r-statistic performance in s2
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LIGO-G040174-00
r-statistic performance in S2
Laura CadonatiLIGO-MIT
LSC meeting – LLO March 18, 2004
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t = - 10 ms t = + 10 ms
r-statistic Cross Correlation TestFor each triple coincidence candidate event produced by the burst pipeline (start time, duration T) process pairs of interferometers:
Data Conditioning: » 100-1600 Hz band-pass » Whitening with linear error predictor filters
Partition the trigger in sub-intervals (50% overlap) of duration integration window (20, 50, 100 ms). For each integration window, time shift up to 10 ms and build an r-statistic series distribution.
If the distribution of the r-statistic is inconsistent with the no-correlation hypothesis: find the time shift yielding maximum correlation confidence CM(j) (j=index
for the sub-interval)
simulated signal, SNR~60, S2 noise
lag [ms]
co
nfi
de
nc
e
0 10-10
15
10
5
0
confidence versus lag
Max confidence:
CM() = 13.2
at lag = - 0.7 ms
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Each point: max confidence CM(j) for
an interval wide
Threshold on :3 interferometers:
=maxj(CM12+ CM
13+ CM23)/3 >
=3: 99.9% correlation probability in a single integration
window
12 =max(CM12)
13 =max(CM13)
23 =max(CM23)
=max(CM12 + CM
13+CM23)/3
Testing 3 integration windows:20ms (20) 50ms (50) 100ms (100)in OR: =max(20,50,100)
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Detection Efficiency for Narrow-Band BurstsSine-Gaussian waveform f0=235Hz Q=9
linear polarization, source at zenith
50% triple coincidence detection probability (beta=3):
hpeak = 3.2e-20 [strain] hrss = 2.3e-21 [strain/rtHz]
SNR: LLO-4km=8 LHO-4km=4 LHO-2km=3
(fchar, hrss) [strain/rtHz] with 50% triple coincidence detection probability (=3)
√2|h(f)| [strain/Hz]~
LHO-2km
LHO-4km
LLO-4km
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Detection Probability versus False Alarm Probability.Parameter: triple coincidence confidence threshold 3
R.O.C. Receiver-Operator
Characteristics
Real S2 dataRandom times 200 ms long
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SG 235Hz Q=9
=3 (2.3e-21/rtHz)
=4 (3.0e-21/rtHz)
=5 (4e-21/rtHz)
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MDC Sine Gaussians – beta=4
SG 153Hz Q=3 1.6e-20 /rtHz
SG 153Hz Q=9 1.9e-20 /rtHz
SG 235Hz Q=3 4.9e-21 /rtHz
SG 235Hz Q=9 4.9e-21 /rtHz
SG 554Hz Q=3 7.6e-21 /rtHz
SG 554Hz Q=9 7.9e-21 /rtHz
standalone WB trigger
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SNR > 30
Detection Efficiency for Broad-Band BurstsGaussian waveform =1ms
linear polarization, source at zenith
50% triple coincidence detection probability (beta=3):
hpeak = 1.6e-19 [strain] hrss = 5.7e-21 [strain/rtHz]
SNR: LLO-4km=11.5 LHO-4km=6 LHO-2km=5
LLO-4km√2|h(f)| [strain/Hz]~
LHO-2km
LHO-4km
(fchar, hrss) [strain/rtHz] with 50% triple coincidence detection probability
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Detection Probability versus False Alarm Probability.Parameter: triple coincidence confidence threshold 3
R.O.C. Receiver-Operator
Characteristics
Real dataRandom times 200 ms long
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MDC Gaussians - beta=4
GA tau=0.1ms 1.6e-20 /rtHz
GA tau=0.5ms 1.1e-20 /rtHz
GA tau=1.0ms 1.4e-20 /rtHz
GA tau=2.5ms 6.0e-20 /rtHz
GA tau=4.0ms 1.2e-20 /rtHz
standalone WB trigger
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BH-BH mergers, sky-averaged
BH-10 7.0e-20 /rtHz BH-20 3.0e-20 /rtHz BH-30 2.5e-20 /rtHz BH-40 2.4e-20 /rtHzBH-50 2.7e-20 /rtHzBH-60 3.4e-20 /rtHzBH-70 4.0e-20 /rtHzBH-80 5.2e-20 /rtHzBH-90 6.9e-20 /rtHzBH-100 8.1e-20 /rtHz
NOTE: 2 different polarizations!
standalone WB trigger
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Rejection of False Coincidences
Tested over the full S2 background (time-lag) events
using =4
» Random events, 0.2 ms long: 99.99 ± 0.01 %
» TFClusters: 99.6 ± 0.2 %
» WaveBurst: 99.5 ± 0.3 %
» BlockNormal > 99.9 %
» Power 99.94 ± 0.06 %
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False Probability versus Threshold
In general: depends on the trigger generators and the previous portion of the analysis pipeline (typical event duration, how stringent are the selection and coincidence cuts)
Shown here: TFCLUSTERS 130-400 Hz in the playground background with “loose” coincidence cuts
False Probability versus threshold (>)
Histogram of max (20,50,100)
Fra
ctio
n o
f su
rviv
ing
even
ts
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False Probability versus Threshold
In general: depends on the trigger generators and the previous portion of the analysis pipeline (typical event duration, how stringent are the selection and coincidence cuts)
Shown here: TFCLUSTERS 130-400 Hz in the playground background with “loose” coincidence cuts
False Probability versus threshold (>)
Histogram of max (20,50,100)
Fra
ctio
n o
f su
rviv
ing
even
ts
15LIGO-G040174-00
False Probability versus Threshold
In general: depends on the trigger generators and the previous portion of the analysis pipeline (typical event duration, how stringent are the selection and coincidence cuts)
Shown here: TFCLUSTERS 130-400 Hz in the playground background with “loose” coincidence cuts
False Probability versus threshold (>)
Histogram of max (20,50,100)
Fra
ctio
n o
f su
rviv
ing
even
ts
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