Optimal Template Banks

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, with a computational cost that is proportional to the number of these points. 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 Voronoï) cells have the smallest covering radius ($\equiv$ smallest maximal mismatch). Mathematically, such a template bank is said to have "minimum thickness". Here, for realistic populations of signal sources, we compute the fraction of potential detections which are "lost" because the template bank is discrete. We show that at fixed computational cost, 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 fraction of lost detections is proportional to a scale-invariant "quantizer constant" G, which measures the average squared distance from the nearest template, i.e., the average expected mismatch. This provides a straightforward way to characterize and compare the effectiveness of different template banks. The template bank which minimizes G is mathematically called the "optimal quantizer", and maximizes the expected number of detections. We review optimal quantizer and minimum thickness template banks that are built as n-dimensional lattices, showing that even the best of these offer only a marginal advantage over template banks based on the humble cubic lattice.

arXiv commentFinal published version, 1 Figure

References in corpus (42)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?
• Observing binary inspiral in gravitational radiation: One interferometer
• FINDCHIRP: an algorithm for detection of gravitational waves from inspiraling compact binaries
• Search templates for gravitational waves from inspiraling binaries: Choice of template spacing
• The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
• Matched filtering of gravitational waves from inspiraling compact binaries: Computational cost and template placement
• A chi-squared time-frequency discriminator for gravitational wave detection
• Searching for periodic sources with LIGO
• Searching for periodic sources with LIGO. II: Hierarchical searches
• Gravitational waves from coalescing binaries: detection strategies and Monte Carlo estimation of parameters
• A stochastic template placement algorithm for gravitational wave data analysis
• Template-based searches for gravitational waves: efficient lattice covering of flat parameter spaces
• Fast and Accurate Sensitivity Estimation for Continuous-Gravitational-Wave Searches
• Improved Stack-Slide Searches for Gravitational-Wave Pulsars
• Random template banks and relaxed lattice coverings
• Estimating the sensitivity of wide-parameter-space searches for gravitational-wave pulsars
• Search for Continuous Gravitational Waves: Optimal StackSlide method at fixed computing cost
• Building a stochastic template bank for detecting massive black hole binaries
• Filtering post-Newtonian gravitational waves from coalescing binaries
• Blandford's Argument: The Strongest Continuous Gravitational Wave Signal
• Sensitivity improvements in the search for periodic gravitational waves using O1 LIGO data
• Results from the first all-sky search for continuous gravitational waves from small-ellipticity sources
• Einstein@Home all-sky search for continuous gravitational waves in LIGO O2 public data
• Template banks to search for compact binaries with spinning components in gravitational wave data
• Designing a template bank to observe compact binary coalescences in Advanced LIGO's second observing run
• Cover art: issues in the metric-guided and metric-less placement of random and stochastic template banks
• Complexity and algorithms for computing Voronoi cells of lattices
• Lattice template placement for coherent all-sky searches for gravitational-wave pulsars
• Implementing a semicoherent search for continuous gravitational waves using optimally-constructed template banks
• Results from high-frequency all-sky search for continuous gravitational waves from small-ellipticity sources
• Exploiting Orbital Constraints from Optical Data to Detect Binary Gamma-ray Pulsars
• Results from an extended Falcon all-sky survey for continuous gravitational waves
• Empirically extending the range of validity of parameter-space metrics for all-sky searches for gravitational-wave pulsars
• Performance of Newtonian filters in detecting gravitational waves from coalescing binaries
• Spherical ansatz for parameter-space metrics
• Optimising the choice of analysis method for all-sky searches for continuous gravitational waves with Einstein@Home
• Continuous Gravitational Waves from Isolated Galactic Neutron Stars in the Advanced Detector Era
• Efficient generation and optimization of stochastic template banks by a neighboring cell algorithm
• A stochastic template bank for gravitational wave searches for precessing neutron-star--black-hole coalescence events
• A generalization of Voronoi's reduction theory and its application
• Optimizing StackSlide setup and data selection for continuous-gravitational-wave searches in realistic detector data

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• Searches for Continuous-Wave Gravitational Radiation
• Searches for continuous gravitational waves from neutron stars: A twenty-year retrospective
• Search methods for continuous gravitational-wave signals from unknown sources in the advanced-detector era
• Application of a hierarchical MCMC follow-up to Advanced LIGO continuous gravitational-wave candidates
• Empirically estimating the distribution of the loudest candidate from a gravitational-wave search
• On the best lattice quantizers
• An implementation of Galactic white dwarf binary data analysis for MLDC-3.1
• A geometric template bank for the detection of spinning low-mass compact binaries with moderate orbital eccentricity
• Scalable data-analysis framework for long-duration gravitational waves from compact binaries using short Fourier transforms
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• Template banks based on ${\mathbb{Z}}^n$ and $A_n^{\ast }$ lattices
• Two sides of the same coin: the F-statistic and the 5-vector method
• Implementation of a new weave-based search pipeline for continuous gravitational waves from known binary systems
• Accounting for the Known Unknowns: A Parametric Framework to Incorporate Systematic Waveform Errors in Gravitational-Wave Parameter Estimation
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• One-stop strategy to search for long-duration gravitational-wave signals
• Signal-to-noise-ratio and SNR-max detection statistics in template bank searches for exotic physics transients with networks of quantum sensors
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• Optimization and Identification of Lattice Quantizers
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