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

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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