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We are living through the dawn of the era of gravitational wave astronomy.Our first glances through this new window upon the sky has revealed a newpopulation of objects. Since it first began observing in late 2015, theadvanced Laser Interferometer Gravitational-Wave Observatory (LIGO) hasdetected gravitational waves three times, along with an additional strongcandidate -- and there shall be orders of magnitude more in the years to come.In all four cases, the waveform's signature is consistent with generalrelativity's predictions for the merging of two black holes. Through parameterestimation studies, estimates on features such as the black holes' masses andspins have been determined. At least two of the black hole pairs lie above themass range spanned by comparable black holes observed through traditionalmeans. This suggests they constitute a separate population, either too elusiveor rare to be found with traditional telescopes.  The most natural questions to ask about these black holes -- how did theyform, how many of them are there, and how can they be categorized -- remainopen ended. We know black holes can form when massive stars die, so it's mostnatural to claim stars as their progenitors. Since we now know black holesmerge into larger black holes, could it be the case that they formed fromprevious mergers? Were the two black holes part of a binary from their birth,or did they become coupled later on in life? The measurements provided by LIGOcan help answer these questions and more.  Throughout this thesis, I will describe and demonstrate results from a numberof novel methods whose purpose is to better understand these black holes andtheir progenitors. At their heart, these methods give answers to a few,critical questions.  [truncated]

Inferences about the distribution, merger rate, and evolutionary processes of compact binaries from gravitational wave observations