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