ROOT   Reference Guide
HybridInstructional.C File Reference

Detailed Description

Example demonstrating usage of HybridCalcultor

A hypothesis testing example based on number counting with background uncertainty.

NOTE: This example must be run with the ACLIC (the + option ) due to the new class that is defined.

This example:

• demonstrates the usage of the HybridCalcultor (Part 4-6)
• demonstrates the numerical integration of RooFit (Part 2)
• validates the RooStats against an example with a known analytic answer
• demonstrates usage of different test statistics
• explains subtle choices in the prior used for hybrid methods
• demonstrates usage of different priors for the nuisance parameters
• demonstrates usage of PROOF

The basic setup here is that a main measurement has observed x events with an expectation of s+b. One can choose an ad hoc prior for the uncertainty on b, or try to base it on an auxiliary measurement. In this case, the auxiliary measurement (aka control measurement, sideband) is another counting experiment with measurement y and expectation tau*b. With an 'original prior' on b, called $$\eta(b)$$ then one can obtain a posterior from the auxiliary measurement $$\pi(b) = \eta(b) * Pois(y|tau*b).$$ This is a principled choice for a prior on b in the main measurement of x, which can then be treated in a hybrid Bayesian/Frequentist way. Additionally, one can try to treat the two measurements simultaneously, which is detailed in Part 6 of the tutorial.

This tutorial is related to the FourBin.C tutorial in the modeling, but focuses on hypothesis testing instead of interval estimation.

More background on this 'prototype problem' can be found in the following papers:

[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby[0m
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
-----------------------------------------
Part 2
Hybrid p-value from direct integration = 0.000774094
Z_Gamma Significance = 3.1655
-----------------------------------------
Part 3
Z_Bi p-value (analytic): 0.00094165
Z_Bi significance (analytic): 3.10804
Real time 0:00:05, CP time 5.060
[#0] WARNING:InputArguments -- The parameter 'b' with range [0, 300] of the RooLognormal 'lognorm_prior' exceeds the safe range of (0, inf). Advise to limit its range.
[#0] WARNING:InputArguments -- The parameter 'y' with range [0, 500] of the RooLognormal 'lognorm_prior' exceeds the safe range of (0, inf). Advise to limit its range.
[#0] WARNING:Eval -- RooStatsUtils::MakeNuisancePdf - no constraints found on nuisance parameters in the input model
[#0] WARNING:Eval -- RooStatsUtils::MakeNuisancePdf - no constraints found on nuisance parameters in the input model
-----------------------------------------
Part 4
Results HypoTestCalculator_result:
- Null p-value = 0.00115 +/- 0.000239654
- Significance = 3.04848 +/- 0.0626148 sigma
- Number of Alt toys: 1000
- Number of Null toys: 20000
- Test statistic evaluated on data: 150
- CL_b: 0.00115 +/- 0.000239654
- CL_s+b: 0.524 +/- 0.0157932
- CL_s: 455.652 +/- 95.9434
Real time 0:00:02, CP time 2.030
[#0] WARNING:Eval -- RooStatsUtils::MakeNuisancePdf - no constraints found on nuisance parameters in the input model
[#0] WARNING:Eval -- RooStatsUtils::MakeNuisancePdf - no constraints found on nuisance parameters in the input model
-----------------------------------------
Part 5
Results HypoTestCalculator_result:
- Null p-value = 0.0009 +/- 0.000212037
- Significance = 3.12139 +/- 0.0693716 sigma
- Number of Alt toys: 1000
- Number of Null toys: 20000
- Test statistic evaluated on data: 10.8198
- CL_b: 0.0009 +/- 0.000212037
- CL_s+b: 0.535 +/- 0.0157726
- CL_s: 594.444 +/- 141.141
Real time 0:00:02, CP time 2.300
[#0] WARNING:Eval -- RooStatsUtils::MakeNuisancePdf - no constraints found on nuisance parameters in the input model
[#0] WARNING:Eval -- RooStatsUtils::MakeNuisancePdf - no constraints found on nuisance parameters in the input model
-----------------------------------------
Part 6
Results HypoTestCalculator_result:
- Null p-value = 0.000666667 +/- 0.000149021
- Significance = 3.20871 +/- 0.0642752 sigma
- Number of Alt toys: 1000
- Number of Null toys: 30000
- Test statistic evaluated on data: 5.03388
- CL_b: 0.000666667 +/- 0.000149021
- CL_s+b: 0.489 +/- 0.0158076
- CL_s: 733.5 +/- 165.667
Real time 0:00:37, CP time 37.250
#include "RooGlobalFunc.h"
#include "RooRealVar.h"
#include "RooProdPdf.h"
#include "RooWorkspace.h"
#include "RooDataSet.h"
#include "TCanvas.h"
#include "TStopwatch.h"
#include "TH1.h"
#include "RooPlot.h"
#include "RooMsgService.h"
using namespace RooFit;
using namespace RooStats;
// ----------------------------------
// A New Test Statistic Class for this example.
// It simply returns the sum of the values in a particular
// column of a dataset.
// You can ignore this class and focus on the macro below
class BinCountTestStat : public TestStatistic {
public:
BinCountTestStat(void) : fColumnName("tmp") {}
BinCountTestStat(string columnName) : fColumnName(columnName) {}
virtual Double_t Evaluate(RooAbsData &data, RooArgSet & /*nullPOI*/)
{
// This is the main method in the interface
Double_t value = 0.0;
for (int i = 0; i < data.numEntries(); i++) {
value += data.get(i)->getRealValue(fColumnName.c_str());
}
return value;
}
virtual const TString GetVarName() const { return fColumnName; }
private:
string fColumnName;
protected:
ClassDef(BinCountTestStat, 1)
};
ClassImp(BinCountTestStat)
// ----------------------------------
// The Actual Tutorial Macro
void HybridInstructional()
{
// This tutorial has 6 parts
// Setup
// 1. Make the model for the 'prototype problem'
// Special cases
// 2. Use RooFit's direct integration to get p-value & significance
// 3. Use RooStats analytic solution for this problem
// RooStats HybridCalculator -- can be generalized
// 4. RooStats ToyMC version of 2. & 3.
// 5. RooStats ToyMC with an equivalent test statistic
// 6. RooStats ToyMC with simultaneous control & main measurement
// It takes ~4 min without PROOF and ~2 min with PROOF on 4 cores.
// Of course, everything looks nicer with more toys, which takes longer.
t.Start();
TCanvas *c = new TCanvas;
c->Divide(2, 2);
// ----------------------------------------------------
// P A R T 1 : D I R E C T I N T E G R A T I O N
// ====================================================
// Make model for prototype on/off problem
// $Pois(x | s+b) * Pois(y | tau b )$
// for Z_Gamma, use uniform prior on b.
RooWorkspace *w = new RooWorkspace("w");
w->factory("Poisson::px(x[150,0,500],sum::splusb(s[0,0,100],b[100,0,300]))");
w->factory("Poisson::py(y[100,0,500],prod::taub(tau[1.],b))");
w->factory("PROD::model(px,py)");
w->factory("Uniform::prior_b(b)");
// We will control the output level in a few places to avoid
// verbose progress messages. We start by keeping track
// of the current threshold on messages.
// Use PROOF-lite on multi-core machines
ProofConfig *pc = NULL;
// uncomment below if you want to use PROOF
// ~~~
// pc = new ProofConfig(*w, 4, "workers=4", kFALSE); // machine with 4 cores
// pc = new ProofConfig(*w, 2, "workers=2", kFALSE); // machine with 2 cores
// ~~~
// ----------------------------------------------------
// P A R T 2 : D I R E C T I N T E G R A T I O N
// ====================================================
// This is not the 'RooStats' way, but in this case the distribution
// of the test statistic is simply x and can be calculated directly
// from the PDF using RooFit's built-in integration.
// Note, this does not generalize to situations in which the test statistic
// depends on many events (rows in a dataset).
// construct the Bayesian-averaged model (eg. a projection pdf)
// $p'(x|s) = \int db p(x|s+b) * [ p(y|b) * prior(b) ]$
w->factory("PROJ::averagedModel(PROD::foo(px|b,py,prior_b),b)");
// plot it, red is averaged model, green is b known exactly, blue is s+b av model
RooPlot *frame = w->var("x")->frame(Range(50, 230));
w->pdf("averagedModel")->plotOn(frame, LineColor(kRed));
w->pdf("px")->plotOn(frame, LineColor(kGreen));
w->var("s")->setVal(50.);
w->pdf("averagedModel")->plotOn(frame, LineColor(kBlue));
c->cd(1);
frame->Draw();
w->var("s")->setVal(0.);
// compare analytic calculation of Z_Bi
// with the numerical RooFit implementation of Z_Gamma
// for an example with x = 150, y = 100
// numeric RooFit Z_Gamma
w->var("y")->setVal(100);
w->var("x")->setVal(150);
RooAbsReal *cdf = w->pdf("averagedModel")->createCdf(*w->var("x"));
cdf->getVal(); // get ugly print messages out of the way
cout << "-----------------------------------------" << endl;
cout << "Part 2" << endl;
cout << "Hybrid p-value from direct integration = " << 1 - cdf->getVal() << endl;
cout << "Z_Gamma Significance = " << PValueToSignificance(1 - cdf->getVal()) << endl;
RooMsgService::instance().setGlobalKillBelow(msglevel); // set it back
// ---------------------------------------------
// P A R T 3 : A N A L Y T I C R E S U L T
// =============================================
// In this special case, the integrals are known analytically
// and they are implemented in RooStats::NumberCountingUtils
// analytic Z_Bi
double p_Bi = NumberCountingUtils::BinomialWithTauObsP(150, 100, 1);
double Z_Bi = NumberCountingUtils::BinomialWithTauObsZ(150, 100, 1);
cout << "-----------------------------------------" << endl;
cout << "Part 3" << endl;
std::cout << "Z_Bi p-value (analytic): " << p_Bi << std::endl;
std::cout << "Z_Bi significance (analytic): " << Z_Bi << std::endl;
t.Stop();
t.Print();
t.Reset();
t.Start();
// -------------------------------------------------------------
// P A R T 4 : U S I N G H Y B R I D C A L C U L A T O R
// =============================================================
// Now we demonstrate the RooStats HybridCalculator.
//
// Like all RooStats calculators it needs the data and a ModelConfig
// for the relevant hypotheses. Since we are doing hypothesis testing
// we need a ModelConfig for the null (background only) and the alternate
// (signal+background) hypotheses. We also need to specify the PDF,
// the parameters of interest, and the observables. Furthermore, since
// the parameter of interest is floating, we need to specify which values
// of the parameter corresponds to the null and alternate (eg. s=0 and s=50)
//
// define some sets of variables obs={x} and poi={s}
// note here, x is the only observable in the main measurement
// and y is treated as a separate measurement, which is used
// to produce the prior that will be used in this calculation
// to randomize the nuisance parameters.
w->defineSet("obs", "x");
w->defineSet("poi", "s");
// create a toy dataset with the x=150
RooDataSet *data = new RooDataSet("d", "d", *w->set("obs"));
// Part 3a : Setup ModelConfigs
// -------------------------------------------------------
// create the null (background-only) ModelConfig with s=0
ModelConfig b_model("B_model", w);
b_model.SetPdf(*w->pdf("px"));
b_model.SetObservables(*w->set("obs"));
b_model.SetParametersOfInterest(*w->set("poi"));
w->var("s")->setVal(0.0); // important!
b_model.SetSnapshot(*w->set("poi"));
// create the alternate (signal+background) ModelConfig with s=50
ModelConfig sb_model("S+B_model", w);
sb_model.SetPdf(*w->pdf("px"));
sb_model.SetObservables(*w->set("obs"));
sb_model.SetParametersOfInterest(*w->set("poi"));
w->var("s")->setVal(50.0); // important!
sb_model.SetSnapshot(*w->set("poi"));
// Part 3b : Choose Test Statistic
// ----------------------------------
// To make an equivalent calculation we need to use x as the test
// statistic. This is not a built-in test statistic in RooStats
// so we define it above. The new class inherits from the
// RooStats::TestStatistic interface, and simply returns the value
// of x in the dataset.
BinCountTestStat binCount("x");
// Part 3c : Define Prior used to randomize nuisance parameters
// -------------------------------------------------------------
//
// The prior used for the hybrid calculator is the posterior
// from the auxiliary measurement y. The model for the aux.
// measurement is Pois(y|tau*b), thus the likelihood function
// is proportional to (has the form of) a Gamma distribution.
// if the 'original prior' $\eta(b)$ is uniform, then from
// Bayes's theorem we have the posterior:
// $\pi(b) = Pois(y|tau*b) * \eta(b)$
// If $\eta(b)$ is flat, then we arrive at a Gamma distribution.
// Since RooFit will normalize the PDF we can actually supply
// $py=Pois(y,tau*b)$ that will be equivalent to multiplying by a uniform.
//
// Alternatively, we could explicitly use a gamma distribution:
// w->factory("Gamma::gamma(b,sum::temp(y,1),1,0)");
//
// or we can use some other ad hoc prior that do not naturally
// follow from the known form of the auxiliary measurement.
// The common choice is the equivalent Gaussian:
w->factory("Gaussian::gauss_prior(b,y, expr::sqrty('sqrt(y)',y))");
// this corresponds to the "Z_N" calculation.
//
// or one could use the analogous log-normal prior
w->factory("Lognormal::lognorm_prior(b,y, expr::kappa('1+1./sqrt(y)',y))");
//
// Ideally, the HybridCalculator would be able to inspect the full
// model $Pois(x | s+b) * Pois(y | tau b )$ and be given the original
// prior $\eta(b)$ to form $\pi(b) = Pois(y|tau*b) * \eta(b)$.
// This is not yet implemented because in the general case
// it is not easy to identify the terms in the PDF that correspond
// to the auxiliary measurement. So for now, it must be set
// explicitly with:
// - ForcePriorNuisanceNull()
// - ForcePriorNuisanceAlt()
// the name "ForcePriorNuisance" was chosen because we anticipate
// this to be auto-detected, but will leave the option open
// to force to a different prior for the nuisance parameters.
// Part 3d : Construct and configure the HybridCalculator
// -------------------------------------------------------
HybridCalculator hc1(*data, sb_model, b_model);
ToyMCSampler *toymcs1 = (ToyMCSampler *)hc1.GetTestStatSampler();
toymcs1->SetNEventsPerToy(1); // because the model is in number counting form
toymcs1->SetTestStatistic(&binCount); // set the test statistic
hc1.SetToys(20000, 1000);
hc1.ForcePriorNuisanceAlt(*w->pdf("py"));
hc1.ForcePriorNuisanceNull(*w->pdf("py"));
// if you wanted to use the ad hoc Gaussian prior instead
// ~~~
// hc1.ForcePriorNuisanceAlt(*w->pdf("gauss_prior"));
// hc1.ForcePriorNuisanceNull(*w->pdf("gauss_prior"));
// ~~~
// if you wanted to use the ad hoc log-normal prior instead
// ~~~
// hc1.ForcePriorNuisanceAlt(*w->pdf("lognorm_prior"));
// hc1.ForcePriorNuisanceNull(*w->pdf("lognorm_prior"));
// ~~~
// enable proof
// NOTE: This test statistic is defined in this macro, and is not
// working with PROOF currently. Luckily test stat is fast to evaluate.
// if(pc) toymcs1->SetProofConfig(pc);
// these lines save current msg level and then kill any messages below ERROR
// Get the result
HypoTestResult *r1 = hc1.GetHypoTest();
RooMsgService::instance().setGlobalKillBelow(msglevel); // set it back
cout << "-----------------------------------------" << endl;
cout << "Part 4" << endl;
r1->Print();
t.Stop();
t.Print();
t.Reset();
t.Start();
c->cd(2);
HypoTestPlot *p1 = new HypoTestPlot(*r1, 30); // 30 bins, TS is discrete
p1->Draw();
// -------------------------------------------------------------------------
// # P A R T 5 : U S I N G H Y B R I D C A L C U L A T O R
// # W I T H A N A L T E R N A T I V E T E S T S T A T I S T I C
//
// A likelihood ratio test statistics should be 1-to-1 with the count x
// when the value of b is fixed in the likelihood. This is implemented
// by the SimpleLikelihoodRatioTestStat
SimpleLikelihoodRatioTestStat slrts(*b_model.GetPdf(), *sb_model.GetPdf());
slrts.SetNullParameters(*b_model.GetSnapshot());
slrts.SetAltParameters(*sb_model.GetSnapshot());
// HYBRID CALCULATOR
HybridCalculator hc2(*data, sb_model, b_model);
ToyMCSampler *toymcs2 = (ToyMCSampler *)hc2.GetTestStatSampler();
toymcs2->SetNEventsPerToy(1);
toymcs2->SetTestStatistic(&slrts);
hc2.SetToys(20000, 1000);
hc2.ForcePriorNuisanceAlt(*w->pdf("py"));
hc2.ForcePriorNuisanceNull(*w->pdf("py"));
// if you wanted to use the ad hoc Gaussian prior instead
// ~~~
// hc2.ForcePriorNuisanceAlt(*w->pdf("gauss_prior"));
// hc2.ForcePriorNuisanceNull(*w->pdf("gauss_prior"));
// ~~~
// if you wanted to use the ad hoc log-normal prior instead
// ~~~
// hc2.ForcePriorNuisanceAlt(*w->pdf("lognorm_prior"));
// hc2.ForcePriorNuisanceNull(*w->pdf("lognorm_prior"));
// ~~~
// enable proof
if (pc)
toymcs2->SetProofConfig(pc);
// these lines save current msg level and then kill any messages below ERROR
// Get the result
HypoTestResult *r2 = hc2.GetHypoTest();
cout << "-----------------------------------------" << endl;
cout << "Part 5" << endl;
r2->Print();
t.Stop();
t.Print();
t.Reset();
t.Start();
c->cd(3);
HypoTestPlot *p2 = new HypoTestPlot(*r2, 30); // 30 bins
p2->Draw();
// -----------------------------------------------------------------------------
// # P A R T 6 : U S I N G H Y B R I D C A L C U L A T O R W I T H A N A L T E R N A T I V E T E S T
// # S T A T I S T I C A N D S I M U L T A N E O U S M O D E L
//
// If one wants to use a test statistic in which the nuisance parameters
// are profiled (in one way or another), then the PDF must constrain b.
// Otherwise any observation x can always be explained with s=0 and b=x/tau.
//
// In this case, one is really thinking about the problem in a
// different way. They are considering x,y simultaneously.
// and the PDF should be $Pois(x | s+b) * Pois(y | tau b )$
// and the set 'obs' should be {x,y}.
w->defineSet("obsXY", "x,y");
// create a toy dataset with the x=150, y=100
w->var("x")->setVal(150.);
w->var("y")->setVal(100.);
RooDataSet *dataXY = new RooDataSet("dXY", "dXY", *w->set("obsXY"));
// now we need new model configs, with PDF="model"
ModelConfig b_modelXY("B_modelXY", w);
b_modelXY.SetPdf(*w->pdf("model")); // IMPORTANT
b_modelXY.SetObservables(*w->set("obsXY"));
b_modelXY.SetParametersOfInterest(*w->set("poi"));
w->var("s")->setVal(0.0); // IMPORTANT
b_modelXY.SetSnapshot(*w->set("poi"));
// create the alternate (signal+background) ModelConfig with s=50
ModelConfig sb_modelXY("S+B_modelXY", w);
sb_modelXY.SetPdf(*w->pdf("model")); // IMPORTANT
sb_modelXY.SetObservables(*w->set("obsXY"));
sb_modelXY.SetParametersOfInterest(*w->set("poi"));
w->var("s")->setVal(50.0); // IMPORTANT
sb_modelXY.SetSnapshot(*w->set("poi"));
// without this print, their can be a crash when using PROOF. Strange.
// w->Print();
// Test statistics like the profile likelihood ratio
// (or the ratio of profiled likelihoods (Tevatron) or the MLE for s)
// will now work, since the nuisance parameter b is constrained by y.
// ratio of alt and null likelihoods with background yield profiled.
//
// NOTE: These are slower because they have to run fits for each toy
// Tevatron-style Ratio of profiled likelihoods
// $Q_Tev = -log L(s=0,\hat\hat{b})/L(s=50,\hat\hat{b})$
RatioOfProfiledLikelihoodsTestStat ropl(*b_modelXY.GetPdf(), *sb_modelXY.GetPdf(), sb_modelXY.GetSnapshot());
ropl.SetSubtractMLE(false);
// profile likelihood where alternate is best fit value of signal yield
// $\lambda(0) = -log L(s=0,\hat\hat{b})/L(\hat{s},\hat{b})$
ProfileLikelihoodTestStat profll(*b_modelXY.GetPdf());
// just use the maximum likelihood estimate of signal yield
// $MLE = \hat{s}$
MaxLikelihoodEstimateTestStat mlets(*sb_modelXY.GetPdf(), *w->var("s"));
// However, it is less clear how to justify the prior used in randomizing
// the nuisance parameters (since that is a property of the ensemble,
// and y is a property of each toy pseudo experiment. In that case,
// one probably wants to consider a different y0 which will be held
// constant and the prior $\pi(b) = Pois(y0 | tau b) * \eta(b)$.
w->factory("y0[100]");
w->factory("Gamma::gamma_y0(b,sum::temp0(y0,1),1,0)");
w->factory("Gaussian::gauss_prior_y0(b,y0, expr::sqrty0('sqrt(y0)',y0))");
// HYBRID CALCULATOR
HybridCalculator hc3(*dataXY, sb_modelXY, b_modelXY);
ToyMCSampler *toymcs3 = (ToyMCSampler *)hc3.GetTestStatSampler();
toymcs3->SetNEventsPerToy(1);
toymcs3->SetTestStatistic(&slrts);
hc3.SetToys(30000, 1000);
hc3.ForcePriorNuisanceAlt(*w->pdf("gamma_y0"));
hc3.ForcePriorNuisanceNull(*w->pdf("gamma_y0"));
// if you wanted to use the ad hoc Gaussian prior instead
// ~~~{.cpp}
// hc3.ForcePriorNuisanceAlt(*w->pdf("gauss_prior_y0"));
// hc3.ForcePriorNuisanceNull(*w->pdf("gauss_prior_y0"));
// ~~~
// choose fit-based test statistic
toymcs3->SetTestStatistic(&profll);
// toymcs3->SetTestStatistic(&ropl);
// toymcs3->SetTestStatistic(&mlets);
// enable proof
if (pc)
toymcs3->SetProofConfig(pc);
// these lines save current msg level and then kill any messages below ERROR
// Get the result
HypoTestResult *r3 = hc3.GetHypoTest();
cout << "-----------------------------------------" << endl;
cout << "Part 6" << endl;
r3->Print();
t.Stop();
t.Print();
t.Reset();
t.Start();
c->cd(4);
HypoTestPlot *p3 = new HypoTestPlot(*r3, 50); // 50 bins
p3->Draw();
c->SaveAs("zbi.pdf");
// -----------------------------------------
// OUTPUT W/O PROOF (2.66 GHz Intel Core i7)
// =========================================
// -----------------------------------------
// Part 2
// Hybrid p-value from direct integration = 0.00094165
// Z_Gamma Significance = 3.10804
// -----------------------------------------
//
// Part 3
// Z_Bi p-value (analytic): 0.00094165
// Z_Bi significance (analytic): 3.10804
// Real time 0:00:00, CP time 0.610
// -----------------------------------------
// Part 4
// Results HybridCalculator_result:
// - Null p-value = 0.00115 +/- 0.000228984
// - Significance = 3.04848 sigma
// - Number of S+B toys: 1000
// - Number of B toys: 20000
// - Test statistic evaluated on data: 150
// - CL_b: 0.99885 +/- 0.000239654
// - CL_s+b: 0.476 +/- 0.0157932
// - CL_s: 0.476548 +/- 0.0158118
// Real time 0:00:07, CP time 7.620
// -----------------------------------------
// Part 5
// Results HybridCalculator_result:
// - Null p-value = 0.0009 +/- 0.000206057
// - Significance = 3.12139 sigma
// - Number of S+B toys: 1000
// - Number of B toys: 20000
// - Test statistic evaluated on data: 10.8198
// - CL_b: 0.9991 +/- 0.000212037
// - CL_s+b: 0.465 +/- 0.0157726
// - CL_s: 0.465419 +/- 0.0157871
// Real time 0:00:34, CP time 34.360
// -----------------------------------------
// Part 6
// Results HybridCalculator_result:
// - Null p-value = 0.000666667 +/- 0.000149021
// - Significance = 3.20871 sigma
// - Number of S+B toys: 1000
// - Number of B toys: 30000
// - Test statistic evaluated on data: 5.03388
// - CL_b: 0.999333 +/- 0.000149021
// - CL_s+b: 0.511 +/- 0.0158076
// - CL_s: 0.511341 +/- 0.0158183
// Real time 0:05:06, CP time 306.330
// ---------------------------------------------------------
// OUTPUT w/ PROOF (2.66 GHz Intel Core i7, 4 virtual cores)
// =========================================================
// -----------------------------------------
// Part 5
// Results HybridCalculator_result:
// - Null p-value = 0.00075 +/- 0.000173124
// - Significance = 3.17468 sigma
// - Number of S+B toys: 1000
// - Number of B toys: 20000
// - Test statistic evaluated on data: 10.8198
// - CL_b: 0.99925 +/- 0.000193577
// - CL_s+b: 0.454 +/- 0.0157443
// - CL_s: 0.454341 +/- 0.0157564
// Real time 0:00:16, CP time 0.990
// -----------------------------------------
// Part 6
// Results HybridCalculator_result:
// - Null p-value = 0.0007 +/- 0.000152699
// - Significance = 3.19465 sigma
// - Number of S+B toys: 1000
// - Number of B toys: 30000
// - Test statistic evaluated on data: 5.03388
// - CL_b: 0.9993 +/- 0.000152699
// - CL_s+b: 0.518 +/- 0.0158011
// - CL_s: 0.518363 +/- 0.0158124
// Real time 0:01:25, CP time 0.580
// ----------------------------------
// Comparison
// ----------------------------------
// LEPStatToolsForLHC
// https://plone4.fnal.gov:4430/P0/phystat/packages/0703002
// Uses Gaussian prior
// CL_b = 6.218476e-04, Significance = 3.228665 sigma
//
// ----------------------------------
// Comparison
// ----------------------------------
// Asymptotic
// From the value of the profile likelihood ratio (5.0338)
// The significance can be estimated using Wilks's theorem
// significance = sqrt(2*profileLR) = 3.1729 sigma
}

Definition in file HybridInstructional.C.

c
#define c(i)
Definition: RSha256.hxx:101
RooAbsRealLValue::frame
RooPlot * frame(const RooCmdArg &arg1, 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
Create a new RooPlot on the heap with a drawing frame initialized for this object,...
Definition: RooAbsRealLValue.cxx:199
RooWorkspace.h
RooPlot::Draw
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:691
RooRealVar::setVal
virtual void setVal(Double_t value)
Set value of variable to 'value'.
Definition: RooRealVar.cxx:257
RooMsgService.h
RooStats::HybridCalculator
Same purpose as HybridCalculatorOriginal, but different implementation.
Definition: HybridCalculator.h:22
RooAbsData
RooAbsData is the common abstract base class for binned and unbinned datasets.
Definition: RooAbsData.h:49
kGreen
@ kGreen
Definition: Rtypes.h:66
RooStats::HypoTestResult::Print
void Print(const Option_t *="") const
Print out some information about the results Note: use Alt/Null labels for the hypotheses here as the...
Definition: HypoTestResult.cxx:339
ClassImp
#define ClassImp(name)
Definition: Rtypes.h:364
TStopwatch.h
RooAbsPdf::createCdf
RooAbsReal * createCdf(const RooArgSet &iset, const RooArgSet &nset=RooArgSet())
Create a cumulative distribution function of this p.d.f in terms of the observables listed in iset.
Definition: RooAbsPdf.cxx:3475
RooAbsReal::getVal
Double_t getVal(const RooArgSet *normalisationSet=nullptr) const
Evaluate object.
Definition: RooAbsReal.h:91
ToyMCSampler.h
RooStats::TestStatistic
TestStatistic is an interface class to provide a facility for construction test statistics distributi...
Definition: TestStatistic.h:31
TGeant4Unit::pc
static constexpr double pc
Definition: TGeant4SystemOfUnits.h:130
RooAbsReal
RooAbsReal is the common abstract base class for objects that represent a real value and implements f...
Definition: RooAbsReal.h:61
NumberCountingUtils.h
TCanvas.h
TString
Basic string class.
Definition: TString.h:136
RooFit::MsgLevel
MsgLevel
Verbosity level for RooMsgService::StreamConfig in RooMsgService.
Definition: RooGlobalFunc.h:65
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
RooDataSet.h
RooAbsPdf::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 RooCmdArg &arg9=RooCmdArg::none(), const RooCmdArg &arg10=RooCmdArg::none()) const
Definition: RooAbsPdf.h:121
RooWorkspace::factory
RooFactoryWSTool & factory()
Return instance to factory tool.
Definition: RooWorkspace.cxx:2166
RooStats::HypoTestPlot
This class provides the plots for the result of a study performed with any of the HypoTestCalculatorG...
Definition: HypoTestPlot.h:22
RooStats::NumberCountingUtils::BinomialWithTauObsZ
Double_t BinomialWithTauObsZ(Double_t nObs, Double_t bExp, Double_t tau)
Definition: NumberCountingUtils.cxx:138
HybridCalculator.h
RooStats::PValueToSignificance
Double_t PValueToSignificance(Double_t pvalue)
returns one-sided significance corresponding to a p-value
Definition: RooStatsUtils.h:51
virtual void add(const RooArgSet &row, Double_t weight=1.0, Double_t weightError=0) override
Add a data point, with its coordinates specified in the 'data' argset, to the data set.
Definition: RooDataSet.cxx:1181
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
RooStats::ToyMCSampler::SetNEventsPerToy
virtual void SetNEventsPerToy(const Int_t nevents)
Forces the generation of exactly n events even for extended PDFs.
Definition: ToyMCSampler.h:151
RooProdPdf.h
RooStats::RatioOfProfiledLikelihoodsTestStat
TestStatistic that returns the ratio of profiled likelihoods.
Definition: RatioOfProfiledLikelihoodsTestStat.h:26
RooFit
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Definition: RooCFunction1Binding.h:29
SimpleLikelihoodRatioTestStat.h
RooAbsCollection::getRealValue
Double_t getRealValue(const char *name, Double_t defVal=0, Bool_t verbose=kFALSE) const
Get value of a RooAbsReal stored in set with given name.
Definition: RooAbsCollection.cxx:856
TStopwatch::Reset
void Reset()
Definition: TStopwatch.h:52
RatioOfProfiledLikelihoodsTestStat.h
RooStats::NumberCountingUtils::BinomialWithTauObsP
Double_t BinomialWithTauObsP(Double_t nObs, Double_t bExp, Double_t tau)
Definition: NumberCountingUtils.cxx:107
RooStats::ProofConfig
Holds configuration options for proof and proof-lite.
Definition: ProofConfig.h:46
RooAbsData::get
virtual const RooArgSet * get() const
Definition: RooAbsData.h:92
RooPlot.h
RooMsgService::setGlobalKillBelow
void setGlobalKillBelow(RooFit::MsgLevel level)
Definition: RooMsgService.h:160
RooPlot
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
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
RooStats::SimpleLikelihoodRatioTestStat
TestStatistic class that returns -log(L[null] / L[alt]) where L is the likelihood.
Definition: SimpleLikelihoodRatioTestStat.h:24
RooAbsData::numEntries
virtual Int_t numEntries() const
Return number of entries in dataset, i.e., count unweighted entries.
Definition: RooAbsData.cxx:304
TStopwatch::Start
void Start(Bool_t reset=kTRUE)
Start the stopwatch.
Definition: TStopwatch.cxx:58
RooRealVar.h
kRed
@ kRed
Definition: Rtypes.h:66
RooGlobalFunc.h
RooStats::ToyMCSampler::SetTestStatistic
virtual void SetTestStatistic(TestStatistic *testStatistic, unsigned int i)
Definition: ToyMCSampler.h:186
RooWorkspace
The RooWorkspace is a persistable container for RooFit projects.
Definition: RooWorkspace.h:43
RooStats::ToyMCSampler::SetProofConfig
void SetProofConfig(ProofConfig *pc=NULL)
Definition: ToyMCSampler.h:235
RooFit::LineColor
RooCmdArg LineColor(Color_t color)
Definition: RooGlobalFunc.cxx:57
Double_t
double Double_t
Definition: RtypesCore.h:59
RooStats::SamplingDistPlot::Draw
void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: SamplingDistPlot.cxx:299
TCanvas
The Canvas class.
Definition: TCanvas.h:23
RooStats
Namespace for the RooStats classes.
Definition: Asimov.h:19
RooStats::ToyMCSampler
ToyMCSampler is an implementation of the TestStatSampler interface.
Definition: ToyMCSampler.h:73
TStopwatch
Stopwatch class.
Definition: TStopwatch.h:28
ClassDef
#define ClassDef(name, id)
Definition: Rtypes.h:325
RooStats::HypoTestResult
HypoTestResult is a base class for results from hypothesis tests.
Definition: HypoTestResult.h:22
RooFit::Range
RooCmdArg Range(const char *rangeName, Bool_t adjustNorm=kTRUE)
Definition: RooGlobalFunc.cxx:53
kBlue
@ kBlue
Definition: Rtypes.h:66
RooFit::ERROR
@ ERROR
Definition: RooGlobalFunc.h:65
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
MaxLikelihoodEstimateTestStat.h
RooDataSet
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:33
RooStats::ProfileLikelihoodTestStat
ProfileLikelihoodTestStat is an implementation of the TestStatistic interface that calculates the pro...
Definition: ProfileLikelihoodTestStat.h:32
TStopwatch::Stop
void Stop()
Stop the stopwatch.
Definition: TStopwatch.cxx:77
RooStats::ModelConfig
ModelConfig is a simple class that holds configuration information specifying how a model should be u...
Definition: ModelConfig.h:30
RooStats::MaxLikelihoodEstimateTestStat
MaxLikelihoodEstimateTestStat: TestStatistic that returns maximum likelihood estimate of a specified ...
Definition: MaxLikelihoodEstimateTestStat.h:39
TH1.h
HypoTestPlot.h
RooMsgService::instance
static RooMsgService & instance()
Return reference to singleton instance.
Definition: RooMsgService.cxx:366
RooMsgService::globalKillBelow
RooFit::MsgLevel globalKillBelow() const
Definition: RooMsgService.h:161
RooArgSet
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:29
ProfileLikelihoodTestStat.h
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