  A common approach in semi-analytic modeling of galaxy formation is to
construct Monte Carlo realizations of merger histories of dark matter halos
whose masses are sampled from a halo mass function. Both the mass function
itself, and the merger rates used to construct merging histories are calibrated
to N-body simulations. Typically, "backsplash" halos (those which were once
subhalos within a larger halo, but which have since moved outside of the halo)
are counted in both the halo mass function, and in the merger rates (or,
equivalently, progenitor mass functions). This leads to a double-counting of
mass in Monte Carlo merger histories which will bias results relative to N-body
results. We measure halo mass functions and merger rates with this
double-counting removed in a large, cosmological N-body simulation with
cosmological parameters consistent with current constraints. Furthermore, we
account for the inherently noisy nature of N-body halo mass estimates when
fitting functions to N-body data, and show that ignoring these errors leads to
a significant systematic bias given the precision statistics available from
state-of-the-art N-body cosmological simulations.
