G.A.Prodi - INFN and Università di Trento, Italy International Gravitational Event Collaboration igec.lnl.infn.it ALLEGRO group:ALLEGRO (LSU) Louisiana State University, Baton Rouge - Louisiana AURIGA group:AURIGA (INFN-LNL) INFN of Padova, Trento, Ferrara, Firenze, LNL Universities of Padova, Trento, Ferrara, Firenze IFN- CNR, Trento – Italia NIOBE group:NIOBE (UWA) University of Western Australia, Perth, Australia ROG group:EXPLORER (CERN) NAUTILUS (INFN-LNF) INFN of Roma and LNF Universities of Roma, L’Aquila CNR IFSI and IESS, Roma - Italia Results of the Search for Burst Gw by IGEC GWDAW 2002

 overview of the EXCHANGED DATA SET sensitivity and observation time candidate burst gw events OUTLINE GWDAW 2002  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  RESULTS accidental coincidences are Poisson r.v. compatibility with null hypothesis upper limit on the rate of detected gw …unfolding the sources (not yet) methods  L.Baggio tomorrow

DETECTOR LOCATIONS GWDAW 2002 almost parallel detectors

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

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

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

amplitude of burst gw OBSERVATION TIME GWDAW 2002 total time when exchange threshold has been lower than gw amplitude

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

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

AMPLITUDE DISTRIBUTIONS of EXCHANGED EVENTS GWDAW 2002 normalized to each detector threshold for trigger search  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

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

FALSE DISMISSAL PROBABILITY GWDAW 2002 data selection as a function of the common search threshold H t 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 > H t at each detector time coincidence search time window is set requiring a conservative false dismissal robust and general method: Tchebyscheff inequality fraction of found gw coincidences fluctuations of accidental background best balance in our case: time coincidence max false dismissal 5%  30% no rejection based on amplitude consistency test  efficiency of detection versus false alarms: maximize the ratio false alarms  k amplitude consistency check: gw generates events with correlated amplitudes testing (same as above)

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

SETTING CONFIDENCE INTERVALS GWDAW 2002 unified & frequentistic approach  tomorrow talk by L. Baggio References: 1.B. Roe and M. Woodroofe, PRD 63, (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: 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

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

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

UPPER LIMIT /1 GWDAW 2002 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 search threshold Hz -1 ensured minimum coverage true rate value is under the curves with a probability = coverage

UPPER LIMIT /2 GWDAW 2002 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 search threshold Hz -1 ensured minimum coverage true rate value is under the curves with a probability = coverage