Renate Meyer (University of Auckland)

Title: Bayesian Spectral Analysis with Applications to Gravitational Wave Astronomy

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Abstract: The new era of gravitational wave astronomy truly began on September 14, 2015 with the sensational first direct observation of gravitational waves, when LIGO recorded the signature of the merger of two black holes. In the subsequent three observing runs of the LIGO/Virgo network, gravitational waves from 90 compact binary mergers have been announced. Moreover, the future space-based observatory LISA will open the low-frequency window on gravitational waves and will be sensitive to a vast range of sources including the white dwarf binaries in our Milky Way and mergers of supermassive black holes at the centre of galaxies. Beyond signal detection, a major challenge has been the development of statistical methodology for estimating the physical waveform parameters and quantifying their uncertainties. Bayesian methods and MCMC have played a key role in this new era of astrophysics. This challenge has also been a key driver for new theoretical and methodological advancements in statistics. The call for a more robust instrumental noise characterization aiming at a simultaneous estimation of noise characteristics and gravitational wave parameters has triggered ongoing research into Bayesian nonparametric analysis of time series. Starting with nonparametric Bayesian approaches to spectral density estimation of univariate Gaussian stationary time series, I will review novel extensions to multivariate, non-Gaussian, and locally stationary time series.

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