Bayesian modelling of stellar core collapse gravitational wave signals and detector noise

Abstract

A new era of astronomy dawned on September 14, 2015, when the Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced LIGO) detectors observed a gravitational wave signal from a binary black hole merger for the first time. This was followed by two more observations of gravitational waves from black hole binary mergers on December 26, 2015, and January 4, 2017. Bayesian data analysis played a key role in inferring the underlying astrophysics of these events. As more detectors come on-line and new discoveries are made, novel data analysis techniques will be critical to accurately model gravitational wave signals and background noise. Though stellar core collapse gravitational waves have not been observed yet, parameter estimation routines that can extract important astrophysical parameters encoded in these signals must be designed for their eventual detection. These methods will need to be different from those of binary black hole mergers as stellar core collapse signals are far more complex. A novel method for parameter estimation of stellar core collapse will be discussed here. The signal will first be reconstructed using principal component regression and implemented using Metropolis-within-Gibbs and reversible jump Markov chain Monte Carlo algorithms. Known astrophysical parameters will be fitted to Monte Carlo estimates of the principal component coefficients. Inferences of important physical quantities will then be made by sampling from the posterior predictive distribution and by applying classification and cross-validation methods. In addition to modelling stellar core collapse signals, the noise spectral density from the groundbased gravitational wave detectors, Advanced LIGO, will be modelled using the methods of Bayesian nonparametrics. Three different approaches will be presented: the Bernstein polynomial prior; a newly developed B-spline prior; and the recently developed nonparametric correction to a parametric likelihood. These methods will address the limitations of the default parametric noise model used in much of the gravitational wave data analysis literature and in practice.