5 Data Analysis

Observing gravitational waves requires a data analysis strategy, which is in many ways different from conventional astronomical data analysis. There are several reasons why this is so:

Data analysis for broadband detectors has been strongly developed since the mid 1980s [362Jump To The Next Citation Point334333]. The field has a regular series of annual Gravitational Wave Data Analysis Workshops; the published proceedings are a good place to find current thinking and challenges. Early coincidence experiments with interferometers [273] and bars [32] provided the first opportunities to apply these techniques. Although the theory is now fairly well understood [207Jump To The Next Citation Point], strategies for implementing data analysis depend on available computer resources, data volumes, astrophysical knowledge, and source modeling, and so are under constant revision.

We will begin with a discussion of the matched filtering algorithm and next use it to estimate the SNRs for binary coalescences in various detectors. After that, we will develop the theory of matched filtering further to work out the computational costs to carry out online searches, that is to search at the same rate as the data is acquired. In the final section, we will use the formalism developed in earlier sections to discuss parameter estimation. The foundations of signal analysis lie in the statistics of making “best estimates” of whether a signal is present in noisy data or not. See the Living Review by Jaranowski and Królak [207] for a discussion of this in the gravitational wave context.

 5.1 Matched filtering and optimal signal-to-noise ratio
  5.1.1 Optimal filter
  5.1.2 Optimal signal-to-noise ratio
  5.1.3 Practical applications of matched filtering
 5.2 Suboptimal filtering methods
 5.3 Measurement of parameters and source reconstruction
  5.3.1 Ambiguity function
  5.3.2 Metric on the space of waveforms
  5.3.3 Covariance matrix
  5.3.4 Bayesian inference

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