2. Kirsten Münich Dortmund University Diffuse Limit with an unfolding method AMANDA Collaboration Meeting Berkeley, March 2005

3. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Overview Method of setting an upper limit Constructing a P robability D ensity F unction (PDF) Building a 90% Confidence Belt (C.B) Changes for the 4 year data set: Higher statistics Better sys. errors estimation Model dependence

4. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 PART I How to build a confidence belt

5. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Constructing the probability density function – pdf Using different signal contributions µ Energy reconstruction using a Neural Network (ANNE) Energy distribution unfolding via RUN (Blobel) 10 -8 E -2 GeV/cm 2 s sr ≤ µ ≤ 10 -6 E -2 GeV/cm 2 s sr

6. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Constructing the pdf For each fixed signal contribution µ i Place an energy cut (e.g. last bin) and count the event rate Histogram the event rate Normalize the histogram e.g. µ = 2*10 -7 E -2 GeV/cm 2 s sr E in GeV Events 1000 times Plot the energy distribution for each of the 1000 MC experiments

7. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Constructing a confidence belt 1.Estimate P μ-max (n) for each counting rate n by using the probability table 2.Calculate the ranking factor (likelihood-ratio) R(n|μ) = P(n|μ)/P μ-max (n) 3. Rank the entries n for each signal contribution 4. Include for each fixed μ all counts n until the wanted degree of belief is reached 5.Plot the acceptance slice for the fixed μ

8. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Constructing the probability table

9. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Find P μ-max (n) 1.Estimate P μ-max (n) for each counting rate n by using the probability table P μ-max (n 1 ) probability table:

10. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Constructing the ranking table 2. Calculate the ranking factor (likelihood-ratio) R(n|μ) = P(n|μ)/P μ-max (n) R(n|μ) = P(n 1 |μ) / P μ-max (n 1 ) 1.Estimate P μ-max (n) for each counting rate n by using the probability table probability table:

11. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Using the ranking table 3. Rank the entries n for each signal contribution Rank (highest first) ranking table: 1.Estimate P μ-max (n) for each counting rate n by using the probability table 2.Calculate the ranking factor (likelihood-ratio) R(n|μ) = P(n|μ)/P μ-max (n) probability table:

12. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Constructing a confidence belt 4. Include for each fixed μ all counts n until the wanted degree of belief is reached 5. Plot the acceptance slice for the fixed μ acceptance slice

13. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 90% F.C. Confidence Belt energy cut: last bin

14. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Determine the limit Calculation of the limit by using the previous shown diffuse analysis. Data: pointsoure data set of the year 2000-2003 First steps: energy reconstruction with neural net (ANNE) unfolding of the energy distribution with RUN (Blobel) Counting the event rate in the last bin Determine the limit by looking in the confidence belt for the given event rate.

15. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Limit from unfolding method Linear Interpolation take into account the shape of the confidence belt Interpolation is done between the limit corresponding to bin “0” and to bin “1” 0.36 = event rate Most accurate way to estimate the limit, so far... 2.15*10 -7 E -2 GeV/cm 2 s sr

16. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 PART II Changes for the 4 year data set

17. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 90% F.C. Confidence Belt Bigger binning getting the shape of the C.B. snd setting a limit by interpolation Smaller binning Building a part of the C.B. with higher statistics and more signal contributions in the event rate region of the data. Region of interest for the year 2000 data

18. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Estimation of the syst. error disagreement of the depth intensity relation < 10% (product of energy loss * propagation * detection probability) uncertainty of the ν μ to μ cross section ~ 10% neutrino oscillation ~ 10% unfolding precision: 17% Systematic error is the dominanting error source

19. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Estimation of the syst. error unfolding precision 17% possible contamination of the data set → flux might be too high up to 7% uncertainty of the atmospheric neutrino flux: 25% error due to the smoothness of the upper CB ~ < 10% systematic error: 33% (2.15+ 0.72)*10 -7 E -2 GeV/cm 2 s sr = 2.87*10 -7 E -2 GeV/cm 2 s sr

20. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Including the syst. error in C.B. Generate MC set which already includes an error Construct pdf's with this MC → broader than the normal pdf's Build the confidence belt Look up the limit + error from this C.B. with the measured event rate

21. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Limits for different models Limits: E -2 Idea: C.B. construct for different spectral index to have model dependences for spectral indices between 1.7 and 2.3

22. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 Summary Changes for the 4 year data set: Higher statistics and smaller binning in signal contribution  Building a second C.B. which includes the errors Using different spectral indices to obtain model dependent limits Unblinding request within the next weeks ICRC Further outlook Using different method for the energy reconstruction – SVM

23. Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005 More Informations http://app.uni-dortmund.de/~muenich