# A self-consistent method to estimate the rate of compact binary coalescences with a Poisson mixture model

## TL;DR

This paper introduces a self-consistent Poisson mixture model to estimate gravitational wave event rates from compact binary coalescences, accounting for multiple source categories and validating the approach with synthetic data.

## Contribution

It develops a formalism that accurately estimates GW event rates and probabilities across multiple astrophysical categories using a Poisson mixture model, improving upon previous methods.

## Key findings

- Method accurately estimates GW event rates from synthetic data.
- Incorporates multiple astrophysical source categories via mass-based weighting.
- Works well for data from first two LIGO-Virgo observing runs.

## Abstract

The recently published GWTC-1 - a journal article summarizing the search for gravitational waves (GWs) from coalescing compact binaries in data produced by the LIGO-Virgo network of ground-based detectors during their first and second observing runs - quoted estimates for the rates of binary neutron star, neutron star black hole binary, and binary black hole mergers, as well as assigned probabilities of astrophysical origin for various significant and marginal GW candidate events. In this paper, we delineate the formalism used to compute these rates and probabilities, which assumes that triggers above a low ranking statistic threshold, whether of terrestrial or astrophysical origin, occur as independent Poisson processes. In particular, we include an arbitrary number of astrophysical categories by redistributing, via mass-based template weighting, the foreground probabilities of candidate events, across source classes. We evaluate this formalism on synthetic GW data, and demonstrate that this method works well for the kind of GW signals observed during the first and second observing runs.