  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.
