Please read TRolke.cxx and TRolke.h for more docs.
Author: Jan Conrad. Johan Lundberg
This notebook tutorial was automatically generated with ROOTBOOK-izer (Beta) from the macro found in the ROOT repository on Thursday, January 19, 2017 at 04:34 PM.
In [1]:
%%cpp -d
#include "TROOT.h"
#include "TSystem.h"
#include "TRolke.h"
#include "Riostream.h"
Variables used throughout the example
In [2]:
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
In [3]:
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
In [4]:
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;
Model 2 assumes:
Poisson uncertainty in the background estimate Gaussian uncertainty in the efficiency estimate
In [5]:
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;
Model 3 assumes:
Gaussian uncertainty in the background estimate Gaussian uncertainty in the efficiency estimate
In [6]:
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;
Model 4 assumes:
Poisson uncertainty in the background estimate known efficiency
In [7]:
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;
Model 5 assumes:
Gaussian uncertainty in the background estimate Known efficiency
In [8]:
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;
Model 6 assumes:
Known background Binomial uncertainty in the efficiency estimate
In [9]:
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;
Model 7 assumes:
Known Background Gaussian uncertainty in the efficiency estimate
In [10]:
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;
Example of bounded and unbounded likelihood Example for Model 1
In [11]:
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;