[PPT] - Parameter Estimation and Model Selection of Gravitational-Wave PowerPoint Presentation

SLIDE 1

Parameter Estimation and Model Selection of Gravitational-Wave Signals Contaminated by Transient Detector Noise Glitches

Jade Powell OzGrav, Swinburne University of Technology

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2. Gravitational Wave Detectors

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3. Detector Locations

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4. Gravitational Wave Sources

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5. Current Black Hole Detections

6 Binary black hole signals detected so far. Estimated distances between 340 and 1000 Mpc. One signal detected by three detectors. Image from first detection paper GW150914 (Phys- RevLett.116.061102)

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6. The Neutron Star Detection GW170817

Source masses 1.36 − 2.26 M⊙ and 0.86 − 1.36 M⊙ Distance 40 Mpc

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7. Parameter Estimation

Measuring parameters of a source is essential for astrophysics with gravitational wave detections. With GW detectors we can measure the chirp mass, spin, eccentricity, distance, and sky position. Chirp mass is given by M = (m1m2)3/5/(m1 + m2)1/5

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8. Astrophysics with Source Parameters

Constrain the mass distribution of black hole binaries. Distinguish between different black hole formation channels. Attempt to constrain parameters in binary evolution using population synthesis models. Measure the evolution of merger rate / mass distribution with redshift.

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9. Bayesian Model Selection

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10. Parameter Estimation

To calculate the evidence for each model we integrate the likelihood multiplied by the prior over all possible parameter values θ p(D|M) =

θ

p(θ|M)p(D|θ, M)dθ. (1) The evidence integral is difficult for a large number of parameters. This problem is solved using nested sampling.

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11. Nested Sampling

First the likelihood is calculated for selected points distributed over the entire prior. The point with the smallest likelihood and largest prior mass is selected and becomes the limiting values. A new point is generated inside the new limits. This is repeated so that it iterates inwards in prior mass and upwards in likelihood until the highest value is found. Produces Bayes factors and posterior distributions on the signal parameters.

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12. Burst Sources

For a burst source we don’t know exactly what a signal should look like. We use sine Gaussian’s as a signal model. They are defined as, hx(t) = h0 sin(2πft) exp(−t2/τ 2) (2) h+(t) = h0 cos(2πft) exp(−t2/τ 2) (3) where τ = Q/ √ 2πf , f is the frequency, Q is the quality factor, t is time of the signal and h0 = hrss/√τ, where hrss is the root sum squared amplitude of the signal. Produces posterior distributions on hrss, Q, f, and sky position.

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13. Glitches

Glitches are short duration excess power noise created by the detector or the environment. The detectors have 1000’s of auxiliary channels of data from monitors around the detector. Some glitches don’t show up in any monitors making it difficult to determine their origin. They limit the sensitivity of gravitational wave searches.

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14. Signals with glitches

106 glitches above SNR 6 were observed in 51.5 days of O1. GW170817 had a large glitch in L1. High probability that as detections increase, more will occur at the same time as a glitch.

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15. Glitch Removal

For GW170817 we already know what we expected the signal to look like. The glitch was very loud and easy to identify as being a glitch. It was removed by gating and subtracting the reconstructed waveform. The glitch is short duration compared to the signal, which means some signal is still left over after gating. It might not be so easy next time!

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16. This Analysis

We inject three different types of gravitational wave signals on top of three different types of glitches. We measure the parameters of the signals at different signal to noise ratios and offsets in time between the signal and glitches. What happens if the glitch is not obvious because it does not

ccur in auxiliary channels and the exact shape of the signal

waveform is unknown? We determine the effects of glitches that can’t be gated. We investigate if the effects of glitches is worse when there is a mis-match between signal and template.

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17. The Glitches

Three types of O1 glitches are used that occur in L1 at the same time as good quality H1 data.

Figure: Images taken from Gravity Spy.

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18. The Signals

We measure parameters of all signals injected near glitches with time offsets

f 0.0 s, 0.1 s and 0.2 s.

IMRPhenomPv2 signal model is used for the CBC signals. A sine Gaussian signal model is used for the sine Gaussian signals. A sine Gaussian model is used for the supernova signals to determine if effects are worse when there is a mis-match between signal and model.

0.10 0.08 0.06 0.04 0.02 0.00 0.02

Time(s)

3 2 1 1 2 3

Binary black hole

0.00 0.25 0.50 0.75 1.00 1.25

Time(s)

0.5 0.0 0.5 1.0

Supernova

0.04 0.02 0.00 0.02 0.04

Time(s)

6 4 2 2 4 6

Sine Gaussian

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19. BBH Bayes Factors

5 10 15 20 25 30

Signal SNR

100 200 300 400 500

log B

ffset 0.0s

scattering blip whistle 5 10 15 20 25 30

Signal SNR

100 200 300 400 500

log B

ffset 0.1s

scattering blip whistle 5 10 15 20 25 30

Signal SNR

100 200 300 400 500

log B

ffset 0.2s

scattering blip whistle 5 10 15 20 25 30

Signal SNR

5 10 15 20 25

Glitch SNR

scattering blip whistle

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20. BBH Example Posteriors

17.5 20.0 22.5 25.0 27.5 30.0 32.5

Chirp mass (M )

500 1000 1500 2000 2500 true value

ffset 0.0s
ffset 0.1s
ffset 0.2s

200 400 600 800 1000 1200 1400

Distance (Mpc)

500 1000 1500 2000 2500 3000 true value

ffset 0.0s
ffset 0.1s
ffset 0.2s

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21. BBH Chirp Mass Summary

20 15 10 5 5 10 15 20 rec true (M ) 5 10 15 20 25 30

Posterior width (M )

ffset 0.0s

scattering blip whistle 20 15 10 5 5 10 15 20 rec true (M ) 5 10 15 20 25 30

Posterior width (M )

ffset 0.1s

scattering blip whistle 20 15 10 5 5 10 15 20 rec true (M ) 5 10 15 20 25 30

Posterior width (M )

ffset 0.2s

scattering blip whistle

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22. BBH Distance Summary

500 500 1000 1500

Distrec Disttrue (Mpc)

500 1000 1500 2000 2500 3000 3500

Posterior width (Mpc)

ffset 0.0s

scattering blip whistle 500 500 1000 1500

Distrec Disttrue (Mpc)

500 1000 1500 2000 2500 3000 3500

Posterior width (Mpc)

ffset 0.1s

scattering blip whistle 500 500 1000 1500

Distrec Disttrue (Mpc)

500 1000 1500 2000 2500 3000 3500

Posterior width (Mpc)

ffset 0.2s

scattering blip whistle

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23. Sine Gaussian Bayes Factors

5 10 15 20 25 30 35

Signal SNR

100 200 300 400 500 600

log B

ffset 0.0s

scattering blip whistle 5 10 15 20 25 30 35

Signal SNR

100 200 300 400 500 600

log B

ffset 0.1s

scattering blip whistle 5 10 15 20 25 30 35

Signal SNR

100 200 300 400 500 600

log B

ffset 0.2s

scattering blip whistle 5 10 15 20 25 30

Signal SNR

5 10 15 20 25

Glitch SNR

scattering blip whistle

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24. Sine Gaussian Example Posteriors

160 180 200 220 240 260 280 300 320

Frequency (Hz)

200 400 600 800 1000 1200 1400 1600 true value

ffset 0.0s
ffset 0.1s
ffset 0.2s

52 51 50 49 48

log hrss

250 500 750 1000 1250 1500 1750 2000 true value

ffset 0.0s
ffset 0.1s
ffset 0.2s

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25. Sine Gaussian Frequency Summary

250 250 500 750 1000 1250 1500 1750

frec ftrue (Hz)

25 50 75 100 125 150 175 200

Posterior width (Hz)

ffset 0.0s

scattering blip whistle 250 250 500 750 1000 1250 1500 1750

frec ftrue (Hz)

25 50 75 100 125 150 175 200

Posterior width (Hz)

ffset 0.1s

scattering blip whistle 250 250 500 750 1000 1250 1500 1750

frec ftrue (Hz)

25 50 75 100 125 150 175 200

Posterior width (Hz)

ffset 0.2s

scattering blip whistle

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26. Sine Gaussian Log Hrss Summary

3 2 1 1 2 3

loghrssrec loghrsstrue

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Posterior width

ffset 0.0s

scattering blip whistle 3 2 1 1 2 3

loghrssrec loghrsstrue

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Posterior width

ffset 0.1s

scattering blip whistle 3 2 1 1 2 3

loghrssrec loghrsstrue

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Posterior width

ffset 0.2s

scattering blip whistle

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27. Supernova Bayes Factors

5 10 15 20 25 30 35

Signal SNR

50 100 150 200 250 300 350 400

log B

ffset 0.0s

scattering blip whistle 5 10 15 20 25 30 35

Signal SNR

50 100 150 200 250 300 350 400

log B

ffset 0.1s

scattering blip whistle 5 10 15 20 25 30 35

Signal SNR

50 100 150 200 250 300 350 400

log B

ffset 0.2s

scattering blip whistle 5 10 15 20 25 30

Signal SNR

5 10 15 20 25

Glitch SNR

scattering blip whistle

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28. Supernova Example Posteriors

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Duration (s)

500 1000 1500 2000 2500 3000 true value

ffset 0.0s
ffset 0.1s
ffset 0.2s

52 51 50 49 48

log hrss

250 500 750 1000 1250 1500 1750 2000 true value

ffset 0.0s
ffset 0.1s
ffset 0.2s

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29. Supernova Duration Summary

6 4 2 2 4 6

durrec durtrue (s)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Posterior width (s)

ffset 0.0s

scattering blip whistle 6 4 2 2 4 6

durrec durtrue (s)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Posterior width (s)

ffset 0.1s

scattering blip whistle 6 4 2 2 4 6

durrec durtrue (s)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Posterior width (s)

ffset 0.2s

scattering blip whistle

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30. Supernova Log Hrss Summary

4 2 2 4

loghrssrec loghrsstrue

1 2 3 4 5

Posterior width

ffset 0.0s

scattering blip whistle 4 2 2 4

loghrssrec loghrsstrue

1 2 3 4 5

Posterior width

ffset 0.1s

scattering blip whistle 4 2 2 4

loghrssrec loghrsstrue

1 2 3 4 5

Posterior width

ffset 0.2s

scattering blip whistle

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31. What’s next?

Next step is to apply techniques designed to reduce the effect

f glitches to the data set.

We are attempting to reconstruct the glitch and the signal at the same time to reduce the error on signal parameters. Currently Bayes factors can be produced to tell you if their is a signal or a glitch in the data. Next we hope to produce a Bayes factor that tells you there is both a signal and a glitch.