# Performance of multi-detector hybrid statistic in targeted compact binary coalescence search

## TL;DR

This study compares the effectiveness of maximum likelihood ratio and hybrid detection statistics in identifying gravitational waves from compact binary coalescences across multiple detector networks, showing the hybrid statistic's improved performance for black hole-neutron star systems.

## Contribution

The paper introduces a comparative analysis of likelihood ratio based detection statistics, highlighting the hybrid statistic's advantages in multi-detector gravitational wave searches.

## Key findings

- Hybrid statistic recovers more injections for black hole-neutron star systems in multi-detector networks.
- Maximum likelihood ratio statistic performs better for binary neutron star injections.
- Performance varies with the number of detectors and the type of binary system.

## Abstract

In this paper we compare the performance of two likelihood ratio based detection statistics namely maximum likelihood ratio statistic and {\it hybrid} statistic designed for the detection of gravitational waves from compact binary coalescence using multiple interferometric detector networks. We perform simulations with non-spinning double neutron star binary system and neutron star-black hole binary systems with spinning as well as non-spinning black hole component masses. The binary injections are distributed uniformly in volume up to 1 Gpc. We observe that, on average, the maximum likelihood ratio statistic recovers $\sim 34.45\%$, $\sim 49.69\%$, $\sim 61.25\%$ and $\sim 69.67\%$ of injections in 2, 3, 4 and 5 detector networks respectively in the case of neutron star-black hole injections for a fixed false alarm probability of $10^{-7}$ in Gaussian noise. Further, we note that, compared to the maximum likelihood ratio statistic, the {\it hybrid} statistic recovers $\sim 7.45\%$, $\sim 4.57\%$, $\sim 2.56\%$ and $\sim 1.22\%$ more injections in 2, 3, 4 and 5 detector networks respectively for the same false alarm probability in Gaussian noise. On the other hand, among binary neutron star injections, the maximum likelihood ratio statistic recovers $\sim 5.587\%$, $\sim 9.917\%$, $\sim 14.73\%$ and $\sim 19.86\%$ of injections in 2, 3, 4 and 5 detector networks respectively and the {\it hybrid} statistic recovers $\sim 14.63\%$, $\sim 12.91\%$, $\sim 11.49\%$ and $\sim 10.29\%$ more injections compared to maximum likelihood ratio statistic in 2, 3, 4 and 5 detector networks respectively.