# Correlator bank detection of gravitational wave chirps--False-alarm probability, template density, and thresholds: Behind and beyond the minimal-match issue

## Abstract

The general problem of computing the false-alarm probability vs the detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves in additive stationary Gaussian noise. Specific reference is made 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 readdress the problem of relating the template density to the fraction of potentially observable sources which could be dismissed as an effect of template space discreteness.

- Authors:

- Wavesgroup, University of Sannio at Benevento, Piazza Roma, Pal. Bosco Lucarelli, 82100 Benevento (Italy)
- Dipartimento di Ingegneria dell' Informazione e Ingegneria Elettrica, University of Salerno, Via Ponte don Melillo, 84084 Fisciano, SA (Italy)

- Publication Date:

- OSTI Identifier:
- 20698200

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 70; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.70.122001; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; BINARY STARS; COMPUTERIZED SIMULATION; CORRELATIONS; DENSITY; DISTRIBUTION; GRAVITATIONAL WAVE DETECTORS; GRAVITATIONAL WAVES; MAXIMUM-LIKELIHOOD FIT; NOISE; PROBABILITY

### Citation Formats

```
Croce, R.P., Demma, Th., Pierro, V., Pinto, I.M., Longo, M., Marano, S., and Matta, V.
```*Correlator bank detection of gravitational wave chirps--False-alarm probability, template density, and thresholds: Behind and beyond the minimal-match issue*. United States: N. p., 2004.
Web. doi:10.1103/PhysRevD.70.122001.

```
Croce, R.P., Demma, Th., Pierro, V., Pinto, I.M., Longo, M., Marano, S., & Matta, V.
```*Correlator bank detection of gravitational wave chirps--False-alarm probability, template density, and thresholds: Behind and beyond the minimal-match issue*. United States. doi:10.1103/PhysRevD.70.122001.

```
Croce, R.P., Demma, Th., Pierro, V., Pinto, I.M., Longo, M., Marano, S., and Matta, V. Wed .
"Correlator bank detection of gravitational wave chirps--False-alarm probability, template density, and thresholds: Behind and beyond the minimal-match issue". United States.
doi:10.1103/PhysRevD.70.122001.
```

```
@article{osti_20698200,
```

title = {Correlator bank detection of gravitational wave chirps--False-alarm probability, template density, and thresholds: Behind and beyond the minimal-match issue},

author = {Croce, R.P. and Demma, Th. and Pierro, V. and Pinto, I.M. and Longo, M. and Marano, S. and Matta, V.},

abstractNote = {The general problem of computing the false-alarm probability vs the detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves in additive stationary Gaussian noise. Specific reference is made 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 readdress the problem of relating the template density to the fraction of potentially observable sources which could be dismissed as an effect of template space discreteness.},

doi = {10.1103/PhysRevD.70.122001},

journal = {Physical Review. D, Particles Fields},

number = 12,

volume = 70,

place = {United States},

year = {Wed Dec 15 00:00:00 EST 2004},

month = {Wed Dec 15 00:00:00 EST 2004}

}