  We develop a Bayesian model for globular clusters composed of multiple
stellar populations, extending earlier statistical models for open clusters
composed of simple (single) stellar populations (vanDyk et al. 2009, Stein et
al. 2013). Specifically, we model globular clusters with two populations that
differ in helium abundance. Our model assumes a hierarchical structuring of the
parameters in which physical properties---age, metallicity, helium abundance,
distance, absorption, and initial mass---are common to (i) the cluster as a
whole or to (ii) individual populations within a cluster, or are unique to
(iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm
is devised for model fitting that greatly improves convergence relative to its
precursor non-adaptive MCMC algorithm. Our model and computational tools are
incorporated into an open-source software suite known as BASE-9. We use
numerical studies to demonstrate that our method can recover parameters of
two-population clusters, and also show model misspecification can potentially
be identified. As a proof of concept, we analyze the two stellar populations of
globular cluster NGC 5272 using our model and methods. (BASE-9 is available
from GitHub: https://github.com/argiopetech/base/releases).
