  The stellar masses, mean ages, metallicities, and star formation histories of
galaxies are now commonly estimated via stellar population synthesis (SPS)
techniques. SPS relies on stellar evolution calculations from the main sequence
to stellar death, stellar spectral libraries, phenomenological dust models, and
stellar initial mass functions (IMFs). The present work is the first in a
series that explores the impact of uncertainties in key phases of stellar
evolution and the IMF on the derived physical properties of galaxies and the
expected luminosity evolution for a passively evolving set of stars. A
Monte-Carlo Markov-Chain approach is taken to fit near-UV through near-IR
photometry of a representative sample of low- and high-redshift galaxies with
this new SPS model. Significant results include the following: 1) including
uncertainties in stellar evolution, stellar masses at z~0 carry errors of ~0.3
dex at 95% CL with little dependence on luminosity or color, while at z~2, the
masses of bright red galaxies are uncertain at the ~0.6 dex level; 2) either
current stellar evolution models, current observational stellar libraries, or
both, do not adequately characterize the metallicity-dependence of the
thermally-pulsating asymptotic giant branch phase; 3) conservative estimates on
the uncertainty of the slope of the IMF in the solar neighborhood imply that
luminosity evolution per unit redshift is uncertain at the ~0.4 mag level in
the K-band, which is a substantial source of uncertainty for interpreting the
evolution of galaxy populations across time; 4) The more plausible assumption
of a distribution of stellar metallicities, rather than a fixed value as is
usually assumed, can have significant effects on the interpretation of colors
blueward of the V-band. (ABRIDGED)

Astrophysics