Study on the improvement from beta information in the Likelihood
Collaboration MeetingCERN, 6-10 Feb 2012
Agustín Sánchez LosaIFIC (CSIC – Universitat de València)
PRELIMINARY
Outline
• Correlation "α vs β"• Likelihood• PEX (PseudoEXperiments)• First results• To-Do List
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 2
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 3
0.0<β<0.1
1.4<β<1.5
αlog
Correlation "α vs β”
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 4
Correlation "α vs β”
0.0<β<0.1
1.4<β<1.5
MEAN(Log(α))
Β slice
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 5
iiibkibkiiisigsigtot
iiibkibkiisigiiisigsigtot
iiibkibkiisigisigsigtot
iibkibkisigisigsigtot
iiiibksigiiisigsigtotbksig
nPPnP
nPPnPnP
nPPnPP
nPPnPP
nPnPL
,,,
,,,
,,
,,,,,log
PS Analysis
β 1st Aprox.
ceevent/sour theofn Declinatio :
event in the hits ofNumber :
matrixerror fromtion reconstrucin estimationerror Angular :
tedreconstruc-real differenceangular Neutrino :
n
Likelihood
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 6
sigiiMC nP ,
PS Analysis
β 1st Aprox.
iDATAiDATA nPP ,
PS Analysis
β 1st Aprox.
DATADATA n,TH2
DATAnTH1
DATATH1
MCMCMC n,,TH3
MCMC n,TH2
MCMCMC n,,TH3
iii nbk ,,
iii nsig ,,
iiMCsigiiMC nPnP , ,
iiiMCsigiiMC nPnP ,, ,
iiDATAiDATA nPP ,,
PEXSimulating signal and background events
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 7
DATA
MC
log(α)
Nhits
Nhits
β
β
Ingredients
log(α)
β
β
Nhi
ts
β
Nhi
ts
Nhi
ts
log(α)
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 8
MCMC n,TH2 DATADATA n,TH2
i
iibkibkiisigisigsigtotbksig nPPnPPL ,,log
i
ibkibkisigisigsigtotbksig nPPnPPL log
DATAnTH1 MCnTH1
MCspline DATAspline
DATAspline MCspline
PS Analysis
β 1st Aprox.
Likelihood"PS Analysis" vs "β 1st Aproximation"
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 9
First results"PS Analysis" vs "β 1st Aproximation"
• Comparison under same conditions:– Fixed search– δ = 0°– Cut N52– Same systematics (OFF for number of hits)– Same ingredients (PDFs)– Same statistics:• 10000 pex for background• 1000 pex for signal up to 20
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 10
nsig 0: 0.14 nsig 1: 0.98 nsig 2: 1.95 nsig 3: 2.96 nsig 4: 3.96 nsig 5: 4.95 nsig 6: 5.92 nsig 7: 6.92 nsig 8: 7.89 nsig 9: 8.90 nsig 10: 9.90
Means
Fitted Signal
First results"β 1st Aprox." fitted signal check
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 11
nsig 0: 0.2 nsig 1: 21.7 nsig 2: 56.2 nsig 3: 81.3 nsig 4: 93.2 nsig 5: 98.0
% events above 3σ
Q distribution
First results"PS Analysis" Q statistic distribution
Q = 3.84
3σ Threshold
PS Analysis
bkbksig LLQ loglog max
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 12
nsig 0: 0.2 nsig 1: 24.7 nsig 2: 55.6 nsig 3: 81.6 nsig 4: 94.0 nsig 5: 98.1
% events above 3σ
Q distribution
First results "β 1st Aprox." Q statistic distribution
Q = 3.58
3σ Threshold
β 1st Aprox.
nsig 0: 0.2 nsig 1: 21.7 nsig 2: 56.2 nsig 3: 81.3 nsig 4: 93.2 nsig 5: 98.0
PS Analysis
bkbksig LLQ loglog max
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 13
nsig 0: 4.1 nsig 1: 51.4 nsig 2: 83.9 nsig 3: 95.9 nsig 4: 98.9 nsig 5: 99.8
% events above 2σ
Q distribution
First results "β 1st Aprox." Q statistic distribution
Q = 1.20
2σ Threshold
β 1st Aprox.
nsig 0: 4.2 nsig 1: 59.3 nsig 2: 86.6 nsig 3: 96.1 nsig 4: 99.1 nsig 5: 99.8
PS Analysis β 1st Aprox.
% events above 2σ
2σ Threshold
Q = 0.96PRELIMINARY
bkbksig LLQ loglog max
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting 14
LikelihoodNext implementations
MCMCMC n,,TH3
MCMC n,TH2
i
iibkibkiisigiiisigsigtotbksig nPPnPnPL ,,,log
DATADATA n,TH2 MCMCMC n,,TH3
i
iibkibkiiisigsigtotbksig nPPnPL ,,,log
DATAnTH1
DATAspline
DATAspline
DATADATA n,TH2
6-10 Feb 2012 Agustín Sánchez Losa – CERN Collaboration Meeting
To-Do List
• Solve the problems with the PDFs• Make additional checks with higher statistics• Compute discovery power curves
• …adapt it for a time dependent search
15
Thank youfor your attention
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