LIGO-G040174-00

r-statistic performance in S2

Laura CadonatiLIGO-MIT

LSC meeting – LLO March 18, 2004

2LIGO-G040174-00

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

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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