Model Selection in Gravitational Wave Astronomy
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The several detections of gravitational waves by the Laser Interferometer Gravitational-wave Observatory (LIGO) and the Virgo detector are providing insights about the nature of gravity in our Universe . As the number of detected gravitational waves increases, it will be necessary to employ computationally inexpensive methods to extract the parameters of the gravitational wave sources. This proof of concept study utilizes principal component analysis (PCA) to try to reduce the number of vectors needed to describe binary black hole (BBH) parameter space. The results of this study suggest that performing PCA on face-on BBH systems, those at zero degrees inclination, adds an unnecessary level of complexity. However, PCA is a beneficial method to apply to waveforms that are morphologically complex such as those from edge-on BBH systems, those at 90 degrees inclination. Running PCA on a catalog of specific waveforms in one area of parameter space can inform how to construct waveforms in other regions of parameter space. If these waveforms can be constructed to a high level of accuracy using only a few principal components (PCs), it will significantly reduce the computational cost associated with generating template waveforms. Instead of creating a waveform template for every parameter combination, the PCs can be used to construct waveforms from similar areas of parameter space.