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 behaviour 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 non-standard behaviours 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.

翻译：贝叶斯合成似然是一种广泛采用的方法，用于在似然评估不可行但假设模型可模拟的复杂模型中进行贝叶斯分析。我们分析了当假设模型与实际数据生成过程存在差异时，贝叶斯合成似然后验的行为。研究表明，根据模型误指定的程度，贝叶斯合成似然后验可能表现出多种非标准行为，包括多峰性和渐近非高斯性。我们的结果表明，似然退火（一种常用的稳健贝叶斯推断方法）在合成似然中失效，而近期提出的稳健合成似然方法能够改善此行为，并在模型误指定下提供可靠的后验推断。所有结果均通过一个简单的运行实例加以说明。