A Link to the Past: Using Markov Chain Monte Carlo Fitting to Constrain
  Fundamental Parameters of High-Redshift Galaxies
  We have a developed a new method for fitting spectral energy distributions
(SEDs) to identify and constrain the physical properties of high-redshift (4 <
z < 8) galaxies. Our approach uses an implementation of Bayesian based Markov
Chain Monte Carlo (PiMC^2) that allows us to compare observations to
arbitrarily complex models and to compute 95% credible intervals that provide
robust constraints for the model parameters. The work is presented in 2
sections. In the first, we test PiMC^2 using simulated SEDs to not only confirm
the recovery of the known inputs but to assess the limitations of the method
and identify potential hazards of SED fitting when applied specifically to high
redshift (z>4) galaxies. Our tests reveal five critical results: 1) the ability
to confidently constrain metallicity, population ages, and Av all require
photometric accuracy better than what is currently achievable (i.e. less than a
few percent); 2) the ability to confidently constrain stellar masses (within a
factor of two) can be achieved without the need for high-precision photometry;
3) the addition of IRAC photometry does not guarantee that tighter constraints
of the stellar masses and ages can be defined; 4) different assumptions about
the star formation history can lead to significant biases in mass and age
estimates; and 5) we are able to constrain stellar age and Av of objects that
are both young and relatively dust free. In the second part of the paper we
apply PiMC^2 to 17 4<z<8 objects, including the GRAPES Ly alpha sample (4<z<6),
supplemented by HST/WFC3 near-IR observations, and several broad band selected
z>6 galaxies. Using PiMC^2, we are able to constrain the stellar mass of these
objects and in some cases their stellar age and find no evidence that any of
these sources formed at a redshift much larger than z_f=8, a time when the
Universe was ~ 0.6 Gyr old.
