Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments conducted at different time points, the typical meta-analysis approach, which assumes homoscedasticity, fails to adequately address this heteroscedasticity among experiments. This paper proposes a new Bayesian estimation method that simultaneously shrinks estimates of the means and variances of experiments using a hierarchical Bayesian approach while accounting for time effects through a Gaussian process. This method connects experiments via the hierarchical framework, enabling "borrowing strength" between experiments to achieve high-precision estimates of each experiment's mean. The method can flexibly capture potential time trends in datasets by modeling time effects with the Gaussian process. We demonstrate the effectiveness of the proposed method through simulation studies and illustrate its practical utility using a real marketing promotions dataset.

翻译：元分析被广泛应用于整合多项实验结果以获取普适性结论。由于元分析数据集常因不同子组及实验时间点差异而产生异方差性，传统假设同方差的元分析方法难以充分处理实验间的异质性。本文提出一种新的贝叶斯估计方法，通过分层贝叶斯框架同步收缩实验均值与方差的估计值，并借助高斯过程纳入时间效应。该方法通过分层结构连接各实验，实现实验间的"信息借用"，从而获得高精度的实验均值估计。利用高斯过程对时间效应建模，本方法能灵活捕捉数据集中潜在的时间趋势。我们通过模拟研究验证了所提方法的有效性，并借助真实营销促销数据集展示了其实用价值。