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.
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