estimation of resolution and reduced likelihood analysis - kai schatto university of mainz
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Estimation of Resolution and reduced Likelihood analysis - Kai Schatto University of Mainz. IceCube Colaboration Meeting, Berlin 21. September 09. Contents. Part 1: Status of Cramer-Rao modul. Part 2: Studies on reduced likelihood. 18/09/09. 2. Cramer-Rao-Bound. - PowerPoint PPT PresentationTRANSCRIPT
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Estimation of Resolution and reduced Likelihood
analysis-
Kai SchattoUniversity of Mainz
IceCube Colaboration Meeting, Berlin 21. September 09
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Contents
Part 1: Status of Cramer-Rao modul
Part 2: Studies on reduced likelihood
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Cramer-Rao-Bound Cramér-Rao inequality expresses lower bound for
resolution of individual track
Cramér-Rao inequality:
Fisher information matrix:
p=propability density function(in our case Pandel function)
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Cramer-Rao-Bound
Fisher information matrix:
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Cramer-Rao-Bound
Fisher information matrix:
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Cramer-Rao-Bound
Fisher information matrix:
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Cramer-Rao-Bound
Fisher information matrix:
precalculated calculated on the run
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Cut efficiency
Cutting the geometric mean of azimuth and zenith estimation
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Cut efficiency
Cutting the geometric mean of azimuth and zenith estimation
50 %
6 %
3 %
1 %
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Real resol vs estimator
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New: Depth-dependent scatter length
we use the Pandel function as pdf, which depends on lambda:
before a fixed lambda value of 33m was used, which is not accurate due to in ice dust layers for instance
now the Cramer-Rao estimation is calculated with the lambda values from:
„Ackermann, M., et al. (2006), Optical properties of deep glacial ice at the South Pole, J. Geophys. Res., 111, D13203, doi:10.1029/2005JD006687“
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New: Depth-dependent scatter length
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New: Convoluted Pandel using gauss convoluted pandel from:
Implementation of a Gauss convoluted Pandel PDFfor track reconstruction in Neutrino Telescopes,N. van Eijndhoven, O. Fadiran and G. Japaridze
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New: Convoluted Pandel using gauss convoluted pandel from:
Implementation of a Gauss convoluted Pandel PDFfor track reconstruction in Neutrino Telescopes,N. van Eijndhoven, O. Fadiran and G. Japaridze
t/ns
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New: Convoluted Pandel
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Still fast to compute using a precalculated table On an Intel Xeon 2.5GHz quad core
0.91ms/event a paraboloid calculation takes 178ms no need for high level reco
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Part 2: Studies on reduced likelihood
Part 1: Status of Cramer-Rao modul
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llh!=Chi^2
definition of reduced likelihood
but likelihood differs from Chi^2
get further information in Studies on reduced likelihood, Lutz Köpke
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reduced Likelihood vs NChannel
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Nchannel independent rLlh
Fit to find rlogl without NChdependency
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Nchannel independent rLlh
Fit to find rlogl without NChdependency
Reduced Llh with (NCh-0.8)
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Nchannel independent rLlh
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Cut comparison
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Correlation
correlation factor for background = 0.1
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Conclusion & status
Cramer Rao module: Cramér-Rao module currently in testing & review stage fast computation and practical for early cuts not correlating too strong with rLlh cuts integration into offline software soon
rLlh:
rLlh cuts are hidden channel cuts other name for that what‘s currently called „reduced Likelihood“ -> effective Likelihood ??? reduced likelihood similar to Chi^2 with (N-0.8)
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Thanks for listening!
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