Methods and challenges for gravitational-wave population analyses

Nearly 100 gravitational-wave signals emitted by stellar-mass compact-binary coalescences were confidently detected by the LIGO-Virgo-KAGRA Collaboration during their first three observing runs. Since the beginning of the fourth run, dozens more candidates have been publicly released. This growing observational catalog has revealed new insights into the nature and properties of compact objects and their mergers, not only for individual sources but also their underlying population. Though improved statistical and astrophysical constraints are made possible, analyzing this increasingly informative dataset is not without significant challenges, as systematic biases due to theoretical and numerical mismodeling are already problematic and computational costs will only increase. In the context of Bayesian hierarchical modeling, I will explain how parametrized inference leads to such issues with a review of current methods in gravitational-wave data analysis, and point to some key examples - such as misestimation of selection effects and measurement of population-level correlations - that demonstrate the need for more robust approaches. Recent promising developments include weakly parametric models that are very flexible on one end of the spectrum and simulation-based inferences that directly constrain physical parameters on the other, as well as likelihood-free methods that remove limiting assumptions from probabilistic models. Looking to the near future, proper characterization of the population of gravitational-wave sources will be crucial to probe their origins and place reliable constraints on the astrophysics of compact-binary formation.