The follow-up observations of the candidate gravitational-wave (GW) transient events with the optical/X-ray/radio telescopes in search of associated electromagnetic (EM) counterparts can potentially provide very rich, complementary information about the GW sources and their environment. If detected the EM counterparts may also increase the overall significance of the GW candidates and thus improve sensitivity of the joint search. We present methodology for a generic joint analysis of GW and EM data that combines information from both observations into a single detection statistic – the composite likelihood-ratio. We illustrate it by considering the recently performed end-to-end analysis of Swift XRT follow-up observations of candidate GW transient events from 2009-2010 LIGO and Virgo scientific run. Using this analysis as an example we identify the key factors determining sensitivity of the joint search (e.g. sky-coverage and latency of observations, background of serendipitous EM transients and GW probability sky-map) and demonstrate through simulations that EM observations may significantly improve detection efficiency of GW signals. We conclude with discussion of the open issues in this and other, similar type analyses and prospects for the future multi-messenger searches.
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