Basic questions of interest about globular cluster systems include how many globular clusters there are, what are the relative fractions of different types of globular clusters, and how are they distributed around their host galaxies. Ideally, these questions could be answered trivially by taking an image of the galaxy, selecting those sources which are globular clusters, and performing our measurements on that subsample. Unfortunately, typical datasets are much messier than this. In a globular cluster dataset, we are dealing with a sample that is both incomplete (globular clusters may exist below the detection threshold of our imaging data) and contaminated (globular clusters in images are easily confused both with foreground stars in the Milky Way and distant galaxies far behind the galaxy of interest). Current approaches to globular cluster selection have use somewhat ad-hoc selection rules to attempt a selection with minimal contamination, but unquantified selection errors muddle inferences from such a method.
I am developing a fully Bayesian framework for modelling the globular cluster populations of nearby galaxies. My method simultaneously models all sources in the image as a mixture model composed of both contaminants and genuine globular clusters, each with their own distributions. I model the contaminants using kernel density estimates trained on control images taken far away from galaxies, then use parametric models for the distribution of globular clusters mixed in with these contaminants. This allows me to easily fold in all measured data from sources in our imaging; while most methods just select globular clusters based on their measured colors, I can easily fold in information about their spatial and luminosity distributions into the selection methodology.
The advantages of these methods are two-fold: first, I get a better sample of likely globular clusters. Rather than simply selecting a sample using ad-hoc criteria, I calculate a probability for every source in the image of how likely it is to be a globular cluster. Any studies requiring a clean sample of clusters will have a clear quantification of their contamination, and follow-up spectroscopic studies with different telescopes will be able to better optimize their target selection. Second, the parameters of the distributions used to model the globular clusters are themselves very interesting astrophysical quantities. Bayesian methods give us full PDFs for quantities like the total number of globular clusters or the relative fractions of red and blue globular clusters, completely folding in any uncertainties introduced by the selection process. The estimates of such parameters with reliable uncertainties attached will offer a useful discriminant between competing models of globular cluster formation which currently exist in the literature.