1. r-statistic performance in S2
Laura Cadonati
LIGO-MIT
LSC meeting – LLO March 18, 2004

2. r-statistic Cross Correlation Test
For each triple coincidence candidate event produced by the burst pipeline (start time, duration DT) process pairs of interferometers:
simulated signal, SNR~60, S2 noise
Data Conditioning:
» Hz band-pass
» Whitening with linear error predictor filters
Partition the trigger in sub-intervals (50% overlap) of duration t = integration window (20, 50, 100 ms).
For each integration window, time shift up to 10 ms and build an r-statistic series distribution.
Dt = - 10 ms
Dt = + 10 ms
lag [ms]
confidence 10
-10 15 5
confidence versus lag
Max confidence:
CM(t0) = 13.2
at lag = ms
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)

3. Each point: max confidence CM(j) for an interval t wide
G12 =max(CM12)
Each point: max confidence CM(j) for an interval t wide
Threshold on G:
3 interferometers:
G=maxj(CM12+ CM13+ CM23)/3 > b
b=3: 99.9% correlation probability
in a single integration window
G13 =max(CM13)
G23 =max(CM23)
G =max(CM12 + CM13+CM23)/3
Testing 3 integration windows:
20ms (G20) 50ms (G50) 100ms (G100)
in OR: G=max(G20,G50,G100)

4. Detection Efficiency for Narrow-Band Bursts
Sine-Gaussian waveform f0=235Hz Q=9
linear polarization, source at zenith
(fchar, hrss) [strain/rtHz] with 50% triple coincidence detection probability (b=3)
√2|h(f)| [strain/Hz] ~
LHO-2km
LHO-4km
LLO-4km
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

5. R.O.C. Receiver-Operator Characteristics
Detection Probability versus False Alarm Probability.
Parameter: triple coincidence confidence threshold b3
R.O.C. Receiver-Operator Characteristics
Real S2 data
Random times 200 ms long

6. SG 235Hz Q=9
b=3 (2.3e-21/rtHz)
b=4 (3.0e-21/rtHz)
b=5 (4e-21/rtHz)

7. MDC Sine Gaussians – beta=4
standalone WB trigger
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

8. Detection Efficiency for Broad-Band Bursts
Gaussian waveform t=1ms
linear polarization, source at zenith
(fchar, hrss) [strain/rtHz] with 50% triple coincidence detection probability
LHO-4km
LHO-2km
LLO-4km
√2|h(f)| [strain/Hz] ~
SNR > 30
50% triple coincidence detection probability (beta=3):
hpeak = 1.6e-19 [strain] hrss = 5.7e-21 [strain/rtHz]
SNR: LLO-4km= LHO-4km=6 LHO-2km=5

9. R.O.C. Receiver-Operator Characteristics
Detection Probability versus False Alarm Probability.
Parameter: triple coincidence confidence threshold b3
R.O.C. Receiver-Operator Characteristics
Real data
Random times 200 ms long

10. MDC Gaussians - beta=4 standalone WB trigger
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

11. BH-BH mergers, sky-averaged
standalone WB trigger
BH e-20 /rtHz
BH e-20 /rtHz
BH e-20 /rtHz
BH e-20 /rtHz
BH e-20 /rtHz
BH e-20 /rtHz
BH e-20 /rtHz
BH e-20 /rtHz
BH e-20 /rtHz
BH e-20 /rtHz
NOTE: 2 different polarizations!

12. Rejection of False Coincidences
Tested over the full S2 background (time-lag) events
using b=4
Random events, 0.2 ms long: ± 0.01 %
TFClusters: ± 0.2 %
WaveBurst: ± 0.3 %
BlockNormal > 99.9 %
Power ± 0.06 %

13. False Probability versus Threshold
Histogram of G= max (G20, G50, G100)
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 Hz in the playground background with “loose” coincidence cuts G
False Probability versus threshold (G>b)
Fraction of surviving events b

14. False Probability versus Threshold
Histogram of G= max (G20, G50, G100)
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 Hz in the playground background with “loose” coincidence cuts G
False Probability versus threshold (G>b)
Fraction of surviving events b

15. False Probability versus Threshold
Histogram of G= max (G20, G50, G100)
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 Hz in the playground background with “loose” coincidence cuts G
False Probability versus threshold (G>b)
Fraction of surviving events b