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

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


PART I

How to build a confidence belt


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/cm2 s sr ≤ µ ≤ 10-6 E-2 GeV/cm2 s sr


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


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


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)


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:


Constructing the ranking table


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:


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


max(n)

probability table:

...

...

...

... ... ... ...

n1

n2

1 P(n1| 1) P(n2| 1)

2

P(n1|

2) P(n

2|

2)


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


90% F.C. Confidence Belt

energy cut: last bin


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.


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


PART II

Changes for the 4 year data set


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


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


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


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


Limits for different models

Limits: E-2

Idea:C.B. construct fordifferent spectral index to havemodel dependencesfor spectral indicesbetween 1.7 and 2.3


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


More Informations

http://app.uni-dortmund.de/~muenich

Documents

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