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

2. 18/09/092 Contents Part 1: Status of Cramer-Rao modul Part 2: Studies on reduced likelihood

3. 18/09/093 Part 1: Status of Cramer-Rao modul

4. 18/09/094 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)

5. 18/09/095 Cramer-Rao-Bound  Fisher information matrix:

6. 18/09/096 Cramer-Rao-Bound  Fisher information matrix:

7. 18/09/097 Cramer-Rao-Bound Fisher information matrix:

8. 18/09/098 Cramer-Rao-Bound Fisher information matrix: precalculatedcalculated on the run

9. 18/09/099 Cut efficiency Cutting the geometric mean of azimuth and zenith estimation

10. 18/09/0910 Cut efficiency Cutting the geometric mean of azimuth and zenith estimation 50 % 6 % 3 % 1 %

11. 18/09/0911 Real resol vs estimator

12. 18/09/0912 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“

13. 18/09/0913 New: Depth-dependent scatter length

14. 18/09/0914 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

15. 18/09/0915 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

16. 18/09/0916 New: Convoluted Pandel

17. 18/09/0917 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. 18/09/0918 Part 2: Studies on reduced likelihood Part 1: Status of Cramer-Rao modul

19. 18/09/0919 llh!=Chi^2  definition of reduced likelihood  but likelihood differs from Chi^2  get further information in Studies on reduced likelihood, Lutz Köpke

20. 18/09/0920 reduced Likelihood vs NChannel

21. 18/09/0921 Nchannel independent rLlh Fit to find rlogl without NCh dependency

22. 18/09/0922 Nchannel independent rLlh Fit to find rlogl without NCh dependency Reduced Llh with (NCh-0.8)

23. 18/09/0923 Nchannel independent rLlh

24. 18/09/0924 Cut comparison

25. 18/09/0925 Correlation correlation factor for background = 0.1

26. 18/09/0926 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)

27. 18/09/0927 Thanks for listening!