  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 new
population of objects. Since it first began observing in late 2015, the
advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) has
detected gravitational waves three times, along with an additional strong
candidate -- and there shall be orders of magnitude more in the years to come.
In all four cases, the waveform's signature is consistent with general
relativity's predictions for the merging of two black holes. Through parameter
estimation studies, estimates on features such as the black holes' masses and
spins have been determined. At least two of the black hole pairs lie above the
mass range spanned by comparable black holes observed through traditional
means. This suggests they constitute a separate population, either too elusive
or rare to be found with traditional telescopes.
  The most natural questions to ask about these black holes -- how did they
form, how many of them are there, and how can they be categorized -- remain
open ended. We know black holes can form when massive stars die, so it's most
natural to claim stars as their progenitors. Since we now know black holes
merge into larger black holes, could it be the case that they formed from
previous 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 LIGO
can help answer these questions and more.
  Throughout this thesis, I will describe and demonstrate results from a number
of novel methods whose purpose is to better understand these black holes and
their progenitors. At their heart, these methods give answers to a few,
critical questions.
  [truncated]
