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 focus on such cases. Three main classes of methods are discussed: restricted likelihood methods, which use a model based on an insufficient summary of the original data; modular inference methods, which use a model constructed from coupled submodels, with some of the submodels 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.

中文翻译：

---

错误指定生成模型的贝叶斯推理


贝叶斯推理是一种强大的工具，用于在复杂环境中组合信息，这是一项在现代应用中越来越重要的任务。但是，使用有缺陷的模型进行贝叶斯推理可能会产生不可靠的结论。这篇综述讨论了在模型指定错误时执行贝叶斯推理的方法，其中，错误指定是指分析师不愿意假装模型是正确的。关于这个主题已经写了很多文章，在大多数情况下，我们认为当存在严重的模型错误指定时，传统的贝叶斯分析没有意义。然而，在某些情况下，可以使用一个明确指定的模型来赋予对错误指定模型的贝叶斯分析以意义，我们专注于此类情况。讨论了三类主要的方法：限制似然法，它使用基于原始数据摘要不足的模型;模块化推理方法，使用由耦合子模型构建的模型，并正确指定了一些子模型;以及使用参考模型为被认为对预测或解释有用的简化模型构建预测的后验或预测分布。