1 / 27

Estimation of Resolution and reduced Likelihood analysis - Kai Schatto University of Mainz

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.

gwen
Download Presentation

Estimation of Resolution and reduced Likelihood analysis - Kai Schatto University of Mainz

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Estimation of Resolution and reduced Likelihood analysis - Kai Schatto University of Mainz IceCube Colaboration Meeting, Berlin 21. September 09

  2. Contents Part 1: Status of Cramer-Rao modul Part 2: Studies on reduced likelihood 18/09/09 2

  3. 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) 18/09/09 4

  4. Cramer-Rao-Bound • Fisher information matrix: 18/09/09 5

  5. Cramer-Rao-Bound • Fisher information matrix: 18/09/09 6

  6. Cramer-Rao-Bound • Fisher information matrix: 18/09/09 7

  7. Cramer-Rao-Bound • Fisher information matrix: precalculated calculated on the run 18/09/09 8

  8. Cut efficiency Cutting the geometric mean of azimuth and zenith estimation 18/09/09 9

  9. Cut efficiency 6 % 3 % 1 % 50 % Cutting the geometric mean of azimuth and zenith estimation 18/09/09 10

  10. Real resol vs estimator 18/09/09 11

  11. 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“ 18/09/09 12

  12. New: Depth-dependent scatter length 18/09/09 13

  13. New: Convoluted Pandel • using gauss convoluted pandel from: • Implementation of a Gauss convoluted Pandel PDF • for track reconstruction in Neutrino Telescopes, • N. van Eijndhoven, O. Fadiran and G. Japaridze 18/09/09 14

  14. New: Convoluted Pandel • using gauss convoluted pandel from: • Implementation of a Gauss convoluted Pandel PDF • for track reconstruction in Neutrino Telescopes, • N. van Eijndhoven, O. Fadiran and G. Japaridze t/ns 18/09/09 15

  15. New: Convoluted Pandel 18/09/09 16

  16. 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 18/09/09 17

  17. Part 1: Status of Cramer-Rao modul Part 2: Studies on reduced likelihood 18/09/09 18

  18. llh!=Chi^2 • definition of reduced likelihood • but likelihood differs from Chi^2 • get further information in • Studies on reduced likelihood, Lutz Köpke 18/09/09 19

  19. reduced Likelihood vs NChannel 18/09/09 20

  20. Nchannel independent rLlh Fit to find rlogl without NCh dependency 18/09/09 21

  21. Nchannel independent rLlh Fit to find rlogl without NCh dependency Reduced Llh with (NCh-0.8) 18/09/09 22

  22. Nchannel independent rLlh 18/09/09 23

  23. Cut comparison 18/09/09 24

  24. Correlation correlation factor for background = 0.1 18/09/09 25

  25. 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) 18/09/09 26

  26. Thanks for listening! 18/09/09 27

More Related