Kirsten Münich Dortmund University Diffuse Limit with an unfolding method AMANDA Collaboration...
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Transcript of Kirsten Münich Dortmund University Diffuse Limit with an unfolding method AMANDA Collaboration...
Kirsten Münich Dortmund University
Diffuse Limit with anunfolding method
AMANDA Collaboration MeetingBerkeley, March 2005
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Overview
Method of setting an upper limitConstructing a Probability Density Function (PDF)Building a 90% Confidence Belt (C.B)
Changes for the 4 year data set:Higher statisticsBetter sys. errors estimationModel dependence
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
PART I
How to build a confidence belt
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Constructing the probability density function –
Using different signal contributions µ
Energy reconstruction using a Neural Network (ANNE)Energy distribution unfolding via RUN (Blobel)
10-8 E-2 GeV/cm2 s sr ≤ µ ≤ 10-6 E-2 GeV/cm2 s sr
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Constructing the pdf
For each fixed signal contribution µi
Place an energy cut (e.g. last bin) and count the event rateHistogram the event rateNormalize the histogram
e.g. µ = 2*10-7 E-2 GeV/cm2s sr
E in
GeV
Event
s
1000 times
Plot the energy distribution for each of the 1000 MC experiments
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Constructing a confidence belt
1. Estimate Pμ-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)/Pμ-
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
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Constructing the probability table
PDF ...
0.42 0.19 0.13 ...
0.15 0.16 0.15 ...
0.00 0.002 0.001 ...
n1=0 n2=1 n3=2
P(n|1=10 -8)
P(n|2=2 . 10 -7)
P(n|3=10 -6)
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Find Pμ-max(n)
...
...
...
... ... ... ...
n1
n2
1 P(n1| 1) P(n2| 1)
2
P(n1|
2) P(n
2|
2)
1. Estimate Pμ-max(n) for each counting rate n by using the probability table
Pμ-max(n1)
probability table:
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)/Pμ-
max(n)
R(n|μ) = P(n1|μ) / Pμ-
max(n1)
1. Estimate Pμ-max(n) for
each counting rate n by using the probability table
...
...
...
... ... ... ...
n1
n2
1 P(n1| 1) P(n2| 1)
2
P(n1|
2) P(n
2|
2)
probability table:
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Using the ranking table
...
...
...
... ... ... ...
n1
n2
1 R(n1| 1) R(n2| 1)
2
R(n1|
2) R(n
2|
2)
3. Rank the entries n for each signal contribution
Rank (highest first)
ranking table:
1. Estimate Pμ-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)/Pμ-
max(n)
probability table:
...
...
...
... ... ... ...
n1
n2
1 P(n1| 1) P(n2| 1)
2
P(n1|
2) P(n
2|
2)
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
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
90% F.C. Confidence Belt
energy cut: last bin
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 2000-2003First steps:
energy reconstruction with neural net (ANNE)
unfolding of the energy distribution with RUN (Blobel)
Counting the event rate in the last binDetermine the limit by looking in the confidence belt for the given event rate.
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Limit from unfolding method
Linear Interpolation
take into account the shapeof 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/cm2s sr
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
PART II
Changes for the 4 year data set
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 byinterpolation
Smaller binning
Building a part of the C.B. with higher statistics and more signal contributions in theevent rate region of the data.
Region of interest for the year 2000 data
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 νμ to μ cross section ~ 10%
neutrino oscillation ~ 10%
unfolding precision: 17%
Systematic error is the dominanting error source
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/cm2s sr = 2.87*10-7 E-2 GeV/cm2s sr
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Including the syst. error in C.B.
Generate MC set which already includes an errorConstruct pdf's with this MC → broader than the normal pdf'sBuild the confidence belt
Look up the limit + error from this C.B. with the measured event rate
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
Limits for different models
Limits: E-2
Idea:C.B. construct fordifferent spectral index to havemodel dependencesfor spectral indicesbetween 1.7 and 2.3
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 errorsUsing different spectral indices to obtain model dependent limitsUnblinding request within the next weeks ICRC
Further outlookUsing different method for the energy reconstruction – SVM
Kirsten Münich AMANDA / IceCube collab. meeting, Berkeley, March. 2005
More Informations
http://app.uni-dortmund.de/~muenich