R statistic performance in s2
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r-statistic performance in S2. Laura Cadonati LIGO-MIT LSC meeting – LLO March 18, 2004. D t = + 10 ms. D t = - 10 ms. confidence versus lag. 15. Max confidence: C M ( t 0 ) = 13.2 at lag = - 0.7 ms. 10. confidence. 5. 0. -10. 0. 10. lag [ms].

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R statistic performance in s2

r-statistic performance in S2

Laura Cadonati

LIGO-MIT

LSC meeting – LLO March 18, 2004


R statistic cross correlation test

Dt = + 10 ms

Dt = - 10 ms

confidence versus lag

15

Max confidence:

CM(t0) = 13.2

at lag = - 0.7 ms

10

confidence

5

0

-10

0

10

lag [ms]

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:

» 100-1600 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.

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)


G12 =max(CM12)

  • Each point: max confidence CM(j) for an interval twide

  • 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)


Detection efficiency for narrow band bursts

(fchar, hrss) [strain/rtHz] with 50% triple coincidence detection probability (b=3)

LHO-4km

LHO-2km

LLO-4km

~

√2|h(f)| [strain/Hz]

Detection Efficiency for Narrow-Band Bursts

Sine-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=4LHO-2km=3


R o c receiver operator characteristics
R.O.C. Receiver-Operator Characteristics

Detection Probability versus False Alarm Probability.

Parameter: triple coincidence confidence threshold b3

Real S2 data

Random times 200 ms long


SG 235Hz Q=9

b=3 (2.3e-21/rtHz)

b=4 (3.0e-21/rtHz)

b=5 (4e-21/rtHz)


Mdc sine gaussians beta 4
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


Detection efficiency for broad band bursts

~

√2|h(f)| [strain/Hz]

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

SNR > 30

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=6LHO-2km=5


R o c receiver operator characteristics1
R.O.C. Receiver-Operator Characteristics

Detection Probability versus False Alarm Probability.

Parameter: triple coincidence confidence threshold b3

Real data

Random times 200 ms long


Mdc gaussians beta 4
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


Bh bh mergers sky averaged
BH-BH mergers, sky-averaged

standalone WB trigger

BH-10 7.0e-20 /rtHz

BH-20 3.0e-20 /rtHz

BH-30 2.5e-20 /rtHz

BH-40 2.4e-20 /rtHz

BH-50 2.7e-20 /rtHz

BH-60 3.4e-20 /rtHz

BH-70 4.0e-20 /rtHz

BH-80 5.2e-20 /rtHz

BH-90 6.9e-20 /rtHz

BH-100 8.1e-20 /rtHz

NOTE: 2 different polarizations!


Rejection of false coincidences
Rejection of False Coincidences

Tested over the full S2 background (time-lag) events

using b=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 %


False probability versus threshold
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 130-400 Hz in the playground background with “loose” coincidence cuts

G

False Probability versus threshold (G>b)

Fraction of surviving events

b


False probability versus threshold1
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 130-400 Hz in the playground background with “loose” coincidence cuts

G

False Probability versus threshold (G>b)

Fraction of surviving events

b


False probability versus threshold2
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 130-400 Hz in the playground background with “loose” coincidence cuts

G

False Probability versus threshold (G>b)

Fraction of surviving events

b


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