r-statistic performance in S2

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Presentation transcript:

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

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. Dt = - 10 ms Dt = + 10 ms lag [ms] confidence 10 -10 15 5 confidence versus lag Max confidence: CM(t0) = 13.2 at lag = - 0.7 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)

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)

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

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

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 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 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=11.5 LHO-4km=6 LHO-2km=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 data Random times 200 ms long

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 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 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 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 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 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