A Comprehensive Analysis of Uncertainties Affecting the Stellar Mass -
  Halo Mass Relation for 0<z<4
  We conduct a comprehensive analysis of the relationship between central
galaxies and their host dark matter halos, as characterized by the stellar
mass-halo mass (SM-HM) relation, with rigorous consideration of uncertainties.
Our analysis focuses on results from the abundance matching technique, which
assumes that every dark matter halo or subhalo above a specific mass threshold
hosts one galaxy. We discuss the quantitative effects of uncertainties in
observed galaxy stellar mass functions (GSMFs) (including stellar mass
estimates and counting uncertainties), halo mass functions (including cosmology
and uncertainties from substructure), and the abundance matching technique used
to link galaxies to halos (including scatter in this connection). Our analysis
results in a robust estimate of the SM-HM relation and its evolution from z=0
to z=4. The shape and evolution are well constrained for z < 1. The largest
uncertainties at these redshifts are due to stellar mass estimates; however,
failure to account for scatter in stellar masses at fixed halo mass can lead to
errors of similar magnitude in the SM-HM relation for central galaxies in
massive halos. We also investigate the SM-HM relation to z=4, although the
shape of the relation at higher redshifts remains fairly unconstrained when
uncertainties are taken into account. These results will provide a powerful
tool to inform galaxy evolution models. [Abridged]
