Upper limits on gravitational-wave signals based on loudest events
  Searches for gravitational-wave bursts have often focused on the loudest event(s) in searching for detections and in determining upper limits on astrophysical populations. Typical upper limits have been reported on event rates and event amplitudes which can then be translated into constraints on astrophysical populations. We describe the mathematical construction of such upper limits. 
Patrick R. Brady, Jolien D. E. Creighton, and Alan G. Wiseman