Farr, BenEdelman, Bruce2024-01-092024-01-092024-01-09https://hdl.handle.net/1794/29177Gravitational Waves (GWs) have quickly emerged as powerful, indispensabletools for studying gravity in the strong field regime and high-energy astrophysical phenomena since they were first directly detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO) on September 14, 2015. Over the course of this dissertation work gravitational-wave astronomy has begun to mature, going from 11 GW observations when I began to 90 at the time of writing, just before the next observing run begins. As the network of GW observatories continues to grow and these observations become a regular occurrence, the entire population of merging compact objects observed with GWs will provide a unique probe of the astrophysics of their formation and evolution along with the cosmic expansion of the universe. In this dissertation I present four studies that I have led using GWs to better understand the astrophysics of the currently most detected GW source, binary black holes (BBHs). We first present a novel data-driven technique to look for deviations from modeled gravitational waveforms in the data, coherent across the network of observatories, along with an analysis of the first gravitational- wave transient catalog (GWTC-1). The following three studies present the three different approaches to modeling populations of BBHs, using parametric, semi- parametric and non-parametric models. The first of these studies uses a parametric model that imposes a gap in the mass distribution of black holes, looking for evidence of effects caused by pair-instability supernovae. The second study introduces a semi-parametric model that aims to take advantage of the benefits of both parametric and non-parametric methods, by imposing a flexible perturbation to an underlying simpler parametric description. This study was among the first data-driven studies revealing possible structure in the mass distribution of BBHs using GWTC-2, namely an additional peak at 10M⊙ . The final study introduces a novel non-parametric model for hierarchically inferring population properties of GW sources, and performs the most comprehensive data-driven study of the BBH population to date. This study is also the first that uses non-parametric models to simultaneously infer the distributions of BBH masses, spins and redshifts. This dissertation contains previously published and unpublished material.en-USAll Rights Reserved.Bayesian StatisticsBlack HolesGravitational WavesElectronic Thesis or Dissertation