The Milky Way Galaxy is surrounded by a population of roughly 150 old star clusters, referred to as globular clusters. Inferring the distribution of stellar mass and velocity in these clusters is vital to testing physical theories about star cluster evolution. Many physically motivated models for globular clusters exist --- including probability distributions for the positions and velocities of stars --- and there is much prior information about these star clusters in the literature. In this talk, I will first review some of the physically motivated probability models and prior information for globular clusters. Next, I will present recent work where we have used repeated simulations of star clusters and a Bayesian analysis framework that uses one of these probability models to estimate model parameters. We show how parameter inference and coverage probabilities are reliable in the case of complete data (Eadie, Webb, and Rosenthal, submitted to ApJ). We also show that selection bias in the data can lead to unreliable credible intervals. The latter is an important result; recent data collection by the Gaia spacecraft and the Hubble Space Telescope has provided a wealth of information about the positions and velocities of individual stars, but these data sets still present statistical challenges such as measurement uncertainty, selection bias, and incompleteness which must be accounted for in a real analysis.
My research is in the interdisciplinary field of astrostatistics, and I am jointly-appointed between the Department of Astronomy & Astrophysics and the Department of Statistical Sciences. I am interested in using and developing modern statistical methods for astronomy applications to answer fundamental questions about the universe. For example, I use hierarchical Bayesian analysis to study the dark matter halo of the Milky Way and other galaxies, and am developing new time series analysis methods to learn about the internal structure of stars.