Synthetic Likelihood in Misspecified Models

• 成果类型: Article
• 署名作者: Frazier, David T.; Nott, David J.; Drovandi, Christopher
• 署名单位: Monash University; National University of Singapore; National University of Singapore; Queensland University of Technology (QUT)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2370594
• 发表日期: 2025
• 页码: 884-895
• 关键词: asymptotic properties; inference

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 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.