Example of the usage of the TRolke class The TRolke class computes the profile likelihood confidence limits for 7 different model assumptions on systematic/statistical uncertainties
Please read TRolke.cxx and TRolke.h for more docs.
Author: Jan Conrad, Johan Lundberg
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, March 19, 2024 at 07:12 PM.
variables used throughout the example
Double_t bm;
Double_t tau;
Int_t mid;
Int_t m;
Int_t z;
Int_t y;
Int_t x;
Double_t e;
Double_t em;
Double_t sde;
Double_t sdb;
Double_t b;
Double_t alpha; //Confidence Level
make TRolke objects
TRolke tr; //
Double_t ul ; // upper limit
Double_t ll ; // lower limit
Model 1 assumes:
Poisson uncertainty in the background estimate Binomial uncertainty in the efficiency estimate
cout << endl<<" ======================================================== " <<endl;
mid =1;
x = 5; // events in the signal region
y = 10; // events observed in the background region
tau = 2.5; // ratio between size of signal/background region
m = 100; // MC events have been produced (signal)
z = 50; // MC events have been observed (signal)
alpha=0.9; //Confidence Level
tr.SetCL(alpha);
tr.SetPoissonBkgBinomEff(x,y,z,tau,m);
tr.GetLimits(ll,ul);
cout << "For model 1: Poisson / Binomial" << endl;
cout << "the Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
======================================================== For model 1: Poisson / Binomial the Profile Likelihood interval is : [0,11.5943]
Model 2 assumes:
Poisson uncertainty in the background estimate Gaussian uncertainty in the efficiency estimate
cout << endl<<" ======================================================== " <<endl;
mid =2;
y = 3 ; // events observed in the background region
x = 10 ; // events in the signal region
tau = 2.5; // ratio between size of signal/background region
em = 0.9; // measured efficiency
sde = 0.05; // standard deviation of efficiency
alpha =0.95; // Confidence L evel
tr.SetCL(alpha);
tr.SetPoissonBkgGaussEff(x,y,em,tau,sde);
tr.GetLimits(ll,ul);
cout << "For model 2 : Poisson / Gaussian" << endl;
cout << "the Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
======================================================== For model 2 : Poisson / Gaussian the Profile Likelihood interval is : [3.88417,18.4584]
Model 3 assumes:
Gaussian uncertainty in the background estimate Gaussian uncertainty in the efficiency estimate
cout << endl<<" ======================================================== " <<endl;
mid =3;
bm = 5; // expected background
x = 10; // events in the signal region
sdb = 0.5; // standard deviation in background estimate
em = 0.9; // measured efficiency
sde = 0.05; // standard deviation of efficiency
alpha =0.99; // Confidence Level
tr.SetCL(alpha);
tr.SetGaussBkgGaussEff(x,bm,em,sde,sdb);
tr.GetLimits(ll,ul);
cout << "For model 3 : Gaussian / Gaussian" << endl;
cout << "the Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
cout << "***************************************" << endl;
cout << "* some more example's for gauss/gauss *" << endl;
cout << "* *" << endl;
Double_t slow,shigh;
tr.GetSensitivity(slow,shigh);
cout << "sensitivity:" << endl;
cout << "[" << slow << "," << shigh << "]" << endl;
int outx;
tr.GetLimitsQuantile(slow,shigh,outx,0.5);
cout << "median limit:" << endl;
cout << "[" << slow << "," << shigh << "] @ x =" << outx <<endl;
tr.GetLimitsML(slow,shigh,outx);
cout << "ML limit:" << endl;
cout << "[" << slow << "," << shigh << "] @ x =" << outx <<endl;
tr.GetSensitivity(slow,shigh);
cout << "sensitivity:" << endl;
cout << "[" << slow << "," << shigh << "]" << endl;
tr.GetLimits(ll,ul);
cout << "the Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
Int_t ncrt;
tr.GetCriticalNumber(ncrt);
cout << "critical number: " << ncrt << endl;
tr.SetCLSigmas(5);
tr.GetCriticalNumber(ncrt);
cout << "critical number for 5 sigma: " << ncrt << endl;
cout << "***************************************" << endl;
======================================================== For model 3 : Gaussian / Gaussian the Profile Likelihood interval is : [0,17.5005] *************************************** * some more example's for gauss/gauss * * * sensitivity: [0.00213408,9.0817] median limit: [0,9.21861] @ x =5 ML limit: [0,9.21861] @ x =5 sensitivity: [0.00213408,18.3004] the Profile Likelihood interval is : [0,17.5005] critical number: 13 critical number for 5 sigma: 21 ***************************************
Model 4 assumes:
Poisson uncertainty in the background estimate known efficiency
cout << endl<<" ======================================================== " <<endl;
mid =4;
y = 7; // events observed in the background region
x = 1; // events in the signal region
tau = 5; // ratio between size of signal/background region
e = 0.25; // efficiency
alpha =0.68; // Confidence L evel
tr.SetCL(alpha);
tr.SetPoissonBkgKnownEff(x,y,tau,e);
tr.GetLimits(ll,ul);
cout << "For model 4 : Poissonian / Known" << endl;
cout << "the Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
======================================================== For model 4 : Poissonian / Known the Profile Likelihood interval is : [0,4.08807]
Model 5 assumes:
Gaussian uncertainty in the background estimate Known efficiency
cout << endl<<" ======================================================== " <<endl;
mid =5;
bm = 0; // measured background expectation
x = 1 ; // events in the signal region
e = 0.65; // known eff
sdb = 1.0; // standard deviation of background estimate
alpha =0.799999; // Confidence Level
tr.SetCL(alpha);
tr.SetGaussBkgKnownEff(x,bm,sdb,e);
tr.GetLimits(ll,ul);
cout << "For model 5 : Gaussian / Known" << endl;
cout << "the Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
======================================================== For model 5 : Gaussian / Known the Profile Likelihood interval is : [0,4.91504]
Model 6 assumes:
Known background Binomial uncertainty in the efficiency estimate
cout << endl<<" ======================================================== " <<endl;
mid =6;
b = 10; // known background
x = 25; // events in the signal region
z = 500; // Number of observed signal MC events
m = 750; // Number of produced MC signal events
alpha =0.9; // Confidence L evel
tr.SetCL(alpha);
tr.SetKnownBkgBinomEff(x, z,m,b);
tr.GetLimits(ll,ul);
cout << "For model 6 : Known / Binomial" << endl;
cout << "the Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
======================================================== For model 6 : Known / Binomial the Profile Likelihood interval is : [11.4655,36.3035]
Model 7 assumes:
Known Background Gaussian uncertainty in the efficiency estimate
cout << endl<<" ======================================================== " <<endl;
mid =7;
x = 15; // events in the signal region
em = 0.77; // measured efficiency
sde = 0.15; // standard deviation of efficiency estimate
b = 10; // known background
alpha =0.95; // Confidence L evel
y = 1;
tr.SetCL(alpha);
tr.SetKnownBkgGaussEff(x,em,sde,b);
tr.GetLimits(ll,ul);
cout << "For model 7 : Known / Gaussian " << endl;
cout << "the Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
======================================================== For model 7 : Known / Gaussian the Profile Likelihood interval is : [0,20.1747]
Example of bounded and unbounded likelihood Example for Model 1
bm = 0.0;
tau = 5;
mid = 1;
m = 100;
z = 90;
y = 15;
x = 0;
alpha = 0.90;
tr.SetCL(alpha);
tr.SetPoissonBkgBinomEff(x,y,z,tau,m);
tr.SetBounding(true); //bounded
tr.GetLimits(ll,ul);
cout << "Example of the effect of bounded vs unbounded, For model 1" << endl;
cout << "the BOUNDED Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
tr.SetBounding(false); //unbounded
tr.GetLimits(ll,ul);
cout << "the UNBOUNDED Profile Likelihood interval is :" << endl;
cout << "[" << ll << "," << ul << "]" << endl;
Example of the effect of bounded vs unbounded, For model 1 the BOUNDED Profile Likelihood interval is : [0,1.1729] the UNBOUNDED Profile Likelihood interval is : [0,0.936334]