  Theoretical studies in gravitational wave astronomy have mostly focused on
the information that can be extracted from individual detections, such as the
mass of a binary system and its location in space. Here we consider how the
information from multiple detections can be used to constrain astrophysical
population models. This seemingly simple problem is made challenging by the
high dimensionality and high degree of correlation in the parameter spaces that
describe the signals, and by the complexity of the astrophysical models, which
can also depend on a large number of parameters, some of which might not be
directly constrained by the observations. We present a method for constraining
population models using a Hierarchical Bayesian modeling approach which
simultaneously infers the source parameters and population model and provides
the joint probability distributions for both. We illustrate this approach by
considering the constraints that can be placed on population models for
galactic white dwarf binaries using a future space based gravitational wave
detector. We find that a mission that is able to resolve ~5000 of the shortest
period binaries will be able to constrain the population model parameters,
including the chirp mass distribution and a characteristic galaxy disk radius
to within a few percent. This compares favorably to existing bounds, where
electromagnetic observations of stars in the galaxy constrain disk radii to
within 20%.
