Gravitational Wave Analysis (I)
lectures: 16, 17 November 2006
1. Response of a GW antenna to an astrophysical signal; GW polarisations; antenna pattern and the inverse problem of reconstructing the source from a knowledge of the response in several detectors.
2. Statistical theory of signal detection: theory of hypothesis testing; matched filtering; frequentist vs. Bayesian approaches to interpretation of data; detection Vs. upper limits. Geometrical theory of signal detection; metric on the signal manifold; effectualness Vs. faithfulness; fitting factor and match; template placement algorithms.
3. Signal detection problem in ground-based vis-a-vis space-based detectors. Detecting weak and rare signals in background Vs. detecting weak and strong signals in confusion background. Frequency noise in LISA:The problem of unequal arms. TDI variables. The first, second and third
generation of TDIs.
4. Detecting compact binary coalescences with spinning and non-spinning components:
a. Template models: post-Newtonian waveforms;
b. resummation methods; evolution beyond the ISCO; comparison of numerical and analytical methods
c. phenomenological waveforms.
5. Deteciting signals of unknwon shape: time-frequency analysis; excess power-statistic.
6. Detecitng continuous waves: accounting for the motion of the antenna.
7. Modelling the noise: gaussian approximation; non-Gaussianity and non-stationarity of data; methods of estimating the PSD (mean- and median-based methods, etc.).
8. Parameter estimation: Covariance matrix, Monte-Carlo simulations, MCMC techniques.