A new method for deriving the stellar birth function of resolved stellar
  populations
  We present a new method for deriving the stellar birth function (SBF) of
resolved stellar populations. The SBF (stars born per unit mass, time, and
metallicity) is the combination of the initial mass function (IMF), the
star-formation history (SFH), and the metallicity distribution function (MDF).
The framework of our analysis is that of Poisson Point Processes (PPPs), a
class of statistical models suitable when dealing with points (stars) in a
multidimensional space (the measurement space of multiple photometric bands).
The theory of PPPs easily accommodates the modeling of measurement errors as
well as that of incompleteness. Compared to most of the tools used to study
resolved stellar populations, our method avoids binning stars in the
color-magnitude diagram and uses the entirety of the information (i.e., the
whole likelihood function) for each data point; the proper combination of the
individual likelihoods allows the computation of the posterior probability for
the global population parameters. This includes unknowns such as the IMF slope
and combination of SFH and MDF, which are rarely solved for simultaneously in
the literature, however entangled and correlated they might be. Our method also
allows proper inclusion of nuisance parameters, such as distance and extinction
distributions. The aim of this paper, is to assess the validity of this new
approach under a range of assumptions, using only simulated data. Forthcoming
work will show applications to real data. Although it has a broad scope of
possible applications, we have developed this method to study multi-band HST
observations of the Milky Way Bulge. Therefore we will focus on simulations
with characteristics similar to those of the Galactic Bulge.
