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We propose a Bayesian meta-analysis to infer the current expansion rate ofthe Universe, called the Hubble constant ($H_0$), via time delay cosmography.Inputs of the meta-analysis are estimates of two properties for each pair ofgravitationally lensed images; time delay and Fermat potential differenceestimates with their standard errors. A meta-analysis can be appealing inpractice because obtaining each estimate from even a single lens systeminvolves substantial human efforts, and thus estimates are often separatelyobtained and published. This work focuses on combining these estimates fromindependent studies to infer $H_0$ in a robust manner. For this purpose, weadopt Student's $t$ error for the inputs of the meta-analysis. We investigateproperties of the resulting $H_0$ estimate via two simulation studies withrealistic 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 applythe 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, ispublicly available for fitting the proposed meta-analysis.

A Robust Bayesian Meta-Analysis for Estimating the Hubble Constant via Time Delay Cosmography