  An excess up-scattering mass bias on a weak lensing cluster mass estimate is
a statistical bias that an observed weak lensing mass ($M_{\rm obs}$) of a
cluster of galaxies is, in a statistical sense, larger than its true mass
($M_{\rm true}$) because of a higher chance of up-scattering than that of
down-scattering due to random noises in a weak lensing cluster shear profile.
This non-symmetric scattering probability is caused by a monotonically
decreasing cluster mass function with increasing mass. We examine this bias
(defined by $b=M_{\rm obs}/M_{\rm true}$) in weak lensing shear-selected
clusters, and present an empirical method for mitigating it. In so doing, we
perform the standard weak lensing mass estimate of realistic mock clusters, and
find that the weak lensing mass estimate based on the standard $\chi^2$
analysis gives a statistically correct confidence intervals, but resulting
best-fitting masses are biased high on average. Our correction method uses the
framework of the standard Bayesian statistics with the prior of the probability
distribution of the cluster mass and concentration parameter from recent
empirical models. We test our correction method using mock weak lensing
clusters, and find that the method works well with resulting corrected $M_{\rm
obs}$-bin averaged mass biases being close to unity within $\sim 10$ percent.
We applied the correction method to weak lensing shear-selected cluster sample
of Hamana et al. (2020), and present bias-corrected weak lensing cluster
masses.
