  We describe a general approach to detection of transient gravitational-wave
signals in the presence of non-Gaussian background noise. We prove that under
quite general conditions, the ratio of the likelihood of observed data to
contain a signal to the likelihood of it being a noise fluctuation provides
optimal ranking for the candidate events found in an experiment. The
likelihood-ratio ranking allows us to combine different kinds of data into a
single analysis. We apply the general framework to the problem of unifying the
results of independent experiments and the problem of accounting for
non-Gaussian artifacts in the searches for gravitational waves from compact
binary coalescence in LIGO data. We show analytically and confirm through
simulations that in both cases the likelihood ratio statistic results in an
improved analysis.
