Performance of Random Template Banks

TL;DR

This paper compares the effectiveness of random versus lattice-based template banks in high-dimensional parameter spaces for gravitational-wave and electromagnetic source detection, revealing that random banks outperform lattices in dimensions greater than eight.

Contribution

It provides a quantitative analysis of signal loss in random template banks and shows their superiority over lattice-based banks in high-dimensional spaces.

Findings

Lattice banks outperform random banks for dimensions less than 4.

Random banks perform comparably to lattices for dimensions greater than 8.

In high dimensions, random banks are more effective than the best known lattices.

Abstract

When searching for new gravitational-wave or electromagnetic sources, the $n$ signal parameters (masses, sky location, frequencies,...) are unknown. In practice, one hunts for signals at a discrete set of points in parameter space, called a template bank. These may be constructed systematically as a lattice, or alternatively, by placing templates at randomly selected points in parameter space. Here, we calculate the fraction of signals lost by an $n$-dimensional random template bank (compared to a very finely spaced bank). This fraction is compared to the corresponding loss fraction for the best possible lattice-based template banks containing the same number of grid points. For dimensions $n<4$ the lattice-based template banks significantly outperform the random ones. However, remarkably, for dimensions $n>8$, the difference is negligible. In high dimensions, random template banks outperform the best known lattices.