Bayesian inference is a powerful tool for combining information in complex settings, a task of increasing importance in modern applications. However, Bayesian inference with a flawed model can produce unreliable conclusions. This review discusses approaches to performing Bayesian inference when the model is misspecified, where by misspecified we mean that the analyst is unwilling to act as if the model is correct. Much has been written about this topic, and in most cases we do not believe that a conventional Bayesian analysis is meaningful when there is serious model misspecification. Nevertheless, in some cases it is possible to use a well-specified model to give meaning to a Bayesian analysis of a misspecified model and we will focus on such cases. Three main classes of methods are discussed - restricted likelihood methods, which use a model based on a non-sufficient summary of the original data; modular inference methods which use a model constructed from coupled submodels and some of the submodels are correctly specified; and the use of a reference model to construct a projected posterior or predictive distribution for a simplified model considered to be useful for prediction or interpretation.

翻译：贝叶斯推断是复杂场景下整合信息的强大工具，这一任务在现代应用中日益重要。然而，基于有缺陷模型的贝叶斯推断可能产生不可靠的结论。本文综述了当模型存在错误设定时（此处"错误设定"指分析者不愿将模型视为正确）进行贝叶斯推断的方法。关于该主题已有大量文献，我们认为在模型存在严重错误设定的情况下，传统贝叶斯分析通常缺乏意义。尽管如此，某些情况下可通过正确设定的模型赋予错误设定模型的贝叶斯分析以实际含义，本文将聚焦此类场景。主要讨论三类方法：受限似然法（基于原始数据的非充分统计量构建模型）、模块化推断法（通过耦合子模型构建模型且部分子模型正确设定），以及使用参考模型为目标简化模型构建投影后验或预测分布的方法（该简化模型被认为对预测或解释具有实用价值）。