  Parametric modeling of galaxy cluster density profiles from weak lensing
observations leads to a mass bias, whose detailed understanding is critical in
deriving accurate mass-observable relations for constraining cosmological
models. Drawing from existing methods, we develop a robust framework for
calculating this mass bias in one-parameter fits to simulations of dark matter
halos. We show that our approach has the advantage of being independent of the
absolute noise level, so that only the number of halos in a given simulation
and the representativeness of the simulated halos for real clusters limit the
accuracy of the bias estimation. While we model the bias as a log-normal
distribution and the halos with a Navarro-Frenk-White profile, our method can
be generalized to any bias distribution and parametric model of the radial mass
distribution. We find that the log-normal assumption is not strictly valid in
the presence of miscentring of halos. We investigate the use of cluster centers
derived from weak lensing in the context of mass bias, and tentatively find
that such centroids can yield sensible mass estimates if the convergence peak
has a signal-to-noise ratio approximately greater than four. In this context we
also find that the standard approach to estimating the positional uncertainty
of weak lensing mass peaks using bootstrapping severely underestimates the true
positional uncertainty for peaks with low signal-to-noise ratios. Though we
determine the mass and redshift dependence of the bias distribution for a few
experimental setups, our focus remains providing a general approach to
computing such distributions.
