We propose a Bayesian meta-analysis to infer the current expansion rate of the Universe, called the Hubble constant ($H_0$), via time delay cosmography. Inputs of the meta-analysis are estimates of two properties for each pair of gravitationally lensed images; time delay and Fermat potential difference estimates with their standard errors. A meta-analysis can be appealing in practice because obtaining each estimate from even a single lens system involves substantial human efforts, and thus estimates are often separately obtained and published. This work focuses on combining these estimates from independent studies to infer $H_0$ in a robust manner. For this purpose, we adopt Student's $t$ error for the inputs of the meta-analysis. We investigate properties of the resulting $H_0$ estimate via two simulation studies with realistic imaging data. It turns out that the meta-analysis can infer $H_0$ with sub-percent bias and about 1 percent level of coefficient of variation, even when 30 percent of inputs are manipulated to be outliers. We also apply the meta-analysis to three gravitationally lensed systems, and estimate $H_0$ by $75.632 \pm 6.918$ (km/second/Mpc), which covers a wide range of $H_0$ estimates obtained under different physical processes. An R package, h0, is publicly available for fitting the proposed meta-analysis.

翻译：本文提出一种贝叶斯元分析方法，通过时间延迟宇宙学推断宇宙当前膨胀速率，即哈勃常数（$H_0$）。元分析的输入为每对引力透镜图像的两种特性估计值：时间延迟和费马势差估计及其标准误差。在实际应用中，元分析具有吸引力，因为即使针对单个透镜系统，获取每组估计值也需要大量人工投入，因此这些估计值通常分别获取并独立发表。本研究重点在于如何稳健地整合来自独立研究的估计值以推断$H_0$。为此，我们对元分析的输入采用学生$t$误差分布。通过两项基于真实成像数据的仿真研究，我们探讨了所得$H_0$估计值的性质。结果表明，即便30%的输入被操控为异常值，元分析仍能以低于1%的偏差和约1%的变异系数推断$H_0$。我们还将该元分析应用于三个引力透镜系统，估算出$H_0 = 75.632 \pm 6.918$（公里/秒/百万秒差距），该结果覆盖了不同物理过程下得到的多种$H_0$估计范围。R语言包h0已公开提供，可用于拟合本文提出的元分析模型。