Keywords:
Gravitational fields -- Measurement -- Statistical methods.
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Electronic books.
Description / Table of Contents:
Introducing gravitational-wave data analysis, this book is an ideal starting point for researchers entering the field, and researchers currently analyzing data. Detailed derivations of the basic formulae enable readers to apply general statistical concepts to the analysis of gravitational-wave signals. It also discusses new ideas on devising the efficient algorithms.
Type of Medium:
Online Resource
Pages:
1 online resource (271 pages)
Edition:
1st ed.
ISBN:
9780511603785
Series Statement:
Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology Series ; v.Series Number 29
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=461090
DDC:
523.01
Language:
English
Note:
Cover -- Half-title -- Series-title -- Title -- Copyright -- Contents -- Preface -- Notation and conventions -- 1 Overview of the theory of gravitational radiation -- 1.1 Linearized general relativity -- 1.1.1 Linearized Einstein equations -- 1.1.2 Global Poincaré transformations -- 1.1.3 Gauge transformations -- 1.1.4 Harmonic coordinates -- 1.2 Plane monochromatic gravitational waves -- 1.3 Description in the TT coordinate system -- 1.4 Description in the observer's proper reference frame -- 1.4.1 Plus polarization -- 1.4.2 Cross polarization -- 1.5 Gravitational waves in the curved background -- 1.6 Energy-momentum tensor for gravitational waves -- 1.7 Generation of gravitational waves and radiation reaction -- 2 Astrophysical sources of gravitational waves -- 2.1 Burst sources -- 2.1.1 Coalescing compact binaries -- 2.1.2 Supernovae -- 2.2 Periodic sources -- 2.3 Stochastic sources -- 2.4 Case study: binary systems -- 2.4.1 Newtonian binary dynamics -- 2.4.2 Post-Newtonian binary dynamics -- 2.5 Case study: a rotating triaxial ellipsoid -- 2.6 Case study: supernova explosion -- 2.7 Case study: stochastic background -- 3 Statistical theory of signal detection -- 3.1 Random variables -- 3.2 Stochastic processes -- 3.3 Hypothesis testing -- 3.3.1 Bayesian approach -- 3.3.2 Minimax approach -- 3.3.3 Neyman-Pearson approach -- 3.3.4 Likelihood ratio test -- 3.4 The matched filter in Gaussian noise: deterministic signal -- 3.4.1 Cameron-Martin formula -- 3.4.2 Stationary noise -- 3.4.3 Matched filtering -- 3.5 Estimation of stochastic signals -- 3.6 Estimation of parameters -- 3.6.1 Uniformly minimum variance unbiased estimators -- 3.6.2 Exponential families of probability distributions -- 3.6.3 Fisher information -- 3.6.4 Kullback-Leibler divergence -- 3.6.5 L1-norm distance -- 3.6.6 Entropy -- 3.6.7 Bayesian estimation.
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3.6.8 Maximum a posteriori probability estimation -- 3.6.9 Maximum-likelihood estimation -- 3.6.10 Lower bounds on the variance of estimators -- 3.6.11 Jeffreys' prior -- 3.7 Non-stationary stochastic processes -- 3.7.1 Karhunen-Loéve expansion -- 3.7.2 Wiener processes -- 3.7.3 Resampled stochastic processes -- 3.7.4 Cyclostationary processes -- 4 Time series analysis -- 4.1 Sample mean and correlation function -- 4.2 Power spectrum estimation -- 4.2.1 Periodogram -- 4.2.2 Averaging -- 4.2.3 Windowing and smoothing -- 4.2.5 Multitapering -- 4.3 Tests for periodicity -- 4.4 Goodness-of-fit tests -- 4.4.1 Pearson's chi2 test -- 4.4.2 Kolmogorov-Smirnov test -- 4.5 Higher-order spectra -- 5 Responses of detectors to gravitational waves -- 5.1 Detectors of gravitational waves -- 5.2 Doppler shift between freely falling observers -- 5.3 Long-wavelength approximation -- 5.4 Responses of the solar-system-based detectors -- 5.4.1 LISA detector: time-delay interferometry -- 5.4.2 Ground-based laser interferometric detector -- 5.4.3 Ground-based resonant-bar detector -- 6 Maximum-likelihood detection in Gaussian noise -- 6.1 Deterministic signals -- 6.1.1 The F-statistic -- 6.1.2 Signal-to-noise ratio and the Fisher matrix -- 6.1.3 False alarm and detection probabilities -- 6.1.4 Number of templates -- 6.1.5 Suboptimal filtering -- 6.2 Case studies: deterministic signals -- 6.2.1 Periodic signal from a spinning neutron star -- 6.2.2 Chirp signal from an inspiraling compact binary -- 6.2.3 Signal from a supernova explosion -- 6.3 Network of detectors -- 6.3.1 Chirp signal from an inspiraling compact binary -- 6.3.2 Periodic signal from a spinning neutron star -- 6.3.3 Detection of periodic signals by LISA -- 6.4 Detection of stochastic signals -- 7 Data analysis tools -- 7.1 Linear signal model -- 7.1.1 Examples -- 7.2 Grid of templates in the parameter space.
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7.2.1 Covering problem -- 7.2.2 The covering problem with constraints -- 7.3 Numerical algorithms to calculate the F-statistic -- 7.3.1 The FFT algorithm -- 7.3.2 Resampling -- 7.3.3 Fourier interpolation -- 7.3.4 Optimization algorithms -- 7.4 Analysis of the candidates -- 7.4.1 Coincidences -- 7.4.2 Signal-to-noise gain -- 7.4.3 Upper limits -- Appendix A The chirp waveform -- Appendix B Proof of the Neyman-Pearson lemma -- Appendix C Detector's beam-pattern functions -- C.1 LISA detector -- C.2 Earth-based detectors -- C.2.1 Interferometric detector -- C.2.2 Resonant-bar detector -- Appendix D Response of the LISA detector to an almost monochromatic wave -- Appendix E Amplitude parameters of periodic waves -- References -- Index.
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