Counting And Confusion: Bayesian Rate Estimation With Multiple Populations

TL;DR

This paper introduces a Bayesian method for estimating signal and background event rates in scenarios with overlapping distributions and uncertain event classification, applicable to gravitational-wave detection and stellar cluster analysis.

Contribution

It presents a novel Bayesian approach for rate estimation that handles overlapping distributions and uncertain event identities, improving analysis in complex background scenarios.

Findings

Effective in estimating rates with overlapping distributions

Applicable to gravitational-wave event detection

Useful for analyzing non-uniform stellar fields

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 non-uniform background density of stars superimposed on the cluster stars.