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NumberCountingUtils.cxx
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1 // @(#)root/roostats:$Id$
2 // Author: Kyle Cranmer 28/07/2008
3 
4 /*************************************************************************
5  * Copyright (C) 1995-2008, Rene Brun and Fons Rademakers. *
6  * All rights reserved. *
7  * *
8  * For the licensing terms see $ROOTSYS/LICENSE. *
9  * For the list of contributors see $ROOTSYS/README/CREDITS. *
10  *************************************************************************/
11 
12 
14 
15 #include "RooStats/RooStatsUtils.h"
16 
17 // // Without this macro the THtml doc can not be generated
18 // #if !defined(R__ALPHA) && !defined(R__SOLARIS) && !defined(R__ACC) && !defined(R__FBSD)
19 // NamespaceImp(RooStats)
20 // //NamespaceImp(NumberCountingUtils)
21 // #endif
22 
23 //using namespace RooStats;
24 
25 Double_t RooStats::NumberCountingUtils::BinomialExpP(Double_t signalExp, Double_t backgroundExp, Double_t relativeBkgUncert){
26  // Expected P-value for s=0 in a ratio of Poisson means.
27  // Here the background and its uncertainty are provided directly and
28  // assumed to be from the double Poisson counting setup described in the
29  // BinomialWithTau functions.
30  // Normally one would know tau directly, but here it is determiend from
31  // the background uncertainty. This is not strictly correct, but a useful
32  // approximation.
33 
34 
35  //SIDE BAND EXAMPLE
36  //See Eqn. (19) of Cranmer and pp. 36-37 of Linnemann.
37  //150 total events in signalExp region, 100 in sideband of equal size
38  Double_t mainInf = signalExp+backgroundExp; //Given
39  Double_t tau = 1./backgroundExp/(relativeBkgUncert*relativeBkgUncert);
40  Double_t auxiliaryInf = backgroundExp*tau; //Given
41 
42  Double_t P_Bi = TMath::BetaIncomplete(1./(1.+tau),mainInf,auxiliaryInf+1);
43  return P_Bi;
44 
45 /*
46 Now, if instead the mean background level b in the signal region is
47 specified, along with Gaussian rms sigb, then one can fake a Poisson
48 sideband (see Linnemann, p. 35, converted to Cranmer's notation) by
49 letting tau = b/(sigb*sigb) and y = b*tau. Thus, for example, if one
50 has x=150 and b = 100 +/- 10, one then derives tau and y. Then one
51 has the same two lines of ROOT calling BetaIncomplete and ErfInverse.
52 Since I chose these numbers to revert to the previous example, we get
53 the same answer:
54 */
55 /*
56 //GAUSSIAN FAKED AS POISSON EXAMPLE
57 x = 150. //Given
58 b = 100. //Given
59 sigb = 10. //Given
60 tau = b/(sigb*sigb)
61 y = tau*b
62 Z_Bi = TMath::BetaIncomplete(1./(1.+tau),x,y+1)
63 S = sqrt(2)*TMath::ErfInverse(1 - 2*Z_Bi)
64 
65 */
66 
67 }
68 
69 
71  // Expected P-value for s=0 in a ratio of Poisson means.
72  // Based on two expectations, a main measurement that might have signal
73  // and an auxiliarly measurement for the background that is signal free.
74  // The expected background in the auxiliary measurement is a factor
75  // tau larger than in the main measurement.
76 
77  Double_t mainInf = signalExp+backgroundExp; //Given
78  Double_t auxiliaryInf = backgroundExp*tau; //Given
79 
80  Double_t P_Bi = TMath::BetaIncomplete(1./(1.+tau),mainInf,auxiliaryInf+1);
81 
82  return P_Bi;
83 
84 }
85 
87  // P-value for s=0 in a ratio of Poisson means.
88  // Here the background and its uncertainty are provided directly and
89  // assumed to be from the double Poisson counting setup.
90  // Normally one would know tau directly, but here it is determiend from
91  // the background uncertainty. This is not strictly correct, but a useful
92  // approximation.
93 
94  Double_t tau = 1./backgroundObs/(relativeBkgUncert*relativeBkgUncert);
95  Double_t auxiliaryInf = backgroundObs*tau; //Given
96 
97 
98  //SIDE BAND EXAMPLE
99  //See Eqn. (19) of Cranmer and pp. 36-37 of Linnemann.
100  Double_t P_Bi = TMath::BetaIncomplete(1./(1.+tau),mainObs,auxiliaryInf+1);
101 
102  return P_Bi;
103 
104 }
105 
106 
108  // P-value for s=0 in a ratio of Poisson means.
109  // Based on two observations, a main measurement that might have signal
110  // and an auxiliarly measurement for the background that is signal free.
111  // The expected background in the auxiliary measurement is a factor
112  // tau larger than in the main measurement.
113 
114  //SIDE BAND EXAMPLE
115  //See Eqn. (19) of Cranmer and pp. 36-37 of Linnemann.
116  Double_t P_Bi = TMath::BetaIncomplete(1./(1.+tau),mainObs,auxiliaryObs+1);
117 
118  return P_Bi;
119 
120 }
121 
122 Double_t RooStats::NumberCountingUtils::BinomialExpZ(Double_t signalExp, Double_t backgroundExp, Double_t relativeBkgUncert) {
123  // See BinomialExpP
124  return RooStats::PValueToSignificance( BinomialExpP(signalExp,backgroundExp,relativeBkgUncert) ) ;
125  }
126 
128  // See BinomialWithTauExpP
129  return RooStats::PValueToSignificance( BinomialWithTauExpP(signalExp,backgroundExp,tau) ) ;
130 }
131 
132 
134  // See BinomialObsP
135  return RooStats::PValueToSignificance( BinomialObsP(mainObs,backgroundObs,relativeBkgUncert) ) ;
136 }
137 
139  // See BinomialWithTauObsP
140  return RooStats::PValueToSignificance( BinomialWithTauObsP(mainObs,auxiliaryObs,tau) ) ;
141 }
RooStats::NumberCountingUtils::BinomialWithTauExpP
Double_t BinomialWithTauExpP(Double_t sExp, Double_t bExp, Double_t tau)
Definition: NumberCountingUtils.cxx:70
RooStats::NumberCountingUtils::BinomialExpZ
Double_t BinomialExpZ(Double_t sExp, Double_t bExp, Double_t fractionalBUncertainty)
Definition: NumberCountingUtils.cxx:122
RooStats::NumberCountingUtils::BinomialObsP
Double_t BinomialObsP(Double_t nObs, Double_t, Double_t fractionalBUncertainty)
Definition: NumberCountingUtils.cxx:86
RooStats::NumberCountingUtils::BinomialObsZ
Double_t BinomialObsZ(Double_t nObs, Double_t bExp, Double_t fractionalBUncertainty)
Definition: NumberCountingUtils.cxx:133
NumberCountingUtils.h
RooStats::NumberCountingUtils::BinomialWithTauObsZ
Double_t BinomialWithTauObsZ(Double_t nObs, Double_t bExp, Double_t tau)
Definition: NumberCountingUtils.cxx:138
RooStats::PValueToSignificance
Double_t PValueToSignificance(Double_t pvalue)
returns one-sided significance corresponding to a p-value
Definition: RooStatsUtils.h:51
RooStats::NumberCountingUtils::BinomialWithTauExpZ
Double_t BinomialWithTauExpZ(Double_t sExp, Double_t bExp, Double_t tau)
Definition: NumberCountingUtils.cxx:127
TMath::BetaIncomplete
Double_t BetaIncomplete(Double_t x, Double_t a, Double_t b)
Calculates the incomplete Beta-function.
Definition: TMath.cxx:2075
RooStats::NumberCountingUtils::BinomialWithTauObsP
Double_t BinomialWithTauObsP(Double_t nObs, Double_t bExp, Double_t tau)
Definition: NumberCountingUtils.cxx:107
RooStatsUtils.h
Double_t
double Double_t
Definition: RtypesCore.h:59
RooStats::NumberCountingUtils::BinomialExpP
Double_t BinomialExpP(Double_t sExp, Double_t bExp, Double_t fractionalBUncertainty)
Definition: NumberCountingUtils.cxx:25