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IntervalExamples.C File Reference
Tutorials » RooStats Tutorials

Detailed Description

View in nbviewer Open in SWAN Example showing confidence intervals with four techniques.

An example that shows confidence intervals with four techniques. The model is a Normal Gaussian G(x|mu,sigma) with 100 samples of x. The answer is known analytically, so this is a good example to validate the RooStats tools.

  • expected interval is [-0.162917, 0.229075]
  • plc interval is [-0.162917, 0.229075]
  • fc interval is [-0.17 , 0.23] // stepsize is 0.01
  • bc interval is [-0.162918, 0.229076]
  • mcmc interval is [-0.166999, 0.230224]
␛[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby␛[0m
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
All rights reserved, please read http://roofit.sourceforge.net/license.txt
[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-1e+30, 1e+30] of the RooGaussian 'normal' exceeds the safe range of (0, inf). Advise to limit its range.
RooDataSet::normalData[x] = 100 entries
[#1] INFO:Minization -- createNLL: caching constraint set under name CONSTR_OF_PDF_normal_FOR_OBS_x with 0 entries
[#0] PROGRESS:Minization -- ProfileLikelihoodCalcultor::DoGLobalFit - find MLE
[#0] PROGRESS:Minization -- ProfileLikelihoodCalcultor::DoMinimizeNLL - using Minuit / Migrad with strategy 1
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization --
RooFitResult: minimized FCN value: 144.292, estimated distance to minimum: 3.63481e-09
covariance matrix quality: Full, accurate covariance matrix
Status : MINIMIZE=0
Floating Parameter FinalValue +/- Error
-------------------- --------------------------
mu 3.3073e-02 +/- 9.98e-02
=== Using the following for Example G(x|mu,1) ===
Observables: RooArgSet:: = (x)
Parameters of Interest: RooArgSet:: = (mu)
PDF: RooGaussian::normal[ x=x mean=mu sigma=sigma ] = 0.999453
FeldmanCousins: ntoys per point: adaptive
FeldmanCousins: nEvents per toy will not fluctuate, will always be 100
FeldmanCousins: Model has no nuisance parameters
FeldmanCousins: # points to test = 100
NeymanConstruction: Prog: 1/100 total MC = 78 this test stat = 52.3345
mu=-0.99 [-1e+30, 1.44394] in interval = 0
NeymanConstruction: Prog: 2/100 total MC = 78 this test stat = 50.3084
mu=-0.97 [-1e+30, 1.79333] in interval = 0
NeymanConstruction: Prog: 3/100 total MC = 78 this test stat = 48.3222
mu=-0.95 [-1e+30, 2.15157] in interval = 0
NeymanConstruction: Prog: 4/100 total MC = 78 this test stat = 46.3761
mu=-0.93 [-1e+30, 1.35751] in interval = 0
NeymanConstruction: Prog: 5/100 total MC = 78 this test stat = 44.4699
mu=-0.91 [-1e+30, 3.34994] in interval = 0
NeymanConstruction: Prog: 6/100 total MC = 78 this test stat = 42.6037
mu=-0.89 [-1e+30, 2.51372] in interval = 0
NeymanConstruction: Prog: 7/100 total MC = 78 this test stat = 40.7776
mu=-0.87 [-1e+30, 2.23515] in interval = 0
NeymanConstruction: Prog: 8/100 total MC = 78 this test stat = 38.9914
mu=-0.85 [-1e+30, 1.58856] in interval = 0
NeymanConstruction: Prog: 9/100 total MC = 78 this test stat = 37.2453
mu=-0.83 [-1e+30, 1.81502] in interval = 0
NeymanConstruction: Prog: 10/100 total MC = 78 this test stat = 35.5391
mu=-0.81 [-1e+30, 2.60219] in interval = 0
NeymanConstruction: Prog: 11/100 total MC = 78 this test stat = 33.873
mu=-0.79 [-1e+30, 1.83579] in interval = 0
NeymanConstruction: Prog: 12/100 total MC = 78 this test stat = 32.2468
mu=-0.77 [-1e+30, 1.80677] in interval = 0
NeymanConstruction: Prog: 13/100 total MC = 78 this test stat = 30.6606
mu=-0.75 [-1e+30, 2.46798] in interval = 0
NeymanConstruction: Prog: 14/100 total MC = 78 this test stat = 29.1145
mu=-0.73 [-1e+30, 1.76469] in interval = 0
NeymanConstruction: Prog: 15/100 total MC = 78 this test stat = 27.6083
mu=-0.71 [-1e+30, 2.10923] in interval = 0
NeymanConstruction: Prog: 16/100 total MC = 78 this test stat = 26.1422
mu=-0.69 [-1e+30, 1.96368] in interval = 0
NeymanConstruction: Prog: 17/100 total MC = 78 this test stat = 24.716
mu=-0.67 [-1e+30, 2.46737] in interval = 0
NeymanConstruction: Prog: 18/100 total MC = 78 this test stat = 23.3298
mu=-0.65 [-1e+30, 2.22208] in interval = 0
NeymanConstruction: Prog: 19/100 total MC = 78 this test stat = 21.9837
mu=-0.63 [-1e+30, 1.92004] in interval = 0
NeymanConstruction: Prog: 20/100 total MC = 78 this test stat = 20.6775
mu=-0.61 [-1e+30, 2.09449] in interval = 0
NeymanConstruction: Prog: 21/100 total MC = 78 this test stat = 19.4114
mu=-0.59 [-1e+30, 2.82615] in interval = 0
NeymanConstruction: Prog: 22/100 total MC = 78 this test stat = 18.1852
mu=-0.57 [-1e+30, 2.44483] in interval = 0
NeymanConstruction: Prog: 23/100 total MC = 78 this test stat = 16.9991
mu=-0.55 [-1e+30, 1.47648] in interval = 0
NeymanConstruction: Prog: 24/100 total MC = 78 this test stat = 15.8529
mu=-0.53 [-1e+30, 1.64253] in interval = 0
NeymanConstruction: Prog: 25/100 total MC = 78 this test stat = 14.7467
mu=-0.51 [-1e+30, 3.23375] in interval = 0
NeymanConstruction: Prog: 26/100 total MC = 78 this test stat = 13.6806
mu=-0.49 [-1e+30, 1.36352] in interval = 0
NeymanConstruction: Prog: 27/100 total MC = 78 this test stat = 12.6544
mu=-0.47 [-1e+30, 2.24046] in interval = 0
NeymanConstruction: Prog: 28/100 total MC = 78 this test stat = 11.6683
mu=-0.45 [-1e+30, 1.99249] in interval = 0
NeymanConstruction: Prog: 29/100 total MC = 78 this test stat = 10.7221
mu=-0.43 [-1e+30, 2.54633] in interval = 0
NeymanConstruction: Prog: 30/100 total MC = 78 this test stat = 9.81595
mu=-0.41 [-1e+30, 2.19145] in interval = 0
NeymanConstruction: Prog: 31/100 total MC = 78 this test stat = 8.94979
mu=-0.39 [-1e+30, 2.25133] in interval = 0
NeymanConstruction: Prog: 32/100 total MC = 78 this test stat = 8.12363
mu=-0.37 [-1e+30, 2.63436] in interval = 0
NeymanConstruction: Prog: 33/100 total MC = 78 this test stat = 7.33748
mu=-0.35 [-1e+30, 1.7752] in interval = 0
NeymanConstruction: Prog: 34/100 total MC = 78 this test stat = 6.59132
mu=-0.33 [-1e+30, 2.63173] in interval = 0
NeymanConstruction: Prog: 35/100 total MC = 78 this test stat = 5.88516
mu=-0.31 [-1e+30, 2.2561] in interval = 0
NeymanConstruction: Prog: 36/100 total MC = 78 this test stat = 5.219
mu=-0.29 [-1e+30, 2.0388] in interval = 0
NeymanConstruction: Prog: 37/100 total MC = 234 this test stat = 4.59284
mu=-0.27 [-1e+30, 1.92574] in interval = 0
NeymanConstruction: Prog: 38/100 total MC = 78 this test stat = 4.00668
mu=-0.25 [-1e+30, 2.51905] in interval = 0
NeymanConstruction: Prog: 39/100 total MC = 234 this test stat = 3.46053
mu=-0.23 [-1e+30, 2.20004] in interval = 0
NeymanConstruction: Prog: 40/100 total MC = 234 this test stat = 2.95437
mu=-0.21 [-1e+30, 1.49924] in interval = 0
NeymanConstruction: Prog: 41/100 total MC = 234 this test stat = 2.48821
mu=-0.19 [-1e+30, 1.88454] in interval = 0
NeymanConstruction: Prog: 42/100 total MC = 78 this test stat = 2.06205
mu=-0.17 [-1e+30, 2.92073] in interval = 1
NeymanConstruction: Prog: 43/100 total MC = 234 this test stat = 1.6759
mu=-0.15 [-1e+30, 2.19199] in interval = 1
NeymanConstruction: Prog: 44/100 total MC = 78 this test stat = 1.32974
mu=-0.13 [-1e+30, 1.94832] in interval = 1
NeymanConstruction: Prog: 45/100 total MC = 78 this test stat = 1.02358
mu=-0.11 [-1e+30, 2.16863] in interval = 1
NeymanConstruction: Prog: 46/100 total MC = 78 this test stat = 0.757422
mu=-0.09 [-1e+30, 1.46141] in interval = 1
NeymanConstruction: Prog: 47/100 total MC = 78 this test stat = 0.531264
mu=-0.07 [-1e+30, 4.11006] in interval = 1
NeymanConstruction: Prog: 48/100 total MC = 78 this test stat = 0.345097
mu=-0.05 [-1e+30, 2.11353] in interval = 1
NeymanConstruction: Prog: 49/100 total MC = 78 this test stat = 0.198947
mu=-0.03 [-1e+30, 2.38127] in interval = 1
NeymanConstruction: Prog: 50/100 total MC = 78 this test stat = 0.09279
mu=-0.01 [-1e+30, 3.0189] in interval = 1
NeymanConstruction: Prog: 51/100 total MC = 78 this test stat = 0.026632
mu=0.01 [-1e+30, 2.23448] in interval = 1
NeymanConstruction: Prog: 52/100 total MC = 78 this test stat = 0.000474009
mu=0.03 [-1e+30, 2.54313] in interval = 1
NeymanConstruction: Prog: 53/100 total MC = 78 this test stat = 0.014316
mu=0.05 [-1e+30, 1.52484] in interval = 1
NeymanConstruction: Prog: 54/100 total MC = 78 this test stat = 0.0681571
mu=0.07 [-1e+30, 2.72021] in interval = 1
NeymanConstruction: Prog: 55/100 total MC = 78 this test stat = 0.161992
mu=0.09 [-1e+30, 3.26474] in interval = 1
NeymanConstruction: Prog: 56/100 total MC = 78 this test stat = 0.295842
mu=0.11 [-1e+30, 2.81134] in interval = 1
NeymanConstruction: Prog: 57/100 total MC = 78 this test stat = 0.469684
mu=0.13 [-1e+30, 2.59127] in interval = 1
NeymanConstruction: Prog: 58/100 total MC = 78 this test stat = 0.683526
mu=0.15 [-1e+30, 2.60194] in interval = 1
NeymanConstruction: Prog: 59/100 total MC = 78 this test stat = 0.937368
mu=0.17 [-1e+30, 1.94974] in interval = 1
NeymanConstruction: Prog: 60/100 total MC = 78 this test stat = 1.23121
mu=0.19 [-1e+30, 1.73838] in interval = 1
NeymanConstruction: Prog: 61/100 total MC = 702 this test stat = 1.56505
mu=0.21 [-1e+30, 1.73023] in interval = 1
NeymanConstruction: Prog: 62/100 total MC = 78 this test stat = 1.93888
mu=0.23 [-1e+30, 3.06401] in interval = 1
NeymanConstruction: Prog: 63/100 total MC = 234 this test stat = 2.35273
mu=0.25 [-1e+30, 1.63166] in interval = 0
NeymanConstruction: Prog: 64/100 total MC = 234 this test stat = 2.80658
mu=0.27 [-1e+30, 1.83441] in interval = 0
NeymanConstruction: Prog: 65/100 total MC = 234 this test stat = 3.30042
mu=0.29 [-1e+30, 2.06725] in interval = 0
NeymanConstruction: Prog: 66/100 total MC = 78 this test stat = 3.83426
mu=0.31 [-1e+30, 2.10484] in interval = 0
NeymanConstruction: Prog: 67/100 total MC = 78 this test stat = 4.4081
mu=0.33 [-1e+30, 2.1714] in interval = 0
NeymanConstruction: Prog: 68/100 total MC = 78 this test stat = 5.02195
mu=0.35 [-1e+30, 2.77418] in interval = 0
NeymanConstruction: Prog: 69/100 total MC = 78 this test stat = 5.67579
mu=0.37 [-1e+30, 2.39844] in interval = 0
NeymanConstruction: Prog: 70/100 total MC = 78 this test stat = 6.36963
mu=0.39 [-1e+30, 1.83585] in interval = 0
NeymanConstruction: Prog: 71/100 total MC = 78 this test stat = 7.10347
mu=0.41 [-1e+30, 1.92776] in interval = 0
NeymanConstruction: Prog: 72/100 total MC = 78 this test stat = 7.87731
mu=0.43 [-1e+30, 1.62539] in interval = 0
NeymanConstruction: Prog: 73/100 total MC = 78 this test stat = 8.69116
mu=0.45 [-1e+30, 1.57241] in interval = 0
NeymanConstruction: Prog: 74/100 total MC = 78 this test stat = 9.545
mu=0.47 [-1e+30, 1.9811] in interval = 0
NeymanConstruction: Prog: 75/100 total MC = 78 this test stat = 10.4388
mu=0.49 [-1e+30, 3.71619] in interval = 0
NeymanConstruction: Prog: 76/100 total MC = 78 this test stat = 11.3727
mu=0.51 [-1e+30, 2.09734] in interval = 0
NeymanConstruction: Prog: 77/100 total MC = 78 this test stat = 12.3465
mu=0.53 [-1e+30, 1.61789] in interval = 0
NeymanConstruction: Prog: 78/100 total MC = 78 this test stat = 13.3604
mu=0.55 [-1e+30, 1.75937] in interval = 0
NeymanConstruction: Prog: 79/100 total MC = 78 this test stat = 14.4142
mu=0.57 [-1e+30, 2.16051] in interval = 0
NeymanConstruction: Prog: 80/100 total MC = 78 this test stat = 15.5081
mu=0.59 [-1e+30, 2.49006] in interval = 0
NeymanConstruction: Prog: 81/100 total MC = 78 this test stat = 16.6419
mu=0.61 [-1e+30, 2.15141] in interval = 0
NeymanConstruction: Prog: 82/100 total MC = 78 this test stat = 17.8157
mu=0.63 [-1e+30, 2.63832] in interval = 0
NeymanConstruction: Prog: 83/100 total MC = 78 this test stat = 19.0296
mu=0.65 [-1e+30, 2.12006] in interval = 0
NeymanConstruction: Prog: 84/100 total MC = 78 this test stat = 20.2834
mu=0.67 [-1e+30, 1.70414] in interval = 0
NeymanConstruction: Prog: 85/100 total MC = 78 this test stat = 21.5773
mu=0.69 [-1e+30, 2.54958] in interval = 0
NeymanConstruction: Prog: 86/100 total MC = 78 this test stat = 22.9111
mu=0.71 [-1e+30, 2.27992] in interval = 0
NeymanConstruction: Prog: 87/100 total MC = 78 this test stat = 24.2849
mu=0.73 [-1e+30, 2.99068] in interval = 0
NeymanConstruction: Prog: 88/100 total MC = 78 this test stat = 25.6988
mu=0.75 [-1e+30, 1.60655] in interval = 0
NeymanConstruction: Prog: 89/100 total MC = 78 this test stat = 27.1526
mu=0.77 [-1e+30, 1.61728] in interval = 0
NeymanConstruction: Prog: 90/100 total MC = 78 this test stat = 28.6465
mu=0.79 [-1e+30, 1.92571] in interval = 0
NeymanConstruction: Prog: 91/100 total MC = 78 this test stat = 30.1803
mu=0.81 [-1e+30, 1.69221] in interval = 0
NeymanConstruction: Prog: 92/100 total MC = 78 this test stat = 31.7542
mu=0.83 [-1e+30, 3.26227] in interval = 0
NeymanConstruction: Prog: 93/100 total MC = 78 this test stat = 33.368
mu=0.85 [-1e+30, 1.75583] in interval = 0
NeymanConstruction: Prog: 94/100 total MC = 78 this test stat = 35.0218
mu=0.87 [-1e+30, 2.54103] in interval = 0
NeymanConstruction: Prog: 95/100 total MC = 78 this test stat = 36.7157
mu=0.89 [-1e+30, 2.267] in interval = 0
NeymanConstruction: Prog: 96/100 total MC = 78 this test stat = 38.4495
mu=0.91 [-1e+30, 2.31167] in interval = 0
NeymanConstruction: Prog: 97/100 total MC = 78 this test stat = 40.2234
mu=0.93 [-1e+30, 2.24794] in interval = 0
NeymanConstruction: Prog: 98/100 total MC = 78 this test stat = 42.0372
mu=0.95 [-1e+30, 1.29779] in interval = 0
NeymanConstruction: Prog: 99/100 total MC = 78 this test stat = 43.891
mu=0.97 [-1e+30, 2.00008] in interval = 0
NeymanConstruction: Prog: 100/100 total MC = 78 this test stat = 45.7849
mu=0.99 [-1e+30, 1.56062] in interval = 0
[#1] INFO:Eval -- 21 points in interval
[#1] INFO:Minization -- createNLL picked up cached constraints from workspace with 0 entries
[#1] INFO:Eval -- BayesianCalculator::GetPosteriorFunction : nll value 190.077 poi value = 0.99
[#1] INFO:Eval -- BayesianCalculator::GetPosteriorFunction : minimum of NLL vs POI for POI = 0.033079 min NLL = 144.292
[#1] INFO:Minization -- Including the following constraint terms in minimization: (prior)
[#1] INFO:Minization -- The following global observables have been defined: ()
[#1] INFO:Eval -- BayesianCalculator: Compute interval using RooFit: posteriorPdf + createCdf + RooBrentRootFinder
[#1] INFO:Eval -- BayesianCalculator::GetInterval - found a valid interval : [-0.162918 , 0.229076 ]
[#1] INFO:Minization -- Including the following constraint terms in minimization: (prior)
[#1] INFO:Minization -- The following global observables have been defined: ()
Metropolis-Hastings progress: ....................................................................................................
[#1] INFO:Eval -- Proposal acceptance rate: 16.013%
[#1] INFO:Eval -- Number of steps in chain: 16013
expected interval is [-1.42571, -1.03372]
plc interval is [-0.162917, 0.229075]
fc interval is [-0.17 , 0.23]
bc interval is [-0.162918, 0.229076]
mc interval is [-0.166999, 0.230224]
is mu=0 in the interval? 1
.
[#1] INFO:Minization -- RooProfileLL::evaluate(nll_normal_normalData_Profile[mu]) Creating instance of MINUIT
[#1] INFO:Minization -- RooProfileLL::evaluate(nll_normal_normalData_Profile[mu]) determining minimum likelihood for current configurations w.r.t all observable
[#0] ERROR:InputArguments -- RooArgSet::checkForDup: ERROR argument with name mu is already in this set
[#1] INFO:Minization -- RooProfileLL::evaluate(nll_normal_normalData_Profile[mu]) minimum found at (mu=0.033079)
..........................................................................................................................................................................................................Real time 0:00:15, CP time 15.540
#include "RooStats/ConfInterval.h"
#include "RooStats/PointSetInterval.h"
#include "RooStats/ConfidenceBelt.h"
#include "RooStats/FeldmanCousins.h"
#include "RooStats/ProfileLikelihoodCalculator.h"
#include "RooStats/MCMCCalculator.h"
#include "RooStats/BayesianCalculator.h"
#include "RooStats/MCMCIntervalPlot.h"
#include "RooStats/LikelihoodIntervalPlot.h"
#include "RooStats/ProofConfig.h"
#include "RooStats/ToyMCSampler.h"
#include "RooRandom.h"
#include "RooDataSet.h"
#include "RooRealVar.h"
#include "RooConstVar.h"
#include "RooAddition.h"
#include "RooDataHist.h"
#include "RooPoisson.h"
#include "RooPlot.h"
#include "TCanvas.h"
#include "TTree.h"
#include "TStyle.h"
#include "TMath.h"
#include "Math/DistFunc.h"
#include "TH1F.h"
#include "TMarker.h"
#include "TStopwatch.h"
#include <iostream>
// use this order for safety on library loading
using namespace RooFit;
using namespace RooStats;
void IntervalExamples()
{
// Time this macro
TStopwatch t;
t.Start();
// set RooFit random seed for reproducible results
RooRandom::randomGenerator()->SetSeed(3001);
// make a simple model via the workspace factory
RooWorkspace *wspace = new RooWorkspace();
wspace->factory("Gaussian::normal(x[-10,10],mu[-1,1],sigma[1])");
wspace->defineSet("poi", "mu");
wspace->defineSet("obs", "x");
// specify components of model for statistical tools
ModelConfig *modelConfig = new ModelConfig("Example G(x|mu,1)");
modelConfig->SetWorkspace(*wspace);
modelConfig->SetPdf(*wspace->pdf("normal"));
modelConfig->SetParametersOfInterest(*wspace->set("poi"));
modelConfig->SetObservables(*wspace->set("obs"));
// create a toy dataset
RooDataSet *data = wspace->pdf("normal")->generate(*wspace->set("obs"), 100);
data->Print();
// for convenience later on
RooRealVar *x = wspace->var("x");
RooRealVar *mu = wspace->var("mu");
// set confidence level
double confidenceLevel = 0.95;
// example use profile likelihood calculator
ProfileLikelihoodCalculator plc(*data, *modelConfig);
plc.SetConfidenceLevel(confidenceLevel);
LikelihoodInterval *plInt = plc.GetInterval();
// example use of Feldman-Cousins
FeldmanCousins fc(*data, *modelConfig);
fc.SetConfidenceLevel(confidenceLevel);
fc.SetNBins(100); // number of points to test per parameter
fc.UseAdaptiveSampling(true); // make it go faster
// Here, we consider only ensembles with 100 events
// The PDF could be extended and this could be removed
fc.FluctuateNumDataEntries(false);
// Proof
// ProofConfig pc(*wspace, 4, "workers=4", kFALSE); // proof-lite
// ProofConfig pc(w, 8, "localhost"); // proof cluster at "localhost"
// ToyMCSampler* toymcsampler = (ToyMCSampler*) fc.GetTestStatSampler();
// toymcsampler->SetProofConfig(&pc); // enable proof
PointSetInterval *interval = (PointSetInterval *)fc.GetInterval();
// example use of BayesianCalculator
// now we also need to specify a prior in the ModelConfig
wspace->factory("Uniform::prior(mu)");
modelConfig->SetPriorPdf(*wspace->pdf("prior"));
// example usage of BayesianCalculator
BayesianCalculator bc(*data, *modelConfig);
bc.SetConfidenceLevel(confidenceLevel);
SimpleInterval *bcInt = bc.GetInterval();
// example use of MCMCInterval
MCMCCalculator mc(*data, *modelConfig);
mc.SetConfidenceLevel(confidenceLevel);
// special options
mc.SetNumBins(200); // bins used internally for representing posterior
mc.SetNumBurnInSteps(500); // first N steps to be ignored as burn-in
mc.SetNumIters(100000); // how long to run chain
mc.SetLeftSideTailFraction(0.5); // for central interval
MCMCInterval *mcInt = mc.GetInterval();
// for this example we know the expected intervals
double expectedLL =
data->mean(*x) + ROOT::Math::normal_quantile((1 - confidenceLevel) / 2, 1) / sqrt(data->numEntries());
double expectedUL =
data->mean(*x) + ROOT::Math::normal_quantile_c((1 - confidenceLevel) / 2, 1) / sqrt(data->numEntries());
// Use the intervals
std::cout << "expected interval is [" << expectedLL << ", " << expectedUL << "]" << endl;
cout << "plc interval is [" << plInt->LowerLimit(*mu) << ", " << plInt->UpperLimit(*mu) << "]" << endl;
std::cout << "fc interval is [" << interval->LowerLimit(*mu) << " , " << interval->UpperLimit(*mu) << "]" << endl;
cout << "bc interval is [" << bcInt->LowerLimit() << ", " << bcInt->UpperLimit() << "]" << endl;
cout << "mc interval is [" << mcInt->LowerLimit(*mu) << ", " << mcInt->UpperLimit(*mu) << "]" << endl;
mu->setVal(0);
cout << "is mu=0 in the interval? " << plInt->IsInInterval(RooArgSet(*mu)) << endl;
// make a reasonable style
gStyle->SetCanvasColor(0);
gStyle->SetCanvasBorderMode(0);
gStyle->SetPadBorderMode(0);
gStyle->SetPadColor(0);
gStyle->SetCanvasColor(0);
gStyle->SetTitleFillColor(0);
gStyle->SetFillColor(0);
gStyle->SetFrameFillColor(0);
gStyle->SetStatColor(0);
// some plots
TCanvas *canvas = new TCanvas("canvas");
canvas->Divide(2, 2);
// plot the data
canvas->cd(1);
RooPlot *frame = x->frame();
data->plotOn(frame);
data->statOn(frame);
frame->Draw();
// plot the profile likelihood
canvas->cd(2);
LikelihoodIntervalPlot plot(plInt);
plot.Draw();
// plot the MCMC interval
canvas->cd(3);
MCMCIntervalPlot *mcPlot = new MCMCIntervalPlot(*mcInt);
mcPlot->SetLineColor(kGreen);
mcPlot->SetLineWidth(2);
mcPlot->Draw();
canvas->cd(4);
RooPlot *bcPlot = bc.GetPosteriorPlot();
bcPlot->Draw();
canvas->Update();
t.Stop();
t.Print();
}
kGreen
@ kGreen
Definition Rtypes.h:66
sqrt
double sqrt(double)
gStyle
R__EXTERN TStyle * gStyle
Definition TStyle.h:412
fc
static struct mg_connection * fc(struct mg_context *ctx)
Definition civetweb.c:3728
RooAbsData::statOn
virtual RooPlot * statOn(RooPlot *frame, const RooCmdArg &arg1=RooCmdArg::none(), const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none(), const RooCmdArg &arg6=RooCmdArg::none(), const RooCmdArg &arg7=RooCmdArg::none(), const RooCmdArg &arg8=RooCmdArg::none())
Add a box with statistics information to the specified frame.
Definition RooAbsData.cxx:1165
RooAbsData::Print
virtual void Print(Option_t *options=0) const
Print TNamed name and title.
Definition RooAbsData.h:193
RooAbsData::numEntries
virtual Int_t numEntries() const
Return number of entries in dataset, i.e., count unweighted entries.
Definition RooAbsData.cxx:307
RooAbsData::plotOn
virtual RooPlot * plotOn(RooPlot *frame, const RooCmdArg &arg1=RooCmdArg::none(), const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none(), const RooCmdArg &arg6=RooCmdArg::none(), const RooCmdArg &arg7=RooCmdArg::none(), const RooCmdArg &arg8=RooCmdArg::none()) const
Definition RooAbsData.cxx:547
RooAbsData::mean
Double_t mean(const RooRealVar &var, const char *cutSpec=0, const char *cutRange=0) const
Definition RooAbsData.h:211
RooAbsPdf::generate
RooDataSet * generate(const RooArgSet &whatVars, Int_t nEvents, const RooCmdArg &arg1, const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none())
See RooAbsPdf::generate(const RooArgSet&,const RooCmdArg&,const RooCmdArg&,const RooCmdArg&,...
Definition RooAbsPdf.h:58
RooArgSet
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition RooArgSet.h:29
RooDataSet
RooDataSet is a container class to hold unbinned data.
Definition RooDataSet.h:33
RooPlot
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition RooPlot.h:44
RooPlot::frame
static RooPlot * frame(const RooAbsRealLValue &var, Double_t xmin, Double_t xmax, Int_t nBins)
Create a new frame for a given variable in x.
Definition RooPlot.cxx:249
RooPlot::Draw
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition RooPlot.cxx:691
RooRandom::randomGenerator
static TRandom * randomGenerator()
Return a pointer to a singleton random-number generator implementation.
Definition RooRandom.cxx:53
RooRealVar
RooRealVar represents a variable that can be changed from the outside.
Definition RooRealVar.h:39
RooRealVar::setVal
virtual void setVal(Double_t value)
Set value of variable to 'value'.
Definition RooRealVar.cxx:282
RooStats::BayesianCalculator
BayesianCalculator is a concrete implementation of IntervalCalculator, providing the computation of a...
Definition BayesianCalculator.h:37
RooStats::FeldmanCousins
The FeldmanCousins class (like the Feldman-Cousins technique) is essentially a specific configuration...
Definition FeldmanCousins.h:33
RooStats::LikelihoodIntervalPlot
This class provides simple and straightforward utilities to plot a LikelihoodInterval object.
Definition LikelihoodIntervalPlot.h:30
RooStats::LikelihoodInterval
LikelihoodInterval is a concrete implementation of the RooStats::ConfInterval interface.
Definition LikelihoodInterval.h:34
RooStats::LikelihoodInterval::LowerLimit
Double_t LowerLimit(const RooRealVar &param)
return the lower bound of the interval on a given parameter
Definition LikelihoodInterval.h:65
RooStats::LikelihoodInterval::UpperLimit
Double_t UpperLimit(const RooRealVar &param)
return the upper bound of the interval on a given parameter
Definition LikelihoodInterval.h:69
RooStats::LikelihoodInterval::IsInInterval
virtual Bool_t IsInInterval(const RooArgSet &) const
check if given point is in the interval
Definition LikelihoodInterval.cxx:117
RooStats::MCMCCalculator
Bayesian Calculator estimating an interval or a credible region using the Markov-Chain Monte Carlo me...
Definition MCMCCalculator.h:31
RooStats::MCMCIntervalPlot
This class provides simple and straightforward utilities to plot a MCMCInterval object.
Definition MCMCIntervalPlot.h:28
RooStats::MCMCIntervalPlot::SetLineColor
void SetLineColor(Color_t color)
Definition MCMCIntervalPlot.h:38
RooStats::MCMCIntervalPlot::SetLineWidth
void SetLineWidth(Int_t width)
Definition MCMCIntervalPlot.h:39
RooStats::MCMCIntervalPlot::Draw
void Draw(const Option_t *options=NULL)
Definition MCMCIntervalPlot.cxx:147
RooStats::MCMCInterval
MCMCInterval is a concrete implementation of the RooStats::ConfInterval interface.
Definition MCMCInterval.h:33
RooStats::MCMCInterval::UpperLimit
virtual Double_t UpperLimit(RooRealVar &param)
get the highest value of param that is within the confidence interval
Definition MCMCInterval.cxx:1021
RooStats::MCMCInterval::LowerLimit
virtual Double_t LowerLimit(RooRealVar &param)
get the lowest value of param that is within the confidence interval
Definition MCMCInterval.cxx:1005
RooStats::ModelConfig
ModelConfig is a simple class that holds configuration information specifying how a model should be u...
Definition ModelConfig.h:30
RooStats::ModelConfig::SetObservables
virtual void SetObservables(const RooArgSet &set)
Specify the observables.
Definition ModelConfig.h:146
RooStats::ModelConfig::SetPriorPdf
virtual void SetPriorPdf(const RooAbsPdf &pdf)
Set the Prior Pdf, add to the the workspace if not already there.
Definition ModelConfig.h:87
RooStats::ModelConfig::SetWorkspace
virtual void SetWorkspace(RooWorkspace &ws)
Definition ModelConfig.h:66
RooStats::ModelConfig::SetParametersOfInterest
virtual void SetParametersOfInterest(const RooArgSet &set)
Specify parameters of interest.
Definition ModelConfig.h:100
RooStats::ModelConfig::SetPdf
virtual void SetPdf(const RooAbsPdf &pdf)
Set the Pdf, add to the the workspace if not already there.
Definition ModelConfig.h:81
RooStats::PointSetInterval
PointSetInterval is a concrete implementation of the ConfInterval interface.
Definition PointSetInterval.h:21
RooStats::PointSetInterval::UpperLimit
Double_t UpperLimit(RooRealVar &param)
return upper limit on a given parameter
Definition PointSetInterval.cxx:147
RooStats::PointSetInterval::LowerLimit
Double_t LowerLimit(RooRealVar &param)
return lower limit on a given parameter
Definition PointSetInterval.cxx:160
RooStats::ProfileLikelihoodCalculator
The ProfileLikelihoodCalculator is a concrete implementation of CombinedCalculator (the interface cla...
Definition ProfileLikelihoodCalculator.h:22
RooStats::SimpleInterval
SimpleInterval is a concrete implementation of the ConfInterval interface.
Definition SimpleInterval.h:20
RooStats::SimpleInterval::UpperLimit
virtual Double_t UpperLimit()
Definition SimpleInterval.h:49
RooStats::SimpleInterval::LowerLimit
virtual Double_t LowerLimit()
Definition SimpleInterval.h:47
RooWorkspace
The RooWorkspace is a persistable container for RooFit projects.
Definition RooWorkspace.h:43
RooWorkspace::defineSet
Bool_t defineSet(const char *name, const RooArgSet &aset, Bool_t importMissing=kFALSE)
Define a named RooArgSet with given constituents.
Definition RooWorkspace.cxx:855
RooWorkspace::var
RooRealVar * var(const char *name) const
Retrieve real-valued variable (RooRealVar) with given name. A null pointer is returned if not found.
Definition RooWorkspace.cxx:1295
RooWorkspace::factory
RooFactoryWSTool & factory()
Return instance to factory tool.
Definition RooWorkspace.cxx:2166
RooWorkspace::set
const RooArgSet * set(const char *name)
Return pointer to previously defined named set with given nmame If no such set is found a null pointe...
Definition RooWorkspace.cxx:977
RooWorkspace::pdf
RooAbsPdf * pdf(const char *name) const
Retrieve p.d.f (RooAbsPdf) with given name. A null pointer is returned if not found.
Definition RooWorkspace.cxx:1277
TAttFill::SetFillColor
virtual void SetFillColor(Color_t fcolor)
Set the fill area color.
Definition TAttFill.h:37
TCanvas
The Canvas class.
Definition TCanvas.h:23
TCanvas::cd
TVirtualPad * cd(Int_t subpadnumber=0) override
Set current canvas & pad.
Definition TCanvas.cxx:708
TCanvas::Update
void Update() override
Update canvas pad buffers.
Definition TCanvas.cxx:2504
TPad::Divide
void Divide(Int_t nx=1, Int_t ny=1, Float_t xmargin=0.01, Float_t ymargin=0.01, Int_t color=0) override
Automatic pad generation by division.
Definition TPad.cxx:1177
TRandom::SetSeed
virtual void SetSeed(ULong_t seed=0)
Set the random generator seed.
Definition TRandom.cxx:608
TStopwatch
Stopwatch class.
Definition TStopwatch.h:28
TStopwatch::Start
void Start(Bool_t reset=kTRUE)
Start the stopwatch.
Definition TStopwatch.cxx:58
TStopwatch::Stop
void Stop()
Stop the stopwatch.
Definition TStopwatch.cxx:77
TStopwatch::Print
void Print(Option_t *option="") const
Print the real and cpu time passed between the start and stop events.
Definition TStopwatch.cxx:219
TStyle::SetPadBorderMode
void SetPadBorderMode(Int_t mode=1)
Definition TStyle.h:340
TStyle::SetFrameFillColor
void SetFrameFillColor(Color_t color=1)
Definition TStyle.h:355
TStyle::SetCanvasColor
void SetCanvasColor(Color_t color=19)
Definition TStyle.h:327
TStyle::SetCanvasBorderMode
void SetCanvasBorderMode(Int_t mode=1)
Definition TStyle.h:329
TStyle::SetTitleFillColor
void SetTitleFillColor(Color_t color=1)
Definition TStyle.h:387
TStyle::SetStatColor
void SetStatColor(Color_t color=19)
Definition TStyle.h:373
TStyle::SetPadColor
void SetPadColor(Color_t color=19)
Definition TStyle.h:338
ROOT::Math::normal_quantile
double normal_quantile(double z, double sigma)
Inverse ( ) of the cumulative distribution function of the lower tail of the normal (Gaussian) distri...
Definition QuantFuncMathCore.cxx:134
ROOT::Math::normal_quantile_c
double normal_quantile_c(double z, double sigma)
Inverse ( ) of the cumulative distribution function of the upper tail of the normal (Gaussian) distri...
Definition QuantFuncMathCore.cxx:126
x
Double_t x[n]
Definition legend1.C:17
RooFit
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Definition RooCFunction1Binding.h:29
RooStats
Namespace for the RooStats classes.
Definition Asimov.h:19
Author
Kyle Cranmer

Definition in file IntervalExamples.C.