Meta-analysis is an important quantitative tool for cumulative science, but its application is frustrated by publication bias. In order to test and adjust for publication bias, we extend model-averaged Bayesian meta-analysis with selection models. The resulting robust Bayesian meta-analysis (RoBMA) methodology does not require all-or-none decisions about the presence of publication bias, can quantify evidence in favor of the absence of publication bias, and performs well under high heterogeneity. By model-averaging over a set of 12 models, RoBMA is relatively robust to model misspecification and simulations show that it outperforms existing methods. We demonstrate that RoBMA finds evidence for the absence of publication bias in Registered Replication Reports and reliably avoids false positives. We provide an implementation in R so that researchers can easily use the new methodology in practice.

中文翻译：

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稳健的贝叶斯荟萃分析：通过模型平均解决发表偏差。

荟萃分析是累积科学的重要定量工具，但其应用因发表偏见而受挫。为了测试和调整发表偏倚，我们用选择模型扩展了模型平均贝叶斯荟萃分析。由此产生的稳健贝叶斯荟萃分析 (RoBMA) 方法不需要对是否存在发表偏倚做出全有或全无的决定，可以量化有利于不存在发表偏倚的证据，并且在高异质性下表现良好。通过对一组 12 个模型进行模型平均，RoBMA 对于模型错误指定相对稳健，并且模拟表明它优于现有方法。我们证明 RoBMA 在注册复制报告中找到了不存在发表偏倚的证据，并可靠地避免了误报。我们提供了 R 中的实现，以便研究人员可以在实践中轻松使用新方法。