CoMaLit – V. Mass forecasting with proxies: method and application to weak lensing calibrated samples

Mass measurements of astronomical objects are most wanted but still elusive. We need them to trace the formation and evolution of cosmic structure but we can get direct measurements only for a minority. This lack can be circumvented with a proxy and a scaling relation. The twofold goal of estimating the unbiased relation and finding the right proxy value to plug in can be hampered by systematics, selection effects, Eddington/Malmquist biases and time evolution. We present a Bayesian hierarchical method which deals with these issues. Masses to be predicted are treated as missing data in the regression and are estimated together with the scaling parameters. The calibration subsample with measured masses does not need to be representative of the full sample as far as it follows the same scaling relation. We apply the method to forecast weak lensing calibrated masses of the Planck, redMaPPer and MCXC clusters. Planck masses are biased low with respect to weak lensing calibrated masses, with a bias more pronounced for high redshift clusters. MCXC masses are under-estimated by ~20 per cent, which may be ascribed to hydrostatic bias. Packages and catalogs are made available with the paper.