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#### Optimal Template Banks

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2102.11254.pdf

(Preprint), 651KB

PhysRevD.104.042005.pdf

(Publisher version), 293KB

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##### Citation

Allen, B. (2021). Optimal Template Banks.* Physical Review D,*
*104*(4): 042005. doi:10.1103/PhysRevD.104.042005.

Cite as: https://hdl.handle.net/21.11116/0000-0009-2490-B

##### 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.

The computational cost is proportional to the number of these points, and if

that is fixed, the question arises, where should the points be placed in

parameter space? The current literature advocates selecting the set of points

(called a "template bank") whose Wigner-Seitz (also called Voronoi) cells have

the smallest covering radius ($\equiv$ smallest maximal mismatch).

Mathematically, such a template bank is said to have "minimum thickness". Here,

we show that at fixed computational cost, for realistic populations of signal

sources, the minimum thickness template bank does NOT maximize the expected

number of detections. Instead, the most detections are obtained for a bank

which minimizes a particular functional of the mismatch. For closely spaced

templates, the most detections are obtained for a template bank which minimizes

the average squared distance from the nearest template, i.e., the average

expected mismatch. Mathematically, such a template bank is said to be the

"optimal quantizer". We review the optimal quantizers for template banks that

are built as $n$-dimensional lattices, and show that even the best of these

offer only a marginal advantage over template banks based on the humble cubic

lattice.

signal parameters (masses, sky location, frequencies,...) are unknown. In

practice, one hunts for signals at a discrete set of points in parameter space.

The computational cost is proportional to the number of these points, and if

that is fixed, the question arises, where should the points be placed in

parameter space? The current literature advocates selecting the set of points

(called a "template bank") whose Wigner-Seitz (also called Voronoi) cells have

the smallest covering radius ($\equiv$ smallest maximal mismatch).

Mathematically, such a template bank is said to have "minimum thickness". Here,

we show that at fixed computational cost, for realistic populations of signal

sources, the minimum thickness template bank does NOT maximize the expected

number of detections. Instead, the most detections are obtained for a bank

which minimizes a particular functional of the mismatch. For closely spaced

templates, the most detections are obtained for a template bank which minimizes

the average squared distance from the nearest template, i.e., the average

expected mismatch. Mathematically, such a template bank is said to be the

"optimal quantizer". We review the optimal quantizers for template banks that

are built as $n$-dimensional lattices, and show that even the best of these

offer only a marginal advantage over template banks based on the humble cubic

lattice.