Banagiri, Narayana Sri Sharan2021-08-162021-08-162021-05https://hdl.handle.net/11299/223186University of Minnesota Ph.D. dissertation. May 2021. Major: Physics. Advisor: Vuk Mandic. 1 computer file (PDF); x, 174pages.The discovery of gravitational waves by LIGO and Virgo have unveiled a sector of the Universe previously hidden from us. Gravitational waves allow us to detect and observe the dynamics of phenomena usually hidden from electromagnetism probes like binary black hole mergers, providing new tools to study astrophysics and cosmology in the process. As the number of detections increase, the statistics of the mergers are starting to inform us about their progenitor distributions. This dissertation consists of three parts. First, analyses to detect potential gravitational waves from a post-merger remnant of the binary neutron star merger GW170817 are described, with particular emphasis on the STAMP pipeline-based search targeting gravitational waves from a long-lived remnant. Bayesian parameter estimation techniques for the poorly modeled post-merger signals are then described. A novel likelihood formalism is developed to account for the inaccuracies in models, focusing in particular on the phase evolution of the waveform. In the second part, techniques are developed, using hierarchical Bayesian modeling to measure N-point correlations of the distributions of black hole mergers, with a focus on two-point correlations. These methods allow us to use black hole mergers as a tool to measure the angular distribution and the large-scale structure of the matter in the Universe. The two-point correlation method is validated with simulations for the angular structure of the mergers in the Universe. Finally, Bayesian methods are devised to probe anisotropies in the angular distribution of the stochastic gravitational-wave backgrounds and foregrounds in the LISA band. A novel decomposition using \cg coefficients in the spherical harmonic basis is developed that allows us to infer the anisotropy of arbitrary distributions of gravitational-wave power. This method is employed and tested using different kinds of simulations, including that of the galactic gravitational-wave foreground from galactic white dwarf binaries.enAstrophysicsGravitational wavesLIGOLISAThesis or Dissertation