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Comparing different searches for gravitational-wave bursts

Comparing different searches for gravitational-wave bursts on simulated LIGO and VIRGO data. Michele Zanolin -MIT on behalf of the LIGO-VIRGO joint working group. Benefits Pipeline Results Future plans.

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Comparing different searches for gravitational-wave bursts

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  1. Comparing different searches for gravitational-wave bursts on simulated LIGO and VIRGO data Michele Zanolin -MIT on behalf of the LIGO-VIRGO joint working group

  2. Benefits • Pipeline • Results • Future plans

  3. Benefits of comparing LIGO and Virgo searcheson single interferometer simulated data • Compare time domain and frequency domain methods over different class of waveforms. • Detector independent measure of performance • Simulated noise (see inspiral talk) allows to test the limit of design sensitivity and improved vetos (and no restrictions due to use of real data) • Single interferometer analysis decouples the properties of the trigger generation from those of coincidence modules • Events might happen when only one interferometer is on lock

  4. Pipeline • 7 methods already involved (3 more will join soon) • Simulated data have been produced • Simulated injections have been generated • Receiver operating characteristics have been computed on the 3 hours of simulated data for false rates from 0.1 to 0.0001 Hz. • Trigger lists ( containing rough time-frequency volume) and sets of figures of merit have been generated • A method independent parameterisation of the triggers is adopted (Sylvestre, Sutton, Lazzarini). A post processing stand alone parameter estimation module is introduced, that uses Maximum likelihood estimators and assumes colored Gaussian noise (Zanolin, Sylvestre).

  5. Time-frequency Methods • Q-pipeline (see talk by S.Chatterji): multiresolution time frequency search for excess power applied on data that are first whitened using zero phase linear prediction. Equivalent to optimal matched filter for minimum uncertainty waveforms of unknown phase in the whitened data. • Kleine Welle (L.D. - L. Blackburn): search for statistically significant clusters of coefficients in the dyadic Haar wavelet decomposition. • S-transform (V.D. - see talk byA.C. Clapson): search for statistically significant clusters of coefficients in the time frequency map generated using a kernel composed of complex exponentials shaped by Gaussian profiles with width inversely proportional to frequency. High pass and line removal applied on Virgo data. • Power Filter (G.Guidi): search for excess power over different time intervals and sets of frequencies.

  6. Time domain methods • Peak Correlator(P.Hello): Search for peaks of Wiener filtered data with Gaussian templates. For Virgo data a high pass filter and a line removal filter are applied to remove the resonance at 0.6 Hz. • Mean Filter (M. A. Bizouard): Search for excess in moving averages of whitened data over intervals containing from 10 to 200 samples. • ALF (M.A.Bizouard): Search for change in slope over moving windows of whitened data over intervals containing from 10 to 300 samples.

  7. Simulated Bursts • Three hours sets of simulated bursts generated (peak times are Poisson distributed with mean rate of 1/60 seconds ) • Bursts amplitude is parameterized in terms of h and snr (tested between 2 to10) • Injected Gaussian have durations of 1 and 4 milliseconds • Cosine Gaussian with central frequencies of 235 820 Hz and Qs of 5 and 15 • Supernovae core collapse waveforms (Dimmelmejer, Font, Muller) with parameters (a=1, b=2, g=1) and (a=2, b=4, g=1)

  8. Burst events 0.01 0.2 • Three species: Dimmelmeier & al. a1b2g1,a2b4g1 Gaussian 1,4 milliseconds sine-gaussian shapes q=5,15 f=235,820 0.1

  9. Method independent event parametrization • central frequency • Bandwidth where • duration where and h_rss. The stand alone parameter estimation gets the time frequency volumes from the searches and computes the burst’s parameters in the presence of noise

  10. Injections locations in the parameter space cg ga dfm . . 3 3 3 10 10 10

  11. Receiver operating characteristics for SG235Q5 snr=5 snr=10

  12. Receiver operating characteristics for SG235Q5 snr=10 snr=5

  13. snr=5 snr=10 Receiver operating characteristics for GA1d0

  14. Receiver operating characteristics for GA1d0 snr=5 snr=5

  15. snr=5 snr=10 Receiver operating characteristics for dfm2b4g1

  16. snr=5 snr=5 Receiver operating characteristics for dfm2b4g1

  17. And/Or combination of methods • Each method is tuned at a false rate = 0.1 Hz • Preliminary, since joint false rate still to be estimated. l LIGO Virgo sg235Q5 GA1d0 DFMa2b4g1 sg235Q5 GA1d0 DFMa2b4g1 Single (snr=5) Q 116 PC 136 PC 84 Q 115 PC 134 PC 75 AND (snr=5) 14 16 9 12 16 10 OR (snr=5) 130 144 98 121 148 93 Single (snr=10) Q PF 190 MF/ALF/PC 178 MF/ALF/PC 178 MF/ALF/PC/Q 170 Q/PC 170 Q/ALF 190 Q Q AND (snr=10) 184 174 166 174 120 164 OR (snr=10) 190 178 170 190 178 170 N injected 190 178 170 190 178 170

  18. What did we learn • Learn to process each others' data, exchange, and compare triggers • Different methods perform differently in different regions of the parameter space • OR combinations of methods increases efficiency (false rates for combinations of the methods still to be investigated) • Confront burst search performance with optimal matched filtering (see S.Chatterji talk)

  19. Future directions • As first project of exchanging simulated noise and signal data of the LIGO and Virgo instruments is successfully carrying out and address the goals set by the joint working group the next steps are approaching: - A program to continue the data exchange within the framework of simulated data but using astrophysical (coherent) waveform injections onto simulations is forthcoming (useful to quantify the scientific potential of a combined analysis ) - Ultimate goal is to operate the instruments as part of a global network. We are defining the details of exchange of triggers (and/or) data will actually take place.

  20. From now on back up material

  21. Q-pipeline • Targets miminum uncertaintly waveforms with 64<f [Hz]<1024 3.5<Q<50 • Space of time, frequency, and Q is tilted for a worst case energy loss of 20 percent for minimum uncertainty waveforms • The data are first whitened using zero-phase linear prediction • Multi-resolution time-frequency search for excess power • The whitened data is projected onto a basis of windowed complex exponentials where the window w(t) has mimimum time-frequency uncertainty and bandwidth • Significant tiles are identified assuming white noise statistics • Only the most significant set of non-overlapping tiles are reported • Equivalent to an optimal matched filter search for minimum uncertainty waveforms of unknown phase in the whitened data stream • See talk by S. Chatterji at this conference.

  22. kleineWelle kleineWelle searches for statistically significant clusters of coefficients in the dyadic wavelet decomposition of a whitened timeseries.

  23. Power Filter (PF) Compute the Power over several windows. Analyze the power in different sets of frequencies. Parameters of the analysis: Window 0: width = 0.03 s. Window 1: width =0.06 s, 10 sets of frequencies. Whitening of the data: Burg algorithm with a learning time of ~180 s 3000 paramaters for the LIGO simulated noise 1000 paramaters for the VIRGO simulated noise.

  24. Peak Correlator (PC) PC : Wiener filtering with Gaussian templates Half-widths  are optimally computed in [0.2 ms; 6ms] according to a minimal match MM = 0.99 ( 9 templates) In the case of the VIRGO simulated noise, a pre-processing is applied in order to kill the huge resonance at 0.6 Hz (Kalman filter).

  25. Mean Filter (MF) MF computes the average of data in some moving window of size N : MF needs a whitening of the data. In the LIGOVIRGO MDC we have used a Burg algorithm with a learning time of 300 s and 3000 paramaters for the LIGO simulated noise and 4000 paramaters for the VIRGO simulated noise. The practical implementation has been done using 10 windows : N (bins) : 10 15 20 25 30 40 50 70 150 200

  26. ALF ALF is based on a detection of change of slope in a window of size N. ALF needs a whitening of the data as MF (same algo and parameters). Assuming data being whitened, the slope a and offset b are computed : where < > means average over a window of size N The variables a and b are then decorrelated using variances and covariance being : All the information (slope and offset) is then combined in ALF : The practical implementation has been done using 10 windows : N (bins) : 10 20 30 40 50 100 150 200 250 300

  27. S transform analysis chain • S transform • Related to the Gabor (or wavelet) transform • Good signal localization (time and frequency) • Restitution of noise psd. • Invertible. • Preprocessing (window length) • High pass filter + Hanning window. • Change to frequency domain (FFT). • Build TF map using S-Transform (resolution) (for each frequency) • Product with Gaussian window. • Bring back to time domain (FFT-1). • Post processing (for each frequency) • Normalize to zero mean and unit standard deviation. • Threshold map element value. (1st threshold) • Data reduction • Clustering of map elements (8 connectivity) • Threshold on total cluster energy. (2nd threshold) Signal visible in map… Issue is reliable extraction!

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