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Results of the 1997-2000 Search for Burst Gw by IGEC

Results of the 1997-2000 Search for Burst Gw by IGEC. G.A.Prodi - INFN and Università di Trento, Italy International Gravitational Event Collaboration. http:// igec .lnl.infn.it. GWDAW 2002. ALLEGRO group : ALLEGRO (LSU) http://gravity.phys.lsu.edu

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Results of the 1997-2000 Search for Burst Gw by IGEC

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  1. Results of the 1997-2000 Search for Burst Gw by IGEC G.A.Prodi - INFN and Università di Trento, Italy International Gravitational Event Collaboration http://igec.lnl.infn.it GWDAW 2002 ALLEGRO group: ALLEGRO (LSU)http://gravity.phys.lsu.edu Louisiana State University, Baton Rouge - Louisiana AURIGA group: AURIGA (INFN-LNL) http://www.auriga.lnl.infn.it INFN of Padova, Trento, Ferrara, Firenze, LNL Universities of Padova, Trento, Ferrara, Firenze IFN- CNR, Trento – Italia NIOBE group: NIOBE (UWA) http://www.gravity.pd.uwa.edu.au University of Western Australia, Perth, Australia ROG group: EXPLORER (CERN) http://www.roma1.infn.it/rog/rogmain.html NAUTILUS (INFN-LNF) INFN of Roma and LNF Universities of Roma, L’Aquila CNR IFSI and IESS, Roma - Italia

  2. OUTLINE GWDAW 2002 • ·overview of the EXCHANGED DATA SET 1997-2000 • sensitivity and observation time • candidate burst gw events • · multiple detector DATA ANALYSIS • directional search strategy • search as a function of amplitude threshold • false dismissal or detection efficiency • estimation of accidental coincidences by time shifts methods  L.Baggio tomorrow • ·RESULTS • accidental coincidences are Poissonr.v. • compatibility with null hypothesis • upper limit on the rate of detected gw • …unfolding the sources (not yet)

  3. GWDAW 2002 DETECTOR LOCATIONS almost parallel detectors

  4. GWDAW 2002 exchange threshold EXCHANGED PERIODS of OBSERVATION 1997-2000 ALLEGRO AURIGA NAUTILUS EXPLORER NIOBE fraction of time in monthly bins Fourier amplitude of burst gw arrival time

  5. DIRECTIONAL SEARCH GWDAW 2002 amplitude directional sensitivity amplitude (Hz-1) time (hours) amplitude (Hz-1) time (hours)

  6. DATA SELECTION GWDAW 2002 amplitude (Hz-1) time (hours)

  7. GWDAW 2002 amplitude of burst gw OBSERVATION TIME 1997-2000 total time when exchange threshold has been lower than gw amplitude

  8. DATA SELECTION GWDAW 2002 amplitude (Hz-1) time (hours) amplitude (Hz-1) time (hours)

  9. RESULTING PERIODS of OBSERVATION and EVENTS GWDAW 2002 no directional search time (hours) directional search time (hours)

  10. GWDAW 2002 AMPLITUDE DISTRIBUTIONS of EXCHANGED EVENTS normalized to each detector threshold for trigger search ·typical SNRoftrigger search thresholds:  3ALLEGRO, NIOBE  5 AURIGA, EXPLORER, NAUTILUS ·amplitude rangemuch wider than expected: non modeled outliers dominating at high SNR

  11. FALSE ALARM REDUCTION GWDAW 2002 by thresholding events natural consequence: AMPLITUDE CONSISTENCY of SELECTED EVENTS

  12. GWDAW 2002 fraction of found gw coincidences fluctuations of accidental background FALSE DISMISSAL PROBABILITY • data selection as a function of the common search thresholdHt • keep the observation time when false dismissal is under control • keep events above threshold • efficiency of detection depends on signal amplitude, direction, polarization … e.g. > 50% with amplitude > Ht at each detector • time coincidence search • time window is set requiring a conservative false dismissal • robust and general method: Tchebyscheff inequality false alarms  k • amplitude consistency check: gw generates events with correlated amplitudes • testing (same as above)  efficiency of detection versus false alarms: maximize the ratio best balance in our case: time coincidence max false dismissal 5%  30% no rejection based on amplitude consistency test

  13. GWDAW 2002 POISSON STATISTICS of ACCIDENTAL COINCIDENCES Poisson fits of accidental concidences: 2 test sample of EX-NA background one-tailprobability = 0.71 agreement with uniform distribution histogram of one-tail2 probabilities for ALL two-fold observations

  14. GWDAW 2002 SETTING CONFIDENCE INTERVALS • unified & frequentistic approach • tomorrow talk by L. Baggio References: • B. Roe and M. Woodroofe, PRD 63, 013009 (2000) • most likely confidence intervals ensuring a given coverage (our choice) • 2. G.J.Feldman and R.D.Cousins, PRD57, 3873 (1998) • Recommendations of the Particle Data Group: http://pdg.lbl.gov/2002/statrpp.pdf • see also the review: F.Porter, Nucl. Instr. Meth A 368 (1996) COVERAGE: probability that the confidence interval contains the true value unified treatment of UPPER LIMIT  DETECTION freedom to chose the confidence of goodness of the fit tests independently from the confidence of the interval

  15. GWDAW 2002 “upper limit” : true value outside with probability  95% Ht SETTING CONFIDENCE INTERVALS / 2 GOAL: estimate the number of gw which are detected with amplitude Ht Example: confidence interval with coverage 95%

  16. GWDAW 2002 SETTING CONFIDENCE INTERVALS / 3 systematic search on thresholds many trials ! all upper limits but one: • testing the null hypothesis • overall false alarm probability 33% • at least one detection in case • NO GW are in the data PDG recommendation A potential difficulty with unified intervals arises if, for example, one constructs such an interval for a Poisson parameter s of some yet to be discovered signal process with, say, 1 - = 0:9. If the true signal parameter is zero, or in any case much less than the expected background, one will usually obtain a one-sided upper limit on s. In a certain fraction of the experiments, however, a two-sided interval for s will result. Since, however, one typically chooses 1 - to be only 0:9 or 0:95 when searching for a new effect, the value s = 0 may be excluded from the interval before the existence of the effect is well established. It must then be communicated carefully that in excluding s = 0 from the interval, one is not necessarily claiming to have discovered the effect. NULL HYPOTHESIS WELL IN AGREEMENT WITH THE OBSERVATIONS

  17. GWDAW 2002 UPPER LIMIT /1 on RATE of BURST GW from the GALACTIC CENTER DIRECTION with measured amplitude  search threshold no model is assumed for the sources, apart from being a random time series rate year -1 ensured minimum coverage search threshold Hz -1 true rate value is under the curves with a probability = coverage

  18. GWDAW 2002 UPPER LIMIT /2 on RATE of BURST GW without performing a directional search measured amplitude  search threshold (amplitudes of gw are referred to the direction of detectors) no model is assumed for the sources, apart from being a random time series rate year -1 ensured minimum coverage search threshold Hz -1 true rate value is under the curves with a probability = coverage

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