T. Demma

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

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.

Gravitational wave chirp search: no-signal cumulative distribution of the maximum likelihood detection statistic

The cumulative distribution of the supremum of a set (bank) of correlators is investigated in the context of maximum likelihood detection of gravitational wave chirps from coalescing binaries with unknown parameters. Accurate (lower-bound) approximants are introduced based on a suitable generalization of previous results by Mohanty. Asymptotic properties (in the limit where the number of correlators goes to infinity) are highlighted. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a Gaussian correlation inequality.