  We review detection methods that are currently in use or have been proposed
to search for a stochastic background of gravitational radiation. We consider
both Bayesian and frequentist searches using ground-based and space-based laser
interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we
allow for anisotropy, non-Gaussianity, and non-standard polarization states.
Our focus is on relevant data analysis issues, and not on the particular
astrophysical or early Universe sources that might give rise to such
backgrounds. We provide a unified treatment of these searches at the level of
detector response functions, detection sensitivity curves, and, more generally,
at the level of the likelihood function, since the choice of signal and noise
models and prior probability distributions are actually what define the search.
Pedagogical examples are given whenever possible to compare and contrast
different approaches. We have tried to make the article as self-contained and
comprehensive as possible, targeting graduate students and new researchers
looking to enter this field.
