Fast likelihood-free reconstruction of gravitational wave backgrounds

Bryan Zaldivar

Abstract: We apply state-of-the-art, likelihood-free statistical inference (machine-learning-based)techniques for reconstructing the spectral shape of a gravitational wave background (GWB). Wefocus on the reconstruction of an arbitrarily shaped signal (approximated by a piecewise power-lawin many frequency bins) by the LISA detector, but the method can be easily extended to eithertemplate-dependent signals, or to other detectors, as long as a characterisation of theinstrumental noise is available. As proof of the technique, we quantify the ability of LISA toreconstruct signals of arbitrary spectral shape (blind reconstruction), considering adiversity of frequency profiles, and including astrophysical backgrounds in some cases. As ateaser of how the method can reconstruct signals characterised by a parameter-dependent template(template reconstruction), we present a dedicated study for power-law signals. While ourtechnique has several advantages with respect to traditional MCMC methods, we validate it with thelatter for concrete cases. This work opens the door for both fast and accurate Bayesian parameterestimation of GWBs, with essentially no computational overhead during the inference step. Our setof tools are integrated into the package GWBackFinder, which is publicly available inGitHub.