Counting and confusion: Bayesian rate estimation with multiple populations

Will M. Farr, Jonathan R. Gair, Ilya Mandel, Curt Cutler

Research output: Contribution to journalArticleResearchpeer-review

42 Citations (Scopus)

Abstract

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 background triggers from a template bank when noise parameters are known and/or can be fit from the trigger data. We also give an example of determining globular-cluster shape, location, and density from an observation of a stellar field that contains a nonuniform background density of stars superimposed on the cluster stars.

Original languageEnglish
Article number023005
Number of pages14
JournalPhysical Review D
Volume91
Issue number2
DOIs
Publication statusPublished - 22 Jan 2015
Externally publishedYes

Keywords

  • gravitational waves
  • gravitational self-force
  • |black holes (astronomy)

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