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It is expected that interferometric gravitational wave detectors such as LIGO\cite{Barish99} will be eventually limited by fundamental noise sources likeshot noise and Brownian motion, as well as by seismic noise. In thecommissioning process, other technical noise sources (electronics noise,alignment fluctuations) limit the sensitivity and are eliminated one by one. Wepropose here a way to correlate the noise in the output of the gravitationalwave detector with other detector and environmental signals not through theirlinear transfer functions (often unknown), but through their statisticalproperties. This could prove useful for identifying the frequency bandsdominated by different noise sources in the final configuration, and also tohelp the commissioning process.Comment: 7 Pages, Latex,figures include

Limiting noises in gravitational wave detectors: guidance from their statistical properties