On the Estimation of Random Uncertainties of Star Formation Histories
  The standard technique for measurement of random uncertainties of star
formation histories (SFHs) is the bootstrap Monte Carlo, in which the
color-magnitude diagram (CMD) is repeatedly resampled. The variation in SFHs
measured from the resampled CMDs is assumed to represent the random uncertainty
in the SFH measured from the original data. However, this technique
systematically and significantly underestimates the uncertainties for times in
which the measured star formation rate is low or zero, leading to overly (and
incorrectly) high confidence in that measurement. This study proposes an
alternative technique, the Markov Chain Monte Carlo (MCMC), which samples the
probability distribution of the parameters used in the original solution to
directly estimate confidence intervals. While the most commonly used MCMC
algorithms are incapable of adequately sampling a probability distribution that
can involve thousands of highly correlated dimensions, the Hybrid Monte Carlo
algorithm is shown to be extremely effective and efficient for this particular
task. Several implementation details, such as the handling of implicit priors
created by parameterization of the SFH, are discussed in detail.
