Correlator Bank Detection of GW chirps. False-Alarm Probability, Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue

TL;DR

This paper develops a statistical framework for evaluating false-alarm probabilities in gravitational wave detection using correlator banks, optimizing template density for efficient detection of binary coalescence signals.

Contribution

It introduces lower-bound approximants for the distribution of the maximum correlator output and extends their validity to large banks using a gaussian-correlation inequality.

Findings

Derived bounds for false-alarm probabilities in correlator banks.

Extended the validity of simulations to large banks.

Estimated optimal template density balancing cost and detection efficiency.

Abstract

The general problem of computing the false-alarm rate vs. detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves, with specific reference to chirps from coalescing binary systems. Accurate (lower-bound) approximants for the cumulative distribution of the whole-bank supremum are deduced from a class of Bonferroni-type inequalities. The asymptotic properties of the cumulative distribution are obtained, in the limit where the number of correlators goes to infinity. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a gaussian-correlation inequality. The result is used to estimate the optimum template density, yielding the best tradeoff between computational cost and detection efficiency, in terms of undetected potentially observable sources at a prescribed false-alarm level, for the simplest case of Newtonian chirps.