  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.
