Results of the 19972000 Search for Burst Gw by IGEC

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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 NAUTIL
US (INFN-LNF) INFN of Roma and LNF Universities
of Roma, LAquila CNR IFSI and IESS, Roma -
Italia
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OUTLINE
      overview of the EXCHANGED DATA SET
1997-2000 sensitivity and observation
time candidate burst gw events
      multiple detector DATA ANALYSIS directio
nal 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)
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DETECTOR LOCATIONS
almost parallel detectors
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EXCHANGED PERIODS of OBSERVATION 1997-2000
ALLEGRO
AURIGA
NAUTILUS
EXPLORER
NIOBE
fraction of time in monthly bins
Fourier amplitude of burst gw
arrival time
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DIRECTIONAL SEARCH
amplitude (Hz-1)
time (hours)
amplitude (Hz-1)
time (hours)
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DATA SELECTION
amplitude (Hz-1)
time (hours)
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OBSERVATION TIME 1997-2000
total time when exchange threshold has been lower
than gw amplitude
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DATA SELECTION
amplitude (Hz-1)
time (hours)
amplitude (Hz-1)
time (hours)
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RESULTING PERIODS of OBSERVATION and EVENTS
no directional search
time (hours)
directional search
time (hours)
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AMPLITUDE DISTRIBUTIONS of EXCHANGED EVENTS
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
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FALSE ALARM REDUCTION
by thresholding events
natural consequence AMPLITUDE CONSISTENCY of
SELECTED EVENTS
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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. gt 50 with amplitude gt 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
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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
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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, PRD 57, 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

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SETTING CONFIDENCE INTERVALS / 2
GOAL estimate the number of gw which are
detected with amplitude ? Ht
Example confidence interval with coverage ? 95
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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 - ? 09. 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
09 or 095 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
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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
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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