Since the Laser Interferometer Gravitational-Wave Observatory (LIGO) made the first direct detection of gravitational waves in 2015, the era of gravitational wave astronomy has begun. LIGO and its counterpart Virgo are detecting an ever-growing sample of merging compact binaries: binary black holes, binary neutron stars, and neutron star--black hole binaries. Each individual detection can be compared against simulated signals with known properties, in order to measure the binary\u27s properties. In order to understand the sample of detections as a whole, however, ensemble methods are needed.
The properties measured from these binary systems have large measurement errors, and the sensitivity of gravitational wave detectors are highly property-dependent, resulting in large selection biases. This dissertation applies the technique of hierarchical Bayesian modeling in order to constrain the underlying, unbiased population of merging compact binaries. We use a number of models to constrain the merger rate, mass distribution, and spin distribution for binary black holes and binary neutron stars. We also use tidal information present in binary neutron stars in order to self-consistently constrain the nuclear equation of state
