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Published January 15, 2015 | Published + Submitted
Journal Article Open

Counting and confusion: Bayesian rate estimation with multiple populations


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.

Additional Information

© 2015 American Physical Society. Received 21 February 2013; published 22 January 2015. We thank Kipp Cannon, Thomas Dent, Chad Hanna, Drew Keppel, Richard O'Shaughnessy, David Hogg, and Ted von Hippel for discussions and suggestions about this manuscript. I.M. and W. M. F. acknowledge the hospitality of KITP, supported in part by the National Science Foundation under NSF Grant No. PHY11-25915. C. C.'s work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract to the National Aeronautics and Space Administration. C. C. also gratefully acknowledges support from NSF Grant No. PHY1068881. J. G.'s work is supported by the Royal Society.

Attached Files

Submitted - 1302.5341.pdf

Published - PhysRevD.91.023005.pdf


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August 20, 2023
August 20, 2023