There's more than one way to ride the wave : a multi-disciplinary approach to gravitational wave data analysis

Since the first detection in 2015, gravitational-wave astronomy has progressed hugely. Several observing runs have been completed, resulting in many more confirmed detections of compact binary coalescence. As the number of detections grows larger, the potential for exciting science also increases, however, this is not without challenges. Specifically efficiently analyzing growing data will present many computational problems going forward. In order to properly interpret and understand this growing data, we must develop new ways to approach these computational problems. When seeking to tackle a difficult problem there are broadly two ways to do this. One can tackle the problem using some physical or mathematical insight, this understanding can then be translated into a simpler formulation or good approximation which makes the problem tractable. This has been the standard way to tackle problems since the beginning of science, recently, however, data-driven methods have become hugely popular. These data-driven methods such as machine learning generally do not use physical insight but make use of large amounts of data efficiently to produce solutions to these intractable problems. This thesis draws on both of these approaches and presents several new methods to analyze gravitational-wave data. In chapters 2-3 we derive a way to describe a precessing waveform as a harmonic decomposition, where each harmonic is a simple non-precessing waveform. With this formulation, we are able to obtain a simple picture of precession as the beating of two waveforms. We then use this understanding to answer questions such as when will we observe precessing waveforms? And where in parameter space will we be able to observe precessing waveforms? The remaining chapters look at data-driven approaches, using machine learning techniques to improve different aspects of gravitational-wave data analysis. Chapter 5 uses Gaussian Processes to interpolate posterior samples, this allows us to have a smooth continuous representation of our posterior as opposed to histograms for example. Chapter 6 uses using advances in waveform modeling and GPUs to potentially make parameter estimation more efficient. In chapters 7 and 8 we look at how reliable machine learning techniques are, we show that often they do not incorporate uncertainty properly into their predictions. We then present a simple algorithm for both classification and regression pipelines that can be used with any machine learning model to address this. Finally, in the conclusions, we review the work presented as a whole and discuss ways in which these two approaches can be combined to get the best of both. We suggest that using our physical insights to guide and constrain our data-driven methods will eventually provide the best path forward for gravitational-wave data analysis.