Avi Vajpeyi Rory Smith Jonah Kanner LIGO SURF 16 Summary Introduction Detection Statistic Bayesian Statistics Selecting Background Events Bayes Factor Results Drawbacks Bayes Coherence Ratio ID: 1021833
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1. Use of the Bayes Factor to Improve the Detection of Binary Black Hole SystemsAvi VajpeyiRory Smith, Jonah KannerLIGO SURF 16
2. SummaryIntroductionDetection StatisticBayesian StatisticsSelecting Background EventsBayes Factor ResultsDrawbacksBayes Coherence RatioResultsComparison with SNR
3. OverviewSome candidate events like LVT151012 have low Signal-to-Noise ratios which fall within the background distribution
4. OverviewCan the Bayes factor help increase the detection confidence for binary black hole systems?
5. Detection StatisticSearch results from the two binary coalescence searches using a combined matched filtering signal-to-noise ratio
6. Detection StatisticThe BackgroundSearch results from the two binary coalescence searches using a combined matched filtering signal-to-noise ratio
7. Detection StatisticSome events stand out from backgroundSearch results from the two binary coalescence searches using a combined matched filtering signal-to-noise ratio
8. Detection StatisticSome events stand out from backgroundSome events fall along the backgroundSearch results from the two binary coalescence searches using a combined matched filtering signal-to-noise ratio
9. A Gentle Introduction - Bayesian Statistics
10. Bayesian Statistics P(H | D) = P(D | H) P(H)P(D)Probability of a hypothesis, H conditional some data D‘Posterior Density’ Probability of Data given Hypothesis‘Likelihood’Probability of the Hypothesis‘Prior’Probability of the data‘Evidence’
11. Bayesian StatisticsOh, man
12. Bayesian StatisticsOh, manHYPOTHESITIS
13. Bayesian StatisticsHYPOTHESITISP(H) = you have hypothesitis
14. Bayesian StatisticsHYPOTHESITISP(H) = you have hypothesitisP(S|H) = Probability of symptoms given the Hypothesis = 0.95 Oh, man
15. Bayesian StatisticsP(H | S) = P(S | H) P(H)P(S)P( You Can Get Hypothesitis)P (You Can Get the Symptoms)
16. Bayesian StatisticsHYPOTHESITISP(H) = you have hypothesitis= 0.00001P(S|H) = Probability of symptoms given the Hypothesis = 0.95 Oh, man
17. Bayesian StatisticsHYPOTHESITISP(H) = you have hypothesitis= 0.00001P(S|H) = Probability of symptoms given the Hypothesis = 0.95 Oh, manP(S) = The Evidence, or probability of having symptoms= 0.01
18. Bayesian StatisticsOh, manP(H | S) = (0.95) (0.00001)(0.01)P(H | E) = 0.00095Ehh, I initially forgot about P(H)
19. Bayesian StatisticsOh, manBayes Theorem tells me how to calculate probabilities of hypothesis, or models
20. Bayesian StatisticsOh, manBayes Theorem tells me how to calculate probabilities of hypothesis, or modelsHelps compare different models!
21. Models in GW Hypothesis 2 : data = Gaussian NoiseHypothesis 1 : data = Gaussian Noise + GW Strain
22. Bayesian StatisticsParameter estimation is what we normally doAnd using parameter estimation for multiple sets of data we get model selection
23. Bayesian StatisticsParameter estimation is what we normally doAnd using parameter estimation for multiple sets of data we get model selectionProduct calculated for every set of parameters, Θ( parameters like masses, spins etc of black holes )
24. Bayes Factor vs SNRBayes Factor Calculated using entire set of parameters (all possible templates)Takes into account spins orientations, and magnitudes
25. Bayes Factor vs SNRBayes Factor Calculated using entire set of parameters (all possible templates)Takes into account spins orientations, and magnitudes All Parameters Considered
26. Bayes Factor vs SNRSignal to Noise RatioMaximum Likelihood Estimator (uses one template)Does not consider spins orientations, and magnitudes
27. Bayes Factor vs SNRSignal to Noise RatioMaximum Likelihood Estimator (uses one template)Does not consider spins orientations, and magnitudes One set of Parameters Considered
28. Project MotivationsBayes Factor may prove to be more robust than the SNR
29. Project MotivationsBayes it bruhBayes Factor may prove to be more robust than the SNR
30. Project GoalsCan we use the Bayes factor as a detection statistic?Bayes it bruh
31. Obtaining the Bayes FactorLn Bayes Factors - GW signals: GW150914 – 289.8 ± 0.3 GW151226 – 60.2 ± 0.2 LVT151012 – 23.0 ± 0.1 Values in ~10’s rangeOnce we run Parameter Estimations for the events, we can calculate the Bayes FactorLn Bayes Factors - Noise:Values in ~1’s range
32. Generating Background DataHanford Strain DataLivingston Strain DataTIMECoherent Data
33. Hanford Strain DataLivingston Strain DataTIMEIncoherent Time Shifted DataTime Shift > light travel time Generating Background Data
34. Generating Background DataFalse Alarm Rate Plotted Against The SNRLower the FAR, louder and rarer the event
35. Bayes Factor ResultsBayes Factor as a Detection Statistic, using only Coalescing Binary Back Hole Templates
36. Bayes Factor ResultsBayes Factor as a Detection Statistic, using only Coalescing Binary Back Hole Templates
37. Bayes Factor ResultsBayes Factor as a Detection Statistic, using only Coalescing Binary Back Hole Templates Y U DO DISBAYES FACTOR?
38. Issue with Bayes FactorReal GW Spectogram
39. Issue with Bayes FactorReal GW SpectogramGlitch Spectograms
40. Hypothesis 2 : data = Gaussian NoiseHypothesis 1 : data = Gaussian Noise + GW StrainIssue with Bayes Factor
41. Issue with Bayes FactorA glitch in one detector’s data inflates the Coherent Bayes FactorLivingston’s Strain Data*Hanford’s Strain Data** Figures are not real, Numbers areCoherent Bayes Factor = 142.82timestrainstraintime
42. Issue with Bayes FactorA glitch in one detector’s data inflates the Coherent Bayes FactorLivingston’s Strain Data*Hanford’s Strain Data*Incoherent Bayes factor = 0.91Incoherent Bayes factor = 152.58* Figures are not real, Numbers areCoherent Bayes Factor = 142.82timestrainstraintime
43. Bayes Coherence RatioThe Bayes Coherence Ratio Reduces the error that appears in the Coherent Bayes Factor Empirically we found this usefullWe can Compute numberator – not sensiive at all.Introduce idea of incoherent analysisExplain how the Bayes CR Show plots with the Bayes Factor to help explain with the Bay R
44. Bayes Coherence RatioEmpirically we found this usefullWe can Compute numberator – not sensiive at all.Introduce idea of incoherent analysisExplain how the Bayes CR Show plots with the Bayes Factor to help explain with the Bay = (0.91) + (152.58)142.820. 93= COHERENT BAYES FACTORSUM OF BOTH DETECTOR’SBAYES FACTORSR
45. Results for Bayes Coherent RatioBayes Coherence Ratio as a Detection Statistic(6.7 x 1011 , 10-10 ) OUTLIER
46. Additional Information AvailableWe have a lot of additional information that we could potentially use to distinguish the outlier as a glitch L1 optimal SNR : 17.2H1 optimal SNR : 2.6
47. Comparing Detection StatisticsBayes Coherence Ratio as a Detection StatisticSignal-to-Noise Ratio as a Detection Statistic
48. Conclusions and Future WorkStudy the low FAR background events Determine if BCR can be used in addition with SNR as a detection statistic Expand the work for more mass binsRepeat the Study with Binary Neutron Star Signals
49. AcknowledgementsThanks to NSF, Dr Rory Smith, Dr Jonah Kanner, Professor Alan Weinstein and the LIGO SURF pen.