misspecification. All results are illustrated using a simple running example. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.