Chairperson, Graduate Committee: Neil J. Cornish; Nicolas Yunes (co-chair)Robson, Travis JamesNeil Cornish and Chang Liu were co-authors of the article, 'The construction and use of LISA sensitivity curves' submitted to the journal 'Classical and quantum gravity' which is contained within this thesis.Neil Cornish was a co-author of the article, 'Impact of galactic foreground characterization on a global analysis for the LISA gravitational wave observatory' in the journal 'Classical and quantum gravity' which is contained within this thesis.Neil Cornish, Nicola Tamanini and Silvia Toonen were co-authors of the article, 'Detecting hierarchical stellar systems with LISA' in the journal 'Physical Review D' which is contained within this thesis.Travis Robson, Blake Moore, Nicholas Loutrel and Nicolas Yunes were all authors of the article, 'A fourier domain waveform for non-spinning binaries with arbitrary eccentricity' in the journal 'Classical and quantum gravity' which is contained within this thesis.Neil Cornish was a co-author of the article, 'Detecting gravitational wave bursts with LISA in the presence of instrumental glitches' submitted to the journal 'Physical review D' which is contained within this thesis.Dissertation contains one article of which Travis Robson is not the main author.2019-03-142019-03-142018https://scholarworks.montana.edu/handle/1/15101The Laser Interferometer Space Antenna (LISA) is a space-based gravitational wave detector in development under a joint venture between ESA and NASA. LISA will be sensitive to a wealth of signals from a variety of sources--both astrophysical and instrumental. Since many of these signals will be overlapping we must carry out a global analysis where we model everything believed to be present in the data simultaneously. To analyze the data this way we must understand what types of signals we expect, develop fast signal generators, and develop data analysis algorithms to handle this problem. We must also be flexible to characterize signals that we do not expect such as instrumental glitches of unknown morphology, or exotic astrophysical sources. We employ the Markov Chain Monte Carlo algorithm to address these multiple facets of the global analysis problem through a Bayesian approach. We have developed fast models for a variety of sources, characterized what we can learn about the sources, and assessed the nature of LISA's global analysis problem.enGravitational wavesMultiple starsGeneral relativity (Physics)Laser interferometryDissertationCopyright 2018 by Travis James Robson