A generalized marginal random effects model is described that enables exact Bayesian inference using either the Jeffreys or Berger-Bernardo non-informative prior distributions without the need for Markov Chain Monte Carlo sampling, requiring only numerical integrations. This contribution focuses on inference for the heterogeneity parameter, often called “dark uncertainty” and denoted τ in this contribution. The proposed models are used for consensus building in meta-analyses of measurement results for the Newtonian constant of gravitation, G , and for the effectiveness of anti-retroviral pre-exposure prophylaxis in preventing HIV infection. The estimates of τ that seventeen alternative different methods produce, including those that we propose, were also compared. The relative impact (gauged in terms of the ratio of the range of estimates to their median) that model choice had on the estimate of τ was very substantial: 79 % for G and 87 %...

中文翻译：

---

贝叶斯推断异质性的荟萃分析

描述了一种通用的边际随机效应模型，该模型可以使用Jeffreys或Berger-Bernardo非信息性先验分布进行精确的贝叶斯推断，而无需进行马尔可夫链蒙特卡洛采样，仅需数值积分即可。该贡献集中于对异质性参数（通常称为“暗不确定性”）的推断，并在此贡献中表示为τ。拟议中的模型用于牛顿引力常数G的测量结果的荟萃分析中的共识建立，以及抗逆转录病毒预暴露预防措施在预防HIV感染中的有效性。还比较了十七种不同方法（包括我们提出的方法）产生的τ的估计值。