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RooStats::ProfileLikelihoodCalculator Class Reference

The ProfileLikelihoodCalculator is a concrete implementation of CombinedCalculator (the interface class for tools which can produce both a RooStats HypoTestResult and ConfInterval).

The tool uses the profile likelihood ratio as a test statistic, and assumes that Wilks' theorem is valid. Wilks' theorem states that $$-2 \cdot \ln(\lambda)$$ (profile likelihood ratio) is asymptotically distributed as a $$\chi^2$$ distribution with $$N$$ degrees of freedom. Thus, $$p$$-values can be constructed, and the profile likelihood ratio can be used to construct a LikelihoodInterval. (In the future, this class could be extended to use toy Monte Carlo to calibrate the distribution of the test statistic).

Usage: It uses the interface of the CombinedCalculator, so that it can be configured by specifying:

• A model common model (e.g. a family of specific models, which includes both the null and alternate)
• A data set
• A set of parameters of interest. The nuisance parameters will be all other parameters of the model.
• A set of parameters which specify the null hypothesis (including values and const/non-const status).

The interface allows one to pass the model, data, and parameters either directly or via a ModelConfig class. The alternate hypothesis leaves the parameter free to take any value other than those specified by the null hypothesis. There is therefore no need to specify the alternate parameters.

After configuring the calculator, one only needs to call GetHypoTest() (which will return a HypoTestResult pointer) or GetInterval() (which will return a ConfInterval pointer).

This calculator can work with both one-dimensional intervals or multi- dimensional ones (contours).

Note that for hypothesis tests, it is often better to use the AsymptoticCalculator, which can compute in addition the expected $$p$$-value using an Asimov data set.

Definition at line 22 of file ProfileLikelihoodCalculator.h.

## Public Member Functions

ProfileLikelihoodCalculator ()
Default constructor (needed for I/O)

ProfileLikelihoodCalculator (RooAbsData &data, ModelConfig &model, Double_t size=0.05)
Constructor from data and a model configuration If the ModelConfig defines a prior pdf for any of the parameters those will be included as constrained terms in the likelihood function.

ProfileLikelihoodCalculator (RooAbsData &data, RooAbsPdf &pdf, const RooArgSet &paramsOfInterest, Double_t size=0.05, const RooArgSet *nullParams=0)
Constructor from data, from a full model pdf describing both parameter of interest and nuisance parameters and from the set specifying the parameter of interest (POI).

virtual ~ProfileLikelihoodCalculator ()
destructor cannot delete prod pdf because it will delete all the composing pdf's if (fOwnPdf) delete fPdf; fPdf = 0;

virtual HypoTestResultGetHypoTest () const
Return the hypothesis test result obtained from the likelihood ratio of the maximum likelihood value with the null parameters fixed to their values, with respect to keeping all parameters floating (global maximum likelihood value).

virtual LikelihoodIntervalGetInterval () const
Return a likelihood interval.

Public Member Functions inherited from RooStats::CombinedCalculator
CombinedCalculator ()

CombinedCalculator (RooAbsData &data, const ModelConfig &model, Double_t size=0.05)
constructor from data and model configuration

CombinedCalculator (RooAbsData &data, RooAbsPdf &pdf, const RooArgSet &paramsOfInterest, Double_t size=0.05, const RooArgSet *nullParams=0, const RooArgSet *altParams=0, const RooArgSet *nuisParams=0)

virtual ~CombinedCalculator ()
destructor.

virtual Double_t ConfidenceLevel () const
Get the Confidence level for the test.

virtual HypoTestResultGetHypoTest () const =0
main interface to get a HypoTestResult, pure virtual

virtual ConfIntervalGetInterval () const =0
Main interface to get a ConfInterval, pure virtual.

virtual void SetAlternateModel (const ModelConfig &)

virtual void SetAlternateParameters (const RooArgSet &set)
set parameter values for the alternate if using a common PDF

virtual void SetConditionalObservables (const RooArgSet &set)
set conditional observables needed for computing the NLL

virtual void SetConfidenceLevel (Double_t cl)
set the confidence level for the interval (eg. 0.95 for a 95% Confidence Interval)

virtual void SetData (RooAbsData &data)
Set the DataSet, add to the the workspace if not already there.

virtual void SetGlobalObservables (const RooArgSet &set)
set global observables needed for computing the NLL

virtual void SetModel (const ModelConfig &model)
set the model (in this case can set only the parameters for the null hypothesis)

virtual void SetNuisanceParameters (const RooArgSet &set)
specify the nuisance parameters (eg. the rest of the parameters)

virtual void SetNullModel (const ModelConfig &)

virtual void SetNullParameters (const RooArgSet &set)
set parameter values for the null if using a common PDF

virtual void SetParameters (const RooArgSet &set)
specify the parameters of interest in the interval

virtual void SetPdf (RooAbsPdf &pdf)
Set the Pdf.

virtual void SetTestSize (Double_t size)
set the size of the test (rate of Type I error) ( Eg. 0.05 for a 95% Confidence Interval)

virtual Double_t Size () const
Get the size of the test (eg. rate of Type I error)

Public Member Functions inherited from RooStats::IntervalCalculator
virtual ~IntervalCalculator ()

virtual Double_t ConfidenceLevel () const =0
Get the Confidence level for the test.

virtual ConfIntervalGetInterval () const =0
Main interface to get a ConfInterval, pure virtual.

virtual void SetConfidenceLevel (Double_t cl)=0
set the confidence level for the interval (e.g. 0.95 for a 95% Confidence Interval)

virtual void SetData (RooAbsData &)=0
Set the DataSet ( add to the the workspace if not already there ?)

virtual void SetModel (const ModelConfig &)=0
Set the Model.

virtual void SetTestSize (Double_t size)=0
set the size of the test (rate of Type I error) ( e.g. 0.05 for a 95% Confidence Interval)

virtual Double_t Size () const =0
Get the size of the test (eg. rate of Type I error)

Public Member Functions inherited from RooStats::HypoTestCalculator
virtual ~HypoTestCalculator ()

virtual HypoTestResultGetHypoTest () const =0

virtual void SetAlternateModel (const ModelConfig &model)=0

virtual void SetCommonModel (const ModelConfig &model)

virtual void SetData (RooAbsData &data)=0

virtual void SetNullModel (const ModelConfig &model)=0

## Protected Member Functions

RooAbsRealDoGlobalFit () const

void DoReset () const

Protected Member Functions inherited from RooStats::CombinedCalculator
RooAbsDataGetData () const

RooAbsPdfGetPdf () const

## Static Protected Member Functions

static RooFitResultDoMinimizeNLL (RooAbsReal *nll)

## Protected Attributes

RooFitResultfFitResult

bool fGlobalFitDone

Protected Attributes inherited from RooStats::CombinedCalculator
RooArgSet fAlternateParams

RooArgSet fConditionalObs

RooAbsDatafData

RooArgSet fGlobalObs

RooArgSet fNuisParams

RooArgSet fNullParams

RooAbsPdffPdf

RooArgSet fPOI

Double_t fSize

#include <RooStats/ProfileLikelihoodCalculator.h>

Inheritance diagram for RooStats::ProfileLikelihoodCalculator:
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## ◆ ProfileLikelihoodCalculator() [1/3]

 ProfileLikelihoodCalculator::ProfileLikelihoodCalculator ( )

Default constructor (needed for I/O)

default constructor

Definition at line 83 of file ProfileLikelihoodCalculator.cxx.

## ◆ ProfileLikelihoodCalculator() [2/3]

 ProfileLikelihoodCalculator::ProfileLikelihoodCalculator ( RooAbsData & data, RooAbsPdf & pdf, const RooArgSet & paramsOfInterest, Double_t size = 0.05, const RooArgSet * nullParams = 0 )

Constructor from data, from a full model pdf describing both parameter of interest and nuisance parameters and from the set specifying the parameter of interest (POI).

There is no need to specify the nuisance parameters since they are all other parameters of the model. When using the calculator for performing an hypothesis test one needs to provide also a snapshot (a copy) defining the null parameters and their value. There is no need to pass the alternate parameters. These will be obtained by the value maximizing the likelihood function

Definition at line 88 of file ProfileLikelihoodCalculator.cxx.

## ◆ ProfileLikelihoodCalculator() [3/3]

 ProfileLikelihoodCalculator::ProfileLikelihoodCalculator ( RooAbsData & data, ModelConfig & model, Double_t size = 0.05 )

Constructor from data and a model configuration If the ModelConfig defines a prior pdf for any of the parameters those will be included as constrained terms in the likelihood function.

Definition at line 97 of file ProfileLikelihoodCalculator.cxx.

## ◆ ~ProfileLikelihoodCalculator()

 ProfileLikelihoodCalculator::~ProfileLikelihoodCalculator ( )
virtual

destructor cannot delete prod pdf because it will delete all the composing pdf's if (fOwnPdf) delete fPdf; fPdf = 0;

Definition at line 113 of file ProfileLikelihoodCalculator.cxx.

## ◆ DoGlobalFit()

 RooAbsReal * ProfileLikelihoodCalculator::DoGlobalFit ( ) const
protected

Definition at line 124 of file ProfileLikelihoodCalculator.cxx.

## ◆ DoMinimizeNLL()

 RooFitResult * ProfileLikelihoodCalculator::DoMinimizeNLL ( RooAbsReal * nll )
staticprotected

Definition at line 169 of file ProfileLikelihoodCalculator.cxx.

## ◆ DoReset()

 void ProfileLikelihoodCalculator::DoReset ( ) const
protected

Definition at line 117 of file ProfileLikelihoodCalculator.cxx.

## ◆ GetHypoTest()

 HypoTestResult * ProfileLikelihoodCalculator::GetHypoTest ( ) const
virtual

Return the hypothesis test result obtained from the likelihood ratio of the maximum likelihood value with the null parameters fixed to their values, with respect to keeping all parameters floating (global maximum likelihood value).

Main interface to get a HypoTestResult.

It does two fits:

1. The first lets the null parameters float, so it's a maximum likelihood estimate.
2. The second is to the null model (fixing null parameters to their specified values): e.g. a conditional maximum likelihood. Since not all parameters are floating, this likelihood will be lower than the unconditional model.

The ratio of the likelihood obtained from the conditional MLE to the MLE is the profile likelihood ratio. Wilks' theorem is used to get $$p$$-values.

Implements RooStats::CombinedCalculator.

Definition at line 301 of file ProfileLikelihoodCalculator.cxx.

## ◆ GetInterval()

 LikelihoodInterval * ProfileLikelihoodCalculator::GetInterval ( ) const
virtual

Return a likelihood interval.

Main interface to get a RooStats::ConfInterval.

A global fit to the likelihood is performed and the interval is constructed using the profile likelihood ratio function of the POI.

It constructs a profile likelihood ratio, and uses that to construct a RooStats::LikelihoodInterval.

Implements RooStats::CombinedCalculator.

Definition at line 223 of file ProfileLikelihoodCalculator.cxx.

## ◆ fFitResult

 RooFitResult* RooStats::ProfileLikelihoodCalculator::fFitResult
mutableprotected

Definition at line 70 of file ProfileLikelihoodCalculator.h.

## ◆ fGlobalFitDone

 bool RooStats::ProfileLikelihoodCalculator::fGlobalFitDone
mutableprotected

Definition at line 71 of file ProfileLikelihoodCalculator.h.

Libraries for RooStats::ProfileLikelihoodCalculator:

The documentation for this class was generated from the following files: