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：贝叶斯推断是在复杂情境中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，使用有缺陷的模型进行贝叶斯推断可能产生不可靠的结论。本文综述了当模型被错误设定时的贝叶斯推断方法——所谓"错误设定"指分析者不愿假定模型正确。该主题已有大量文献讨论，在多数情况下我们认为，当模型存在严重错误设定时，常规贝叶斯分析缺乏意义。尽管如此，在某些场景下，利用正确设定的模型赋予错误设定模型贝叶斯分析以意义是可行的，我们将聚焦此类情况。本文讨论三类主要方法：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，其中部分子模型被正确设定），以及使用参考模型为简化模型（被认为适用于预测或解释）构建投影后验或预测分布的方法。