在不恰当模型中的合成似然
Synthetic likelihood in misspecified models
AI总结：
研究分析了在模型不恰当情况下合成似然后验行为，揭示其可能呈现非标准特性如多模态和非高斯性，并指出传统鲁棒方法在合成似然中的不足。
摘要：
贝叶斯合成似然是一种在复杂模型中进行贝叶斯分析的常用方法，当无法评估似然但可以模拟假设模型时。我们分析了当假设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行为。我们展示了贝叶斯合成似然后验在模型不恰当程度不同下可以表现出广泛非标准行为，包括多模态和渐近非高斯性。我们的结果表明，传统用于稳健贝叶斯推断的似然降温方法在合成似然中失效，而最近提出的稳健合成似然方法可以缓解这一行为并在模型不恰当情况下提供可靠的后验推断。所有结果均通过一个简单的运行例子进行说明。
英文摘要：
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.
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