Likelihood-ratio ranking of gravitational-wave candidates in a non-Gaussian background

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 applying the likelihood-ratio ranking results in an improved analysis.