Statistics – Applications
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010cqgra..27x9003f&link_type=abstract
Classical and Quantum Gravity, Volume 27, Issue 24, pp. 249003 (2010).
Statistics
Applications
Scientific paper
The field of gravitational-wave data analysis has expanded greatly over the past decade and significant developments have been made in methods of analyzing the data taken by resonant bar and interferometric detectors, as well as analysis of mock LISA data. This book introduces much of the required theoretical background in gravitational physics, statistics and time series analysis before moving on to a discussion of gravitational-wave data analysis techniques themselves.
The book opens with an overview of the theory of gravitational radiation, providing a comprehensive discussion of various introductory topics: linearized gravity, transverse traceless gauge, the effects of gravitational waves (via geodesic deviation), energy and momentum carried by the waves, and generation of gravitational waves.
The second chapter provides an introduction to the various sources of gravitational waves, followed by more detailed expositions on some of the primary sources. For example, the description of compact binary coalescence is thorough and includes a brief exposition of the post-Newtonian formalism and the effective one body method. There also follows extended derivations of gravitational waves from distorted neutron stars, supernovae and a stochastic background.
Chapter three provides an introduction to the statistical theory of signal detection, including a discussion of parameter estimation via the Fisher matrix formalism. This is presented from a very mathematical, postulate based, standpoint and I expect that even established gravitational-wave data analysts will find the derivations here more formal than they are used to. The discussion of likelihood ratio tests and the importance of prior probabilities are presented particularly clearly.
The fourth chapter covers time series analysis, with power spectrum estimation, extraction of periodic signals and goodness of fit tests. Chapter five switches topics and gives the details of the response of gravitational-wave detectors. The derivation is kept general at the outset, so that a detailed discussion of the response of the LISA detector is possible, before restricting to the long wavelength approximation for discussion of ground based detectors.
Chapter six provides a detailed exposition of the maximum likelihood method for searching for signals in Gaussian noise. Jaranowski and Królak developed the F-statistic search method, which has become standard in searches for continuous waves and is also used in LISA data analysis. Perhaps then, it is unsurprising that the discussion of matched filtering is couched in terms of a generalized F-statistic method. This chapter also covers parameter estimation via the Fisher matrix and applications to networks of detectors. As in other chapters, the initial formalism is rather general but, in later sections, specific examples are given, such as the application to continuous wave, compact binary coalescence and stochastic signals.
The seventh, and final, chapter provides examples of concrete methods for analyzing data. The focus is on methods which the authors are most familiar with and consequently these are mostly relevant for the analysis of resonant bar data and searches for continuous wave signals. The discussion of complexities arising in creating banks of template waveforms is likely to be of more general interest.
The last two chapters of the book, which contain the meat of the subject of gravitational-wave data analysis, are regrettably short. Several large research areas are not discussed at all, including: time-frequency excess power search methods; Bayesian parameter estimation techniques (e.g. Markov Chain Monte Carlo) to go past the Fisher matrix approximation; signal consistency tests and other methods of dealing with non-Gaussian data.
On the back cover, it states that `this book introduces researchers entering the field ... to gravitational-wave data analysis'. While this book certainly does contain much of the necessary introductory material, the presentation will likely prove too technical to be easily accessible to beginning researchers, especially those without a strong mathematical grounding. I expect, however, that this book will serve as a useful reference, containing detailed derivations and descriptions of many central topics in gravitational-wave data analysis.
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