Counting and confusion: Bayesian rate estimation with multiple populations

@article{Farr2015CountingAC,
  title={Counting and confusion: Bayesian rate estimation with multiple populations},
  author={Will M. Farr and Jonathan R. Gair and Ilya Mandel and Curt Cutler},
  journal={Physical Review D},
  year={2015},
  volume={91},
  pages={023005}
}
We show how to obtain a Bayesian estimate of the rates or numbers of signal and background events from a set of events when the shapes of the signal and background distributions are known, can be estimated, or approximated; our method works well even if the foreground and background event distributions overlap significantly and the nature of any individual event cannot be determined with any certainty. We give examples of determining the rates of gravitational-wave events in the presence of… 
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