Bayesian power spectral estimation of gravitational wave detector noise revisited

The analysis of gravitational wave interferometer data requires estimates for the noise covariance matrix. For stationary noise, this amounts to estimating the power spectrum. Classical methods such as Welch averaging are used in many analyses, but this method require large stretches of ``off-source'' data, where the assumption of stationarity may break down. For this reason, Bayesian spectral estimates using only ``on-source'' data are becoming more widely used, but the Bayesian approach tends to be slower, and more computationally expensive than classical methods. Here we introduce numerous improvements in speed and performance for the BayesWave trans-dimensional Bayesian spectral estimation algorithm, and introduce a new, low-latency fixed dimension Bayesian spectral estimation algorithm, FastSpec, which serves as both a starting point for the BayesWave analysis, and as a stand-alone fast spectral estimation tool. The performance of the Welch, BayesWave and FastSpec algorithms are compared by applying statistical tests for normality to the whitened frequency domain data. Bayesian spectral estimation methods are shown to significantly outperform the classical approach.