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.
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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 GWDAW 2002 OUTLINE 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 Poisson r.v. compatibility with null hypothesis upper limit on the rate of detected gw …unfolding the sources (not yet) GWDAW 2002 DETECTOR LOCATIONS almost parallel detectors LIGHT TRAVEL TIME (ms) AL-NI 41.8 EX-NI 39.0 NA-NI 39.0 AU-NI 38.7 AL-AU 20.5 AL-EX 20.0 AL-NA 19.7 EX-NA 2.4 AU-EX 1.6 AU-NA 1.3 GWDAW 2002 EXCHANGED PERIODS of OBSERVATION 1997-2000 ALLEGRO AURIGA NAUTILUS EXPLORER NIOBE fraction of time in monthly bins exchange threshold 6 1021 Hz 1 3 6 1021 Hz 1 3 1021 Hz 1 Fourier amplitude of burst gw h(t ) H0 (t t0 ) arrival time GWDAW 2002 amplitude (Hz-1) DIRECTIONAL SEARCH 10 9 8 7 6 5 4 3 2 1 0 0 6 12 18 24 30 36 42 48 54 60 amplitude (Hz-1) time (hours) 1.0 5 10 0.9 9 amplitude directional sensitivity 0.8 8 4 0.7 7 0.6 6 3 sin2 GC 0.5 5 sin 2 GC 0.4 4 2 0.3 3 0.2 2 1 0.1 1 0 0.0 0 6 12 18 24 30 36 42 48 54 54 60 time (hours) GWDAW 2002 amplitude (Hz-1) DATA SELECTION 10 9 8 7 6 5 4 3 2 1 0 0 6 12 18 24 30 36 42 48 54 60 time (hours) GWDAW 2002 OBSERVATION TIME 1997-2000 total time when exchange threshold has been lower than gw amplitude amplitude of burst gw GWDAW 2002 amplitude (Hz-1) DATA SELECTION 10 9 8 7 6 5 4 3 2 1 0 0 6 12 18 24 30 36 42 48 54 60 amplitude (Hz-1) time (hours) 10 9 8 7 6 5 4 3 2 1 0 0 6 12 18 24 30 36 42 48 54 60 time (hours) GWDAW 2002 RESULTING PERIODS of OBSERVATION and EVENTS no directional search time (hours) directional search time (hours) GWDAW 2002 AMPLITUDE DISTRIBUTIONS of EXCHANGED EVENTS normalized to each detector threshold for trigger search 1 -1 relative counts 10 -2 10 -3 10 -4 10 -5 10 1 10 AMP/THR ALLEGRO 1 10 AMP/THR AURIGA 1 10 AMP/THR EXPLORER 1 10 AMP/THR NAUTILUS typical SNR of trigger search thresholds: 3 ALLEGRO, NIOBE 5 AURIGA, EXPLORER, NAUTILUS · amplitude range much wider than expected: non modeled outliers dominating at high SNR 1 10 NIOBE GWDAW 2002 FALSE ALARM REDUCTION by thresholding events amplitude time natural consequence: AMPLITUDE CONSISTENCY of SELECTED EVENTS GWDAW 2002 FALSE DISMISSAL PROBABILITY • data selection as a function of the common search threshold Ht 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 1 ti t j k i2 2j false dismissal 2 k false alarms k • amplitude consistency check: gw generates events with correlated amplitudes testing Ai Aj A (same as above) efficiency of detection versus false alarms: fraction of found gw coincidences maximize the ratio fluctuations of accidental background best balance in our case: time coincidence max false dismissal 5% 30% no rejection based on amplitude consistency test GWDAW 2002 POISSON STATISTICS of ACCIDENTAL COINCIDENCES Poisson fits of accidental concidences: 2 test sample of EX-NA background one-tail probability = 0.71 agreement with uniform distribution histogram of one-tail 2 probabilities for ALL two-fold observations GWDAW 2002 SETTING CONFIDENCE INTERVALS unified & frequentistic approach tomorrow talk by L. Baggio References: 1. 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, PRD 57, 3873 (1998) 3. 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 GWDAW 2002 SETTING CONFIDENCE INTERVALS / 2 GOAL: estimate the number of gw which are detected with amplitude Ht Example: confidence interval with coverage 95% “upper limit” : true value outside with probability 95% 18 16 14 12 Ngw 10 8 6 Ht 4 2 0 1.0 10.0 search threshold [10-21/Hz] 100.0 GWDAW 2002 SETTING CONFIDENCE INTERVALS / 3 18 16 systematic search on thresholds many trials ! 14 12 Ngw 10 8 all upper limits but one: 6 testing the null hypothesis 4 2 0 1.0 overall false alarm probability 33% search threshold [10-21/Hz] at least one detection in case PDG recommendation NO GW are in the data 10.0 100.0 A potential difficulty with unified intervals arises if, for example, one constructs such an interval for a Poisson parameter s of some yet toIN be discovered signal process NULL HYPOTHESIS WELL with, AGREEMENT WITH THE say, 1 - = 0:9. If the true signal parameter is zero, or in any case much less than OBSERVATIONS 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 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 1,000 rate year -1 100 0.60 0.80 0.90 0.95 10 1 1E-21 1E-20 ensured minimum coverage 1E-19 search threshold Hz -1 true rate value is under the curves with a probability = coverage 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 1,000 rate year -1 100 0.60 0.80 0.90 0.95 ensured minimum coverage 10 1 1E-21 1E-20 1E-19 search threshold Hz -1 true rate value is under the curves with a probability = coverage