Bayesian non-parametric methods for gravitational-wave astrophysics

In this dissertation, we introduce "a Hierarchy of Dirichlet Process Gaussian Mixture Models", or (H)DPGMM for short, the first fully non-parametric hierarchical model in the context of gravitational-wave astronomy aimed at studying the properties of compact objects, and FIGARO, the publicly available python code we developed to perform inferences with it. After providing the reader with a turnkey introduction to Dirichlet processes, we present the mathematical derivation for (H)DPGMM. We then describe the inference scheme behind FIGARO as well as demonstrate the effectiveness of this method at reconstructing probability densities in a hierarchical fashion using simulated data sets. To demonstrate the flexibility and potential of these methods, throughout the dissertation we present the results obtained by applying (H)DPGMM and FIGARO to a variety of problems, even beyond black hole astrophysics: with several collaborators, we successfully applied these techniques to the problem of promptly localising the electromagnetic counterpart of a gravitational wave signal, to mitigate the impact of potential population biases in gravitational wave lensing, to provide a consensus value for the gravitational constant G, to provide robust evidence in favour of the first observation of the electromagnetic counterpart of a binary black hole merger and, most importantly, to provide evidence for the evolution of the black hole mass distribution with redshift.