Weak Lensing Peak Finding: Estimators, Filters, and Biases
  Large catalogs of shear-selected peaks have recently become a reality. In
order to properly interpret the abundance and properties of these peaks, it is
necessary to take into account the effects of the clustering of source
galaxies, among themselves and with the lens. In addition, the preferred
selection of lensed galaxies in a flux- and size-limited sample leads to
fluctuations in the apparent source density which correlate with the lensing
field (lensing bias). In this paper, we investigate these issues for two
different choices of shear estimators which are commonly in use today:
globally-normalized and locally-normalized estimators. While in principle
equivalent, in practice these estimators respond differently to systematic
effects such as lensing bias and cluster member dilution. Furthermore, we find
that which estimator is statistically superior depends on the specific shape of
the filter employed for peak finding; suboptimal choices of the
estimator+filter combination can result in a suppression of the number of high
peaks by orders of magnitude. Lensing bias generally acts to increase the
signal-to-noise \nu of shear peaks; for high peaks the boost can be as large as
\Delta \nu ~ 1-2. Due to the steepness of the peak abundance function, these
boosts can result in a significant increase in the abundance of shear peaks. A
companion paper (Rozo et al., 2010) investigates these same issues within the
context of stacked weak lensing mass estimates.
