= Coincidence and noise controls for GW150914
The modeled <matched filter> search found an arrival difference of about $7\,\mathrm{ms}$, within the roughly $10\,\mathrm{ms}$ intersite light travel time. Background events were obtained by shifting one detector's timestamps far beyond that time and repeating the coincidence analysis. The binary search bounded the <false alarm rate> below one event per $203\,000$ years. That is an empirically estimated background rate, not a probability that the source interpretation is false.<GW150914: First results from the search for binary black hole coalescence with Advanced LIGO by B. P. Abbott and others>[Abstract; I Introduction; time-shift background analysis, Fig. 5]{ref}
The logic is to destroy a common astronomical arrival while retaining each instrument's real glitches. A <Poisson distribution> approximation would turn a background rate $r$ into $1-e^{-rT}$ for at least one equally strong noise event during live time $T$, only after accounting for the search's ranking and trials. Repeated time slides reuse data; their accumulated background duration is not an equally long series of independent new observations. Correlated disturbances also require separate controls because shifting timestamps can erase them along with a true signal.
The dedicated noise study inspected auxiliary channels and deliberately applied magnetic, acoustic and mechanical disturbances to measure their coupling into strain. For <GW150914>, checks included environmental coincidences, instrument state, and exclusion of an intentional hardware injection. It also examined potentially correlated global magnetic disturbances, which time slides alone cannot exclude.<Characterization of transient noise in Advanced LIGO relevant to gravitational wave signal GW150914 by B. P. Abbott and others>[2 Identifying noise sources, Fig. 2; 6 Validation of GW150914; Appendix B physical environment monitors]{ref} The point of an injection test is quantitative: a quiet environmental monitor is informative only if its sensitivity and coupling bound the disturbance needed to explain the candidate.
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