Random template banks and relaxed lattice coverings
Abstract
Templatebased searches for gravitational waves are often limited by the computational cost associated with searching large parameter spaces. The study of efficient template banks, in the sense of using the smallest number of templates, is therefore of great practical interest. The traditional approach to templatebank construction requires every point in parameter space to be covered by at least one template, which rapidly becomes inefficient at higher dimensions. Here we study an alternative approach, where any point in parameter space is covered only with a given probability η<1. We find that by giving up complete coverage in this way, large reductions in the number of templates are possible, especially at higher dimensions. The prime examples studied here are random template banks in which templates are placed randomly with uniform probability over the parameter space. In addition to its obvious simplicity, this method turns out to be surprisingly efficient. We analyze the statistical properties of such random template banks, and compare their efficiency to traditional lattice coverings. We further study relaxed lattice coverings (using Z_{n} and A_{n}^{*} lattices), which similarly cover any signal location only with probability η. The relaxed A_{n}^{*} lattice is found to yield the most efficient template banks at low dimensions (n≲10), while random template banks increasingly outperform any other method at higher dimensions.
 Publication:

Physical Review D
 Pub Date:
 May 2009
 DOI:
 10.1103/PhysRevD.79.104017
 arXiv:
 arXiv:0809.5223
 Bibcode:
 2009PhRvD..79j4017M
 Keywords:

 04.30.Tv;
 95.75.z;
 29.85.Fj;
 Gravitationalwave astrophysics;
 Observation and data reduction techniques;
 computer modeling and simulation;
 Data analysis;
 General Relativity and Quantum Cosmology
 EPrint:
 13 pages, 10 figures, submitted to PRD