We analyse the behaviour of approximate Bayesian computation (ABC) when the model generating the simulated data differs from the actual data‐generating process, i.e. when the data simulator in ABC is misspecified. We demonstrate both theoretically and in simple, but practically relevant, examples that when the model is misspecified different versions of ABC can yield substantially different results. Our theoretical results demonstrate that even though the model is misspecified, under regularity conditions, the accept–reject ABC approach concentrates posterior mass on an appropriately defined pseudotrue parameter value. However, under model misspecification the ABC posterior does not yield credible sets with valid frequentist coverage and has non‐standard asymptotic behaviour. In addition, we examine the theoretical behaviour of the popular local regression adjustment to ABC under model misspecification and demonstrate that this approach concentrates posterior mass on a pseudotrue value that is completely different from accept–reject ABC. Using our theoretical results, we suggest two approaches to diagnose model misspecification in ABC. All theoretical results and diagnostics are illustrated in a simple running example.

中文翻译：

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近似贝叶斯计算中的模型错误指定：后果和诊断

当生成模拟数据的模型与实际数据生成过程不同时，即当ABC中的数据模拟器指定不正确时，我们将分析近似贝叶斯计算（ABC）的行为。我们在理论上和简单但实际相关的示例中都进行了演示，这些示例表明，当模型被错误指定时，不同版本的ABC可能会产生实质上不同的结果。我们的理论结果表明，即使模型指定不正确，在规则性条件下，接受拒绝ABC方法也会将后验质量集中在适当定义的伪真实参数值上。但是，在模型错误指定的情况下，ABC后验不能产生可靠的频次覆盖有效范围的集合，并且具有非标准的渐近行为。此外，我们研究了在模型错误指定情况下对ABC进行的流行的局部回归调整的理论行为，并证明了该方法将后验质量集中在与接受拒绝ABC完全不同的伪真实值上。使用我们的理论结果，我们建议了两种方法来诊断ABC中的模型错误指定。在一个简单的运行示例中说明了所有理论结果和诊断。