G.A.Prodi - INFN and Università di Trento, ItalyInternational Gravitational Event Collaboration

http://igec.lnl.infn.it

ALLEGRO group: ALLEGRO (LSU) http://gravity.phys.lsu.eduLouisiana State University, Baton Rouge - Louisiana

AURIGA group: AURIGA (INFN-LNL) http://www.auriga.lnl.infn.itINFN of Padova, Trento, Ferrara, Firenze, LNLUniversities of Padova, Trento, Ferrara, FirenzeIFN- CNR, Trento – Italia

NIOBE group: NIOBE (UWA) http://www.gravity.pd.uwa.edu.auUniversity of Western Australia, Perth, Australia

ROG group: EXPLORER (CERN) http://www.roma1.infn.it/rog/rogmain.htmlNAUTILUS (INFN-LNF)

INFN of Roma and LNFUniversities of Roma, L’AquilaCNR IFSI and IESS, Roma - Italia

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

GWDAW 2002

      overview of the EXCHANGED DATA SET 1997-2000sensitivity and observation timecandidate burst gw events

OUTLINEGWDAW 2002

      multiple detector DATA ANALYSISdirectional search strategy search as a function of amplitude threshold false dismissal or detection efficiencyestimation of accidental coincidences by time shifts

      RESULTSaccidental coincidences are Poisson r.v.compatibility with null hypothesisupper limit on the rate of detected gw…unfolding the sources (not yet)

methods L.Baggio tomorrow

DETECTOR LOCATIONS

GWDAW 2002

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

almost parallel detectors

EXCHANGED PERIODS of OBSERVATION 1997-2000

GWDAW 2002

fraction of time in monthly bins

exchange threshold

21 16 10 Hz 21 13 6 10 Hz

21 13 10 Hz

Fourier amplitude of burst gw

0 0( ) ( )h Ht tt arrival time

ALLEGRO

AURIGA

NAUTILUS

EXPLORER

NIOBE

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 6 12 18 24 30 36 42 48 54 60

amplitude directional sensitivity

2sin GC

0

1

2

3

4

5

0 6 12 18 24 30 36 42 48 54 60

2sin GC

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

time (hours)

ampl

itude

(H

z-1)

time (hours)

ampl

itude

(H

z-1)

GWDAW 2002

DIRECTIONAL SEARCH

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

time (hours)

ampl

itude

(H

z-1)

GWDAW 2002DATA SELECTION

amplitude of burst gw

OBSERVATION TIME 1997-2000

GWDAW 2002

total time when exchange threshold has been lower than gw amplitude

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

0

1

2

3

4

5

6

7

8

9

10

0 6 12 18 24 30 36 42 48 54 60

time (hours)

ampl

itude

(H

z-1)

ampl

itude

(H

z-1)

time (hours)

GWDAW 2002DATA SELECTION

time (hours)

time (hours)

GWDAW 2002

RESULTING PERIODS of OBSERVATION and EVENTS

no directional search

directional search

AMPLITUDE DISTRIBUTIONS of EXCHANGED EVENTS

GWDAW 2002

relat

ive c

ount

s

10-5

10-4

10-3

10-2

10-1

1

relat

ive c

ount

s

10-5

10-4

10-3

10-2

10-1

1

NIOBENIOBEAMP/THR1 10

NAUTILUSNAUTILUSAMP/THR1 10

AURIGAAURIGAAMP/THR1 10

ALLEGROALLEGROAMP/THR1 10

EXPLOREREXPLORERAMP/THR1 10

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

time

amplitude

time

amplitude

time

amplitude

time

amplitude

A

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 Ht

keep the observation time when false dismissal is under controlkeep events above threshold

efficiency of detection depends on signal amplitude, direction, polarization …e.g. > 50% with amplitude > Ht at each detector

• time coincidence searchtime window is set requiring a conservative false dismissalrobust and general method: Tchebyscheff inequality

fraction of found gw coincidences

fluctuations of accidental background

2 22

1i j i jt t k false dismissal

k

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) i jA A A

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, 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

SETTING CONFIDENCE INTERVALS / 2

GWDAW 2002

Example: confidence interval with coverage 95%

0

2

4

6

8

10

12

14

16

18

1.0 10.0 100.0

search threshold [10-21/Hz]

Ngw

Ht

“upper limit” : true value outside with probability 95%

GOAL: estimate the number of gw which are detected with amplitude Ht

0

2

4

6

8

10

12

14

16

18

1.0 10.0 100.0

search threshold [10-21/Hz]

Ngw

GWDAW 2002

SETTING CONFIDENCE INTERVALS / 3

systematic search on thresholdsmany 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 dataPDG recommendation

A potential difficulty with unified intervals arises if, for example, one constructs suchan 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 theexpected background, one will usually obtain a one-sided upper limit on s. In a certainfraction 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

1

10

100

1,000

1E-21 1E-20 1E-19

0.60

0.80

0.90

0.95

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

rateyear -1

search thresholdHz -1

ensured minimumcoverage

true rate value is under the curves with a probability = coverage

1

10

100

1,000

1E-21 1E-20 1E-19

0.60

0.80

0.90

0.95

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

rateyear -1

search thresholdHz -1

ensured minimumcoverage

true rate value is under the curves with a probability = coverage