empirical method for mitigating an excess up-scattering mass bias on the weak lensing mass estimates for shear-selected cluster samples.

This article focuses on the excess up-scattering mass bias affecting weak lensing cluster mass estimates, where observed weak lensing masses (M_obs) tend to be statistically overestimated relative to true cluster masses (M_true) due to asymmetric noise scatter combined with a decreasing cluster mass function. The authors develop and test an empirical Bayesian correction method that incorporates prior knowledge of the cluster mass function and concentration parameter distributions to mitigate this bias without relying on extensive mock simulations. Using realistic mock weak lensing cluster catalogs, the method reduces the average mass bias to within approximately 10% for clusters with sufficiently high signal-to-noise ratios (SN_γ ≳ 5). The correction is applied to a sample of 61 shear-selected clusters from the Hyper Suprime-Cam survey, yielding bias-corrected masses for 37 clusters, with corrected masses on average about 58% of the uncorrected estimates. The study emphasizes appropriate contexts for using the corrected masses and notes limitations of the method, particularly its dependence on high signal-to-noise data and the need for further refinement of priors to avoid non-physical posterior behavior at low masses.